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3 years ago

What is the first step in finding the unit price on a box of 20 pencils?

1 answer:

7 0

You would need to know the cost of the box of 20, then you would divide the total cost by the number of pencils in the box. This would give you the cost of one pencil - which is the unit cost.

Example:

Lets say the box of 20 pencils cost $10.

Divide the total cost by the number of pencils:

10 / 20 = 0.50 - This means each pencil cost 50 cents, so the unit cost would be 50 cents per pencil.

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Solve the system of linear equations by elimination −2x+3y=7 and 5x+8y=−2

forsale [732]

You would need to make them eliminate so I would multiply the entire first one by 2.5 to make the X's cancel out. So you would end up with -5X+7.5Y=17.5. The X's would cancel and you would be left with 15.5Y=15.5. So Y=1. Then replace Y into one of the equations. I'm going to use the top again. -2X+3(1)=7. Subtract 3 from both sides to get -2x=4. Divide both sides by negative 2 to get X=-2. So the solution would be (-2,1)

4 0

3 years ago

What system of inequalities is represented by the graph?

yarga [219]

As shown in the figure, we have two straight line. One of them has a negative slope and the other has a positive one. In two dimensions, the equation for non-vertical lines is often given in the slope-intercept form by:

$y=mx+b$

being m the slope of the line and b the y-intercept of it.

On the other hand, if x = 0 then y = b.

First of all we will order the equations above without inequalities like this:

A. $y = 5x-1$ , $y = 3x+4$
B. $y = 5x-1$ , $y = -3x+4$
C. $y = 5x+1$ , $y = -3x+4$
D. $y = 5x-1$ , $y = -3x-4$ 

As shown in the figure b = -1 for one straight and b = 4 for the second one. This values take place when x = 0. So, we discard C and D, because if x = 0, then:

For C, b = 1 and b = 4
For D, b = -1 and b = -4

Let's analyze A and B. So:

For A, m = 5 and m = 3
For B, m = 5 and m = -3

Therefore, we discard A because of the statement above.

Finally the answer is B. So, the inequalities are:

(1) $y\ \textless \ 5x-1$
(2) $3x+y \geq 4$

Let's prove this answer. We will take the point (2, 0) that is in the region in gray. So, substituting this point in the inequalities, we have:

(1) $0\ \textless \ 9$
(2) $6 \geq 4$

In fact, this is true.

7 0

3 years ago

WILL GIVE BRAINLIEST.

Elena L [17]

Answer:

$\tan(\theta) =$ undefined

Step-by-step explanation:

Given

$\sin(\theta) = -1$

Required

Determine $\tan(\theta)$

We know that:

$\sin^2(\theta) + \cos^2(\theta) = 1$

This gives:

$(-1)^2 + \cos^2(\theta) = 1$

$1 + \cos^2(\theta) = 1$

Collect like terms

$\cos^2(\theta) = 1 -1$

$\cos^2(\theta) = 0$

Take square roots

$\cos(\theta) = \sqrt 0$

$\cos(\theta) = 0$

By tan identity

$\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$

$\tan(\theta) = \frac{-1}{0}$

$\tan(\theta) =$ undefined

6 0

3 years ago

working together it takes two computers 10 minutes to send out a company's email. If it takes the slower computer 30 minutes to

allochka39001 [22]

Answer: it will take the faster computer 15 minutes to do the job on its own.

Step-by-step explanation:

Let t represent the number of minutes it will take the faster computer to do the job on its own. It means that the rate at which it does the job per minute is 1/t

If it takes the slower computer 30 minutes to do the job on its own. It means that the rate at which it does the job on its own per minute is 1/30

By working together, they would work simultaneously and their individual rates are additive. Working together it takes two computers 10 minutes to send out a company's email. It means that the rate at which both computers work together per minute is 1/10 Therefore,

1/t + 1/30 = 1/10

Cross multiplying by 30x, it becomes

3x = x + 30

3x - x = 30

2x = 30

x = 30/2

x = 15 minutes

5 0

3 years ago

Write the sum of 8x^2 - x + 4 and x - 5 Show all work

tigry1 [53]

okey

you needed the sum or division?

3 0

3 years ago