. A certain rectangular prism is
4 inches long, 2 inches wide, and
3 inches high. Sketch the figure
and find its volume.

Answer:

Step-by-step explanation:

Lateral surface area of the triangular prism = Perimeter of the triangular base × Height

By applying Pythagoras theorem in ΔABC,

AC² = AB² + BC²

(34)² = (16)² + BC²

BC = [tex]\sqrt{1156-256}[/tex]

     = [tex]\sqrt{900}[/tex]

     = 30 in.

Perimeter of the triangular base = AB + BC + AC

                                                      = 16 + 30 + 34

                                                      = 80 in

Lateral surface area = 80 × 22

                                  = 1760 in²

Total Surface area = Lateral surface area + 2(Surface area of the triangular base)

Surface area of the triangular base = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

                                                           = [tex]\frac{1}{2}(30)(16)[/tex]

                                                           = 240 in²

Total surface area = 1760 + 2(240)

                               = 1760 + 480

                               = 2240 in²

Volume = Area of the triangular base × Height

             = 240 × 20

             = 4800 in³

Complete the table below to show the differences between algebraic

expression and equation.

Describe each to show their differences.

Give 3 examples of each.

Answer:

Explained below with examples

Step-by-step explanation:

1. Algebraic expression in mathematics are basically expressions that are formed from variables, integer constants, and also algebraic operations.

Examples include;

>> 2x² − xy

>> 3ab + 2b²

>> x² + y²

2. An algebraic equation is a phrase where the two sides of the equation which are the left and right hand sides are connected by the equal to sign (=).

Examples are;

>> 3y - y² = 2y² + 2

>> 3x - 4y = x + 2

>> 5a + 3b = 2b - 1

Answer:

603.35%

Step-by-step explanation:

Given that a book costs $ 1.49 and is sold in a retail store for $ 8.99, to determine what is the percentage in mark up, the following calculation must be performed:

1.49 = 100

8.99 = X

8.99 x 100 / 1.49 = X

899 / 1.49 = X

603.35 = X

Thus, the mark up percentage of the book is 603.35%, which implies an increase of more than 6 times its initial value.

Answer:

smaller r =-21

larger r =-7

The vertex of the parabola is at

(-14,-49)

Answer: 5 ounces

Step-by-step explanation:

volume is 20*250*2=10000 cubic mm

10,000*0.0005=5

Answer:

The answer is C or B i dont really know

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

5/6 x 2 2/5 = 2

Step-by-step explanation:

https://www.fractioncalc.com/

This calculator link will help you with fraction equations

:))

Answer:

(x+8)^2=77    and   x=negative 8±√77

Step-by-step explanation:

After watching a video, I got it right on Khan

The equation with completing the squares is (x + 8)² = 77.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

x² + 16x - 2 = 11

We can make complete squares.

x² + 16x - 2 - 11 = 0

x² + 16x - 13 = 0

x² + 2 x 8 x (x) -8² + 8² - 13 = 0

(x² + 16x + 8²) - 64 - 13 = 0

(x + 8)² - 77 = 0

(x + 8)² = 77

Thus,

The equation is (x + 8)² = 77.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ2

Answer:

2 2/3

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

First convert to mixed fractions 7 1/2-> 15/2

Then multiply by the reciprocal---> 15/2 x 4/3

The answer is 60/6

Then simplify---> 10/1 or 10

Answer:

(-10,0)

Step-by-step explanation:

y = 3/2 x + 15

To find the x intercept let y =0 and solve for x

0 = 3/2x +15

Subtract 15 from each side

-15 = 3/2x -15+15

-15 = 3/2x

Multiply each side by 2/3

2/3 *-15 = 2/3 * 3/2x

-10 =x

The x intercept is

(-10,0)

Answer: (-10,0)

Step-by-step explanation:

Answer:

A. 12 ft², 16 ft², and 20 ft²

Step-by-step explanation:

Answer:

502 cubic feet

Step-by-step explanation:

The Volume of the tank is 502 cubic feet.

Answer:

c - 6

Step-by-step explanation:

differnce is subtraction

so subtract.

Answer:

it depends on his chores, how many he has, and how he does them

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

I had the same question his chores only last for 15 minutes so yes he would be done in time

Answer:

The base is 4.2426.

Step-by-step explanation:

Logarithm definition:

Suppose we have that:

[tex]\log_{a}{b} = c[/tex]

It means that;

[tex]b = a^c[/tex]

In this question:

[tex]\log_{x}{(5832)} = 6[/tex]

It means that:

[tex]x^6 = 5832[/tex]

[tex]x = \sqrt[6]{5832}[/tex]

[tex]x = (5832)^{\frac{1}{6}}[/tex]

[tex]x = 4.2626[/tex]

The base is 4.2426.

Answer:

[tex]60%[/tex]%

Step-by-step explanation:

[tex]17+23=40[/tex][tex], 40[/tex] in total.

[tex]10+14=24[/tex], 24 students trying out.

24 of 40 as a percent[tex]=60[/tex]

Answer:

60%

Step-by-step explanation:

According to formula if finding percent, given number(10+14)divide by total number(17+23) multiply 100% which is 24/40*100= 60%

Step-by-step explanation:

-6-9<3x<21-9

-15<3x<12

1) -15<3x

-5<x

2) 3x<12

x<4

so the range of the solution is -5<x<4

Answer:

it's 700 so last one

Step-by-step explanation:

since it's 1 to 20 you multiply 35×20 and you get 700

Answer:

m=√180

Step-by-step explanation:

n² = 6×24

n² = 144

m² = n² + 6²

m² = 144 + 36

m² = 180

m =√180

Answer:

D

Step-by-step explanation:

the 80*10=800

8 in 183= 80

8 in 4879 = 800

Answer:

no solution

Step-by-step explanation:

The given equation is :

2 - 3(x+ 4) = 3(3 - x)

We need to solve the equation. It can be done as follows :

2-3x-12 = 9-3x

As -3x gets canceled from both sides. It means the given equation has no solution.

Answer:

Step-by-step explanation:

Sorry but im struggling with this too :(

Answer:

[tex] \tan(55) = \frac{x}{8} \\ x = \tan(55) \times 8[/tex]

Answer:

B $45.26

Step-by-step explanation:

After 10 years

Emily will have 500 * 1.045^10 = $795.26

Erica will have 500 + 10*0.05*500 = 500 * 1.5 = 750$

Emily will have $45.26 more.

Answer:

120 Miles

Step-by-step explanation:

The answer choice which correctly describe s the function g (x) for a restricted domain as required to be determined in the task content is; g (x) = ³√(x + 4) , x ≥ -4.

As evident in the task content, the function which correctly represents the function g (x) for a restricted domain is to be identified.

By observation of the function;

g (x) = ³√(x + 4) , x ≥ -4.

As evident in the task content; the lowest value of g(x) is; 0.

By checking; when x = -4; the corresponding value of g (x) is;

g (-4) = ³√(-4 + 4)

g (-4) = 0.

On this note, the required function is; g (x) = ³√(x + 4) , x ≥ -4.

Read more on functions and domain;

https://brainly.com/question/20253960

#SPJ1