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Marta_Voda [28]
3 years ago
9

|9x-7|=|6x+3| Solve the inequality

Mathematics
1 answer:
dexar [7]3 years ago
8 0

Answer:

x = 4/15 and x= 10/3

Step-by-step explanation:

|9x-7|=|6x+3|

There are two solutions, one positive and one negative.

(9x-7)=6x+3                   - (9x-7)=6x+3

We will take the positive one first

(9x-7)=6x+3

Subtract 6x from each side

(9x-6x-7)=6x-6x+3

3x -7=3

Add 7 to each side

3x-7+7 = 3+7

3x = 10

Divide by 3x/3 = 10/3

x = 10/3


Now we will take the negative solution

- (9x-7)=6x+3

Distribute the negative sign

-9x+7 = 6x+3

Add 9x to each side

-9x+9x+7 = 6x+9x+3

7 = 15x+3

Subtract 3 from each side

7-3 = 15x +3-3

4 = 15x

Divide by 15 on each side

4/15 =15x/15

4/15 =x

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Answer: PART A : \frac{4.4}{x} = \frac{3}{4}

PART B : 5.9 FEET

Step-by-step explanation:

Length of the first sign = 4.4 feet

height of the first sign = 3 feet

Length of the second sign = x feet

height of the second sign = 4 feet

If two shapes are similar , then the ratio of their sides are equal,

That is ;

\frac{h_{1}}{h_{2} } = \frac{L_{1}}{L_{2} }

PART A

\frac{4.4}{x} = \frac{3}{4}

PART B

\frac{4.4}{x} = \frac{3}{4}

cross multiplying , we have

3x = 4.4 x 4

3x = 17.6

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x = 17.6/3

x = 5.86666666666667

x≈ 5.9 feet

Therefore , the length of the new sign is 5.9 feet

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3 years ago
Jerome is going to draw a marble from the bag shown below, replace it, and then draw another marble. What is the probability tha
alexira [117]
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Event B - get a pink marble

Events A and B are independent because we draw a marble from a bag with 20 marbles in both cases.
P(A)= \frac{3+4}{3+4+5+8}= \frac{7}{20}  
\\P(B)= \frac{8}{3+4+5+8}= \frac{8}{20} = \frac{2}{5}

Probability of combined events is 
P(A) \times P(B)=\frac{7}{20} \times \frac{2}{5} =\frac{7}{50}
7 0
3 years ago
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Find the quotient of 812.30 divided by 83. Round to the nearest tenth.
elena-14-01-66 [18.8K]
812.30/83 = 9.78674698.....
Nearest tenth means one number under decimal place so...

812.30/83 ~ 9.8

Explanation: The 9.7... rounded up to 9.8 because the number after the tenths place (in this case the number after the 7) is greater or equal to 5.
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3 years ago
The sum of all but one interior angle of a heptagon is 776°. what is the measure of the final interior angle? 42º 56º 124º 304º
Mekhanik [1.2K]

A heptagon has seven sides. The measure of the final interior angle of the heptagon is 124°.

<h3>What is heptagon?</h3>

A heptagon, sometimes known as a septagon, is a seven-sided polygon. The heptagon is also known as the septagon, which combines the prefix "sept-" with the Greek suffix "-agon," which means "angle."

A heptagon has 7 sides therefore, the sum of the interior angle of the heptagon can be written as,

\text{Sum of intetrior angles of a polygon with n sides} = (n-2)\times 180^o\\\\\text{Sum of all the angle of heptagon} = (7-2) \times 180^o = 900^o

As it is said in the problem that the sum of the all the angles of the heptagon  except one is 776°, therefore, the measure of the last angle of the heptagon is,

The measure of the last angle = 900° - 776° = 124°

Hence, the measure of the final interior angle of the heptagon is 124°.

Learn more about Heptagon:

brainly.com/question/12630702

3 0
2 years ago
Read 2 more answers
Can anyone help me pls ( if you can, can you do it on paper and post it with the answer)
Alla [95]

Answer:

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44 - 20 = 5x + 2x - 3x add/subtract like terms

24 = 4x divide both side by 4

6 = x

8 0
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