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almond37 [142]
4 years ago
13

SOLVING ABSOLUTE VALUE EQUATION

Mathematics
1 answer:
Ratling [72]4 years ago
7 0

Answer:

1. x=27

2. x=11 or x=-7

3. x=4

4. x=1 or x=\frac{1}{3}

5. x=12

6. x=11 or x=-1

7. x=8

8. x=3 or x=1

9. x=\frac{13}{2} or x=-4

10.x=7 or x=1

Step-by-step explanation:

For the first 8, the absolute value portion is just substituted in for x, so we can skip some of the repeated work that would occur in these. For the absolute value problems, there are two solutions each. When you remove an absolute value, you have to add a plus or minus to each side and solve for each.

1. 5x+9=144\\5x=135\\x=27

2. |3x-6|=27\\3x-6=27\\3x=33\\x=11\\\\3x-6=-27\\3x=-27\\x= -7

3. \frac{x}{7-3} =1\\\frac{x}{4} =1\\x=4

4. |12x-8|=4\\12x-8=4\\12x=12\\x=1\\\\12x-8=-4\\12x=4\\x=\frac{4}{12} \\\\x=\frac{1}{3}

5. \frac{2}{3}x-11=-3\\\frac{2}{3}x=8\\x=\frac{24}{2}\\ x=12

6. |2x-10|=12\\2x-10=12\\2x=22\\x=11\\\\2x-10=-12\\2x=-2\\x=-1

7. \frac{4x-5}{3} =9\\4x-5=27\\4x=32\\x=8

8. |8x-16|=8\\8x-16=8\\8x=24\\x=3\\\\8x-16=-8\\8x=8\\x=1

9. |4x-5| +15=36\\|4x-5|=21\\4x-5=21\\4x=26\\x=\frac{26}{4} \\x=\frac{13}{2} \\\\4x-5=-21\\4x=-16\\x=-4

10. 6|3x-12|-5=49\\6|3x-12|=54\\|3x-12|=9\\3x-12=9\\3x=21\\x=7\\\\3x-12=-9\\3x=3\\x=1

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A TEACHER IS CONSTRUCTING A MATHEMATICS TEST
Nuetrik [128]

The number of ways of constructing questions from the pool of 28 questions if her test is to have 3 difficult, 4 average and 3 easy questions is  924, 000 ways

<h3>How to determine the combination</h3>

Note that the formula for combination is given as;

Combination = \frac{n!}{r!(n-r)!}

From the information we have that;

There are 28 questions in the pool

The test should have a total of 10 questions;

6 difficult , 10 average and 12 easy questions

We are asked to determine the combination of;

3 difficult questions

4 average questions

3 easy questions

6C3 = \frac{6!}{3!(6-3)!}

6C3 = \frac{720}{36}

6C3 = 20

10C4 = \frac{10!}{4!(10-4)!}

10C4 = \frac{3628800}{17280}

10C4 = 210

12C4 = \frac{12!}{4!(12-4)!}

12C4 = 220

The number of ways of constructing the questions is

= 20 × 210 × 220

= 924, 000 ways

Thus, the number of ways of constructing questions from the pool of 28 questions if her test is to have 3 difficult, 4 average and 3 easy questions is  924, 000 ways

Learn more about combination here:

brainly.com/question/4658834

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7 0
2 years ago
A rectangle is twice as long as it is wide. If its length and width are both
puteri [66]

Answer:

a rectangle is twice as long as it is wide . if both its dimensions are increased 4 m , its area is increaed by 88 m squared make a sketch and find its original dimensions of the original rectangle

Step-by-step explanation:

Let l = the original length of the original rectangle

Let w = the original width of the original rectangle

From the description of the problem, we can construct the following two equations

l=2*w (Equation #1)

(l+4)*(w+4)=l*w+88 (Equation #2)

Substitute equation #1 into equation #2

(2w+4)*(w+4)=(2w*w)+88

2w^2+4w+8w+16=2w^2+88

collect like terms on the same side of the equation

2w^2+2w^2 +12w+16-88=0

4w^2+12w-72=0

Since 4 is afactor of each term, divide both sides of the equation by 4

w^2+3w-18=0

The quadratic equation can be factored into (w+6)*(w-3)=0

Therefore w=-6 or w=3

w=-6 can be rejected because the length of a rectangle can't be negative so

w=3 and from equation #1 l=2*w=2*3=6

I hope that this helps. The difficult part of the problem probably was to construct equation #1 and to factor the equation after performing all of the arithmetic operations.

5 0
3 years ago
a five-digth number has a3 in the hundreds place, a 7 in the greatest place-value position, a 9 in the ones place, an 8 in the t
Triss [41]
It will surely be 37986
8 0
3 years ago
With the beam being held still at a height of 40 m, the crane breaks and the beam falls to the ground. Assuming no air resistanc
lapo4ka [179]
What we have so far:
Kinetic energy = 0. The reason behind that is because the beam is not moving at a height of 40m.
Gavity, g = 9.8m/s²
Height = 40m
Potential energy = mgh; this is equal to 0 because m, stands for mass and in this problem, we do not have a value for the mass of the beam. Hence, 0 x 9.8m/s² x 40m = 0. Potential energy = 0.

Solution:
We will use the equation of Total energy:
TE = potential energy + kinetic energy

TE = 0 + 0

∴ TE = 0

The answer is: Assuming no air resistance, the total energy of the beam as it hits the ground is 0.
8 0
3 years ago
6th grade math help me plzzzz
tiny-mole [99]

Answer:

-0.9

Step-by-step explanation:

First we have to distribute. -1 times t is -1t and -1 times 8 is -8. Now, our equation will look like this: -1t - 8 = -7.1  

Next, we have to carry our -8 to the other side of the euqation. So, we have to plus 8 on both sides. -7.1 plus 8 is 0.9. Now, our equation will look like this,

-1t = 0.9.

Lastly, we have to divide -1 from both sides. 0.9 divided by -1 is -0.9. So therefore, t = -0.9.

6 0
3 years ago
Read 2 more answers
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