The volume of a rectangular prism is represented by the function x3 + 11x2 + 20x – 32. The width of the box is x – 1 while the height is x + 8. Find the expression representing the length of the box
Answers
The length of the rectangular prism obtained by finding the quotient of the volume divided by the product of height and width. Hence, the length of the box is x + 4
The volume of a rectangular prism is given calculated using the formula :
Volume = Length × width × height
- Width = x - 1
- Height = x + 8
- Volume = x³ + 11x² + 20x – 32.
From the formula :
Length =
Width × height = (x - 1)(x + 8)
(x - 1)(x + 8) = x² + 8x - x - 8
= x² + 7x - 8
- Divisor = x² + 7x - 8
- Dividend=x³ + 11x² + 20x – 32
Using long divison :
______ | x + 4
______ | _______________
x²+7x-8 | x³ + 11x² + 20x – 32
______ | x³ + 7x² - 8x
-______| ___ 4x²+28x
___________4x²+28x - 32
-___________0__0 ___0
Therefore, the quotient, which is the value of the length of the rectangular prism ls x+ 4
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we know that
the volume of a rectangular prism is equal to
where
L is the length of the box
W is the width of the box
H is is the height of the box
in this problem we have
Find the length of the box
Using a graph tool-------> we will determine the roots of the equation of volume
see the attached figure
the roots are
so
therefore
the answer is
the length of the box is equal to
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The measure of each angle will be 10° and 170°.
A supplementary angle refers to an angle that has the sum to be equal to 180°.
Let the small angle be represented by x
Therefore, the big angle will be: = 17 × x = 17x
Therefore, the value of both angles will be:
x + 17x = 180
18x = 180
Divide both side by 18
18x/18 = 180/18
x = 10
Therefore, the bigger angle will be:
17x = 17 × 10 = 170
Therefore, the angles are 10° and 170°
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The supplement of an angle is 180 - n.
n = 17(180 - n)
n = 3060 - 17n
n + 17n = 3060
18n = 3060
n = 3060/18
n = 170
so the unknown angle (n) = 170 degrees and its supplement = (180 - 170 = 10)......= 10 degrees.
Answers
Maisha can calculate the total cost by multiplying the total amount of paint by the price per cup, Maisha will pay $71.25 for the paint she needs.
What is multiplication?
Multiplication is an arithmetic operation in mathematics that involves combining two or more quantities to form a product. It is a way of finding the total amount or size when there are multiple equal groups or units of the same size.
Maisha needs to calculate the total cost of the paint she needs to buy for her artwork.
First, she needs to convert the units of paint to cups since the price is given in terms of cups of paint:
2 pints of blue paint = 2 x 2 x 8 = 32 cups of blue paint (1 pint = 2 cups, and 1 cup = 8 ounces)
1 1/2 quarts of orange paint = 1.5 x 4 x 2 = 12 cups of orange paint (1 quart = 4 cups, and 1 cup = 8 ounces)
1/2 cup of yellow paint = 0.5 cups of yellow paint
Now, Maisha can add up the total amount of paint she needs:
32 cups of blue paint
3 cups of green paint
12 cups of orange paint
0.5 cups of yellow paint
The total amount of paint is:
32 + 3 + 12 + 0.5 = 47.5 cups
Finally, Maisha can calculate the total cost by multiplying the total amount of paint by the price per cup:
47.5 x $1.50 = $71.25
Therefore, Maisha will pay $71.25 for the paint she needs.
To learn more about multiplication visit:
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A
B
C
D
Answers
We can say
(angle 1) + (angle 3) = 90
(angle 2) + (angle 3) = 90
notice the replacement in bold
The second equation is an algebraic way of saying "angle 2 and angle 3 are complementary"
Answer: Choice C
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cylinder surface area formula is 2*pi*a(a+h) where a is radius and h is height.
plug in your numbers in the right places and you have your answer!
food has a mean fish weight of 12 lbs. and a standard deviation of 1 lb. A fish is measured to be
11.25 lbs. Which brand of fish food, Nacho Average Minos or Impossible Minos, is more likely to have
been used to feed this fish?
Answers
Answer:
i'll see if a friend knows ill work on it
Step-by-step explanation:
Answers
Answer:
y = 8, −8
Step-by-step explanation:
Solve for y by simplifying both sides of the equation, then isolating the variable.