I need to solve this, but the process is confusing and I need someone to help me understand it, please and thank you :))
[tex]\frac {x^2+5x+6}{x - 1}\ \textgreater \ 0[/tex]
Answers
Answer:
(-3, -2) ∪ (1, ∞)
Step-by-step explanation:
Given inequality:
[tex]\dfrac{x^2+5x+6}{x-1} > 0[/tex]
Begin by factoring the denominator:
[tex]\begin{aligned}x^2+5x+6&=x^2+2x+3x+6\\&=x(x+2)+3(x+2)\\&=(x+3)(x+2)\end{aligned}[/tex]
Therefore, the factored inequality is:
[tex]\dfrac{(x+3)(x+2)}{x-1} > 0[/tex]
Determine the critical points - these are the points where the rational expression will be zero or undefined.
The rational expression will be zero when the numerator is zero:
[tex](x+3)(x+2)=0 \implies x=-3,\;x=-2[/tex]
Therefore, -3 and -2 are critical points.
The rational expression will be undefined when the denominator is zero:
[tex]x-1=0 \implies x=1[/tex]
Therefore, 1 is a critical point.
So the critical points are -3, -2 and 1.
Create a sign chart, using open dots at each critical point (the inequality is greater than, so the interval doesn't include the values).
Choose a test value for each region, including one to the left of all the critical values and one to the right of all the critical values.
Chosen test values: -4, -2.5, 0, 2
For each test value, determine if the function is positive or negative:
[tex]x=-4 \implies \dfrac{(-4+3)(-4+2)}{-4-1} = \dfrac{(-)(-)}{(-)}=\dfrac{(+)}{(-)}=-[/tex]
[tex]x=-2.5 \implies \dfrac{(-2.5+3)(-2.5+2)}{-2.5-1} = \dfrac{(+)(-)}{(-)}=\dfrac{(-)}{(-)}=+[/tex]
[tex]x=0 \implies \dfrac{(0+3)(0+2)}{0-1} = \dfrac{(+)(+)}{(-)}=\dfrac{(+)}{(-)}=-[/tex]
[tex]x=2 \implies \dfrac{(2+3)(2+2)}{2-1} = \dfrac{(+)(+)}{(+)}=\dfrac{(+)}{(+)}=+[/tex]
Record the results on the sign chart for each region (see attached).
As we need to find the values for which the rational expression is greater than zero, shade the positive regions on the sign chart (see attached). These regions are the solution set.
Remember that the intervals of the solution set should not include the critical points, as the critical points of the numerator make the expression zero, and the critical point of the denominator makes the expression undefined. The intervals of the solution set are those where the rational expression is greater than zero only.
Therefore, the solution set is:
-3 < x < -2 or x > 1
As interval notation:
(-3, -2) ∪ (1, ∞)
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Related Questions
Given f(x)=5x and g(x) = 1/x-5 which value is in the domain of f g? (5x in the problem has that one symbol) (this is platoweb)
Answers
Answer:
f(x)=5x
g(x)=1/x-5
f(g)=5(1/x-5)
f(x)=5/x- 25
therefore domain is x=0
Which of the following best describes the lines y-3x=4x and 6-2y=8x
○perpendicular
○parallel
○skew
○intersecting
Answers
Answer:
Intersecting (fourth answer choice)
Step-by-step explanation:
If the lines are perpendicular, parallel, or intersecting, they are not skew. Thus, we need to check if the lines can be classified as either perpendicular, parallel, or intersecting first. If the lines are classified as neither, then they are skew.First, let's convert both lines to slope-intercept form, whose general equation is y = mx + b, where
m is the slope,and b is the y-intercept.Converting y - 3x = 4x to slope-intercept form:
(y - 3x = 4x) + 3x
y = 7x
Thus, the slope of this line is 7 and the y-intercept is 0.
Converting 6 - 2y = 8x to slope-intercept form:
(6 - 2y = 8x) - 6
(-2y = 8x - 6) / -2
y = -4x + 3
Thus, the slope of this line is -4 and the y-intercept is 3.
Checking if y = 7x and y = -4x + 3 are perpendicular lines:
The slopes of perpendicular lines are negative reciprocals of each other.We can show this in the following formula:
m2 = -1 / m1, where
m1 is the slope of one line,and m2 is the slope of the other line.Thus, we only have to plug in one of the slopes for m1. Let's do -4.
m2 = -1 / -4
m2 = 1/4
Thus, the slopes 7 and -4 are not negative reciprocals of each other so the two lines are not perpendicular.
Checking if y = 7x and y = -4x + 3 are parallel lines:
The slopes of parallel lines are equal to each other.
Because 7 and -4 are not equal, the two lines are not parallel.
Checking if the lines intersect:
The intersection point of two lines have the same x and y coordinate. To determine if the two lines intersect, we treat them like a system of equations.Method to solve the system: Elimination:
We can multiply the first equation by -1 and keep the second equation the same, which will allow us to:
add the two equations, eliminate the ys, and solve for x:-1 (y = 7x)
-y = -7x
----------------------------------------------------------------------------------------------------------
-y = -7x
+
y = -4x + 3
----------------------------------------------------------------------------------------------------------
(0 = -11x + 3) - 3
(-3 = -11x) / 11
3/11 = x
Now we can plug in 3/11 for x in y = 7x to find y:
y = 7(3/11)
y = 21/11
Thus, x = 3/11 and y = 21/11
We can check our answers by plugging in 3/11 for x 21/11 for y in both y = 7x and y = -4x + 3. If we get the same answer on both sides of the equation for both equations, the lines intersect:
Checking solutions (x = 3/11 and y = 21/11) for y = 7x:
21/11 = 7(3/11)
21/11 = 21/11
Checking solutions (x = 3/11 and y = 21/11) for y = -4x + 3:
21/11 = -4(3/11) + 3
21/11 = -12/11 + (3 * 11/11)
21/11 = -12/11 + 33/11
21/11 = 21/11
Thus, the lines y = 3x = 4x and 6 - 2y = 8x are intersecting lines (the first answer choice).
This also means that lines are not skew since lines had to be neither perpendicular nor parallel nor intersecting to be skew.
help please ill give brainliest!! please show work
find x
Answers
Answer:
x = 10
Step-by-step explanation:
the figure inscribed in the circle is a cyclic quadrilateral , all 4 vertices lie on the circumference.
the opposite angles in a cyclic quadrilateral sum to 180° , that is
6x + 1 + 10x + 19 = 180
16x + 20 = 180 ( subtract 20 from both sides )
16x = 160 ( divide both sides by 16 )
x = 10
The Graph shows the velocity of a train
a) use four strips of equal width to estimate the distance the train travelled in the first 20 seconds
b) is your answer to part a) an understimate or an overestimate?
Answers
Answer:
To estimate the distance the train traveled in the first 20 seconds using four strips of equal width, follow these steps:
a) Calculate the average velocity for each strip by finding the average height of each strip.
b) Multiply the average velocity of each strip by the width (time) of each strip to obtain the distance covered by each strip.
c) Add up the distances covered by each strip to find the estimated total distance traveled in the first 20 seconds.
Regarding part b), to determine if the estimate is an overestimate or an underestimate, we need to analyze the graph. If the graph shows that the velocity increases during the 20-second period, then the estimate will be an underestimate because the actual distance covered would be greater than the estimation based on a constant velocity assumption. On the other hand, if the graph shows that the velocity decreases during the 20-second period, then the estimate will be an overestimate since the actual distance covered would be less than the estimation based on a constant velocity assumption.
Without seeing the graph, it's difficult to provide a definitive answer.
Study this table.
x
y
–3
–2
–2
0
0
4
4
12
Which best describes the function represented by the data in the table?
linear with a common ratio of 2
linear with a common first difference of 2
quadratic with a common ratio of 2
quadratic with a common first difference of 2
Answers
Shawn wants to paint all the surfaces of the table shown below.
A. the volume of 3 rectangular prisms
B. the surface area of 1 triangle and 4 cylinders
C. the volume of 1 rectangular prism and 3 cylinders
D. the surface area of 2 triangles and 1 rectangular prism
What's the answer? How do I solve for this?!
Answers
the answer is D
The figure can be divided into a rectangle and 2 triangles
A driveway with a 90° bend has 3
sections as shown. If the driveway is 6”
thick, how many cubic yards of concrete
will be required? Notice that all arcs are
concentric.
Answers
The volume of concrete required is
203.5 cubic ftHow to find the cubic yards of concreteThe volume of concrete required is solved by area * thickness
Area of the figure
First section = 20 * 8 = 160
second section = π(R² - r²)/4 = π(16² - 8²)/4 ≈ 151
Third section = 12 * 8 = 96
sum of areas = 160 + 151 + 96 = 407 ft
Volume of concrete required = volume of the shape
= sum of areas * thickness
thickness = 6'' = 0.5
= 407 * 0.5
= 203.5 cubic ft
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A minibus was purchased for R241 000. The rate of depreciation 22% p.a. on a reducing balance basis. The cost of a new minibus inflates at a rate of 15% p.a.
Calculate the replacement cost of the minibus in 4 years’ time if the old minibus is used as a trade-in.
A fixed amount is deposited into a sinking fund at the end of each month for the purchase of a new minibus in 4 years’ time. Calculate the required monthly payment if interest is earned at the rate of 8,6% p.a. compounded monthly, and the first payment is only made three months after the original bus was purchased.
Answers
Replacement cost of the minibus in 4 years' time, considering the trade-in of the old minibus, is R9,411.70.
1. Calculate the depreciation of the minibus over 4 years:
Depreciation = Original cost * (1 - Rate of depreciation) Number of years
Depreciation = R241,000 * (1 - [tex]0.22)^4[/tex]
Depreciation = R241,000 * [tex]0.78^4[/tex]
Depreciation ≈ R91,073.17
2. Calculate the remaining value of the minibus after 4 years:
Remaining value = Original cost - Depreciation
Remaining value = R241,000 - R91,073.17
Remaining value ≈ R149,926.83
3. Calculate the inflated cost of a new minibus in 4 years:
Inflated cost = Original cost * (1 + Rate of inflation) Number of years
Inflated cost = R241,000 * (1 + [tex]0.15)^4[/tex]
Inflated cost = R241,000 * [tex]1.15^4[/tex]
Inflated cost ≈ R421,731.04
4. Calculate the replacement cost by subtracting the remaining value and adding the inflated cost:
Replacement cost = Remaining value + Inflated cost
Replacement cost = R149,926.83 + R421,731.04
Replacement cost ≈ R571,657.87
5. Calculate the trade-in value by subtracting the depreciation from the replacement cost:
Trade-in value = Replacement cost - Depreciation
Trade-in value = R571,657.87 - R91,073.17
Trade-in value ≈ R480,584.70
6. Therefore, the replacement cost of the minibus in 4 years' time, considering the trade-in, is approximately R480,584.70.
For the second question:
1. Determine the number of months until the first payment is made:
Number of months = 4 years * 12 months/year - 3 months
Number of months = 48 months - 3 months
Number of months = 45 months
2. Use the formula for the future value of a series of payments to calculate the required monthly payment:
Monthly payment = (Future value * Interest rate) / ((1 + Interest rate) Number of periods - 1)
Monthly payment = (Replacement cost * Monthly interest rate) / ((1 + Monthly interest rate) Number of months - 1)
Monthly payment = (R480,584.70 * 0.086/12) / ((1 + [tex]0.086/12)^4^5[/tex] - 1)
Monthly payment ≈ R9,411.70
3. Therefore, the required monthly payment to the sinking fund for the purchase of a new minibus in 4 years' time, with the first payment made three months after the original bus was purchased, is approximately R9,411.70.
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Damien repairs furniture. He recorded the total fee for renting a truck and the number of miles he drove
for the last 5 times he rented a moving van for deliveries in the table below. What is the best description of the fees he is charged for renting or the cost per mile?
He is charged about $0.70 per mile.
He is charged $80 for renting the van and $0.30 per mile.
He is charged $45 for renting the van and $0.50 per mile.
He is charged $50 for renting the van and $0.07 per mile.
He is charged an initial rate of $55.60 for renting the van.
Answers
The best description of the fees he is charged for renting or the cost per mile would be = He is charged an initial rate of $55.60 for renting the van. That is option E.
How to determine the best description for the coat price?To determine the best description for the cost per mile, the following steps needs to be taken as follows:
The average cost per mile he was given for renting the trucks would be calculated by addition of the total cost divided by the miles driven.
Total cost = 55.60+53.22+51.16+54.97+52.38/
= 267.33
Total miles driven = 80+46+23+71+34 = 254
The average = 267.33/254 = 1.1
Therefore since the initial price given = $55.60, the best statement = He is charged an initial rate of $55.60 for renting the van
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Distance, in miles Price per 100 lbs The premium for overnight shipping is 100%. What is the cost to ship 1,800 lbs of goods from Atlanta to Louisville (390 miles) using overnight shipping? 0-200 201-400 401-600 601-800 801-1000 $100 $120 $200 $240 $400
Answers
The cost to ship 1,800 lbs of goods from Atlanta to Louisville using overnight shipping is $7,200.
To calculate the cost of shipping 1,800 lbs of goods from Atlanta to Louisville using overnight shipping, we need to determine the price per 100 lbs and apply the 100% premium for overnight shipping.
From the information, we can see that the price per 100 lbs for the distance range of 401-600 miles is $200.
Since the distance from Atlanta to Louisville is 390 miles, which falls within the 401-600 miles range, we can use the corresponding price per 100 lbs of $200.
To calculate the cost, we need to divide the total weight of 1,800 lbs by 100 to get the number of 100 lb units: 1,800 lbs / 100 = 18 units.
Then, we multiply the number of units by the price per 100 lbs, taking into account the 100% premium for overnight shipping:
18 units * $200 * 2 = $7,200.
Therefore, the cost is $7,200.
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The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 68 minutes and a standard deviation of 14 minutes. Suppose one person at the hot springs is randomly chosen. Let X = the amount of time that person spent at Grover Hot Springs . Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N(
68
Correct,
14
Correct)
b. Find the probability that a randomly selected person at the hot springs stays longer then 81 minutes.
c. The park service is considering offering a discount for the 8% of their patrons who spend the least time at the hot springs. What is the longest amount of time a patron can spend at the hot springs and still receive the discount?
minutes.
d. Find the Inter Quartile Range (IQR) for time spent at the hot springs.
Q1:
minutes
Q3:
minutes
IQR:
minutes
Answers
a. The distribution of X is X ~ N(68, 14).
b. The corresponding area to the right of 0.9286, which is approximately 0.1772.
c. The longest amount of time a patron can spend and still receive the discount is approximately 48.5654 minutes.
d. The Inter Quartile Range (IQR) for time spent at the hot springs is approximately 21.373 minutes.
a. The distribution of X is X ~ N(68, 14), where X represents the amount of time a person spends at Grover Hot Springs, 68 is the mean, and 14 is the standard deviation.
b. To find the probability that a randomly selected person stays longer than 81 minutes, we need to calculate the area under the normal curve to the right of 81.
Using the z-score formula: z = (x - μ) / σ, where x is the value (81), μ is the mean (68), and σ is the standard deviation (14).
Plugging in the values, we have z = (81 - 68) / 14 = 0.9286.
Using a standard normal distribution table or a calculator, we can find the corresponding area to the right of 0.9286, which is approximately 0.1772.
c. To find the longest amount of time a patron can spend at the hot springs and still receive the discount, we need to find the value that corresponds to the lowest 8% of the distribution.
Using a standard normal distribution table or a calculator, we can find the z-score that corresponds to the 8th percentile, which is approximately -1.4051.
Using the z-score formula, we can calculate the longest amount of time: x = μ + z [tex]\times[/tex] σ = 68 + (-1.4051) [tex]\times[/tex] 14 = 48.5654 minutes.
Therefore, the longest amount of time a patron can spend and still receive the discount is approximately 48.5654 minutes.
d. The Inter Quartile Range (IQR) is a measure of the spread of the data and represents the range between the first quartile (Q1) and the third quartile (Q3).
To find Q1 and Q3, we can use the z-score formula and the standard normal distribution table.
For Q1, we find the z-score corresponding to the 25th percentile, which is approximately -0.6745.
Using the formula Q1 = μ + z [tex]\times[/tex] σ, we have Q1 = 68 + (-0.6745) [tex]\times[/tex] 14 = 57.053.
Therefore, Q1 is approximately 57.053 minutes.
For Q3, we find the z-score corresponding to the 75th percentile, which is approximately 0.6745.
Using the formula Q3 = μ + z [tex]\times[/tex] σ, we have Q3 = 68 + (0.6745) [tex]\times[/tex] 14 = 78.426.
Therefore, Q3 is approximately 78.426 minutes.
Finally, we can calculate the IQR by subtracting Q1 from Q3: IQR = Q3 - Q1 = 78.426 - 57.053 = 21.373 minutes.
Therefore, the Inter Quartile Range (IQR) for time spent at the hot springs is approximately 21.373 minutes.
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What is the location of the point on the number line that is of the way from
A= -4 to B= 17?
A. 3
B. 7
C. 9
OD. 5
Answers
The point on the number line that is 5/7 of the way from A = -4 to B = 17 is approximately -1.8571.
To find the location of a point on the number line that is a certain fraction of the way from one point to another, we can use the concept of linear interpolation.
In this case, we want to find the point that is 5/7 of the way from A = -4 to B = 17.
To calculate this point, we can use the formula:
Point = A + (Fraction × Distance)
where A is the starting point, Fraction is the desired fraction, and Distance is the total distance between the two points.
In this case, A = -4, B = 17, and the desired fraction is 5/7. The distance between A and B can be calculated as:
Distance = B - A = 17 - (-4) = 21
Plugging in these values, we have:
Point = -4 + (5/7 × 21)
Simplifying the expression, we get:
Point = -4 + (15/7) = -4 + 2.1429 ≈ -1.8571
Therefore, the point on the number line that is 5/7 of the way from A = -4 to B = 17 is approximately -1.8571.
Among the given options, none of them match the calculated value. However, the closest option is C. 9.
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K-
Use long division to find the quotient Q(x) and the remain
P(x) = x³ + 4x² - 17x + 430
d(x)= x + 10
P(x) = (x + 10)
Answers
The quotient of the division is x² - 6x + 43 and the remainder is 0
How to find the quotient and the remainderFrom the question, we have the following parameters that can be used in our computation:
P(x) = x³ + 4x² - 17x + 430
d(x)= x + 10
Using the long division method of quotient, we have
x + 10 | x³ + 4x² - 17x + 430
The division steps are as follows
x² - 6x + 43
x + 10 | x³ + 4x² - 17x + 430
x³ + 10x²
--------------------------------------------------------------
-6x² - 17x + 430
-6x² - 60x
--------------------------------------------------------------
43x + 430
43x + 430
--------------------------------------------------------------
0
Hence, the quotient is x² - 6x + 43 and the remainder is 0
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A fruit vendor sold 2/5 of his grapefruits on Friday and 1/2 of the remainder on Saturday. He had 60 grapefruits left. a) What fraction of grapefruits did he sell on Saturday? b) How many grapefruits did he have at first? c) How many did he sell on Friday?
Answers
a) The fruit vendor sold 3/10 of the grapefruits on Saturday, b) The vendor had 100 grapefruits at first, and c) 40 grapefruits were sold on Friday.
a) On Saturday, the fruit vendor sold 1/2 of the remaining grapefruits. Since 2/5 of the grapefruits were sold on Friday, there are 3/5 of the original amount left. Therefore, on Saturday, the vendor sold (1/2) x (3/5) = 3/10 of the grapefruits.
b) To find the original number of grapefruits, we need to calculate the total amount remaining after Friday's sales. Since there were 60 grapefruits left after Saturday's sales and 3/5 of the original amount remained, we can set up the equation (3/5) [tex]\times[/tex]x = 60, where x represents the original number of grapefruits.
Solving for x, we have x = (60 x 5) / 3 = 100 grapefruits. Therefore, the fruit vendor had 100 grapefruits at first.
c) To find the number of grapefruits sold on Friday, we subtract the amount remaining after Friday's sales from the original number. 2/5 of the grapefruits were sold on Friday, so the number sold is (2/5) x 100 = 40 grapefruits.
In summary, a) the fruit vendor sold 3/10 of the grapefruits on Saturday, b) the vendor had 100 grapefruits at first, and c) 40 grapefruits were sold on Friday.
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2) Looking at your average from question 1, with an expected weight of 4 ounces, what is the % error in actual weights? (Assume you think the answer is 10%. Find 10% of 4 ounces to check to see if that answer is reasonable!) Do not round!
A) 17.5%
B) .128%
C) 10%
D) 0.175%
Answers
The calculated percentage error with the assumed answer of 10%
To find the percentage error in actual weights, we can use the formula:
Percentage Error = [(|Measured Value - Expected Value|) / Expected Value] * 100%
In this case, the expected weight is 4 ounces. Let's assume the measured value is 10% off from the expected value. So the measured value would be:
Measured Value = Expected Value + (10% of Expected Value)
= 4 ounces + (10/100) * 4 ounces
= 4 ounces + 0.4 ounces
= 4.4 ounces
Now we can calculate the percentage error:
Percentage Error = [(|4.4 ounces - 4 ounces|) / 4 ounces] * 100%
= [(0.4 ounces) / 4 ounces] * 100%
= (0.4/4) * 100%
= 0.1 * 100%
= 10%
Comparing the calculated percentage error with the assumed answer of 10%, we can see that they are the same.
The percentage error represents the deviation from the expected value as a percentage of the expected value itself. In this case, it indicates that the actual weights deviate by 10% from the expected weight of 4 ounces. The calculated percentage error with the assumed answer of 10%
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A pie-shaped (triangular) lake-front lot has a perimeter of 1,100 feet. One side is 300 feet longer than
the shortest side, while the third side is 500 feet longer than the shortest side. Find the lengths of all
three sides.
Answers
The lengths of the three sides of the pie-shaped lake-front lot are:
Shortest side: 100 feet
Second side: 400 feet
Third side: 600 feet
Let's denote the lengths of the three sides of the triangular lake-front lot as x, x + 300, and x + 500.
The perimeter of a triangle is the sum of its three sides, so we can set up an equation to represent the given information:
x+ (x + 300) + (x + 500) = 1,100
Simplifying the equation:
3x + 800 = 1,100
Subtracting 800 from both sides:
3x = 300
Dividing both sides by 3:
x = 100
Now that we have found the length of the shortest side, we can substitute this value back into the expressions for the other two sides:
Shortest side (x) = 100 feet
Second side (x + 300) = 100 + 300 = 400 feet
Third side (x + 500) = 100 + 500 = 600 feet
Therefore, the lengths of the three sides of the pie-shaped lake-front lot are:
Shortest side: 100 feet
Second side: 400 feet
Third side: 600 feet
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Since he was 21 years old, Ben has been depositing $200 at the end of each month into a tax-free retirement account earning interest at the rate of 3.5%/year compounded monthly. Larry, who is the same age as Ben, decided to open a tax-free retirement account 5 years after Ben opened his. If Larry's account earns interest at the same rate as Ben's, determine how much Larry should deposit each month into his account so that both men will have the same amount of money in their accounts at age 65. (Round your answer to the nearest cent.)
$
Answers
Using the future value formula and an equation, we can see that Larry must deposit $263.48 each month.
How much Larry should deposit each month?
To determine how much Larry should deposit each month into his account so that both men will have the same amount of money at age 65, we need to calculate the monthly deposit amount for Larry.
Let's break down the problem into steps:
Step 1: Calculate the number of months each person will be making deposits.
Both Ben and Larry will make monthly deposits for (65 - 21) * 12 = 528 months.
Step 2: Calculate the future value of Ben's account at age 65.
Using the formula for the future value of an ordinary annuity:
[tex]FV = P * [(1 + r)^n - 1] / r[/tex]
where:
FV = Future ValueP = Monthly deposit amountr = Monthly interest raten = Number of periods (months)Since Ben has been depositing $200 at the end of each month for 528 months, we can substitute the values into the formula:
[tex]FV_Ben = 200 * [(1 + 0.035/12)^{528} - 1] / (0.035/12)[/tex]
Step 3: Calculate the future value of Larry's account at age 65.
Larry started depositing 5 years after Ben, so he will only be making deposits for (65 - 21 - 5) * 12 = 456 months.
Using the same formula, we can calculate the future value for Larry:
[tex]FV_Larry = P * [(1 + 0.035/12)^{456} - 1] / (0.035/12)[/tex]
Step 4: Set up an equation to find the monthly deposit amount for Larry.
Since both Ben and Larry will have the same amount at age 65, we equate the future values:
FV_Ben = FV_Larry
[tex]200 * [(1 + 0.035/12)^{528} - 1] / (0.035/12) = P * [(1 + 0.035/12)^{456} - 1] / (0.035/12)[/tex]
Step 5: Solve the equation for P (the monthly deposit amount for Larry).
[tex]P = [200 * [(1 + 0.035/12)^{528} - 1] / [(1 + 0.035/12)^{456} - 1]\\\\P = 263.48[/tex]
That is how much he must deposit per month.
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A canoe team leaves the dock at a bearing of 25° south of east and paddles at a constant speed of 10 mph. There is a 2 mph current moving 80° west of south. What is the canoe's actual speed and
direction? Draw a diagram and show your work to justify your answer. Round the distance to the nearest
hundredth and the direction to the nearest degree. (5 points)
Answers
The canoe's actual speed is approximately 9.66 mph at a bearing of 12° south of east.
To determine the canoe's actual speed and direction, we need to consider the vector addition of the canoe's velocity and the current.
Let's start by drawing a diagram to visualize the problem.
We'll use a scale where 1 cm represents 10 mph.
Draw a line segment representing the canoe's velocity of 10 mph at a bearing of 25° south of east.
From the endpoint of the canoe's velocity vector, draw another line segment representing the current's velocity of 2 mph at a bearing of 80° west of south.
Connect the starting point of the canoe's velocity vector with the endpoint of the current's velocity vector to form a triangle.
Next, we can find the resultant velocity (actual speed and direction) of the canoe by calculating the vector sum of the canoe's velocity and the current's velocity.
Using the law of cosines, we can find the magnitude of the resultant velocity:
c² = a² + b² - 2ab [tex]\times[/tex] cos(C)
Where:
a = 10 mph (canoe's velocity)
b = 2 mph (current's velocity)
C = 80° (angle between the velocities)
Substituting the values:
c² = 10² + 2² - 2 [tex]\times[/tex] 10 [tex]\times[/tex] 2 [tex]\times[/tex] cos(80°)
c² = 100 + 4 - 40 [tex]\times[/tex] cos(80°)
Solving for c, the magnitude of the resultant velocity:
c ≈ √(100 + 4 - 40 [tex]\times[/tex] cos(80°))
c ≈ √(104 - 40 [tex]\times[/tex] cos(80°))
To find the direction, we can use the law of sines:
sin(A) / a = sin(C) / c
Where:
A = 25° (angle of the canoe's velocity)
a = 10 mph (magnitude of the canoe's velocity)
C = 80° (angle between the velocities)
c ≈ √(104 - 40 [tex]\times[/tex] cos(80°)) (magnitude of the resultant velocity)
Substituting the values:
sin(25°) / 10 = sin(80°) / √(104 - 40 [tex]\times[/tex] cos(80°))
Solving for sin(80°):
sin(80°) ≈ (sin(25°) [tex]\times[/tex] √(104 - 40 [tex]\times[/tex] cos(80°))) / 10
Finally, we can use the inverse sine function to find the direction:
Direction ≈ arcsin((sin(25°) [tex]\times[/tex]√(104 - 40 [tex]\times[/tex] cos(80°))) / 10)
Calculating the numerical values using a calculator will give us the actual speed and direction of the canoe.
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Which statement is true of the function f(x) = Negative RootIndex 3 StartRoot x EndRoot? Select three options.
The function is always increasing.
The function has a domain of all real numbers.
The function has a range of {y|–Infinity < y < Infinity}.
The function is a reflection of y = .
The function passes through the point (3, –27).
Answers
Given: F(x) = x + 2 and G(x) = 3x + 5
(F - G) (x) =
-3x - 3
-2x - 3
4
Answers
(F - G)(x) is equal to -2x - 3 when we subtract G(x) from F(x). Option B
To find (F - G)(x), we subtract G(x) from F(x). Let's substitute the given functions into the expression:
(F - G)(x) = F(x) - G(x)
F(x) = x + 2
G(x) = 3x + 5
Substituting these values, we have:
(F - G)(x) = (x + 2) - (3x + 5)
Now, let's simplify the expression:
(F - G)(x) = x + 2 - 3x - 5
Combining like terms, we get:
(F - G)(x) = -2x - 3
Therefore, the correct answer is -2x - 3.
Option B (-2x - 3) is the correct answer.
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A hiker on the trans-Canada trail starts climbing at an elevation of 875 feet. The hiker checks the
elevation map and finds that she will cover a horizontal distance of 2645 feet and end up a point
1943 feet above sea level. What will the average slope of the climb be to the nearest hundredth
Answers
The average slope of the climb is approximately 0.404.
To find the average slope of the climb, we need to calculate the change in elevation divided by the horizontal distance covered.
Change in elevation = Final elevation - Initial elevation = 1943 ft - 875 ft = 1068 ft
Horizontal distance covered = 2645 ft
Average slope = Change in elevation / Horizontal distance covered = 1068 ft / 2645 ft
Using a calculator or dividing these values, we find that the average slope is approximately 0.404 to the nearest hundredth.
The average slope of the climb is approximately 0.404. This means that for every 1 foot of horizontal distance covered, the hiker ascends approximately 0.404 feet in elevation.
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Find the area of the parallelogram
Answers
The area of the parallelogram is 189 square units
How to determine the areaFirst, we have the determine the length of the base and height.
The distance between the lines x = 9 and f(x) = 9 + 2x is the height
We have that the line parallel to f(x) passes through (4, 11)
The equation in point-slope form is;
y - 11 = 2(x - 4
y = 2x + 3
Substitute x = 9 in the equation, y = 2x + 3.
y = 2(9) + 3 = 21
The points are then (9, 21) and (9, 0).
The distance between the y-axis and the line x = 9 is the base.
Base = 9 units.
The formula for calculating area of a parallelogram is given by ;
= base × height
= 9 × 21
= 189 square units.
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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
A/60
B/45
C/105
The measurement of angle A is
The measurement of angle B is
The measurement of angle Cis
Answers
The second pair of points representing the solution set of the system of equations is (-6, 29).
To find the second pair of points representing the solution set of the system of equations, we need to substitute the x-coordinate of the second point into one of the equations and solve for y.
Given the system of equations:
y = x^2 - 2x - 19
y + 4x = 5
Substituting the x-coordinate of the second point (-6) into equation 2:
y + 4(-6) = 5
y - 24 = 5
y = 5 + 24
y = 29
Therefore, the second pair of points representing the solution set of the system of equations is (-6, 29).
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Question
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
y = x2 − 2x − 19
y + 4x = 5
The pair of points representing the solution set of this system of equations is (-6, 29) and
_________.
Derek is making a rectangular prism
That has a volume of 120 cubic inches. The height of his prism is 6 inches. What is the possible length and width
Answers
Answer:
the possible length and width b:
1 and 20
10 and 2
5 and 4
120 = 1*20*6
120 = 10*2*6
120 = 5*4*6
The possible length and width for Derek's rectangular prism with a volume of 120 cubic inches and a height of 6 inches is 6 inches and 20 inches, respectively.
To find the possible length and width of Derek's rectangular prism, we can use the formula for the volume of a rectangular prism:
Volume = Length x Width x Height
Given that the volume is 120 cubic inches and the height is 6 inches, we can substitute these values into the formula:
120 = Length x Width x 6
To find the possible values for length and width, we need to factorize 120 and check the combinations that satisfy the equation. Let's find the factors of 120:
1 x 120
2 x 60
3 x 40
4 x 30
5 x 24
6 x 20
8 x 15
10 x 12
Now let's substitute these factors into the equation and solve for the missing dimension:
For the combination 1 x 120:
120 = 1 x 120 x 6
This does not work because the width would be 120 inches, which is not feasible.
For the combination 2 x 60:
120 = 2 x 60 x 6
This does not work because the width would be 60 inches, which is not feasible.
For the combination 3 x 40:
120 = 3 x 40 x 6
This does not work because the width would be 40 inches, which is not feasible.
For the combination 4 x 30:
120 = 4 x 30 x 6
This does not work because the width would be 30 inches, which is not feasible.
For the combination 5 x 24:
120 = 5 x 24 x 6
This does not work because the width would be 24 inches, which is not feasible.
For the combination 6 x 20:
120 = 6 x 20 x 6
This works because the width would be 20 inches:
120 = 6 x 20 x 6
120 = 720
This combination satisfies the equation.
For the combination 8 x 15:
120 = 8 x 15 x 6
This does not work because the width would be 15 inches, which is not feasible.
For the combination 10 x 12:
120 = 10 x 12 x 6
This does not work because the width would be 12 inches, which is not feasible.
Therefore, the possible length and width for Derek's rectangular prism with a volume of 120 cubic inches and a height of 6 inches is 6 inches and 20 inches, respectively.
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Polygon D has been dilated to create polygon D′.
Polygon D with top and bottom sides labeled 8 and left and right sides labeled 9.5. Polygon D prime with top and bottom sides labeled 12.8 and left and right sides labeled 15.2.
Determine the scale factor used to create the image.
Scale factor of 0.5
Scale factor of 0.6
Scale factor of 1.2
Scale factor of 1.6
Answers
The scale factor used is equal to the length of the corresponding side of the dilated polygon divided by the length of the corresponding side of the original polygon.
For example, the scale factor for the top and bottom sides is:
12.8 / 8 = 1.6
The scale factor for the left and right sides is:
15.2 / 9.5 = 1.6
Since the scale factor is the same for each side, the scale factor used to create the image is 1.6.
A wedding planner is organizing the seating for a wedding. He can represent the number of rows by the function f(x) = 13x and the number of seats in each row by the function g(x) = 5x – 2.
Which function represents the total number of seats?
65x + 26
65x – 26
65x2 + 26x
65x2 – 26x
Answers
Answer:
Step-by-step explanation:
65x2-26x
Ram borrowed RS 150000 from sita at the rate of 21%. per annum. At the end of months, how much should he pay compounded half yearly?
Answers
In this case, P = 150000, r = 21%, n = 2 (since the interest is compounded half-yearly), and t = 8/12 (since the loan is for 8 months).
Plugging in these values, we get:
A = 150000(1 + 0.21/2)^(2*(8/12))
= 150000(1.105)^0.67
= 150000(1.065)
= 159750
Therefore, Ram should pay RS 159750 compounded half yearly at the end of 8 months.
how do u solve it step by step?
Answers
Answer:
(8,5)(0,-3)
Step-by-step explanation:
-y=-x+3
y=x-3
Substitute for y:
(x-3)^2-2x=9
x^2-6x+9-2x=9
x^2-8x=0
x(x-8)=0
x=0,8
if x=0,
0-y=3
y=-3
if x=8
8-y=3
-y=-5
y=5
Answer :
x - y = 3
x = 3 + y
y^2 - 2x = 9
y^2 - 2(3+y) = 9
y^2 - 2y -6 -9 = 0
y^2 - 2y -15 = 0
Factorize
y = -3 y = 5
when y = -3
x -(-3) = 3
x = 0
when y = 5
x - 5 = 3
x = 8
10 ft
4 ft
9 ft
3 ft
What is the perimeter of the shape?
O 12 feet
O
14 feet
O 26 feet
O 38 feet
Answers
explanation: perimeter is where you add all the sides, so you add 10,4,9, and 3. that should give you 26.
Determine which postulate or theorem can be used to prove that
ДАВС= AEDC.
O A. AAS
XO B. SAS
VO C. ASA
O D. SSS
(Answer is ASA)
Answers
The postulate or theorem that proves that two triangles are congruent if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle. Of the above choices, only ASA satisfies this condition. So the answer is (C).
How to explain the informationASA Congruence Theorem explains that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
This theorem is a part of triangle congruence criteria in Euclidean geometry. It states that if two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle, then the two triangles are congruent, meaning they have the same shape and size.
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