Jae is constructing an open box from a piece of cardboard that is 9 in. wide and 12 in. long. He cuts squares of equal size from each comer of
the cardboard, as shown in the picture, and then folds up the sides of the box. Write and simplify a polynomial function V for the volume of the box in terms of x
Answers
Answer:
The polynomial function for the volume of the box ([tex]V[/tex]) in terms of [tex]x[/tex] is
[tex]V(x)= 108\cdot x -42\cdot x^{2}+4\cdot x^{3}[/tex].
Step-by-step explanation:
We present a representation of the specifications of the open box in a image attached below. The volume of the open box ([tex]V[/tex]), measured in cubic inches, is represented by this expression:
[tex]V = w\cdot h \cdot l[/tex]
Where:
[tex]w[/tex] - Width, measured in inches.
[tex]h[/tex] - Height, measured in inches.
[tex]l[/tex] - Length, measured in inches.
Polynomial functions in standard form are represented by the following form:
[tex]y = \Sigma_{i=0}^{n} c_{i}\cdot x^{i}[/tex]
Where:
[tex]n[/tex] - Order of the polynomial, dimensionless.
[tex]c_{i}[/tex] - i-th Coefficient, dimensionless.
[tex]x[/tex] - Indepedent variable, dimensionless.
[tex]y[/tex] - Dependent variable, dimensionless.
If we get from figure that [tex]w = 12 - 2\cdot x[/tex], [tex]h = x[/tex] and [tex]l = 9 - 2\cdot x[/tex], then:
[tex]V = (12-2\cdot x) \cdot x \cdot (9-2\cdot x)[/tex]
[tex]V = (12\cdot x -2\cdot x^{2})\cdot (9-2\cdot x)[/tex]
[tex]V = 108\cdot x-18\cdot x^{2}-24\cdot x^{2}+4\cdot x^{3}[/tex]
[tex]V = 108\cdot x -42\cdot x^{2}+4\cdot x^{3}[/tex]
The polynomial function for the volume of the box ([tex]V[/tex]) in terms of [tex]x[/tex] is
[tex]V(x)= 108\cdot x -42\cdot x^{2}+4\cdot x^{3}[/tex].
The volume of a box is the amount of space the box can occupy.
The polynomial function is: [tex]\mathbf{V(x) = 4x^3 -42x^2 + 108x }[/tex]
The dimension of the cardboard is given as:
[tex]\mathbf{Length = 12}[/tex]
[tex]\mathbf{Width = 9}[/tex]
Assume the size removed from the box is x
The dimension of the box becomes
[tex]\mathbf{Length = 12 -2x}[/tex]
[tex]\mathbf{Width = 9 -2x}[/tex]
[tex]\mathbf{Height = x}[/tex]
So, the volume (V) of the box is:
[tex]\mathbf{V = Length \times Width \times Height}[/tex]
Substitute known values
[tex]\mathbf{V = (12 -2x) \times (9 - 2x) \times x}[/tex]
Open brackets
[tex]\mathbf{V = (12 -2x) \times (9x - 2x^2)}[/tex]
Open brackets
[tex]\mathbf{V = 108x -24x^2 - 18x^2 + 4x^3}[/tex]
[tex]\mathbf{V = 108x -42x^2 + 4x^3}[/tex]
Rewrite as:
[tex]\mathbf{V = 4x^3 -42x^2 + 108x }[/tex]
Express as a function
[tex]\mathbf{V(x) = 4x^3 -42x^2 + 108x }[/tex]
Hence, the polynomial function is:
[tex]\mathbf{V(x) = 4x^3 -42x^2 + 108x }[/tex]
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Related Questions
11. For any integer x, x x will always produce an even value. true or false
Answers
Two samples were taken of fish caught on Small Lake and are shown in the table below. It is estimated that the Small Lake fish population is roughly 1,000 fish. What is the average number of brown trout in the lake? Small Lake Fish Sample 15 Sample 1 Rainbow Trout Brown Trout Largemouth Bass 11 Sample 2 Rainbow Trout Brown Trout Largemouth Bass 3 1 9 11 43 ООО 80 160 333.
Answers
Answer:
b or 80
Step-by-step explanation:
80 is the average number of brown trout in the lake.
What is Mean?The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.
given, Two samples were taken of fish caught on Small Lake and are shown in the table given.
Total fish were taken in both samples = 9 + 3+ 15 + 11 + 1 + 11
Total fish were taken in both samples = 50
Brown fish in both samples = 3 + 1
Brown fish in both samples = 4
Thus,
the average number of brown trout in the lake = 4/50 * 1000
Since there are 1000 fish in total in the lake
the average number of brown trout in the lake = 80
Therefore, the average number of brown trout in the lake is 80.
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Complete question:
FInd the slope y = -2
Answers
Answer:
The slope is ZERO. It has no slope
Step-by-step explanation:
the length of a rectangle is 3 inches m ore that its width. if the perimeter is 42 inches, what are the dimensions of the rectangle
Answers
Answer:
width is 9 length is 12 :)
Step-by-step explanation:
I'm doing this stuff rn
the sum of 3 consecutive integers is -69. Find the largest
Answers
x = the first integer
x + 1 = the second integer
x + 2 = the third integer.
Let's set each of our variables equal to -69
x + x + 1 + x + 2 = -69
Combine like terms
3x + 3 = -69
Subtract 3 from both sides.
3x = -72
Divide both sides by 3
x = -24
The first integer = x = -24
The second integer = x + 1 = -24 + 1 = -23
The third Integer = x + 2 = -24 + 2 = -22
Solve the equation 3(m + 5) = 3 + 3(2m + 2) for m.
Answers
Answer:
m=2
Step-by-step explanation:
Answer:
[tex]m=2[/tex]
Step-by-step explanation:
[tex]3\left(m+5\right)=3+3\left(2m+2\right)[/tex]
Expand:
[tex]3m+3\times5=3+3\times2m+3\times2[/tex]
[tex]3m+15=3+6m+6[/tex]
[tex]3m+15=6m+9[/tex]
Subtract 15 from both sides:
[tex]3m+15-15=6m+9-15[/tex]
[tex]3m=6m-6[/tex]
Subtract 6m from both sides:
[tex]3m-6m=6m-6-6m[/tex]
[tex]-3m=-6[/tex]
Divide both sides by -3:
[tex]\frac{-3m}{-3}=\frac{-6}{-3}[/tex]
[tex]m=2[/tex]
How many cups are in 1 liter? Which conversions show a path to the solution? Check all that apply. cups Right-arrow liters Right-arrow quarts liters Right-arrow quarts Right-arrow cups cups Right-arrow gallons Right-arrow liters liters Right-arrow gallons Right-arrow cups
Answers
Answer:
I cant answer everything but I know that there are 8 cups in a liter
Step-by-step explanation:
Answer:
B,D
Step-by-step explanation:
helpppp !
expand and simplify (x+y) (x+y)
Answers
Answer:
Step-by-step explanation:
(x+y) (x+y)
=x^2+xy+yx+y^2
=x^2+2xy+y^2
Hope it helps
pls mark as Brainliest
= x*x +xy +yx + y*y
= x^2 + 2xy + y^2
Hope can help you
FREE BRAINLIEST! Are waffles really pancakes with abs?
Answers
are you ok
and yes
waffles are way hotter than pancakes sorry i dont make the rules here
HELP ME PLEASE !!!!!!!!!
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Answer:
12 units right 6 units down
I like to give easy points so what is 35+50+20 super easy
Answers
35
50
20
——
105
Jin has 34 feet of garden fence. He wants the shape of his garden to be a rectangle 5 feet wide.
Which should be the length of Jin's garden?
O A 42 feet
OB 24 feet
O c. 12 feet
D. 6 feet
Answers
Form equation 34=2x+10 (2 unknown lengths which are x and two 5 feet widths. They add up to his 34 feet of fence total).
Subtract 10 from both sides to whet 24=2x.
Divide both sides by 2 to isolate x and get the length is 12 feet.
plz help me i dont understand this one
Answers
Answer:
x^2y^5
Step-by-step explanation:
Simplify the expressions.
what is the equation represented
Answers
Answer:
y=-8x-6, y=-4x, y=-2x+3, x=6
Step-by-step explanation:
y=mx+b
use that formula to make you're equations but remember m represents slope and b what is going up by
I need help on this question
Answers
Answer:
x=32
Step-by-step explanation:
Answer:
x= 32
Step-by-step explanation:
Remember all triangles sum up to 180 degrees.
Equation= 98+50+x=180
Step 1- Add to simplify
148+x= 180
Step 2- Subtract 148 to both sides.
148+x= 180
-148 148
x= 32
HELP ME. ASAP HELP ME PLS. PLSSSS
I will give brainlist for the right answer.
Three cars are for sale car a £14240 or car b £15870 or car c £11690 The price of car is rounded to the nearest £100. Which price changes by the greatest amount
Answers
Answer:
1st car is the answer to you question and even explanation is given.
Answer:
when rounded off to nearest 1000
14200, 15900 11700
first car by 40 second car by 30 and third car by 10
so first car
Step-by-step explanation:
What is the value of 9+21(13+5)? A.287 B.395 C.387 D.540
Answers
Answer:
The answer would be C
Step-by-step explanation:
This is because you would use the distributive property, so you would distribute the 21 to the 13 and the 5. Then you would multiply those two, and then add them, and add the separate 9 to them. Hope this helps :)
Answer:
C.
Step-by-step explanation:
if the other answer gets deleted or they delete it or something im here .<.
This is the second questsions!!! Please helpers!!
Answers
B) < is the answer
C) = is the answer
D) > is the answer
Brainliest?
Max bought two items that were both on sale one item was 10% off and one item was 20% off max says that he saved 15% althogether is he correct?
Answers
Answer:
yes
Step-by-step explanation:
No, Max was wrong about his claim. Max saved 30% altogether.
Let the first item be (a) Let the second item be (b)Discount Offer
a = 10%b = 20%For the two items, the total discount that Max saved was
= (10 + 20)%
= 30%.
Averagely, if we are to determine the average discount for each of the items, we have:
= 30% ÷ 2
= 15%
So, on each item, Max saved 15% on average.
Therefore, we can conclude that Max saved 30% altogether for the two items.
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Can someone please explain to me how I solve a problem like this? I'm learning about proving parallel Lines right now. Thank you!
Answers
Answer:
x = 12
I apologize if it is wrong.
HELP PLEASE GIVING BRAINLIEST
Answers
Answer:
4 3/5
Step-by-step explanation:
i can’t figure this out
Answers
Answer:
B: 2 1/3 > 2 1/6
is the correct answer
A,C, and D are false answers and are incorrect
Answer:
2 1/3 > 2 1/6
Step-by-step explanation:
5/6 < - 1/3
2 < -2 1/2
negative cannot be bigger than positive
1 1/4 > 1 1/3 if you divide them you would get 1.25 > 1.333333, so 1 1/4 not bigger than 1 1/4
grade 7. i actually already learnt this but this whole quarantine thing made me forget lolz. what are factors?
example : is 3 a factor of 372?
please answer and explain <3
Answers
Answer:
A number in a multiplication equation that makes up the total. For example,
2 x 3= 6.
2 and 3 are the factors.
Answer:
A factor is basically a number that derives from another without leaving a remainder. It sounds somewhat confusing when put into words but I'll give you some examples.
Step-by-step explanation:
in the problem you stated the answer would be yes. 3 is a factor of 372 because you can multiply 3 times another number (which in this case is 124) to get 372.
In addition, a number can have several factors. For example, these are all the factors for the number 10: 1, 2, 5, 10
notice how all these numbers multiplied by another of these same numbers on the list give you 10.
hope this helped :)
solve for T
10t = -50
Answers
Answer: t=-5
Step-by-step explanation:
if 10t=-50, you have to solve for the equation. to solve, you have to get the variable by itself. to get the variable by itself, you have to divide both sides by 10. 10t/10=-50/10. t=-5
E varies directly with G. When G is 6, E is 10. Find the value of G when E is 18.
Answers
Answer:
10.8
Step-by-step explanation:
E has increased by a factor of 18/10 = 1.8, so G will increase by that factor. The corresponding value of G is ...
6 × 1.8 = 10.8 = G
__
If you like, you can write an equation relating G to E:
E = kG
10 = k(6)
k = 10/6 = 5/3
Now for E = 18, we have ...
18 = (5/3)G
18(3/5) = G = 10.8
What is 12 to the 3rd power in multiplication expression standard form
Answers
12 to the 3rd power in multiplication expression standard form is 12 ×12 ×12
What are index forms?Index forms are defined as mathematical forms that are used in the representation of numbers or variables that are too large or too small in more convenient forms.
Other names for these index forms are;
Scientific notationStandard formsFrom the information given, we have that;
12 to the 3rd power in multiplication expression standard form
This is represented as;
12³
Expand the expression , we get;
12 ×12 ×12
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Alex's wardrobe is 2 yards tall. How tall is the wardrobe in feet?
feet
Answers
how to subtract 5/8 from 1 7/8
Answers
Answer:
7/8 - 5/8 = 2/8. Therefore the answer is 1 2/8.
Step-by-step explanation:
Answer: 1 2/8
Step-by-step explanation:
you take away 5 from seven so it becomes 2 then you put the 8 under and you still keep the one there
what is the perfect score between 144 and 169
Answers
Answer:
154
Step-by-step explanation:
if you write down all the numbers in a line then you go from 169 and 144 equally to the middle you would reach 154
Answer:
Pfffftttt i wish i knew
Step-by-step explanation:
Please help quick!!!!
Answers
Answer:
they all fit correctly