1. what is the value of x in the equation −x = 2 − 3x + 6?

8
4
−4
−8

2. the work of a student to solve the equation 2(3x − 4) = 8 + 2x + 4 is shown below:

step 1: 2(3x − 4) = 8 + 2x + 4
step 2: 5x − 6 = 12 + 2x
step 3: 5x − 2x = 12 + 6
step 4: 3x = 18
step 5: x = 6

in which step did the student first make an error and what is the correct step?

step 2; 6x − 6 = 2(6 + x + 2)
step 2; 6x − 8 = 12 + 2x
step 3; 5x − 2x = 12 − 6
step 3; 5x + 2x = 12 + 6

3. the steps below show the incomplete solution to find the value of m for the equation 4m − 2m + 4 = −1 + 13:

step 1: 4m − 2m + 4 = −1 + 13
step 2: 4m − 2m + 4 = 12
step 3: 2m + 4 = 12

which of these is most likely the next step?

2m = 3
2m = 8
2m = 16
2m = 18

1. The correct option is 2.

2. The correct option is 2.

3. The correct option is 2.

Step-by-step explanation:

Part 1.

The given equation is

Add 3x on both sides.

Combine like terms.

Divide both sides by 2.

The value of x is 4. Therefore option 2 is correct.

Part 2.

The given equation is

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Student make his first mistake in step 2 and the correct step is 6x-8 = 12 + 2x. Therefore the correct option is 2.

Part 3.

The given equation is

Step 1:

Step 2:

Step 3:

Step 4: Subtract 4 from both sides.

The next step is 2m= 8. Therefore the correct option is 2.

the answer for this question is : 360°

step-by-step explanation:

we have been given a triangle   we need to tell which one of these is a triangle below to map onto itself.

360° rotation is the complete rotation which eventually leads to the same figure which is given.

the correct will be, that is 360° that will cause the triangle below to map onto itself.

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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