Question

circle the letter of the correct answer. 1. add. -8 + 3 a. 11 b. 5 c. -5 d. 10 2. subtract. 12 - (-4) a. 16 b. -16 c. 8 d. 3 3. use the information in the diagram to find the value of x. a. 6 b. 2 c. 10 d. 15 4. line k bisects cd at point x. find the length of cd. a. 12.25 cm b. 6.2 cm c. 12.5 cm d. 24.7 cm 5. find the length of tv in the diagram. a. 12.8 ft b. 15.3 ft c. 10.3 ft d. 2.5 ft 6. betty is driving a total of 193 miles on the highway. after driving for 63 miles, she stops for gas. how many miles does she have left to drive? a. 130 miles b. 256 miles c. 63 miles d. 65 miles

Explanation:

Step1: Solve -8 + 3

Adding a positive and a negative number, we subtract the absolute - values and take the sign of the number with the larger absolute - value. $|-8| = 8$ and $|3| = 3$, $8-3 = 5$, and since $-8$ has a negative sign, $-8 + 3=-5$.

Step2: Solve 12-(-4)

Subtracting a negative number is the same as adding its positive counterpart. So, $12-(-4)=12 + 4=16$.

Step3: Solve for x in the equation 5x-10 = 20

Add 10 to both sides of the equation: $5x-10 + 10=20 + 10$, which simplifies to $5x=30$. Then divide both sides by 5: $\frac{5x}{5}=\frac{30}{5}$, so $x = 6$.

Step4: Find the length of CD

If a line k bisects $\overline{CD}$ at point X and $CX = 12.35$ cm, then $CD=2\times CX$. So, $CD = 2\times12.35=24.7$ cm.

Step5: Find the length of $\overline{TV}$

If $TU = 12.8$ ft and $UV = 2.5$ ft, then $TV=TU - UV=12.8-2.5 = 10.3$ ft.

Step6: Find the remaining miles

If Betty is driving a total of 193 miles and has already driven 63 miles, then the remaining miles are $193 - 63=130$ miles.

Answer:

1. C. -5
2. A. 16
3. A. 6
4. D. 24.7 cm
5. C. 10.3 ft
6. A. 130 miles