A dumpster in the shape of a rectangular prism has a volume of 528 cubic feet. The length of the dumpster is 5 feet less than twice the width w, and the height is 2 foot less than the width. Find the equation, in terms of w, that could be used to find the dimensions of the dumpster in feet. Your answer should be in the form of a polynomial equals a constant.
Answers
answer: 2w^3 - 9w^2 + 10w = 528
The dimensions of the dumpster will be 8 feet by 11 feet by 6 feet.
What is the volume of the rectangular prism?Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as
V = L x W x H
A dumpster in the shape of a rectangular prism has a volume of 528 cubic feet. The length of the dumpster is 5 feet less than twice the width w, and the height is 2 feet less than the width. Then the equation will be
L = 2W - 5 ...1
H = W - 2 ...2
Then the polynomial is given as,
V = L x W x H
528 = (2W - 5)(W - 2)W
528 = (2W² - 5W)(W - 2)
528 = 2W³ - 4W² - 5W² + 10W
0 = 2W³ - 9W² + 10W - 528
Factorize the equation, then we have
2W³ - 4W² - 5W² + 10W - 528 = 0
(W - 8)(4W + 7)² = 0
W = 8, 1.75i, and -1.75i
Then the length and height will be
L = 2 x 8 - 5
L = 11 feet
H = 8 - 2
H = 6 feet
The dimensions of the dumpster will be 8 feet by 11 feet by 6 feet.
More about the volume of the rectangular prism link is given below.
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Related Questions
A jewelry store bought a gold necklace and marked it up 110% from the original cost of $23.52. Later on, Dean purchased the gold necklace and paid 14.75% sales tax. How much, including tax, did he pay for the gold
necklace?
Answers
9514 1404 393
Answer:
$56.68
Step-by-step explanation:
The final price is ...
(cost price) × (1 +110%) × (1 +14.75%) = (cost price)×2.10×1.1475
= $23.52×2.40975 ≈ $56.68
Dean paid $56.68 for the necklace.
Whats the answer? ( BRANLIEST )
Answers
Answer:
14/2 i think
Step-by-step explanation:
f(x) = 732
g(x) = 3x + 2
Find
(1) (a). Include any restrictions on the domain.
, 3 > 0
OA () (x) = 0 + 0
B. (4) (z) = 2, 3
c. (4) (x) = x +
OD. () () + -1
Answers
Answer:
Option DStep-by-step explanation:
Given:
[tex]f(x) = \sqrt[3]{3x}[/tex][tex]g(x)=3x+2[/tex]Find (f/g)(x):
[tex](f/g)(x)=f(x)/g(x)=\sqrt[3]{3x}/(3x+2)[/tex]The restriction is, the denominator can't be zero:
3x + 2 ≠ 0 ⇒ 3x ≠ -2 ⇒ x ≠ -2/3Correct choice is D
solve pls brainliest
Answers
Here it should be this
a) 300
b) 1732
a
1
=
3
and
a
n
=
a
n
−
1
−
1
a
1
=3 and a
n
=a
n−1
−1
Answers
Answer:????????
Step-by-step explanation:?
Question below..................
Answers
Evaluate the expression ab2 + 2ab + a2 for a = 6 and b = 3.
a) 128
b) 126
c) 130
c) 124
Answers
Answer:
I believe there is an error with the problem
Step-by-step explanation:
3*6*2 + 2*6*3 + 6*2 = 36+36+12 = 84
The answer of the expression ab² + 2ab + a² for a = 6 and b = 3 will be 126 so option (b) will be correct.
What is an expression?
A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
An expression is a mathematical proof of the equality of two mathematical expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
Given the expression
ab² + 2ab + a²
Now,
a = 6 and b= 3
So,
⇒ 6(3)² + 2(6)(3) + 6²
⇒ 36 + 54 + 36
⇒ 126
Hence "The answer of the expression ab² + 2ab + a² for a = 6 and b = 3 will be 126".
To learn more about expression,
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Fishing Hook G is let down 2 times its present depth. Where is Fishing Hook G?
Answers
Answer:
[tex]2g[/tex]
Step-by-step explanation:
In other words, this problem is asking where Fishing Hook G is after it's 2 times deeper. Let g = its previous depth. We do 2 * g = 2g.
Four hundred dollars is deposited into an account that compounds interest quarterly. After 10 quarters the account balance is $441.85. Determine the nominal interest paid on the account?
Answers
Answer:
Step-by-step explanation:
(41.85:400)*100%=....
what are the coefficient in the expression 8a+b+9
Answers
Answer:
8 is the coefficient
Step-by-step explanation:
The definition of coefficient is:
a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g. 4 in 4x y).
2.
HELP PLEASE. which equation describes a line parallel to line g that has a y-intercept at (0, -1)
Answers
Answer:
Line C is parallel to the given line.
Step-by-step explanation:
The given graph slopes down, and thus has a negative slope: m = -1/2.
Of the possible choices, only C has this slope: y = (-1/2)x + b. The y-intercepts b and (0, 6) need not be the same, as the quality of parallelness is all that we care about here.
Write 5288 as a product of its prime factors
Answers
Answer:677
Step-by-step explanation i dont know
Here is the answer:
Rocco loves making spaghetti with his grandmother. They make homemade tomato sauce by adding pureed tomatoes, sugar, salt, olive oil, and water. He notices that after he stops stirring, he sees a greasy film at the top of the red liquid. What does this tell you about his sauce mixture?
Answers
Oil floats on water because it is less dense I believe. So that would be the oil on top of the sauce(the oil is on top because of the water that was also added).
Hi everyone, God bless you all, I need help on this, Select each correct answer, thx.
Answers
Answer:
answer is the first one (all trapezoids are quadrilaterals)
Step-by-step explanation:
Simplify:
3 square root 216/343
Answers
Answer:
answer is .........6/7....
Answer: 6/7
Step-by-step explanation:
Subtract the linear expressions.
(−7.6x+7.4)−(3.5x+6.5)
What is the difference?
Enter your answer in the box.
Answers
Step-by-step explanation:
-7.6x+7.4-3.5x-6.5
-7.6x-3.5x+7.4-6.5
-11.1x+0.9
d. What is the number sentence?
Answers
Answer:
Combination of numbers and mathematical operations that children are often required to solve
Summary
Rita solved a linear equation in one variable and got How many solutions does it's equation have?
How do you know?
Answers
Answer:
i!^dkk
Step-by-step explanation:
more than
Answer:
4 or less
Step-by-step explanation:
because that's how many it has
A line passes through the point (−3,−10) , and it’s perpendicular to the line y=0 . Find an equation for this line.
Answers
Answer:
Step-by-step explanation:
y = 0 is actually the x axis.
All the points on the line you want have an x value of - 3
-3,-10 is actually one of those points
The equation you want is x = - 3
help me figure this out.
Answers
Answer:
30; -5 is 5 units away from 0 and V is 25 units away from 0, and 5 + 25 = 30.
Step-by-step explanation:
To find the distance between point T, which has a value of -5, and V, which has a value of 25, we should find the absolute value of each number and then add those numbers together.
So, the absolute value of -5 is 5 and the absolute value of 25 is 25. 25 + 5 = 30, and this is the length of TV.
If you have any further questions or need clarification on anything, let me know!
A store owner had nine employees and bought nine hundred fifty-one uniforms for them. If he wanted to give each employee the same number of uniforms, how many more should he buy so he doesn’t have any extra?
Answers
Answer:
105
Step-by-step explanation:
Divide 951 by 9
Kristen babysits 38 hours a week for $6.80 per hour. She earns an additional $224.00 in tips . How much did she make in 1 week?
Answers
Answer:
$502.40
Step-by-step explanation:
Kristen works 38 hours for $6.80 per hour.
We multiply her pay and the hours she worked:
38 × 6.8 = 258.4
Thus, she makes $258.40/week
Now we add her tips, which would be the equation 258.4 + 224
258.4 + 224 = 502.4
So, she made $502.40 in 1 week
Please show the work. 5256÷52, 5624÷46, 756÷36, 2760÷12. It's a lot to do, so I'm making this 40 points.
Answers
Which graph and equation shows a proportional relationship between and y? NEED HELP ASAP!!!
Answers
Answer:
y = 0.45x
Step-by-step explanation:
proportional relationships must pass through the point 0,0
both the x and y intercepts must equal 0
3. For the pair of polynomials given, select all points of intersection.
f(x) = (x + 7)(x – 5)
g(x) = x-5
a. (-8, -13)
b. (-7,0)
C. (-5, -10)
d. (-6, -11)
e. (5,0)
Answers
Answer:
-6, -11 and 5, 0
Step-by-step explanation:
Graphing calculators can help you a lot with this type of Algebra. I suggest GeoGebra.org
(6-9d4)-(3d4+4) polynomials
Answers
Answer:
2(1 - 6d⁴)
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Terms/CoefficientsFactoringStep-by-step explanation:
Step 1: Define
Identify
(6 - 9d⁴) - (3d⁴ + 4)
Step 2: Simplify
(Parenthesis) Distribute negative: 6 - 9d⁴ - 3d⁴ - 4Combine like terms: 2 - 12d⁴Factor: 2(1 - 6d⁴)Explain the three different ways of writing a ratio and provide an example
Answers
Answer: The most common way to write a ratio is as a fraction, 3/6. We could also write it using the word "to," as "3 to 6."
Step-by-step explanation:
you can write ratios as 3/6 , 3 to 6, or 3:6
What is the equation of a line parallel to y= -1/2x+6 that passes through (-4, 1)?
Answers
Given the value of slope (m) = -1/2, and the other point, (-4, 1), we can substitute its values into the slope-intercept form, y = mx + b to solve for the y-intercept of the other line.
y = mx + b
1 = -1/2(-4) + b
1 = 2 + b
Subtract 2 from both sides to solve for b:
1 -2 = 2 - 2 + b
-1 = b
Therefore, the y-intercept of the other line is b = -1.
The equation of the line parallel to y = -1/2x + 6 is:
y = -1/2x - 1
Attached is a screenshot of the graph of both lines to show that y = -1/2x - 1 is parallel to y = -1/2x + 6.
Please mark my answers as the Brainliest if you find this helpful :).
Solve the system of equations by using substitution.
6r + 7s = –1
2r + 4s = –12
1) (–4, –8)
2) (–8, –4)
3) (–7, 8)
4) (8, –7)
Answers
Answer:
r = 8 and
s = -7
Step-by-step explanation:
(2r + 4s = - 12)/2 =
r +2s = -6
r = -2s - 6
Substitution:
6 (-2s -6) + 7s = -1
-12s - 36 + 7s = -1
-5s = 36-1
s = 35/-5
s = -7
6r + 7(-7) = -1
6r - 49 = -1
6r = 49-1
r = 48/6
r = 8
A duck is 2 feet below the surface of a pond. If its position can be recorded as −2 feet, what would the position of 0 represent?
A 2 feet below water
B 2 feet above water
C The bottom of the pond
D On the surface of the pond
Answers
Answer:
0 will be the right answer
Step-by-step explanation:
so im guessing either 2 feet below or the bottom of the pond