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julsineya [31]
4 years ago
9

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

Mathematics
1 answer:
umka2103 [35]4 years ago
5 0

Answer:

x^2 +23x +49

Step-by-step explanation:

Find the area of the large rectangle

(x+10) * (2x+5)

FOIL

2x^2 +5x+20x+50 = 2x^2 +25x +50

Find  the area of the unshaded square

(x+1) (x+1)

FOIL

x^2 +x+x+1 = x^2 +2x+1

To find the area of the shaded region

Take the area of the large rectangle and subtract the area of the square

2x^2 +25x +50 - (x^2 +2x+1)

Distribute the minus sign

2x^2 +25x +50 - x^2 -2x-1

Combine like terms

x^2 +23x +49

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Name three solutions to the inequality. x<7
Gnom [1K]

Answer:

x=anything less than 7

x=5

x=-2

x=-7

x= anything less than 7

Step-by-step explanation:

7 0
3 years ago
Sandy wants to carpet the game room in her house. How many square feet of carpet will she need to complete her project if the di
AfilCa [17]

Answer:

72ft^2

Step-by-step explanation:

3 0
3 years ago
Tracy wants to earn at least 100 dollars from her two jobs next week. At most she can work 12 hours. Her first job pays 8 an hou
exis [7]

Answer:

Step-by-step explanation:

You didn't list the options from which we are to choose as your system of inequalities, but that doesn't matter...we'll come up with them on our own and then you can match them to your options.  The first inequality is going to be about the number of hours worked.  The second inequality is going to be about the money earned.  Hours worked and money earned have to be in 2 different inequalities because they are not the same.  If x is one job and y is the other, and the combination of these jobs cannot be more than 12 hours total, then the inequality for this is:

x + y ≤ 12

That represents the hours worked.  As far as the money goes, she makes $8 per hour, x, at the first job, and $9 per hour, y, at the second job.  She wants the combination of these wages to be at least $100.  The inequality that represents the money earned is:

8x + 9y ≥ 100

That is the system that represents your situation.

7 0
3 years ago
Four times the sum of half a number and 6 is 48
katrin [286]

Answer:

<h3>The number is 12</h3>

Step-by-step explanation:

Let the number be x

Half a number is written as 1/2x

So we have

Four times the sum of half a number and 6 is 48 is written as

4( \frac{1}{2} x + 6) = 48 \\ 2x + 24 = 48 \\ 2x = 48 - 24 \\ 2x = 24

Divide both sides by 2

That's

\frac{2x}{2}  =  \frac{24}{2}

We have the final answer as

<h3>x = 12</h3>

Hope this helps you

6 0
3 years ago
What is the maximum number of consecutive positive integers that can be added together to create a sum less than 400?
nikitadnepr [17]
X + x + 1 + x + 2 < 400
3x + 3 < 400
3x < 397
x < 132.33333...

the smallest number has to be smaller than 132. 33
7 0
3 years ago
Read 2 more answers
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