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Rainbow [258]
3 years ago
10

Triangle ABC is a right triangle. Point D is the midpoint of side AB and point E is the midpoint of side AC. The measure of angl

e ADE is 28°.
The flow chart with missing statements and reasons proves that the measure of angle ECB is 62°.

Which statement and reason can be used to fill in the numbered blank spaces?

Base angle theorem
Corresponding angle are congruent
Measure of angle AED is 28°.

Alternate interior angles are congruent
Base angle theorem
Measure of angle AED is 62°.

Corresponding angles are congruent
Triangle Sum Theorem
Measure of angle AED is 28°.>> my answer?

Corresponding angles are congruent
Triangle Sum Theorem
Measure of angle AED is 62°.

Mathematics
2 answers:
DedPeter [7]3 years ago
5 0

Answer:

the answer is D. I just took the exam.

Step-by-step explanation:


xeze [42]3 years ago
5 0

Answer:

(D)

Step-by-step explanation:

Given: Triangle ABC is a right triangle. Point D is the midpoint of side AB and point E is the midpoint of side AC. The measure of angle ADE is 28°.

To prove: The measure of angle ECB is 62°.

Proof:

Step1. Segment DE joins the mid points of segments AB and AC (GIVEN).

Step 2. Segment DE is parallel to segment BC (MIDSEGMENT THEOREM)

Step3. Angle ECB is congruent to angle AED (CORRESPONDING ANGLES ARE CONGRUENT) that is ∠AED≅∠ACB.

Step 4. Measure of angle DAE is 90° (Definition of right angle)

Step 5.  Measure of angle ADE is 28° (Given)

Step 6. Thus, by triangle sum theorem, we have

∠DAE+∠ADE+∠AED=180°

∠AED=180-118

∠AED=62°

Step 7. Thus, by substitution, we have

∠AED≅∠ACB that is ∠ECB=62°

Hence proved.

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John invested $17,500 that
babymother [125]

Answer:

<u>The future value of the investment after 10 years is $ 29,240.53</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Principal = $ 17,500

Interest rate = 5.2% = 0.052 compounded semiannually

Time = 10 years = 20 semesters

2. What is the future value of the investment after 10 years​?

Let's use the formula of the Future Value, to calculate it for this investment:

FV = P * (1 + r) ⁿ

Let's replace with the real values:

FV = 17,500 * (1 + 0.052/2)²⁰

FV = 17,500 * 1.670887521

<u>FV = 29,240.53</u>

6 0
3 years ago
There are 96 students in a speech contest. Yesterday, 1/4 of them gave their speeches. Today, 1/8 of the remaining students gave
sattari [20]
5/8 still havent given their speech or 60 students
6 0
3 years ago
Read 2 more answers
12,430,000 and expanded form
valentina_108 [34]

10,000,000+2,000,000+400,000+30,000

7 0
3 years ago
Read 2 more answers
Jeff can weed the garden twice as fast as his sister Julia. Together they can weed the garden in 3 hours. How long would it take
Leona [35]
<h2>Hello!</h2>

The answer is:

The correct option is:

A) Jeff, 4.5 hours; Julia 9 hours.

<h2>Why?</h2>

To solve the problem, we need to write two equations using the given information.

So, writing the first equation we have:

We know that Jeff can weed the garden twice as fas as his sister Julia, so:

JeffRate=2JuliaRate

Also, from the statement we know that they can weed the garden in 3 hours, so, writing the second equation we have:

JeffRate+JuliaRate=\frac{1garden}{3hours}

Then, we need to substitute the first equation into the second equation in order to isolate Julia's rate, so, solving we have:

JeffRate+JuliaRate=\frac{1garden}{3hours}

2JuliaRate+JuliaRate=\frac{1garden}{3hours}

2JuliaRate+JuliaRate=\frac{1garden}{3hours}

3JuliaRate=\frac{1garden}{3hours}

JuliaRate=\frac{1garden}{3hours*3}=\frac{1garden}{9hours}

We have that Julia could weed the garden by herself in 9 hours.

So, calculating how long will it take to Jeff, we have:

JeffRate=2*JuliaRate\\\\JeffRate=2*\frac{1garden}{9hours}=\frac{2garden}{9hours}=\frac{1garden}{4.5hours}

We have that Jeff could weed the same garden by himself in 4.5 hours.

Hence, the correct option is:

A) Jeff, 4.5 hours; Julia 9 hours.

Have a nice day!

8 0
3 years ago
Consider the following matrix. A = 1 k 2 −5 6 1 Assume that the matrix is the augmented matrix of a system of linear equations.
DedPeter [7]

Answer: 2 eqautions and 2 variables

Step-by-step explanation: To solve linear systems, the equations can be represented by an augmented matrix.

To create one, each row represents the coeficients and constants (the numbers after the equal sign) from one equation and each column exhibit all the coeficients for a single variable. This means that the first column of an augmented matrix is for the coeficients of the x-terms, the second for the coeficients of the y-terms, the third column for the z-terms and so on.

For this question:

A = \left[\begin{array}{ccc}1&k&2\\-5&6&1\end{array}\right] or it can be written as

x + ky = 2

-5x + 6y = 1

Thus, the system has 2 equations and 2 variables.

7 0
3 years ago
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