Question

show all steps!
1/9/2026

1. bob is a bad math student because

he did not show his steps!
solve the equation (show all steps)
which statement is true?
a. bob solved the equation correctly
b. step 1 should be 7 + 8x = 9x + 3
c. step 2 should be 8x = 16
d. step 3 should be x = -2
show work here
6(1 + 2x) = 5(4x - 2)
6 + 12x = 20x - 10
8x = -4
x = -1/2

1. classify each as rational or irrational. shade the correct box.

-9.2 5 √12 2.4895 3π
□rat □irrat | □rat □irrat | □rat □irrat | □rat □irrat | □rat □irrat
determine the transformation used on point m (4, -8) to create the image of m.
match the image coordinate with the transformation

1. m’(2, -4) a. rotate 90° clockwise b. reflect over the y axis
2. m’(8, 4) c. dilate by a scale factor of 2 d. translate 2 up and 8 right
3. m’(-4, -8) e. translate 8 up and 2 right f. rotate 90° counterclockwise
4. m’(6, 0) g. reflect over the x axis h. dilate by a scale factor of 1/2
5. you spin the spinner then roll a standard number cube. what is the probability the spinner will land on

an even number then you roll a 4? (write as a fraction)
(spinner with numbers 5,9,3,12,9,10,1)

Explanation:

Step1: Solve the given equation

Start with $6(1 + 2x) = 5(4x - 2)$
Apply distributive property:
$6 + 12x = 20x - 10$

Step2: Isolate x terms

Subtract $12x$ from both sides:
$6 = 8x - 10$
Add 10 to both sides:
$16 = 8x$

Step3: Solve for x

Divide both sides by 8:
$x = 2$

Step4: Verify true statement

Compare to given steps:

• Step 2 in the table is wrong; correct step is $8x=16$, so option C is true.

Step5: Classify rational/irrational

• $-9.\overline{2}$: Repeating decimal → Rational
• $5$: Integer → Rational
• $\sqrt{12}=2\sqrt{3}$: Non-terminating, non-repeating → Irrational
• $2.4895$: Terminating decimal → Rational
• $3\pi$: Non-terminating, non-repeating → Irrational

Step6: Match coordinate transformations

1. $M(4,-8)→M'(2,-4)$: Multiply by $\frac{1}{2}$ → Dilate by $\frac{1}{2}$ (H)
2. $M(4,-8)→M'(8,4)$: Rotate $90^\circ$ clockwise: $(x,y)→(y,-x)$ → $( -8,-4)$ no; Rotate $90^\circ$ counterclockwise: $(x,y)→(-y,x)$ → $(8,4)$ (F)
3. $M(4,-8)→M'(-4,-8)$: Flip x-coordinate → Reflect over y-axis (B)
4. $M(4,-8)→M'(6,0)$: $4+2=6$, $-8+8=0$ → Translate 8 up, 2 right (E)

Step7: Calculate probability

Spinner has 8 sections; even numbers: 10,12 → 2 options.
Probability spinner even: $\frac{2}{8}=\frac{1}{4}$
Probability roll 4 on cube: $\frac{1}{6}$
Combine probabilities: $\frac{1}{4} \times \frac{1}{6} = \frac{1}{24}$

Answer:

1. C. Step 2 should be $8x = 16$

2.
$-9.\overline{2}$: $\square$Rat $\square$Irrat
$5$: $\square$Rat $\square$Irrat
$\sqrt{12}$: $\square$Rat $\square$Irrat
$2.4895$: $\square$Rat $\square$Irrat
$3\pi$: $\square$Rat $\square$Irrat

1. H. dilate by a scale factor of $\frac{1}{2}$
2. F. rotate $90^\circ$ counterclockwise
3. B. reflect over the y axis
4. E. translate 8 up and 2 right
5. $\frac{1}{24}$