32. in the figure below, $overleftrightarrow{ab}$ and $overleftrightarrow{ce}$ intersect at $o$…

32. in the figure below, $overleftrightarrow{ab}$ and $overleftrightarrow{ce}$ intersect at $o$. $overrightarrow{oc}$ bisects $angle bod$, and the measure of $angle aod$ is $40^{circ}$. what is the measure of $angle aoe$? f. $40^{circ}$ g. $50^{circ}$ h. $60^{circ}$ j. $70^{circ}$ k. $80^{circ}$ 33. the entire length of a rope is coiled into 6 circular loops, each with a diameter of 10 inches, as shown below. which of the following is closest to the length, in inches, of the rope? a. 30 b. 80 c. 95 d. 190 e. 315 34. given the matrix equation below, what is the value of $ab$? $\begin{bmatrix}5& - 6\\3&12end{bmatrix}+\begin{bmatrix}a&2\\0&bend{bmatrix}=\begin{bmatrix}10& - 4\\3&4end{bmatrix}$ f. - 40 g. - 3 h. - 2 j. $-\frac{1}{5}$ k. $\frac{2}{3}$

32. in the figure below, $overleftrightarrow{ab}$ and $overleftrightarrow{ce}$ intersect at $o$. $overrightarrow{oc}$ bisects $angle bod$, and the measure of $angle aod$ is $40^{circ}$. what is the measure of $angle aoe$? f. $40^{circ}$ g. $50^{circ}$ h. $60^{circ}$ j. $70^{circ}$ k. $80^{circ}$ 33. the entire length of a rope is coiled into 6 circular loops, each with a diameter of 10 inches, as shown below. which of the following is closest to the length, in inches, of the rope? a. 30 b. 80 c. 95 d. 190 e. 315 34. given the matrix equation below, what is the value of $ab$? $\begin{bmatrix}5& - 6\\3&12end{bmatrix}+\begin{bmatrix}a&2\\0&bend{bmatrix}=\begin{bmatrix}10& - 4\\3&4end{bmatrix}$ f. - 40 g. - 3 h. - 2 j. $-\frac{1}{5}$ k. $\frac{2}{3}$

Answer

32.

Explanation:

Step1: Find ∠BOD

Since ∠AOD and ∠BOD are a linear - pair, and ∠AOD = 40°, then ∠AOD+∠BOD = 180°. So, ∠BOD=180° - ∠AOD. ∠BOD = 180°-40°=140°

Step2: Use the angle - bisector property

OC bisects ∠BOD, so ∠BOC = ∠DOC=\frac{1}{2}∠BOD. Then ∠BOC=\frac{1}{2}×140° = 70°.

Step3: Find ∠AOE

∠AOE and ∠BOC are vertical angles. Vertical angles are equal. So ∠AOE = ∠BOC = 70°.

Answer:

J. 70°

33.

Explanation:

Step1: Recall the formula for the circumference of a circle

The formula for the circumference of a circle is C = πd, where d is the diameter. Given d = 10 inches, then C=π×10 = 10π inches.

Step2: Calculate the length of the rope

The rope is coiled into 6 circular loops. The length of the rope L is the sum of the circumferences of the 6 loops. So L = 6C. Substituting C = 10π, we get L=6×10π=60π inches. Using π≈3.14, L≈60×3.14 = 188.4 inches.

Answer:

D. 190

34.

Explanation:

Step1: Add the matrices

When adding matrices (\begin{bmatrix}5&- 6\3&12\end{bmatrix}+\begin{bmatrix}a&2\0&b\end{bmatrix}=\begin{bmatrix}5 + a&-6 + 2\3+0&12 + b\end{bmatrix}=\begin{bmatrix}10&-4\3&4\end{bmatrix})

Step2: Solve for a and b

We have the following two - equations: For the top - left elements: 5 + a=10, so a=10 - 5=5. For the bottom - right elements: 12 + b=4, so b=4 - 12=-8.

Step3: Calculate ab

ab=5×(-8)=-40

Answer:

F. - 40