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liq [111]
3 years ago
12

Solve for the variable, please show work.

Mathematics
1 answer:
JulsSmile [24]3 years ago
7 0
The answer is c = 0

Explanation, see the picture

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Solve each inequality, and then drag the correct solution graph to the inequality.
Nesterboy [21]

The correct solution graph to the inequalities are

4(9x-18)>3(8x+12)  →  C

-\frac{1}{3}(12x+6) \geq -2x +14  → A

1.6(x+8)\geq 38.4  →  B

(NOTE: The graphs are labelled A, B and C from left to right)

For the first inequality,

4(9x-18)>3(8x+12)

First, clear the brackets,

36x-72>24x+36

Then, collect like terms

36x-24x>36+72\\12x >108

Now divide both sides by 12

\frac{12x}{12} > \frac{108}{12}

∴ x > 9

For the second inequality

-\frac{1}{3}(12x+6) \geq -2x +14

First, clear the fraction by multiplying both sides by 3

3 \times[-\frac{1}{3}(12x+6)] \geq3 \times( -2x +14)

-1(12x+6) \geq -6x +42

Now, open the bracket

-12x-6 \geq -6x +42

Collect like terms

-6 -42\geq -6x +12x

-48\geq 6x

Divide both sides by 6

\frac{-48}{6} \geq \frac{6x}{6}

-8\geq x

∴ x\leq  -8

For the third inequality,

1.6(x+8)\geq 38.4

First, clear the brackets

1.6x + 12.8\geq 38.4

Collect likes terms

1.6x \geq 38.4-12.8

1.6x \geq 25.6

Divide both sides by 1.6

\frac{1.6x}{1.6}\geq  \frac{25.6}{1.6}

∴ x \geq  16

Let the graphs be A, B and C from left to right

The first graph (A) shows x\leq  -8 and this matches the 2nd inequality

The second graph (B) shows x \geq  16 and this matches the 3rd inequality

The third graph (C) shows x > 9 and this matches the 1st inequality

Hence, the correct solution graph to the inequalities are

4(9x-18)>3(8x+12)  →  C

-\frac{1}{3}(12x+6) \geq -2x +14  → A

1.6(x+8)\geq 38.4  →  B

Learn more here: brainly.com/question/17448505

8 0
2 years ago
a water wheel has a radius of 18 feet. The wheel is rotating at 10 revolutions per minute. Find the linear​ speed, in feet per​
Yuri [45]

Answer:

The linear speed is 1,130.4\frac{ft}{min}

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference is equal to

C=2\pi r

we have

r=18\ ft

\pi =3.14

substitute

C=2(3.14)(18)

C=113.04\ ft

step 2

Find the linear speed in feet per minute

we know that

The wheel is rotating at 10 revolutions per minute

Convert revolutions to feet

Remember that

One revolution is equal to the circumference of the circle

so

10 revolutions is equal to

(10)113.04=1,130.4\ ft

therefore

The linear speed is 1,130.4\frac{ft}{min}

3 0
3 years ago
5 1/6 divided by 2 5/12= 2 4/29 true or false
Alex_Xolod [135]
5 1/6 divided by 2 5/12 is 2 4/29 so it is true
3 0
3 years ago
I need some heeelp please
VARVARA [1.3K]

Answer:

Min:  3

Q1:  7

Med:  10

Q3:  13

Max:  16

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Help me please :/// help
gayaneshka [121]
It’s not scaled. You can see it’s not the same shape as image A. 1 is only added to the height. If a shape is scaled, then the shape will remain the same, however it’s size will not. Therefore, the answer is “not a scaled copy of image A because 1 is added to the height”
7 0
2 years ago
Read 2 more answers
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