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Vesnalui [34]
3 years ago
11

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

th length x plus 10 and width 2 x plus 5. The inside of the rectangle is shaded other than an unshaded square with length x plus 1 and width x plus 1. Write an expression for the area of the shaded region in its simplest form. Show all of your steps.

Mathematics
1 answer:
Verizon [17]3 years ago
3 0

Answer:

x² + 23x + 49

Step-by-step explanation:

Since the area of a rectangle is: A = l x w, where l = length and w = width, we can find the overall area of the shaded region by multiplying the entire area and subtracting the smaller area of the unshaded square:

(2x + 5)(x + 10) - (x + 1)² or (2x + 5)(x + 10) - (x² + 2x + 1)

Distribute/FOIL:  

2x² + 20x + 5x + 50 - x² - 2x -1

Combine like terms:

x² + 23x + 49

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Answer:

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Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
James has dimes and quarters saved up in his change jar. He has a total of 162 coins totaling $31.20. James has dimes
SashulF [63]

The question is incomplete:

James has dimes and quarters saved up in his change jar. He has a total of 162 coins totaling $31.20 what is the total amount james has in quarters?

a. $10.00

b. $6.20

c.$15.50

d.$25.00

Answer:

d.$25.00

Step-by-step explanation:

With the information provided, you can write the following equations given that dimes are equal to 0.10 and quarters to 0.25 to determine the number of dimes and quarters that James has:

x+y=162 (1)

0.10x+0.25y=31.20 (2), where:

x is the number of dimes

y is the number of quarters

First, you can solve for x in (1):

x=162-y (3)

Then, you have to replace (3) in (2) and solve for y:

0.10(162-y)+0.25y=31.20

16.2-0.10y+0.25y=31.20

0.15y=31.20-16.2

0.15y=15

y=15/0.15

y=100

Finally, you have to replace the value of y in (3) to find x:

x=162-100

x=62

Now, you know that James has 100 quarters and you can multiply this number for the value of a quarter to find the amount James has in quarters:

100*0.25=25

According to this, the answer is that James has $25 in quarters.

4 0
3 years ago
How would I find the Max/min of this function f(x) = 2x squared +18x +16
slamgirl [31]
F(x)=2x²+18x+16
1) we have to calculate the first derived.

f´(x)=4x+18

2) Now, we equalize the first derived to "0" and find out the value of "x"
4x+18=0
4x=-18
x=-18/4=-4.5

3)we calculate the second derived
f´´(x)=4>0  ⇒we have a minimum at x=-4.5

4) Now we calculate the value of "y".
f(-4.5)=2(-4.5)²+18(-4.5)+16=40.5-81+16=-24.5

Therefore; Exist a minimum at (-4.5 , -24.5)
7 0
3 years ago
The ratio of 1.5 to 33 is the same as the ratio of 4.5 to
Mandarinka [93]

Answer:

132

Step-by-step explanation:

7 0
3 years ago
Solve the system of equations.
expeople1 [14]

Answer:(-5,-6)

Step-by-step explanation:

Solve for one variable then solve for the other. Don’t worry you will get a big fraction before you get to the whole number.

8 0
3 years ago
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