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OLEGan [10]
3 years ago
12

Find the area of the figure

Mathematics
1 answer:
Pavlova-9 [17]3 years ago
3 0
Triangle
1+1+5=7
7×4=28
28÷2=12

rectangle
12×5=60

whole shape
60+12=72in squared
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Can someone please help me on number 16-ABC
melomori [17]

Answer:

Please check the explanation.

Step-by-step explanation:

Given the inequality

-2x < 10

-6 < -2x

<u>Part a) Is x = 0 a solution to both inequalities</u>

FOR  -2x < 10

substituting x = 0 in -2x < 10

-2x < 10

-3(0) < 10

0 < 10

TRUE!

Thus, x = 0 satisfies the inequality -2x < 10.

∴ x = 0 is the solution to the inequality -2x < 10.

FOR  -6 < -2x

substituting x = 0 in -6 < -2x

-6 < -2x

-6 < -2(0)

-6 < 0

TRUE!

Thus, x = 0 satisfies the inequality -6 < -2x

∴ x = 0 is the solution to the inequality -6 < -2x

Conclusion:

x = 0 is a solution to both inequalites.

<u>Part b) Is x = 4 a solution to both inequalities</u>

FOR  -2x < 10

substituting x = 4 in -2x < 10

-2x < 10

-3(4) < 10

-12 < 10

TRUE!

Thus, x = 4 satisfies the inequality -2x < 10.

∴ x = 4 is the solution to the inequality -2x < 10.

FOR  -6 < -2x

substituting x = 4 in -6 < -2x

-6 < -2x

-6 < -2(4)

-6 < -8

FALSE!

Thus, x = 4 does not satisfiy the inequality -6 < -2x

∴ x = 4 is the NOT a solution to the inequality -6 < -2x.

Conclusion:

x = 4 is NOT a solution to both inequalites.

Part c) Find another value of x that is a solution to both inequalities.

<u>solving -2x < 10</u>

-2x\:

Multiply both sides by -1 (reverses the inequality)

\left(-2x\right)\left(-1\right)>10\left(-1\right)

Simplify

2x>-10

Divide both sides by 2

\frac{2x}{2}>\frac{-10}{2}

x>-5

-2x-5\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-5,\:\infty \:\right)\end{bmatrix}

<u>solving -6 < -2x</u>

-6 < -2x

switch sides

-2x>-6

Multiply both sides by -1 (reverses the inequality)

\left(-2x\right)\left(-1\right)

Simplify

2x

Divide both sides by 2

\frac{2x}{2}

x

-6

Thus, the two intervals:

\left(-\infty \:,\:3\right)

\left(-5,\:\infty \:\right)

The intersection of these two intervals would be the solution to both inequalities.

\left(-\infty \:,\:3\right)  and \left(-5,\:\infty \:\right)

As x = 1 is included in both intervals.

so x = 1 would be another solution common to both inequalities.

<h3>SUBSTITUTING x = 1</h3>

FOR  -2x < 10

substituting x = 1 in -2x < 10

-2x < 10

-3(1) < 10

-3 < 10

TRUE!

Thus, x = 1 satisfies the inequality -2x < 10.

∴ x = 1 is the solution to the inequality -2x < 10.

FOR  -6 < -2x

substituting x = 1 in -6 < -2x

-6 < -2x

-6 < -2(1)

-6 < -2

TRUE!

Thus, x = 1 satisfies the inequality -6 < -2x

∴ x = 1 is the solution to the inequality -6 < -2x.

Conclusion:

x = 1 is a solution common to both inequalites.

7 0
3 years ago
You deposit 1200 in an account. the annual interest is 3 percent. how long will it take you to earn 108 in simple interest
AleksandrR [38]

1200 + 108 = 1200( 1 + 0.03x)

1308 = 1200 + 36x

36x = 108

x = 3 years

3 0
3 years ago
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If g = 77 cm and h = 85 cm, what is the length of f?
puteri [66]
<span>Your answer is: D. 115 cm</span>
3 0
3 years ago
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Solve the following system of equations.<br> -7x +4y = 10<br> -5x +3y = 8<br><br> x=<br> y=
Virty [35]

Answer:x=2

              y=6

Step-by-step explanation:

-7*x+4*y=10

     ║minus

-5*x+3*y=8

----------------

-2*x+y=2

y=2+2*x

-------------

-5*x+3*(2+2*x)=8

-5*x+6+6x=8

x=8-6

x=2

-------------------------

-7*2+4*y=10

4*y=10+14

4*y=24

y=24/4

y=6

4 0
3 years ago
sharita does special typing jobs for scientist. she charges 16$ for the first 3 pages and 3$ for each additional page of scienti
liq [111]

Answer: 33 pages

Step-by-step explanation:

Let x represent the total number of pages typed by Sharita.

The cost of the first 3 pages = $ 16

Each additional page cost $3

Total amount paid = $106

since the first 3 pages cost $16 , and x represent the total pages , then the remaining pages will be x - 3

Also , since each additional page cost $3 , the cost of the remaining pages will be 3 ( x - 3)

Combining this , we have

16 + 3 ( x -3 ) = 106

16 + 3x - 9 = 106

7 + 3x      = 106

      3x = 106 - 7

       3x = 99

        x = 33

therefore ,Sonia's paper was 33 pages long

6 0
3 years ago
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