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evablogger [386]
3 years ago
9

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 following flowchart 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?

Mathematics
2 answers:
Effectus [21]3 years ago
7 0

Answer:

Because  \angle ECB=62^{\circ}= \angle ADE ( coresponding angles are equal )

Step-by-step explanation:

Given triangle ABC is a right triangle.

It means one angle of triangle ABC is of90^{\circ}.

\angle mA=90^{\circ}

D is the mid point of side AB and E is the mid point of side AC.

Meet D to E . Now DE\parallelBC

In triangle ADE

m\angle ADE=28^{\circ}  ( given )

m\angle DAE=90^{\circ}  ( given)

Now,

Statement : m\angle ADE+ m\angle DAE +m\angle AED=180^{\circ}.

Reason: Angle sum property of traingle.

Statement: 28^{\circ}+ 90^{\circ} + m\angle AED = 180^{\circ}

Reason: By using substitution property .

Statement: \angle AED=62^{\circ}

Reason: By usin subtarction property of equality.

Statement: m\angle AED=m\angle ECB=62^{\circ}

Reason: Corresponding angles are congruent when transversal line intersect two parallel lines.

Hence proved.

icang [17]3 years ago
3 0
Iwould think its Corresponding angles are congruent
Triangle Sum Theorem
<span>Measure of angle AED is 28°


I hope I helped


Brainliest would be appreciated



Have a great day!</span>
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juin [17]
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8 0
3 years ago
F(x)=-x^2+6x+14 vertex
sasho [114]

Answer:

Vertex: (3, 23)

Step-by-step explanation:

a = -1   b = 6   c = 14

x vertex = \frac{-b}{2a}

\frac{-6}{-2}=3

f(x)-x^{2} +6x+14\\f(3) = -(3)^{2}+6(3) + 14 \\f(3)=-9+18+14\\f(3)=23

4 0
3 years ago
Read 2 more answers
-2(3x+9)=-54<br><br> AND 2(3x+4) -3x=35 <br><br> SHOW WORK PLEASE
Naily [24]

Answer:

1. x=6

2. x=9

Step-by-step explanation:

1.

-2(3x+9)=-54\\-6x-18=-54\\+18 +18\\-6x=-36\\\frac{-6x}{-6} = \frac{-36}{-6}\\x=6

2.

2(3x+4)-3x=35\\6x+8-3x=35\\3x+8=35\\-8 -8\\3x=27\\\frac{3x}{3} =\frac{27}{3} \\x=9

<u>Written Explanation: </u>

1.

-2x(3x+9)=-54

-6x-`8=54 (Distributive property)

Add 18 to both sides

-6x=-36

Divide both sides by -6 (negative divided by a negative equals a positive)

x=6

2.

2(3x+4)-3x=35

6x+8-3x=35 (distributive property)

3x+8=35 (combine Iike terms and then subtract them 6x-3x=3x)

Subtract 8 from both sides

3x=27

Divide both sides by 3

x=9

5 0
3 years ago
I NEED HELP WITH THIS ASAP I CAN NOT FIND ANY COMMON GROUND FOR THESE NUMBERS ALL HELP IS APPRECIATED THANK YOU
poizon [28]

Answer:

45 is um 9x+xy-4y

Step-by-step explanation:

I did it it was a simplify type thing

3 0
2 years ago
One pump can fill a swimming pool in 8 hours and another pump can fill it in 10 hours. If both pumps are opened at the same time
Norma-Jean [14]

Answer: It will take 4.4 hours to fill the pool.

Step-by-step explanation: One pump can fill a swimming pool in 8 hours and another pump can fill it in 10 hours. If both pumps are opened at the same time, how many hours will it take to fill the pool?

Aprox. 4.4 hours.

Hope this Helps!

6 0
3 years ago
Read 2 more answers
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