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3 years ago

What is the equation and solution for the sentence?

Mathematics

1 answer:

frez [133]3 years ago

4 0

Answer:

Write the equation as n + 31 = 113 and subtract 31 from both sides. The answer is 82.

Step-by-step explanation:

The sum of a number and 31 would be 'n + 31'. The sum equaling 113 would be '= 113'.

You would get 'n' by subtracting 31 for each side.

$n+31 = 113\\n+31-31=113-31 \leftarrow \text{Subtraction Property of Equality} \\\boxed{n=82}$

The statement: "Write the equation as n + 31 = 113 and subtract 31 from both sides. The answer is 82." should be the correct answer.

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Jermaine, Keira, and Leon are buying supplies for an art class. Jermaine bought 2 canvases, 4 tubes of paint, and 2 paint brushe

maria [59]

Answer:

canvas $3

tube of paint $5

paint brush $4

Step-by-step explanation:

We need to choose variables for the prices of the different items, translate the sentences into equations, and solve a system of equations.

1. Define variables

Let c = price of 1 canvas, t = price of 1 tube of paint, and b = price of 1 brush.

2. Translate sentences into equations

"Jermaine bought 2 canvases, 4 tubes of paint, and 2 paint brushes for $34."

2c + 4t + 2b = 34

"Keira spent $22 on 1 canvas, 3 tubes of paint, and 1 paint brush."

c + 3t + b = 22

"Leon already has plenty of paint, so he bought 3 canvases and 2 paint brushes for $17."

3c + 2b = 17

The system of equations is

2c + 4t + 2b = 34 Eq. 1

c + 3t + b = 22 Eq. 2

3c + 2b = 17 Eq. 3

Since the third equation has only the variables c and b, we use the first equations to eliminate variable t and give us an equation in only c and b.

3 * Eq. 1 - 4 * Eq. 2

2c + 2b = 14

c + b = 7 Eq. 4

Eq. 3 and Eq. 4 form a system of equations in two variables.

3c + 2b = 17 Eq. 3

c + b = 7 Eq. 4

Solve Eq. 4 for b.

b = 7 - c Eq. 5

Substitute into Eq. 3.

3c + 2(7 - c) = 17

3c + 14 - 2c = 17

c = 3

Plug in c = 3 into Eq. 5.

b = 7 - 3

b = 4

Plug in c = 3 and b = 3 into Eq. 2.

c + 3t + b = 22 Eq. 2

3 + 3t + 4 = 22

3t + 7 = 22

3t = 15

t = 5

Answer:

canvas $3

tube of paint $5

paint brush $4

7 0

3 years ago

You guys are life savers but does anyone know the answers to these questions? I’m so confused rn

timofeeve [1]

Answer:

The third choice

Step-by-step explanation:

We need to find the slope and y-intercept of the line and then put it into y = mx = b form. To find the slope, pick a point on the line; I will use (-2, 5); count how many units up you need to go to get to the next point on the line, which in this case it would be 3. The count how many to the right or left you would need to go, which is 1 to the left. Moving left means a negative, so it is -1. Your slope fraction would be $\frac{3}{-1}$ , since slope is rise over run. You can sub this fraction in for m in y = mx + b, which will give you a revised equation of y = -3x = b. To find the y intercept, or b, just find the point where the line crosses the y-axis, which is -1. So, the equation is now y = -3x - 1.The correct answer is third choice.