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3 years ago

Which of the following equations has a solution x = 4? Select all that apply.

Mathematics

2 answers:

Savatey [412]3 years ago

7 0

Answer: 1st and 3rd

Step-by-step explanation:

natka813 [3]3 years ago

6 0

Answer:

$-2(3x - 4) = -16$ and $20- 15x = 6 - 2(4x + 7)$

Step-by-step explanation:

Given

$-2(3x - 4) = -16$

$\frac{1}{2}(10x + 2) = 6$

$20- 15x = 6 - 2(4x + 7)$

$\frac{1}{3}(9x - 12) + 6=-10$

Required

Equations with $x = 4$ as a solution

$-2(3x - 4) = -16$

Divide both sides by -2

$3x - 4 = 8$

Add 4 to both sides

$3x - 4 +4= 8+4$

$3x =12$

Divide both sides by 3

$x = 4$

$\frac{1}{2}(10x + 2) = 6$

Multiply both sides by 2

$10x + 2 = 12$

Subtract 2 from both sides

$10x + 2 -2= 12-2$

$10x = 10$

Divide both sides by 1

$x = 1$

$20- 15x = 6 - 2(4x + 7)$

Open bracket

$20 - 15x = 6 - 8x - 14$

Collect like terms

$8x - 15x = 6 - 14 - 20$

$-7x = -28$

Divide both sides by -7

$x = 4$

$\frac{1}{3}(9x - 12) + 6=-10$

Subtract 6 from both sides

$\frac{1}{3}(9x - 12) + 6-6=-10-6$

$\frac{1}{3}(9x - 12) =-16$

Multiply both sides by 3

$9x - 12 = -48$

Add 12 to both sides

$9x - 12 +12= -48+12$

$9x = -36$

Divide both sides by 4

$x =-4$

$-2(3x - 4) = -16$ and $20- 15x = 6 - 2(4x + 7)$ have $x = 4$ has a solution

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3 years ago

Semenov [28]

Answer:

Yes, because m<UVW is congruent to m<XVY and m<VUW is congruent to m<VXY

Step-by-step explanation:

we know that

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In this problem

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3 years ago

) An instructor gives his class a set of 18 problems with the information that the next quiz will consist of a random selection

RSB [31]

Answer:

The probability the he or she will answer correctly is 1.5%

Step-by-step explanation:

In all, there are 18 problems. In this question, the order of which the problems are sorted for the quiz makes no difference. For example, if the question A of the quiz is P1 and question B P2, and question A P2 and question B P1, it is the same thing.

There are 18 problems and 9 are going to be selected. So, there is going to be a combination of 9 elements from a set of 18 elements.

A combination of n elements from a set of m objects has the following formula:

$C_{(m,n)} = \frac{m!}{n!(m-n)!}$

In this question, m = 18, n = 9. So the total number of possibilities is:

$T_{p} = C_{(18,9)} = \frac{18!}{9!(18-9)!} = 48620$

Now we have to calculate the number of desired outcomes. This number is a combination of 9 elements from a set of 13 elements(13 is the number of problems that the student has figured out how to do).

Now, m = 13, n = 9. The number of desired possibilities is:

$D_{p} = C_{(13,9)} = \frac{13!}{9!(13-9)!} = 715$

The probability is the number of desired possibilities divided by the number of total possibilities. So

$P = \frac{715}{48620} = 0.015 = 1.5%$

The probability the he or she will answer correctly is 1.5%

3 0

3 years ago

Which expression is equivalent to this expression? thank you :)

CaHeK987 [17]

Answer:

C. -4x - 1

Step-by-step explanation:

$-\frac{1}{2}(8x+2)$

Distribute the term outside of the parenthesis, Multiply each term in the parenthesis by the term outside (do not forget to include the negative sign when multiplying);

$(-\frac{1}{2}(8x))+(-\frac{1}{2}(2))$