A rectangular box has a square base. The combined length of a side of the square
base, and the height is 20 in. Let x be the length of a side of the base of the box.
a. Write a polynomial function in factored form modeling the volume V of the box.
b. What is the maximum possible volume of the box?
c. Explain how you found the maximum possible volume.

Answer:

8

Step-by-step explanation:

Corresponding sides of similar triangles are proportional, so:

[tex]\frac{A'B'}{12}=\frac{4}{6} \implies A'B'=8[/tex]

Answer:Yes, the obtuse angles for both triangles are equailateral

Step-by-step explanation:

The inverse of the given function is (f^-1)(x) = (1/2)×(√x  - 1) for x ≥ 0.

We are given a function f(x). The function f(x) is defined as (2x + 1)². The domain of the given function f(x) is x ≥ -1/2. We need to find the inverse of the function f(x).

Let us suppose that the function f(x) is represented by the variable "y".

y = f(x)

y = (2x + 1)²

Now we will take the square root on both sides of the equation.

√y = √[(2x + 1)²]

When we cancel out the even powers, we need to take the absolute value using modulus.

√y = |2x + 1|

We already know that x ≥ -1/2, so, modulus will open with a positive sign.

√y = +(2x + 1)

√y = 2x + 1

√y  - 1 = 2x

x = (1/2)×(√y  - 1)

At last, we replace the variables y and x by x and (f^-1)(x).

(f^-1)(x) = (1/2)×(√x  - 1) for x ≥ 0

To learn more about functions, visit :

https://brainly.com/question/5975436

#SPJ1

Answer:

[tex]\frac{13}{4}[/tex]

(Decimal: 3.25)

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

Answer:

5.25

Step-by-step explanation:

1/4+1/3(10-1)

*do what's in parenthesis first!*

10 - 1 = 9

1/4 + 1/3 = 7/12

then you multiply 7/12 x 9 = 5.25

DONT FORGET!

Please Excuse My Dear Aunt Sally

P  E M D A S

Using the GCF to factor and the distributive property 28 + 24 = 4(7 + 6)

28 + 24 as a product of the two factors using greatest common factor and the distributive property can be represented as follows:

The greatest common factor is defined as the largest number that is a factor of two or more numbers.

The distributive property states that an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC.

Therefore, lets solve 28 + 24 using GCF and the distributive property.

The GCF of 28 and 24 is 4. Hence,

28 + 24 = 4(7 + 6)

Therefore,

28 + 24 = 4(7 + 6)

learn more on GCF  here; https://brainly.com/question/18994312

#SPJ1

According to the Pythagoras theorem, the value of the slope of the ramp is 10.44

Pythagoras theorem

Pythagoras theorem states that the sum of squares of the sides equal to the square of the hypotenuse.

The general form of the Pythagoras theorem is,

c² =  a² + b²

where

c refers the hypotenuse

a and b refers the sides of the triangle.

Given,

Here we have the ramp with the side values 3 and 10.

Now, we have to find the value of the slope.

Let us consider x be the hypotenuse or slope of the ramp.

We know that the Pythagoras theorem states that the square of the hypotenuse is equal to the sum of square of the sides.

So, it can be written based on these,

x² = 3² + 10²

x² = 9 + 100

x² = 109

x = √109

When we simplify this one then we get the value of slope as 10.44.

To know more about Pythagoras theorem here.

https://brainly.com/question/343682

#SPJ1

The conclusion from the equation |y + 6| = 2 is that it has two solutions , the correct option is (b) .

In the question ,

it is given that ,

the equation is given as |y [tex]+[/tex] 6| [tex]=[/tex] 2 ,

after removing the modulus  , we get the two equations , that are

y + 6 = 2 and y + 6 = -2

Solving y + 6 = 2 , we get

y + 6 = 2

Subtracting 6 from both LHS and RHS ,

we get

y = 2 - 6

y = -4

On Solving y + 6 = -2 ,

we get

y + 6 = -2,

Subtracting 6 from both LHS and RHS ,

we get

y = - 2 - 6

y = -8 .

the two solutions are y = -8 and y = -4 .

Therefore , The conclusion from the equation |y + 6| = 2 is that it has two solutions , the correct option is (b) .

The given question is incomplete , the complete question is

Consider this equation. |y + 6| = 2 what can be concluded of the equation? check all that apply.

(a) There will be one solution

(b) There will be two solutions.

Learn more about Equations here

https://brainly.com/question/12056813

#SPJ4

Answer:

Step-by-step explanation

TS=13 as opp sides in an isosceles triangle are equal

AngleT=60

as 60+60+T=180

The equation to show the net effect of these transactions is x - 45 + 150.

The equation is x + 105.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, the customer withdrew $45 from a bank account and the customer then deposited $150 into the bank account the next day.

Let the initial amount in the account be x. The amount after the transaction will be:

= x - 45 + 150

= x + 105

The equation is x + 105.

Learn more about equations on:

brainly.com/question/2972832

#SPJ1

The growth rates in 1950, 1988 and 2010 are 13.9%, 23.4 and 29.8% respectively

The function of the growth rate equation is given as:

y = -0.0000081x^3+0.00267x^2+8.231

Rewrite properly

So, we have

y = -0.0000081x³ + 0.00267x² + 8.231

From the question, we have

x represents the number of years after 1900

In 1950, x = 50

So, we have

Growth rate in 1950, y = -0.0000081 x 50³ + 0.00267 x 50² + 8.231

Growth rate in 1950, y = 13.9

In 1988, x = 88

So, we have

Growth rate in 1988, y = -0.0000081 x 88³ + 0.00267 x 88² + 8.231

Growth rate in 1988, y = 23.4

In 2010, x = 110

So, we have

Growth rate in 2010, y = -0.0000081 x 110³ + 0.00267 x 110² + 8.231

Growth rate in 2010, y = 29.8

Hence, the growth rate in 2010 is 29.8%

Read more about population functions at

https://brainly.com/question/25896797

#SPJ1

slope = m = (8 - (-6)) / (8 - 6) = 7

y = mx + b

y = 2x + b

plug in (8, 8) to find b

8 = 2(8) + b

b = -8

y = 2x - 8

We must combine 3 servings of Ta-sty Pocket, 2 serving of P-ita Roll, and 1 serving of In-sta Pancake to get 754 calories, 19.2 g of f-at, and 78.9 g of carbohydrates.

According to the question,

Three brands of breakfast food represents the calories , f-at, and carbohydrates.

To get 754 calories, we should combine

= 450 + 238 + 66

= 3 (150) + 2 ( 119) + 1 (66)

= 3 serving of Ta-sty Pocket + 2 serving of P-ita Roll + 1 serving of In-sta Pancake

To get 19.2g of f-at, we should combine

= 14.4 + 4.6 + 0.2

= 3(4.8) + 2( 2.3) + 1(0.2)

= 3 serving of Ta-sty Pocket +2 serving of P-ita Roll +1 serving of In-sta Pancake

To get 78.9 g of carbohydrates, we should combine

= 29.4 + 28 + 21.5

= 3(9.8) + 2( 14) + 1 (21.5)

= 3 serving of Ta-sty Pocket +2 serving of P-ita Roll +1 serving of In-sta Pancake

Hence, we should combine 3 serving of Tasty Pocket, 2 serving of P-ita Roll, 1 serving of In-sta Pancake

Learn more about serving here

https://brainly.com/question/14544303

#SPJ1

Solving for f(-2) in the function f(x) = 3x^2 + 2x + 4 gave the solution

From the given function f(x) = 3x^2 + 2x + 4 we substitute for x = -2  which is same as function of -2

f(x) = 3x^2 + 2x + 4

pugging in x = -2

f(-2) = 3(-2)^2 + 2(-2) + 4

solving the squared and opening the parentheses

f(-2) = 3 * 4 + -4 + 4

f(-2) = 12 - 4 + 4

f(-2) = 12

Learn more about quadratic terms here:

https://brainly.com/question/29395779
#SPJ1

12x³ - 39x² -   111x + 30 is polynomial in standard form .

What in mathematics is a polynomial?

Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an expression made up of variables, constants, and exponents.

standard form g(x) = 3(x + 2)(4x - 1)(x - 5)

                      g(X) = 3[ 4x² - x + 8x - 2 )( x - 5 ) ]

                             = 3[ ( 4x² + 7x - 2 ) ( x - 5 )]

                             = 3 [ 4x³ + 7x² - 2x - 20x² - 35x + 10 )]

                             = 3[ 4x³ - 13x² - 37x + 10 ]

                             = 12x³ - 39x² -   111x + 30

Learn more about polynomial

brainly.com/question/11536910

#SPJ1

The values of x and y will be 10 and 4 respectively, using congruent of the triangle.

What is congruent of the triangle?

The shapes maintain their equality regardless of how they are turned, flipped, or rotated before being cut out and stacked. We'll see that they'll be placed entirely on top of one another and will superimpose one another. Due to their identical radius and ability to be positioned directly on top of one another, the following circles are considered to be congruent.

Any two figures can be perfectly positioned over one another to demonstrate their congruence. The relationship between two figures that are said to be congruent is described using the word "congruence."

Here, ΔRWS ≅ ΔTUV

Here 2y + 10 = 30

2y = 30-10

y=20/2

y=10.

Agian ∠R = ∠T

Here ∠T = 90 -32 =58°

So 8x+26 = 58°

8x = 58-26

x = 32/8

x = 4.

Hence the values of x and y will be 10 and 4 respectively.

Learn more about congruent, by the following link.

https://brainly.com/question/1675117

#SPJ1

To determine what satisfying assumptions 1-3 would mean by considering the variable under consideration.

The regression-inference Assumptions 1-3 must be satisfied if β°, β¹ and σ are constants, which ensures the x dimensions and price of every custom home to be normal, with β° + β¹ and a σ standard deviation.

The residuals should not be linear if the normal probability plot is followed.

In the diagram above, the assumptions for regression inferences appear to be unsatisfactory.

To learn more about regression analysis visit the link- https://brainly.com/question/26755306

#SPJ4

Answer:

$250

Step-by-step explanation:

He expected to collect 37.5% less than $400.

First, we find 37.5% of $400.

Then we subtract that amount from $400.

37.5% of $400 is:

37.5% of $400 = 0.375 × $400 = $150

Now, subtract $150 from $400:

$400 - $150 = $250

Answer: $250

The price of one sweater - x

The price of one shirt - y

From what the problem states, we can assume:

x + 4y = 55

4x + 5y = 110

Multiply both sides of x +4y = 55 by four. This results in 4x + 16y = 220. We then subtract 16y on both sides, resulting in 4x = 220 - 16y. We then insert this into the other equation, which, as a reminder, is 4x + 5y = 110. We replace 4x with 220 - 16y, which results in 220 - 16y + 5y = 110. Now, we can solve it.

Now that we have found out the value of y, we can replace all instances of y in the first equation.

Answer:

36 = 2x + y

x = y

x = 12

y = 12

Step-by-step explanation:

Answer:A=12 C=24

Step-by-step explanation:

there are 3 shares[2x and theunknown]

36=3shares so 1 share=36divided by3=12

ad=12

ch=12x2=24

12+24=36

Answer:

5u - 4u = 1u

1u = 15

9u = 135

∴ Both girls have 135 yo-yos together.

We know that:

                      x = 10 + y

In the next equation {-3x + y = -28}  x is the same as the first, so:

-3(10 + y) + y = -28

-30 - 3y + y = -28

-30 - 2y = -28            

We add 30 to both sides:

-2y = 2

and divide both sides by (-2):

y = -1

Now we can put y = -1 to the first equation:

  x = 10 + y

  x = 10 - 1

   x = 9

So,

Answer:

540= 2x2x3x3x3x5

       or

540= [tex]2^{2}[/tex]x[tex]3^{3}[/tex]x5

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

Since 6 *6 = 36 , the square root of 36 is 6

In other words:

[tex]\sqrt{36} \\= 6\\[/tex]

Since 9*9 = 81, the square root of 81 is 9

[tex]\\\/\sqrt{81}\\ = 9[/tex]

Now we have the fraction [tex]\frac{6}{9}[/tex]

Now we reduce [tex]\frac{6}{9}[/tex] to lowest terms:

[tex]\frac{6}{9 } = \frac{2}{3}[/tex]

Therefore, the answer is  [tex]\frac{2}{3}[/tex]

Hope this helps :)

Answer: 16\/729

Step-by-step explanation:

Answer:

six raised to the fourth power divided by three raised to the tenth power

Step-by-step explanation:

(6^−2 • 3^5)^−2 = 6^(-2*-2) * 3^(5*-2) = 6^4 * 3^(-10) = 6^4 / 3^10

The total number of votes which is reduced by the ratios of yes and no votes will be: 4580; + 6412 = 10992;

What are Ratios?

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings. For instance, a class has a 12:15 boy-to-girl ratio, whereas the part-to-whole ratio refers to the relationship between a particular group and the entire. For instance, five out of every ten people enjoy reading. As a result, the ratio of the part to the whole is 5: 10, meaning that 5 out of every 10 people enjoy reading.

In the given question, we have:

The ratio of yes votes to no votes was 7 to 5.

Total Number of Yes votes = 6412;

So, Let us assume the total number of no votes be x;

So, according to the question,

[tex]\frac{7}{5} = \frac{6412}{x}[/tex]

Cross Multiplying the terms:

⇒7 × x = 6412 ×5

⇒x = 4580;

So, The total number of no votes is 4580;

So, The total number of votes will be: 4580; + 6412 = 10992;

Hence,

The total number of votes will be: 4580; + 6412 = 10992;

To learn more about Ratios, visit:

https://brainly.com/question/12024093

#SPJ1

Answer:

======================

Sum of interior angles of 6-sides polygon is:

Set equation for the sum of interior angles and solve for x:

Find the measure of angle L:

Correct choice is C.

[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ S = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ n=6 \end{cases}\implies S=180(6-2)\implies S=720 \\\\[-0.35em] ~\dotfill\\\\ (120)+(8x)+(6x-7)+\stackrel{\measuredangle L}{(7x-3)}+(5x)+\stackrel{\measuredangle O}{(90)}=720\implies 26x+200=720 \\\\\\ 26x=520\implies x=\cfrac{520}{26}\implies x=20~\hfill \underset{\measuredangle L}{\stackrel{7(20)~~ - ~~3}{\text{\LARGE 137}}}[/tex]

Answer:

9:5

5:14

Step-by-step explanation:

If the dimensions of a right rectangular prism are (8)/(5)cm,(10)/(3)cm, and (7)/(4)cm. Then volume of the prism is 401/60 cm³

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases

The dimensions of a right rectangular prism are width is 8/5 cm, Length is 10/3cm and Height is 7/4cm

Volume=Width×Height×Length

=8/5×10/3×7/4

=96+200+105/60

=401/60 cm³

Hence volume of the right rectangular prism is 401/60 cm³

To learn more on Three dimensional figure click:

https://brainly.com/question/2400003

#SPJ1