Answer:
1. 9 2/7 = (63+2)/7 = 65/7
2. 2 4/5 = (10+4)/5 = 14/5
3. 65/7 * 14/5 = 910/35 = 26
Can someone help me with this question?
Answer: - 27
Step-by-step explanation:
Plug in for x = 3 and y = -6
I'll start with x to make it easier.
Plugging in x =3
[tex]\sqrt{x^4}[/tex]
Means that first we find x^4, and take the square root of that result.
1. Find x^4
x = 3
3^4 = 3 * 3 * 3 *3 = 81
2. Take the square root of x^4
Square root of 81 = 9
So [tex]\sqrt{x^4}[/tex] = 9
Plugging in y = -6
Let's move onto plugging in y, which appears in the expression as y²
y = -6
so y² = -6 * -6 = 36
Putting this together into the expression
[tex]\sqrt{x^4}[/tex] - y²
9 - 36 = -27
help please ill give brainliest!! please show work
find x
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
A merchant mixed 12 lb of a cinnamon tea with 5 lb of spice tea. The 17-pound mixture cost $28. A second mixture included 14 lb of the cinnamon tea and 6 lb of the spice tea. The 20-pound mixture cost $33. Find the cost per pound of the cinnamon tea and of the spice tea.
Cinnamon tea costs $1.50 per pound, and spice tea costs $2.75 per pound.
To solve this problem, we can set up a system of equations based on the given information.
Let's denote the cost per pound of the cinnamon tea as C, and the cost per pound of the spice tea as S.
From the first mixture, we know that the total weight is 17 pounds, so we can write the equation:
12C + 5S = 28 ----(Equation 1)
From the second mixture, we know that the total weight is 20 pounds, so we can write the equation:
14C + 6S = 33 ----(Equation 2)
To solve this system of equations, we can use a method like substitution or elimination.
Let's use the elimination method to eliminate the variable C:
Multiply Equation 1 by 2 and Equation 2 by -3 to eliminate the C terms:
24C + 10S = 56 ----(Equation 3)
-42C - 18S = -99 ----(Equation 4)
Add Equation 3 and Equation 4:
-18C - 8S = -43
Solve for S:
8S = 43 - 18C
S = (43 - 18C)/8 ----(Equation 5)
Now substitute Equation 5 into Equation 1:
12C + 5((43 - 18C)/8) = 28
Multiply through by 8 to eliminate the fraction:
96C + 215 - 90C = 224
6C = 9
C = 9/6 = 1.5
Substitute the value of C back into Equation 5 to find S:
S = (43 - 18(1.5))/8 = 2.75
Therefore, the cost per pound of the cinnamon tea is $1.50, and the cost per pound of the spice tea is $2.75.
In summary, the cost per pound of the cinnamon tea is $1.50, and the cost per pound of the spice tea is $2.75.
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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
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
_________.
how do u solve it step by step?
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
2. Sara had 1/6 of a pound of pastry. She has to divide it equally into 4 pieces. What was the weight of each piece of pastry?
Answer:
1/24 of a pound-------------------
Divide 1/6 by 4:
1/6 ÷ 4 = 1/6 × 1/4 = 1/ (6 × 4) = 1/24Each piece is 1/24 of a pound.
Luis has $190,000 in his retirement account at his present company. Because he is assuming a position with another company, Luis is planning to "roll over" his assets to a new account. Luis also plans to put $2000/quarter into the new account until his retirement 25 years from now. If the new account earns interest at the rate of 3.5%/year compounded quarterly, how much will Luis have in his account at the time of his retirement? Hint: Use the compound interest formula and the annuity formula. (Round your answer to the nearest cent.)
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.
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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If 10 marbles weigh 6.2 ounces, how many marbles in a 7 pound bag?
Answer:
180 marbles in a 7-pound bag.
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
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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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.)
$
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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Toula owns the Pita Pan restaurant. She needs to order supplies for the upcoming weekend rush. She needs 150 bags of pita bread. The bread come in crates of 50, and each crate costs $15.00. She also needs 65 containers of hummus dip. There are 5 containers in a box, and each box costs $20.00 What expressions can Toula use to determine how much the pita bread and hummus dips will cost? What will the total be?
The total cost of the pita bread and hummus dips will be $305.00.
To determine the cost of the pita bread and hummus dips, Toula can use the following expressions:
Cost of pita bread:
Number of crates needed = (150 bags) / (50 bags/crate) = 3 crates
Cost of each crate = $15.00
Total cost of pita bread = (Number of crates needed) × (Cost of each crate) = 3 crates × $15.00/crate = $45.00
Cost of hummus dips:
Number of boxes needed = (65 containers) / (5 containers/box) = 13 boxes
Cost of each box = $20.00
Total cost of hummus dips = (Number of boxes needed) × (Cost of each box) = 13 boxes × $20.00/box = $260.00
Therefore, the expressions Toula can use to determine the costs are:
Cost of pita bread = 3 crates × $15.00/crate
Cost of hummus dips = 13 boxes × $20.00/box
The total cost will be the sum of the costs of pita bread and hummus dips:
Total cost = Cost of pita bread + Cost of hummus dips
Total cost = $45.00 + $260.00
Total cost = $305.00
Therefore, the total cost of the pita bread and hummus dips will be $305.00.
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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
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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Is this relation a function yes or no?
Answer:
Yes
Step-by-step explanation:
Yes, it is a function. If you perform the vertical-line test, the line only touches a point once.
What is the volume of a triangle prism 9cm 8cm 9cm
Answer:
324 cm^3
Step-by-step explanation:
Because this is a triangular prism, we can take the base area times the height. The base area is 9*8/2=36.
The height is 9.
So 36*9=324.
Answer:
324 cm³
Step-by-step explanation:
Area of triangle = 1/2 × base × height
Area of triangle = 1/2 × 9 cm × 8 cm
Area of triangle = 36 cm²
The height of the triangular prism is given as 9 cm.
To find the volume of the triangular prism, we multiply the area of the base triangle by the height of the prism:
Volume of triangular prism = area of base × height
Volume of triangular prism = 36 cm² × 9 cm
Volume of triangular prism = 324 cm³
Therefore, the volume of the triangular prism is 324 cubic centimeters (cm³).
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?
Which of the following best describes the lines y-3x=4x and 6-2y=8x
○perpendicular
○parallel
○skew
○intersecting
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.
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?!
the answer is D
The figure can be divided into a rectangle and 2 triangles
What is the measure of angle jnk?
The hourly wage, the number of hours and the number of days Jaxon works indicates that the amount Jaxon gets paid is $192
What is the formula for calculating hourly wage?The formula for hourly wage can be presented as follows;
Hourly wage = Total earnings/Total hours worked
The question in the link is presented as follows;
Jaxon gets paid $6 an hour. He works for 8 hours each day for four days. How much will Jaxon get paid
The amount Jaxon gets paid per hour (his hourly wage) = $6
The number of hours he works each day = 8 hours
The number of days Jaxon works = Four days
The amount Jaxin gets paid = Hourly wage × Hours per day × Number of days
Therefore we get;
Amount he gets paid = $6 per hour × 8 hours/day × 4 days = $192
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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)
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
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.
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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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
¿Cual es el capital final de $1200al 8% anual durante 8 años?
Answer:
Por lo tanto, el capital final después de 8 años sería de aproximadamente $2061.68.
Step-by-step explanation:
Para calcular el capital final, utilizaremos la fórmula del interés compuesto:
Capital Final = Capital Inicial * (1 + Tasa de Interés)^Tiempo
Donde:
Capital Inicial = $1200
Tasa de Interés = 8% = 0.08 (expresada como decimal)
Tiempo = 8 años
Sustituyendo los valores en la fórmula:
Capital Final = $1200 * (1 + 0.08)^8
Calculando el resultado:
Capital Final = $1200 * (1.08)^8 ≈ $2061.68
Por lo tanto, el capital final después de 8 años sería de aproximadamente $2061.68.
Find a polynomial with real coefficients that has the given zeros. 5+2i, 5-2i, -1 One such polynomial P(x) can be defined as P(x) = x³ - 9x² + x + 29.
The polynomial with real coefficients from the zeros is P(x) = 2x³ - 18x² + 2x + 58
Find a polynomial with real coefficients from the zeros.From the question, we have the following parameters that can be used in our computation:
zeros = 5+2i, 5-2i, -1
One such polynomial P(x) can be defined as
P(x) = x³ - 9x² + x + 29.
When this polynomial is multiplied by a costant, the roots and zeros remain the same
Let the constant be 2
So, we have
New P(x) = 2(x³ - 9x² + x + 29)
Evaluate
New P(x) = 2x³ - 18x² + 2x + 58
Hence, the function is P(x) = 2x³ - 18x² + 2x + 58
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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
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)
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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Given: F(x) = x + 2 and G(x) = 3x + 5
(F - G) (x) =
-3x - 3
-2x - 3
4
(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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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
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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Aright cylinder with a lateral area of 75 units squared and a height of 6 units has a surface area of 100 units squared (if the SA is rounded to the nearest whole).
False
True
True, the surface area of the cylinder is 100units²
What is surface area of cylinder?The surface area of a three-dimensional object is the sum of the area of all the outer surfaces, it is also measured in square units.
The surface area of a cylinder is expressed as;
SA = 2πrh + 2πr²
where 2πr² is the area of the bases
2πrh = lateral area
75 = 2 × 3.14 × 6 × r
r = 75/37.68
r = 1.99 unit
base area = 2 × 3.14 × 1.99²
= 25 units ( nearest whole number)
The surface area = 75+25
= 100units²
Therefore the surface area of the cylinder to nearest whole number is 100units².
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In 1995, wolves were introduced into Yellowstone Park.
The function `w\left(x\right)=14\cdot1.08^{x}` models the number of wolves, `w`, in the years since 1995, `x`.
Determine the value of `w(25)`.
What does this value say about the wolf population?
Answer:
w(25) = 96
There are 96 wolves in the year 2020
Step-by-step explanation:
Given:
[tex]w(x)=14\cdot 1.08^{x}[/tex]
w(25) =
[tex]w(25)=14\cdot 1.08^{25}\\\\= 14 * (6.848)\\\\=95.872\\\\\approx 96[/tex]
Number of years : 1995 + 25 = 2020
In 2020, there are 96 wolves
