Mathematics Middle School

In triangle DEF, m∠D = (4x + 15)°, m∠E = (5x + 32)°, and m∠F = 70°. Determine the degree measure of the exterior angle to ∠D.

137°
113°
67°
43°

Answers

Answer 1
D) 67° is the answer
Answer 2

The measure of the exterior angle to ∠D will be 137°.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In triangle DEF,

m ∠D = (4x + 15)°, m ∠E = (5x + 32)°, and m ∠F = 70°

Now,

Sum of the measure of angle in a triangle is 180°.

So, We can formulate;

⇒ m ∠D + m ∠E + m ∠F  = 180°

Substitute all the values, we get;

⇒ (4x + 15) + (5x + 32) + 70 = 180

⇒ 9x + 117 = 180

⇒ 9x = 180 - 117

⇒ 9x = 63

⇒ x = 7

Thus, We get;

m ∠D = (4x + 15)°

m ∠D = (4 x 7 + 15)°

m ∠D = (28 + 15)°

m ∠D = (43)°

And, m ∠E = (5x + 32)°

m ∠E = (5 x 7 + 32)°

m ∠E = (35 + 32)°

m ∠E = 67°

Since, The measure of the exterior angle to ∠D = m ∠E + m ∠F

                                                                          = 67° + 70°

                                                                          = 137°

Thus, The measure of the exterior angle to ∠D will be 137°.

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Related Questions

Find the next 3 numbers in the sequence: 2, 9, 11, 18, 20, 27

Answers

Answer:

the numbers are 7,, and 2

Step-by-step explanation:

2 plus 7 equals 9 plus 2 equals eleven so the pattern is plus then plus 2

Answer: next 3 numbers are 34,41,48

there is a difference of 7 between each number

Find two numbers whose sum is 21 and their product is 104.
( Make sure you explain how you got the two numbers.
Show both equations as well )

Answers

Answer:

13x8=104     13+8=21    

Step-by-step explanation:

Hope this helps!

13•8=104. 13+8=21. To be honest I just used process of elimination. You can do this by listing the factors of 104, which are 1 & 104, 2 &52, 4 & 26, and 8 & 13. Then you add the pairs. 104+1=105, 105 does not equal 21. 52+2=54, 54 does not equal 21. 26+4=30, 30 does not equal 21. This means the answer has to be 13 & 8 because 13+8=21, and 21 is equal to 21.

Ben earns $940 for working 80 hours on his job
a. Write an equation to represent the amount of pay Ben will earn for any number of hours worked.
b. Use your equation to determine how many hours Ben worked if he earned a total of $411.25

Answers

Answer:

5.1 or 5.140625 (The equation would be 411.25/80=5.140625)

Step-by-step explanation:

80x=940

x=11.75

80x=411.25

x=5.140625

The equation would be

411.25/80=hours

hours =5.140625

And if you're supposed to round your answer it'd be

5.1

A. Y:11.75x
B. 35 hours

can anyone help me find these answers?
thank you if you can!

Answers

Answer:

1. 7/30

2. -3.5

3. -29/9

4. -15/4

5. 60/7

6. -15.73

7. -6/5

8. 60/7

9. 17.64

10. -3/2

Step-by-step explanation:

Question 1
7/30

Question 2
-3.5

Question 3
-29-9 or -3 2/9

Question 4
-15/4 or -3 3/4

Question 5
15

Question 6
-15.73

Question 7
-6/5 or -1 1/5

Question 8
-65/7 or -9 2/7

Question 9
-15.74

Question 10
-3/2 or -1 1/2

I need a very described answer please.

Answers

Answer: D. 140

Step-by-step explanation:

Goal: Find x and solve the equation

1) Since they are parallel angles, you can move QXY up to SQR.

Note: I don't really know how to explain this... Hope this is enough.

2) Set up the equation and solve

4x+40+2x-10 = 180

6x+30=180

6x = 150

x = 25

3) Solve the PQS equation

4x+40

4(25)+40 (Substitute x here.)

100+40

140

The answer would be D.one hundred and 40

Estimate 25.46 ⋅ 18.73 by rounding to the nearest whole number.

A: 475
B: 44
C: 468
D: 6

Answers

A. 475
That is 100% the answer to this problem
A. 475 god day to you

Emilio has a gift card with $250 on it. He uses the gift card to buy 5 DVD's.

Adam has a gift card with $150 and uses it to purchase 4 DVD's.

If they both now have the same amount left on their gift cards, how much did each DVD cost?

Answers

Answer: Each DVD cost $100

Step-by-step explanation:

So it's a system of equations, where x = DVD price and y = remainder...

250 - 5x = y

150 - 4x = y

Now let's find x by making the y's cancel out.

In order to do this, multiply one equation by -1!

-250 + 5x = -y

150 - 4x = y

Which equals to...

-100 + x = 0

Add 100 to both sides...

x = 100

MEANING that each DVD cost $100. Quite pricey if you ask me!

$100 is the answer i believe

Determine whether each equation has one​ solution, no​ solution, or infinitely many solutions

3/2(2x+6)=3x+9

3x+5=3(x+5)

x+4x+4=3(2x-1)

6x+4x+1=2(5x+1)

Answers

Answer: Let's solve each equation step by step to determine the number of solutions:

3/2(2x+6)=3x+9

First, we distribute the 3/2 on the left side:

3x + 9 = 3x + 9

Subtracting 3x from both sides, we get:

9 = 9

This means that the equation is an identity and is true for all values of x. Therefore, it has infinitely many solutions.

3x+5=3(x+5)

Expanding the right side:

3x + 5 = 3x + 15

Subtracting 3x from both sides, we get:

5 = 15

This is a contradiction, so the equation has no solution.

x+4x+4=3(2x-1)

Simplifying the left side:

5x + 4 = 6x - 3

Adding 3 to both sides and subtracting 5x from both sides, we get:

7 = x

Therefore, the equation has one solution, x = 7.

6x+4x+1=2(5x+1)

Simplifying both sides:

10x + 1 = 10x + 2

Subtracting 10x from both sides, we get:

1 = 2

This is a contradiction, so the equation has no solution.

Step-by-step explanation:

A soccer coach is ordering jerseys for members of the soccer team and can choose between small, medium, and large jerseys. The cost of a small jersey is x dollars. The cost of a medium jersey is 3 dollars more than the small jersey, and the cost of a large jersey is 5 dollars more than the medium jersey.

The coach orders 5 medium jerseys and 6 large jerseys for a total cost of $100. Find the cost, in dollars, of one small jersey.

Answers

Answer: X equals 1$

Step-by-step explanation: I think this is the answer cause I

did 3 divided by five and then added one I came up with 1

47

This is because 3x5= 15 and 5x6= 30

You need to at 15 because of the first multiplication problem 3x5 which = 15

Which will be 45 and in the word problem it stayed the large was 5 dollars more then the medium and the medium was 3 dollars more then the small

A given data set has:
Mean -26.5
Interquartile Range - 5.5
Minimum - 21
Maximum - 29
Which measure describes all the values in the data set?
5.5
021
26.5
29

Answers

Answer: 26.5- mean-

Step-by-step explanation:

the mean is all the numbers added up and divided- so it describes all the data in the set

The mean -26.5 the other ones are incorrect

The following angles are supplementary to each other.

m∠A = (3x + 21)° and m∠B = (6x − 21)°

Determine x.

10
20
36
60

Answers

Answer: X=20

Step-by-step explanation: Supplementary angles, by definition, add up to 180.

(3x + 21) + (6x - 21) = 180

3x + 6x + 21 - 21 = 180

9x = 180

9x/9 = 180/9

x = 20

x = 20 . Option B is correct.

What are supplementary angles?

Two angles are supplementary to each other if their sum is equal to 180°.

Given,

          ∠A = (3x + 21)°

And  ∠B = (6x − 21)°

Also, ∠A and ∠B are supplementary angles.

Therefore,    ∠A + ∠B = 180°

           (3x + 21)° + (6x − 21)° = 180°

                (9x + 0)° = 180°

Hence, x = 20.

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ABC computers sold 30 tablets this week. Their goal is to sell at least 33% more next week. Graph an inequality that represents their goal.

Answers

So 30 + 33% = 39.9 which I’m assuming will round up to 40

I could use some help on my homework please. Don't really understand and would like the steps in solving

Answers

x= -29+2y/4

-4(-29+2y/4)+2y=-16

+116-8y/4 +2y=-18

The system has no solutions.
1. 4x=-29+2y
-4x+2y=-16 (rearrange this equation to find 2y)

2. 2y=-16+4x (rearranged equation)
Plug the rearranged equation into the first one.

3. 4x=-29+(-16+4x) (new equation)
Now solve for X

4. Once you solve the equation you’ll find 0=-45 which means there’s no solution

Pls pls help me I will give 20 points

Answers

Answer: False- True- 0.2- 2.5- 5.0-

for the last one it's dilated by 1.25

Step-by-step explanation: for each dash its a different question

the first question, scale factor is .2

Determine the length of the line segment shown.


6 units
8 units
10 units
36 units

Answers

8 units is the answer

Answer:

10 units

Step-by-step explanation:

Determine which integer will make the inequality 18 > 3x + 9 true.

S:{−3}
S:{3}
S:{9}
S:{14}

Answers

Answer: -3

Step-by-step explanation:

X < 3

So the answer is: S{3}

Help me pleased whoever's right will get brainiest :")
1

Answers

Answer:

B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

HHHHHHHHHHHEEEEEEEEEEEEEEEEEEEEELLLLLLLLLLLLLLLLLLPPPPPPPPPP
25 POINTS AND BRAINLIEST
Directions: Evaluate and solve for the variable and graph the resulting solution set, showing ALL work.

a) x/4 > 10

b) -5g < 15


c) t - 4 ≤ -3


d) 4d > -12


e) u + 12 ≤ 5


f) j - 4 ≥ - 4

Answers

Answer:

a) x/4 > 10

x > 10*4

x > 40

--------------------------
b)-5g < 15

g > 15/-5

g > -3

--------------------------

c) t - 4 ≤ -3

t ≤ -3 + 4

t ≤ 1

--------------------------

d)4d > -12

d > -12/4

d > -3

--------------------------

e)u + 12 ≤ 5

u ≤ 5 -12

u ≤ -7

-------------------------
f)j - 4 ≥ - 4

j ≥ -4 + 4

j ≥ 0

Answer:a) x/4 > 10

x > 10*4

x > 40

--------------------------

b)-5g < 15

g > 15/-5

g > -3

--------------------------

c) t - 4 ≤ -3

t ≤ -3 + 4

t ≤ 1

--------------------------

d)4d > -12

d > -12/4

d > -3

--------------------------

e)u + 12 ≤ 5

u ≤ 5 -12

u ≤ -7

-------------------------

f)j - 4 ≥ - 4

j ≥ -4 + 4

j ≥ 0

Step-by-step explanation:

..........................................................................................................

Answers

Line g: 3/4
Line k: -5/6
Line m: -2
Answer: g =3/4

Answer: k = -5/6

Answer: m = -2

If one book is 1.6 inches wide and another is 1.471 inches wide, how much wider is the first?

A: 1.29 inches
B: 0.129
C: 3.071
D: 0.307

Answers

Answer:

B. 0.129

Step-by-step explanation:

If one book is 1.6 inches wide and another is 1.471 inches wide, how much wider is the first?

A: 1.29 inches

B: 0.129

C: 3.071

D: 0.307

1.6 - 1.471 = 0.129

Answer: B

Step-by-step explanation:

HELP CAN SOMEONE ANWSER THIS FOR MEE?

Answers

Answer:

$1.89

Step-by-step explanation:

This is a simple unit-rate proportion. We're trying to find the rate of 1 gallon to unknown money. To get 1 gallon, we have to divide it by 13, because that's the total gallons we start with.

13 = 24.57

/13

_________

1=24.57

Whatever we do to one side of the equation, we have to do to the other, so we divide 24.57 by 13, too.

1 = 24.57

    /13

_________

1=1.89

For every gallon of gas, you pay 1.89 dollars.

Hope this helps!

It is $1.89
Divide the number of dollars to 13 gallons and you get your answer :)

Is -12.161616... rational or not​ rational?

Answers

Answer:

NOT rational_ irrational

Step-by-step explanation:

Not because u have it in ur notes

Can someone pls help?

Answers

Answer:

simplify = 9.61

evaluate = 9.61

Step-by-step explanation:

9.16 for both the words kinda means the same thing

I need help please show your work

Answers

Pauli's pizzeria- y=15x = slope m=$15 per pizza sold
Leo's pizzeria-y=12x = slope m=$12 per pizza sold
$15 per pizza sold is more than $12 per pizza sold
So Pauli's makes more money per pizza than Leo

Answer: Pauli's pizzeria- y=15x = slope m=$15 per pizza sold

Leo's pizzeria-y=12x = slope m=$12 per pizza sold

$15 per pizza sold is more than $12 per pizza sold

So Pauli's makes more money per pizza than Leo

Step-by-step explanation: I thank that is right

Could someone please help me?

Answers

Answer:

y=-x+5

Step-by-step explanation:

3=-(2)+5

3=-2+5

3=3

4=-1+5

4=4

6=-(-1)+5

6=6

9=-(-4)+5

9=9

11=-(-6)+5

11=11

the answer is y=-x+5

A motorcycle travels 93 miles in 3 hours. What is the unit rate in miles per hour?

15 points

Answers

93/3= 31 mph

hope this helps lol

Answer:

31

Step-by-step explanation:

93/3=31

31mph

Can someone please help?

Answers

answers are in the picture

goodluck :)

1. Do the product rule:
Since the base of both numbers are the same, keep the base. In this case, it’s 2. Next add the exponents together. 3 + 2 = 5.
So the simplified one would be 2^5 (two to the fifth power)

2. Multiply 2 by itself five times; 2 • 2 • 2 • 2 • 2 = 64
So evaluated (calculated) the answer would be 64.

HELP ASAP PLEASE NOW!!!!!!

Answers

Answer:

The answer is the second graph

Step-by-step explanation:

The dot is closed meaning no more than 52

The answer is the second paragraph

help me please icxdis

Answers

The answer is QR and CD

DP 2.6 Similar Polygons

Triangle DEF is a dilation of triangle ABC with scale factor 2. In triangle ABC, the largest angle measures 82o. What is the largest angle measure in triangle DEF?
41∘
82∘
180∘
164∘

What characteristics are needed to determine that two polygons are similar?



The quadrilateral PQRS in the diagram is a parallelogram. Which of the following statements would be true if P′Q′R′S′ is the image of PQRS after applying a dilation centered at a point O with scale factor 3?
P′Q′=PQ
P′Q′=3PQ
PQ=3P′Q′
Cannot be determined from the information given

Answers

A. Because changing the size of a polygon doesn't change its angles, it would stay at 82°.

B. The characteristics needed to prove they are similar are just their angles.

C. The scale factor is 3, so P'Q'=3PQ.

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