Translate each verbal description into an algebraic expression. Simplify the expression if you can.

The surface area, S, of a right rectangular prism with length, l, width, w, and height, h can be found using the formula below.

anygoal [31]

Answer:

246 in^2

Step-by-step explanation:

Given data

Length= 8 in

Width= 3 in

Height= 9 in

SA= 2( lw + wh + hl)

substitute

SA= 2(8*3+ 3*9+ 9*8)

SA= 2(24+ 27+72)

SA= 2(123)

SA= 246 in^2

Hence the SA is 246 in^2

4 0

2 years ago

Choose the equation below that represents the line passing through the point (−3, −1) with a slope of 4. (1 point)

tangare [24]

It would be the first one

6 0

3 years ago

Read 2 more answers

Which values are solutions to the inequality below? <br><br>Check all that apply.<br><br>x2 < 81

11111nata11111 [884]

A(6) and D(-4) are solutions to the equations

(6)^2 < 81 | 36 < 81

(-4)^2 < 81 | 16 < 81

5 0

3 years ago

Read 2 more answers

Which of the following equations could represent the points in the table? Select all that apply.

schepotkina [342]

Answer:

Options (A) and (C)

Step-by-step explanation:

From table attached,

Let the equation of a linear equation that represents the input-output values in the table is,

y - y' = m(x - x')

Where (x', y') is a point lying on the graph.

And m = slope of the line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$

m = $\frac{y_2-y_1}{x_2-x_1}$

Slope of the line passing through (0, 11) and (1, 5) will be,

m = $\frac{11-5}{0-1}$

m = -6

Therefore, equation of the line passing through (0, 11) and slope = -6 will be,

y - 11 = -6(x - 0)

Equation of a line passing through (1, 5) and slope = -6 will be,

y - 5 = -6(x - 1)

Equation of a line passing through (2, -1) and slope = -6 will be,

y + 1 = -6(x - 2)

Equation of a line passing through (3, -7) and slope = -6 will be,

y + 7 = -6(x - 3)

Therefore, Options (A) and (C) are the correct options.

4 0

3 years ago

What is the probability that a randomly selected permutation of the letters A, A, C, C, L, L, O, R, T, U would spell "calculator

kirill [66]

Answer:

See explanation

Step-by-step explanation:

Total number of letters = n! = 10

Permutation for 10 letters = n!

= 10!

= 10*9*8*7*6*5*4*3*2*1

= 3628800

From n letters:

Number of A = 2

Number of C = 2

Number of L = 2

A₁, A₂, C₁, C₂, L₁, L₂, O, R, T, U

Out of 3628800 permutations the word calculator can be spelled as:

C₁ A₁ L₁ C₂ U L₂ A₂ T O R

C₂ A₂ L₂ C₁ U L₁ A₁ T O R

and so on

So total number of different permutations are

(permutation of number of letters) / permutation of (number of As * number of Cs * number of Ls)

= 10! / (2! 2! 2 !)

= 10*9*8*7*6*5*4*3*2*1 / (2*1) (2*1) (2*1)

= 3628800 / 2 * 2 * 2

= 3628800 / 8

= 453600

Hence probability that a randomly selected permutation of the letters A, A, C, C, L, L, O, R, T, U would spell "calculator" is:

1 / total number of different permutations

= 1 / 10! / (2! 2! 2 !)

= 1/453600

= 0.000002

8 0

3 years ago