MATHEMATICS HIGH SCHOOL

A square with side length c has an area of 81 square centimeters. The following equation shows the area of the square. c^2 = 81. What is the side length of the square in centimeters?

Answers

Answer 1

Answer:

Answer:

9 cm

Step-by-step explanation:

c^2=81

Take the square root of both sides.

The square root of c^2 is c.

The square root of 81 is 9.

c=9

Answer 2

Answer:

Answer:

C = 9 centimeters

Step-by-step explanation:

First, look at the area of a square, which formula is c^2 or in standard format - s^2. Thus, we can say, c^2 = 81. Then, we can simplify, and put c = √81. Since 81 is a perfect square, 9 * 9 = 81. Thus the answer is 9 centimeters.

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Tony had 1 1/2 gallons of orange juice. He drank 2/7 of the orange juice he had. How mucj orange juice did Tony drink?

Can someone help me whit this?!?

Answers

The answer would be 40 because if you take the the line in which angle b is in it would be 180 and then we would subtract 140 which gives you 40 , good luck ! :)

HELP PLEASE!!!!

WILL MARK BRAINLIST IF YOU HAVE AN EXPLANATION!!

Answers

Answer:

Options B and D

Step-by-step explanation:

$. \n \angle \: 1 \cong \angle 5 \n (exterior \: alternate \: \angle s) \n$

$\angle \: 1 \cong \angle 7 \n (vertical \: \angle s) \n$

A colored chip is yellow on one side and red on the other. The chip was flipped 50 times and landed red side facing up 20 times. What is the relative frequency of the chip landing with the red side facing up?20%
30%
40%
60%

Answers

Number of times red side faced up = 20

Total number of times thrown = 50

Frequency of red side = No of red side / Total    * 100%

= (20 / 50) * 100%

   = 0.4 * 100%

   = 40%

Hope this explains it.

20/50 is equal to 40/100 so the answer is 40%

if 10 800 cm2 of material is available to make a box with a square base and an open top find the largest possible volume of the box.

Answers

Let

x--------> the length side of the square base of the box

y-------> the height of the box

we know that

The surface area of the box is equal to

$SA=4xy+x^(2)$

$SA=10,800\ cm^(2)$

$10,800=4xy+x^(2)$

$y=(10,800-x^(2))/(4x)$

$y=(2,700-0.25x^(2))/(x)$ --------> equation A

the volume of the box is equal to

$V=x^(2)y$ --------> equation B

Substitute the equation A in the equation B

$V=x^(2)*(2,700-0.25x^(2))/(x)$

$V=x*(2,700-0.25x^(2))$

$V=(2,700x-0.25x^(3))$

using a graphing tool

see the attached figure

For $x=60\ cm$

$Volume=108,000\ cm^(3)$

the point $(60,108,000)$ is a maximum of the function

Find the dimensions of the box

$x=60\ cm$

Find the value of y

$V=x^(2)y$

$y=V/x^(2)$

$y=108,000/60^(2)$

$y=30\ cm$

The dimensions of the box are

$60\ cm*60\ cm*30\ cm$

The largest possible volume of the box is

$108,000\ cm^(3)$

The largest possible volume of the box is $\boxed{108000{\text{ c}}{{\text{m}}^3}}.$

Further explanation:

Given:

The area of the material is $10800{\text{ c}}{{\text{m}}^2}.$

Explanation:

Consider the base length of the square box as “x”.

Consider the height of the box as “y”.

The surface area of the open box can be expressed as follows,

$\boxed{{\text{Surface Area}} = 4xy + {x^2}}$

The surface area of the box is $10800{\text{ c}}{{\text{m}}^2}.$

$\begin{aligned}4xy + {x^2}&= 10800\n4xy&= 10800 - {x^2}\ny&= \frac{{10800 - {x^2}}}{{4x}}\ny&=\frac{{2700 - 0.25{x^2}}}{x}\n\end{aligned}$

The volume of the box can be expressed as follows,

$\begin{aligned}V&= {x^2}y\n&= {x^2}* \left({\frac{{2700 - 0.25{x^2}}}{x}} \right)\n&= \left( x \right)* \left({2700 - 0.25{x^2}} \right)\n&= 2700x - 0.25{x^3}\n\end{aligned}$

Differentiate the volume with respect to “x”.

$\begin{aligned}\frac{{dV}}{{dx}}&= \frac{d}{{dx}}\left({2700x - 0.25{x^3}}\right)\n&= 2700 - 0.75{x^2}\n\end{aligned}$

Substitute 0 for $\frac{{dV}}{{dx}}$ in above equation to obtain the value of x.

$\begin{aligned}0&= 2700 - 0.75{x^2}\n0.75{x^2} &= 2700\n{x^2}&= \frac{{2700}}{{0.75}}\n{x^2}&= 3600\nx&= 60\n\end{aligned}$

The side of the base is $60{\text{ cm}}.$

The height of the box can be obtained as follows,

$\begin{aligned}y&= \frac{{2700 - 0.25{{\left( {60} \right)}^2}}}{{60}}\n&=\frac{{2700 - 900}}{{60}}\n&=\frac{{1800}}{{60}}\n&=30\n\end{aligned}$

The height of the box is $y = 30{\text{ cm}}.$

The volume of the box can be calculated as follows,

$\begin{aligned}V&={\left(60}\right)^2}*\left({30}\right)\n&=3600*30\n&=108000 \n\end{aligned}$

The largest possible volume of the boxis $\boxed{108000{\text{ c}}{{\text{m}}^3}}$ .

Learn more:

1. Learn more about inverse of the functionbrainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Application of Derivatives

Keywords: square, box, material, square base, volume of the box, largest, open from the top derivative, surface area.

Rewrite in simplest terms:

10(7g-9h)-4h-8(-h+8g)10(7g−9h)−4h−8(−h+8g)

ASAP

Answers

The answer is 2(3g-43h)

F(x) = 3x - 3
g(x) = 4x + 5

find (f+g) (3)

Answers

Answer:

Step-by-step explanation:

(f + g)(3) = f(3) + g(3)

f(3) = 3(3) - 3 = 9 - 3 = 6

g(3) = 4(3) + 5 = 12 + 5 = 17

Then

(f + g)(3) = 6 + 17 = 23

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