Answer:
Step-by-step explanation:
d
A culture of bacteria has an initial population of 350 bacteria and doubles every 6
hours. Using the formula P = Po 22, where Pt is the population after t hours, Po
is the initial population, t is the time in hours and d is the doubling time, what is the
population of bacteria in the culture after 7 hours, to the nearest whole number?
.
The population to the nearest whole number, the population of bacteria in the culture after 7 hours is approximately 816.
How to determine the the population of bacteria in the culture after 7 hoursBased on the given formula P = Po * 2[tex]^{(t/d)}[/tex], we can calculate the population of bacteria in the culture after 7 hours.
The initial population (Po) is 350 bacteria, and the doubling time (d) is 6 hours.
Let's substitute the values into the formula and calculate:
P = Po * 2[tex]^{(t/d)}[/tex]
P = 350 * 2[tex]^{(7/6)}[/tex]
Using a calculator or simplifying the exponent manually, we have:
P ≈ 350 * 2[tex]^{(1.1667)}[/tex]
Calculating 2^(1.1667), we get approximately 2.3323.
P ≈ 350 * 2.3323
P ≈ 816.31
Rounding the population to the nearest whole number, the population of bacteria in the culture after 7 hours is approximately 816.
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Use the table, along with dimensional analysis to convert the given square unit indicated.
14cm^2 to in^2
To convert 14 cm² to in² using dimensional analysis, we can use the following conversion factors:
1 cm = 0.393701 in (exact conversion factor)
1 in = 2.54 cm (exact conversion factor)
We want to convert cm² to in², so we need to use the conversion factor that relates cm² to in². This is:
1 cm² = (0.393701 in)² = 0.15500031 in² (approximate conversion factor)
To set up the dimensional analysis, we start with the given quantity and multiply it by the appropriate conversion factors so that the units cancel out and we are left with the desired units. We can set it up as follows:
14 cm² * (0.15500031 in² / 1 cm²) = 2.17000434 in² (approximate answer)
Therefore, 14 cm² is approximately equal to 2.17000434 in².
Which values of a, b, and c correctly complete the division?
1/5 5/6= x b/c
O a-4,b-5,c-8
○a-1,b-8,c-5
O a-1,b-5,c-8
O a-4,b-8,c-5
The values of `a, b,` and `c` correctly complete the division of [tex]$$\frac{1}{5}\div \frac{5}{6}[/tex] = [tex]\frac{6}{25}$$[/tex] is `a-1, b-5, c-8`. The correct option is $\boxed{\textbf{(C)}\ a-1,b-5,c-8}$.
To complete the division in the correct manner, the value of `x, b, and c` is to be calculated.
The given fraction is:
[tex]\frac{1}{5}\div \frac{5}{6}[/tex]
= [tex]\frac{1}{5}\cdot \frac{6}{5}[/tex]
= [tex]\frac{6}{25}$$[/tex]
Therefore, the value of `x` is `6`.
Now, we have the equation `5/6 = 6/bc` that is to be solved for `b` and `c`.
Multiplying both sides of the above equation with `bc`,
we get:
[tex]\frac{5bc}{6} = 6$$[/tex]
Multiplying both sides of the equation by `6/5`, we get:
[tex]bc = \frac{36}{5}$$[/tex]
Therefore, the values of `a, b,` and `c` correctly complete the division of [tex]$$\frac{1}{5}\div \frac{5}{6}[/tex] = [tex]\frac{6}{25}$$[/tex] is `a-1, b-5, c-8`.
Hence, the correct option is $\boxed{\textbf{(C)}\ a-1,b-5,c-8}$.
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The values of a, b and c in the expression are a = 1, b = 1 and c = 6
How to determine the values of a, b and cFrom the question, we have the following parameters that can be used in our computation:
1/5 * 5/6 = a * b/c
From the above, we have
1/5 * 5/6 = a * b/c
Evaluate the products
1/6 = a * b/c
Rewrite the expression as
1 * 1/6 = a * b/c
By comparison, we have
a = 1, b = 1 and c = 6
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The inequality 5m − 7 > 16 holds true for all numbers
than
in the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
The inequality 5m - 7 > 16 holds true for the values m = 6, 7, 8, 9, and 10, in the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
To determine the values for which the inequality 5m - 7 > 16 holds true, we can solve it algebraically and then check if each value in the given set satisfies the inequality.
Let's solve the inequality:
5m - 7 > 16
Adding 7 to both sides, we have:
5m > 23
Dividing both sides by 5, we get:
m > 23/5
Now we need to check if each number in the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} satisfies the inequality m > 23/5.
For m = 1:
1 is not greater than 23/5, so the inequality does not hold true.
For m = 2:
2 is not greater than 23/5, so the inequality does not hold true.
For m = 3:
3 is not greater than 23/5, so the inequality does not hold true.
For m = 4:
4 is not greater than 23/5, so the inequality does not hold true.
For m = 5:
5 is not greater than 23/5, so the inequality does not hold true.
For m = 6:
6 is greater than 23/5, so the inequality holds true.
For m = 7, 8, 9, and 10:
All these values are also greater than 23/5, so the inequality holds true for them as well.visit
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Work out 80 000 000 ÷ 200 Give your answer in standard form.
[tex]{\huge{\blue{\bold{\mathfrak{Step\:by\:step\: solution}}}}}[/tex]
To divide 80,000,000 by 200, we can follow these steps:
1. Write out the division problem: 80,000,000 ÷ 200
2. Divide the first digit of the dividend (8) by the divisor (2), which gives us 4.
3. Write 4 above the second digit of the dividend (0), which gives us 40.
4. Subtract 40 from 80, which gives us 40.
5. Bring down the next digit of the dividend (0), which gives us 400.
6. Divide 400 by 200, which gives us 2.
7. Write 2 above the 0 in the dividend, which gives us 4000.
8. Subtract 4000 from 4000, which gives us 0.
So the answer is 400,000. To write it in standard form, we move the decimal point 5 places to the left, which gives us:
[tex]\purple{4 \times {10}^{5}} [/tex]
The answer is:
400,000
Work/explanation:
Divide:
80 000 000 ÷ 200
[tex]\sf{400,000}[/tex]
The answer is already in standard form.
) You are the manager of a firm that produces output in two plants. The demand for your firm's product is P = 78 − 15Q, where Q = Q1 + Q2. The marginal costs associated with producing in the two plants are MC1 = 3Q1 and MC2 = 2Q2. What price should be charged to maximize profits? 2) _______ A) $80.5 B) $40.5 C) $60.5 D) $20.5
The price that should be charged to maximize profits: $80.5 (option a).
To determine the price that should be charged to maximize profits, we need to find the quantity that maximizes the firm's profit function. The profit function can be calculated by subtracting the total costs from the total revenue.
First, let's find the total revenue function. The demand equation given is P = 78 − 15Q, where Q = Q1 + Q2. We can rearrange this equation to express Q in terms of P: Q = (78 - P) / 15.
The total revenue function is calculated by multiplying the price (P) by the quantity (Q): TR = P * Q. Substituting Q, we get TR = P * [(78 - P) / 15].
Next, we need to find the total cost function. The marginal costs associated with producing in the two plants are MC1 = 3Q1 and MC2 = 2Q2. The total cost is the sum of the costs in both plants: TC = MC1 + MC2. Substituting the respective marginal cost equations, we get TC = 3Q1 + 2Q2.
Finally, we can calculate the profit function by subtracting the total cost from the total revenue: Profit = TR - TC.
Now, to find the price that maximizes profits, we need to differentiate the profit function with respect to price (P) and set it equal to zero. By solving this equation, we can find the value of P that maximizes profits.
Taking the derivative of the profit function with respect to P and setting it equal to zero, we get d(Profit)/dP = 0. Solving this equation will give us the value of P that maximizes profits.
After solving the equation, we find that P = $80.5 maximizes profits. Therefore, the price that should be charged to maximize profits is A) $80.5.
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A new city park will have a path from the southeast corner to the northwest corner. The shape of the park is rectangular. With the information given, determine how many yards long the path will be. The rectangles length is 50 yd and the width is 120 yd
The length of the path is 130 yards
How to determine the value
To determine the value of the path, c, we need to know the Pythagorean theorem
Using the Pythagorean theorem which states that the square of the longest leg of a triangle is equal to the sum of the squares of the other two sides of the triangle.
In this case, we have that;
c² = length² + width²
Substitute the values from the information given, we have that;
c² = 50²+ 120²
Find the squares, we get;
c² = 2500 + 14, 400
add the values, we get;
c² = 16900
c = 130 yards
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please help with the questions on the photo
a. The relative frequency of landing on the number 4 is 0.24
b. The relative frequency of landing on a prime number is 0.20
What is relative frequency?Relative frequency is the ratio of the frequency of a particular event in a statistical experiment to the total frequency.
This means to find the relative frequency of a particular outcome of an event, we divide the frequency of the event with the total frequency.
Here, the total frequency is
= 14+9+6+12+4+5
= 50
a. The frequency of 4 is 12
therefore the relative frequency of landing on 4 =
12/50 = 0.24
b. A prime number is a number that can only be divided by itself. Therefore 3 and 5 are the prime numbers in the outcome.
landing on 3 = 6/50 = 0.12
landing on 5 = 4/50 = 0.08
On a prime number = 0.12 + 0.08
= 0.20
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46. Divide $5000 along A, B and C so that A may receive
1/4th much as B and C together and B gets 1/3rd of
what A and C received together. Find how much B
gets?
A. 1000
C. 1250
B. 2750
D. 2500
Amount received by B can be calculated by solving the equation, Amount received by B = $2750So, the amount B gets is $2750.
The correct option for the given question is B. 2750.Divide $5000 along A, B and C so that A may receive 1/4th much as B and C together and B gets 1/3rd of what A and C received together.
The amount that B gets.
Let's suppose the amount B gets is x.
Now, we can proceed as given below:
Given that the total amount = $5000
Amount received by A = (1/4) * (Amount received by B and C)
Amount received by B = (1/3) * (Amount received by A and C)
Amount received by C = (Amount received by B and A) - (Amount received by B)
Now, we have,Amount received by B + Amount received by C = 3 * Amount received by B/3 + Amount received by A/3
Amount received by A = (1/4) * [Amount received by B + Amount received by C]
Amount received by B = (1/3) * [Amount received by A + Amount received by C]
Amount received by C = [Amount received by B + Amount received by A] - [Amount received by B]
Let's solve this problem in detail: Amount received by A = (1/4) * (Amount received by B + Amount received by C)
Now, Amount received by A = (1/4) * ($5000 - Amount received by A)
By solving the above equation,
Amount received by A = $1000Amount received by B = (1/3) * (Amount received by A + Amount received by C)
Also, Amount received by B + Amount received by C = 3 * Amount received by B/3 + Amount received by A/3
Again, $5000 - Amount received by A = 2 * (Amount received by B + Amount received by C)
By substituting the value of Amount received by A in the above equation,Amount received by B + Amount received by C = $3000
Amount received by B = (1/3) * [Amount received by A + Amount received by C]
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table represents an exponential function.
What is the interval between neighboring
x-values shown in the table?
What is the ratio between neighboring y-values?
The interval between neighboring x value is 1
the ratio between neighboring y-values 1
How to find the interval between neighboring x valueTo find interval between neighboring x value, we subtract as follows
interval = 2 - 1 = 3 - 2 = 4 - 3 = 5 - 4 = 1
To find the ratio between neighboring y-values, we divide
ratio = 4 / 1 = 16/4 = 256 / 16 = 1024 / 256 = 4
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complete question
The table below represents an exponential function.
x
1
2
3
4
5
y
1
4
16
256
1,024
What is the interval between neighboring
X-values shown in the table?
What is the ratio between neighboring y-values?
Sara and Steve each bought a pair of pants and some socks .The pants that they purchased cost the exact same amount and the pair of socks are also the same amount.
Sara paid $60 for one pair of pants and two pairs of socks
Steve paid $75 for one pair of pants and three pairs of socks
What was the cost of 1 pair of pants?
Equations
1P+2S=60
1P+3S=75
Answer:
These are two linear equations with two unknowns, P (price of pants) and S (price of socks). You can solve them by using either substitution or elimination methods.
Let's use the elimination method.
First, let's subtract the second equation from the first:
1P + 2S - (1P + 3S) = 60 - 75
After simplifying this, we get:
-1S = -15
Dividing both sides by -1, we find:
S = 15
Now, we can substitute S = 15 into the first equation to find the price of pants (P):
1P + 2(15) = 60
1P + 30 = 60
Subtract 30 from both sides to get:
1P = 60 - 30
1P = 30
So, the price of one pair of pants (P) is $30.
im not sure what goes in the blanks i need answers please
Step-by-step explanation:
Remember that
[tex](a + b) {}^{2} = {a}^{2} + 2ab + {b}^{2} [/tex]
So
[tex](2x) {}^{2} = 4 {x}^{2} [/tex]
So the first blank is 4
[tex]2ab = 2(2x)(3) = 12x[/tex]
So the second blank is 12
And finally
[tex]3 {}^{2} = 9[/tex]
So the final blank is 9.
Select the correct answer.
A department store's customer parking lot has 4 rows with an equal number of parking spots in each row. The lot also has 15 parking spots for store
employees. If c cars can be parked in each of the 4 main rows of the parking lot, what is the expression for the maximum number of cars that can be
parked in the parking lot?
O A. 150-4
OB. 15-4)
OC. 40+15
OD.
4(0+15)
The correct expression for the maximum number of cars that can be parked in the parking lot is 4c + 15. Option C
Given that there are 4 main rows with an equal number of parking spots in each row, and each row can accommodate c cars, the total number of parking spots in the main rows is 4c.
Additionally, there are 15 parking spots specifically allocated for store employees.
To find the maximum number of cars that can be parked in the parking lot, we need to add the number of parking spots in the main rows and the number of parking spots for employees.
Expression:
Total number of cars = Number of cars in main rows + Number of cars in employee spots
Number of cars in main rows = 4c
Number of cars in employee spots = 15
Therefore, the maximum number of cars that can be parked in the parking lot is:
Total number of cars = 4c + 15
This expression represents the sum of cars parked in the main rows and the cars parked in the employee spots, giving us the maximum capacity of the parking lot. Option C.
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What type of transformation takes the graph of f(x)=|x| to the graph of g(x)=2.5|x|?
Answer:
Vertical Stretch
Step-by-step explanation:
The parent function [tex]f(x)=|x|[/tex] when multiplied by 2.5 is a vertical stretch of the absolute value equation. I've attached a graph so you can see the difference between the two functions.
Instructions: Identify the type of sequence and write the explicit rule. write Explicit Rule Sequence: -39, -45, 51, 57,... Type: Arithmetic e Explicit Rule:
The given sequence does not follow a simple arithmetic or geometric pattern, making it challenging to determine an explicit rule based on the given terms.
To identify the type of sequence and write the explicit rule, we need to examine the pattern of the given sequence: -39, -45, 51, 57, ...
By observing the differences between consecutive terms, we can determine if it follows an arithmetic or geometric pattern.
Arithmetic sequences have a common difference between each term, meaning that by adding (or subtracting) the same value repeatedly, we can generate the sequence. Geometric sequences, on the other hand, have a common ratio between each term, meaning that by multiplying (or dividing) by the same value repeatedly, we can generate the sequence.
Let's calculate the differences between consecutive terms:
-45 - (-39) = -6
51 - (-45) = 96
57 - 51 = 6
From the differences, we can see that the sequence is not arithmetic since the differences are not constant. However, the differences alternate between -6 and 6, indicating a possible geometric pattern.
Let's calculate the ratios between consecutive terms:
-45 / (-39) ≈ 1.1538
51 / (-45) ≈ -1.1333
57 / 51 ≈ 1.1176
The ratios are not constant, indicating that the sequence is neither geometric nor arithmetic.
Therefore, the given sequence does not follow a simple arithmetic or geometric pattern, and it is difficult to determine the explicit rule based on the given terms. It is possible that the sequence follows a more complex pattern or rule that is not apparent from the given terms.
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What is the sum of 12-5i and -3+4i?
Answer:
9 and -i
Step-by-step explanation:
12-3 + 5i-4i
9 + -i
9-i
Find the inverse of function f.
ƒ(x) = 1/3 - 1/21 x
The Inverse of ƒ(x) is given by y = 21x + 7 For the given function, the inverse is y = 21x + 7.
Given,ƒ(x) = 1/3 - 1/21x
To find the inverse of ƒ(x)
We can use the following steps,
Replace ƒ(x) with y, y = 1/3 - 1/21x
Swap x and y, then we get x = 1/3 - 1/21y
Solve for y
We have to isolate y on one side and other terms on the other side,
Add 1/21 y to both sides + 1/21 y = 1/3
Now, Multiply both sides by 21 to get rid of the denominator.21x + y = 7
Then the inverse of ƒ(x) is given by y = 21x + 7 For the given function, the inverse is y = 21x + 7.
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find two functions f and g
a. f(x) =
b. f(x) =
The functions f and g are:
a. f(x) = 1/x
b. g(x) = x + 2
a) To find two functions f and g such that (fog)(x) = 1/(x + 2), we need to determine how the composition of the two functions f and g produces the given expression.
Let's start by assuming g(x) = x + a, where a is a constant. This means that g(x) adds the constant a to the input x.
Next, let's determine the function f(x) such that (fog)(x) results in the desired expression. We have:
(fog)(x) = f(g(x)) = f(x + a)
b) To simplify the expression 1/(x + 2) and make it match f(g(x)), we can consider f(x) = 1/x.
Substituting the expressions for f(x) and g(x) into (fog)(x), we have:
(fog)(x) = f(g(x)) = f(x + a) = 1/(x + a)
Comparing this with the desired expression 1/(x + 2), we see that a = 2. Therefore, the functions f and g are:
a. f(x) = 1/x
b. g(x) = x + 2
Using these functions, we can verify the composition (fog)(x):
(fog)(x) = f(g(x)) = f(x + 2) = 1/(x + 2)
Thus, (fog)(x) = 1/(x + 2), which matches the desired expression.
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If the coordinates of point A are (8 , 0) and the coordinates of point B are (3 , 7), the y-intercept of what
Answer: Assuming that you're asking what the y-intercept is, 11.2.
Step-by-step explanation:
y = mx + c,
where m is the slope and c is the y-intercept.
To calculate the slope, we use the formula:
m = (y2 - y1) / (x2 - x1),
where (x1, y1) and (x2, y2) are the coordinates of points A and B, respectively.
Using the coordinates of points A and B, we have:
m = (7 - 0) / (3 - 8)
m = 7 / (-5)
m = -7/5
Now we can substitute the values of the slope (m) and the coordinates of one point (A) into the slope-intercept form to solve for the y-intercept (c):
0 = (-7/5)(8) + c
0 = -56/5 + c
To isolate c, we can add 56/5 to both sides:
56/5 = c
Therefore, the y-intercept of the line passing through points A (8, 0) and B (3, 7) is (0, 56/5) or 11.2 when expressed as a decimal.
f(x)=x-1. Find the inverse of f(x).
Answer: D
Step-by-step explanation: X is being subtracted by 1 so it will now add 1 in the inverse
Help me plssssssssssssssss
Answer:
a) 13
b) B
Step-by-step explanation:
y = x² - 3, where x= 4
• y= 4²-3
•y = 16-3
•y = 13.
(Hope I answered your question)
A cruise ship is traveling south going approximately 22 mph when it hits the Gulf
Stream flowing east at 4mph.
Show your work.
Find the resultant direction. Round to the nearest tenth.
The cruise ship's resultant velocity is approximately 22.67 mph, and its direction is approximately 10.2 degrees south of east.
To find the resultant direction, we can use vector addition. Let's represent the southward velocity of the cruise ship as vector A and the eastward velocity of the Gulf Stream as vector B.
Given:
Magnitude of vector A (southward velocity of the cruise ship) = 22 mph
Magnitude of vector B (eastward velocity of the Gulf Stream) = 4 mph
To find the resultant velocity, we add the two vectors together. Since the vectors are perpendicular to each other, we can use the Pythagorean theorem to find the magnitude of the resultant vector:
Resultant velocity = √(A^2 + B^2) = √(22^2 + 4^2) ≈ 22.67 mph
Now, to find the direction of the resultant vector, we can use trigonometry. The angle between the resultant vector and the south direction can be calculated as:
θ = arctan(B / A) = arctan(4 / 22) ≈ 10.17 degrees
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What terms do not apply to a rhombus
The terms that do not apply to a rhombus are:
Right angle: A rhombus does not have any right angles. Its angles are typically acute or obtuse, but never right angles.
Perpendicular sides: In a rhombus, the opposite sides are parallel to each other, but they are not perpendicular. Perpendicular sides are characteristic of rectangles and squares.
The terms that do not apply to a rhombus are:
Right angle: A rhombus does not have any right angles. Its angles are typically acute or obtuse, but never right angles.
Perpendicular sides: In a rhombus, the opposite sides are parallel to each other, but they are not perpendicular. Perpendicular sides are characteristic of rectangles and squares.
Congruent angles: While the opposite angles in a rhombus are equal to each other, the adjacent angles are not necessarily congruent. Congruent angles are a characteristic of rectangles and squares.
Right triangle: A rhombus does not contain any right angles, so it cannot be classified as a right triangle. A right triangle is a triangle that has one right angle.
Equilateral: A rhombus is not an equilateral polygon. An equilateral polygon has all sides of equal length, while a rhombus has all sides equal in length but does not require all angles to be equal.
It's important to note that a rhombus is a quadrilateral with opposite sides that are parallel and equal in length, but it does not possess the characteristics mentioned above.
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please, answer! 50 pts!
Slope = 4
y-intercept = -1
Step-by-step explanation:Slope-intercept form is one of the most common ways to write a linear equation when graphing.
Slope-intercept Form
Slope-intercept form is written as y = mx + b. In this equation, m is the slope. Slope represents the rate of change of the equation. The slope can also be described as the change in y over the change in x.
Additionally, the b represents the y-intercept. The y-intercept is the y-value where the graph intersects with the y-axis.
Finding Slope and Y-intercept
The equation we are given is y = 4x - 1. This means that the slope is 4. So, the rate of change for the equation is 4 units up per 1 unit right. Additionally, the y-intercept is -1. This means that the function will intersect the y-axis when y = -1. Using this information, we could graph the function if we wanted.
Which of the following statements are true about the given rational equation? Check all of the boxes that
apply.
4
1 x+10
+1=
x+622³+62²
Ox=1is a solution.
Ox=0 is a solution.
O x=-1 is a solution.
Ox=-6 is a solution.
DONE
The statements that are true about the rational equations are options A and C.
How is this so?[tex]\frac{4}{x + 6} + \frac{1}{x^{2} } = \frac{x+10}{x^{3} +6x^{2} }[/tex]
Note that x ≠ 0, and x ≠ -6
The left side of the equation is equal to
[tex]\frac{4}{x + 6} + \frac{1}{x^{2} } = \frac{4*x^{2} + (x+6)}{(x+6)x^{2} } = \frac{4x^{2} + x + 6 }{x^{3} + 6x^{2} }[/tex]
Since the left side of the equation have the same denominators, their numerators are equal. Hence
4x² + x + 6 = x + 10
then
4x² = 10-6
4x² = 4
x² = 1,
x₁ = 1, and x₂ = -1
Thus, both numbers are the solution of the given problem.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
Which of the following statements are true about the given rational equation?
4/x+6 +1/x²=x+10/x³+6x²
Check all of the boxes that apply.
A. x = 1 is a solution.
B. x = 0 is an extraneous solution.=
C. x = –1 is a solution.
D. x = –6 is an extraneous solution.
A garden is designed in the shape of a rhombus formed from 4 identical 30°-60°-90° triangles. The shorter distance across the middle of the garden measures 30 feet.
What is the distance around the perimeter of the garden?
Find x and y for the figure below
The values for x and y derived using trigonometric ratios are:
3). x = 3 and y = 3+ √3
4). x = 6 and y = 12
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
3). Considering right triangle ADB:
sin45 = x/3√2 {opposite/hypotenuse}
√2/2 = x/3√2
x = (3√2 × √2)/2 {cross multiplication}
x = 3
cos45 = BD/3√2
√2/2 = BD/3√2
BD = 3
Considering that triangle ADC:
tan60 = 3/DC
√3 = 3/DC
DC = √3
y = BD + DC = 3 + √3
y = 15 × tan23 {cross multiplication}
y = 6.3671
cos23 = 15/x {adjacent/hypotenuse}
x = 15/cos23
x = 16.2954
4). Considering right triangle ADB:
sin60 = 3√3/x
√3/2 = 3√3/x
x = 6
cos60 = BD/6
1/2 = BD/6
BD = 3
considering right triangle ADC:
tan30 = 3√3/DC
√3/3 = 3√3/DC
DC = 9
y = 3 + 9 = 12
Therefore, the values for x and y derived using trigonometric ratios are:
3). x = 3 and y = 3+ √3
4). x = 6 and y = 12
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The highest point in California
is Mt. Whitney at 14,494 ft
above sea level. The lowest
point in California is Death
Valley, which has an "altitude"
of -282 ft (282 ft below sea
level). Find the difference in
the elevations of the highest
point and lowest point in
California.
The difference in elevations is 14,212 feet.
What is elevation?The action or fact of raising or being raised to a higher or more important level, state, or position. Elevation is distance above sea level. Elevations are usually measured in meters or feet. They can be shown on maps by contour lines, which connect points with the same elevation; by bands of color; or by numbers giving the exact elevations of particular points on the Earths surface.
Given:
The highest point in California is Mount Whitney at 14,494 feet above sea level. The lowest point is the Death Valley at 282 feet below sea level
The positive 14,494 minus 282 feet would be a difference of 14,212 feet.
So, the difference is 14,212 feet.
Therefore, the difference in elevations is 14,212 feet.
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How many solutions exist for the absolute value of 1/2x+1=5
There exists two solutions to the absolute value function |0.5x + 1| = 5.
How to solve the absolute value function?The absolute value function in this problem is defined as follows:
|0.5x + 1| = 5.
The first solution is obtained as follows:
0.5x + 1 = -5
0.5x = -6
x = -6/0.5
x = -12.
The second solution is obtained as follows:
0.5x + 1 = 5
0.5x = 4
x = 4/0.5
x = 8.
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A recycling bin is in the shape of a rectangular box. Find the height of the box if its length is 16 ft, its width is 9 ft, and its surface area is 638ft^2 (In the figure h=height, Assume that the given surface area includes that of the top lid of the box.)
The height of the rectangular recycling bin is 7 ft.
How to calculate the height of the boxTo find the height of the rectangular recycling bin, we can use the formula for the surface area of a rectangular box:
Surface Area = 2lw + 2lh + 2wh
Given:
Length (l) = 16 ft
Width (w) = 9 ft
Surface Area = 638 ft²
Substituting these values into the surface area formula, we have:
638 = 2(16)(9) + 2(16)h + 2(9)h
638 = 288 + 32h + 18h
638 = 288 + 50h
350 = 50h
h = 350 / 50
h = 7
Therefore, the height of the rectangular recycling bin is 7 ft.
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