(03.05 MC)

Given that Ray E B bisects ∠CEA, which statements must be true? Select three options. m∠CEA = 90° m∠CEF = m∠CEA + m∠BEF m∠CEB =

tester [12383]

Answer:

Attached is the question in consideration.

$m\angle CEA =90 \ (deg)$

$m\angle BEF=135\ (deg)$

$\angle CEF$ forms a straight line.

$\angle AEF$ depicts a right triangle.

The options $1,4,5,6$ represent the correct answers.

Step-by-step explanation:

⇒ Given that $\ ray\ AE$ is ⊥ $FEC$ it constitutes a right triangle, leading to $m\angle CEA =90\ (deg)$ .

⇒ The measure for $\angle BEF =135\ (deg)$ equals $\angle BEF =\angle AEB +\angle AEF = (45+90)=135\ (deg)$ as $\angle AEB$ bisects $\angle AEC$ , implying that $\angle AEB$ is half of $\angle AEC$ , thus $\angle AEB = 45\ (deg)$ .

⇒ $\angle CEF$ represents a straight line, as the angle measures across it yield $180\ (deg)$ .

⇒ The angle measure for $\angle AEF = 90\ (deg)$ is derived from the linear pair concept.

Since $\angle CEA + \angle AEF = 180\ (deg)$ , inserting the values of $m\angle CEA =90\ (deg)$ leads to $\angle AEF = 90\ (deg)$ .

The other two options are incorrect as:

$m\angle CEF=m\angle CEA + m\angle BEF = (90+135)=225$

it surpasses $180\ (deg)$ while $\angle CEF$ is a

straight line.

Also, $m\angle CEB=2(m\angle CEA)$ is inaccurate.

As $\angle CEA = 90\ (deg)$ and $\angle CEB=45\ (deg)$

Thus, we have a total $4$ valid answers.

The confirmed options are $1,4,5,6$ .

5 0

2 months ago

Read 2 more answers

2. Santiago wants the lateral surfaces of the

Inessa [12570]

Answer:

Red paint will cover 262 square feet

of the ramp.

Step-by-step explanation:

The lateral surface area represents the surface area of the sides of the ramp without including the top and bottom surfaces

This ramp has three surfaces

The two sides are triangular with dimensions of length 20 and height 8.5

The back consists of a rectangular shape with length 12 and height 8.5

Step 1: Calculating the Area of Triangle

The area of the triangular side = $\frac{1}{2} length \times height$

The area of the triangle = $\frac{1}{2} (20 \times 8.5)$

The area of the triangle = $\frac{170}{2}$

Thus, the area of the triangle = 85 square feet

Area of both triangles = $85 \times 2$ = 170

Step 2: Finding the Area of Rectangle

Area of rectangle = $length \times height$

therefore,

Area of the rectangular back = $12 \times 8.5$ = 102 square feet

Step 3: Calculating the total lateral surface area

Overall Lateral Surface Area

= Area of triangles + Area of Rectangle

= 272 square feet

8 0

2 months ago

Eric is studying people's typing habits. He surveyed 525 people and asked whether they leave one space or two spaces after a per

lawyer [12517]

Response: (0.8115, 0.8645)

Step-by-step outline:

Define p as the proportion of individuals who leave one space after a sentence.

Provided: Sample size: n= 525

Number of respondents indicating they leave one space: 440

Thus, the sample proportion is: $\hat{p}=\dfrac{440}{525}\approx0.838$

The z-score for a 90% confidence interval is: 1.645

The formula for determining the confidence interval:

$\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$0.838\pm (1.645)\sqrt{\dfrac{0.838(1-0.838)}{525}}\\\\=0.838\pm (1.645)\sqrt{0.00025858285}\\\\=0.838\pm (1.645)(0.01608)\\\\= 0.838\pm0.0265\\\\=(0.838-0.0265,\ 0.838+0.0265)\\\\=(0.8115,\ 0.8645)$

Consequently, a 90% confidence interval for the proportion of people who leave one space after a period is: (0.8115, 0.8645)

3 0

2 months ago

Help me please,Thanks

tester [12383]

The solution is 24m^2; I just completed that test and that was the result.<span />

4 0

1 month ago