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belka [17]
3 years ago
7

One angle of a triangle measures

align="absmiddle" class="latex-formula"> more than the second. The measure of the third angle is twice the sum of the first two angles. What is the measure of each angle?
Mathematics
1 answer:
iVinArrow [24]3 years ago
5 0

Answer:

One\ angle: 35^o\\Second\ angle: 25^o\\Third\ angle: 120^o

Step-by-step explanation:

Let

x ----> the measure of one angle of the triangle

y ---> the measure of the second angle

z ----> the measure of the third angle

we know that

The sum of the measure of the interior angles in any triangle must be equal to 180 degrees

x+y+z=180^o -----> equation A

One angle of a triangle measures  10 degrees more than the second

x=y+10 ----> equation B

The measure of the third angle is twice the sum of the first two angles

z=2(x+y) ---> equation C

substitute equation B in equation C

z=2(y+10+y)

z=4y+20 ----> equation D

substitute equation D and equation B in equation A

(y+10)+y+(4y+20)=180^o

solve for y

6y=180-30\\6y=150\\y=25^o

Find the value of x

x=25+10=35^o

Find the value of z

z=4(25)+20=120^o

therefore

One\ angle: 35^o\\Second\ angle: 25^o\\Third\ angle: 120^o

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Reil [10]

Answer:

i hope this helps

Step-by-step explanation:

2x^{2} -16=0

+16        +16

2x^{2} =16

÷2    ÷2

x^{2} = 8

\sqrt{x^{2} }= \sqrt{8}

x= \sqrt{8}

-5x^{2} +9=0

-9          -9

-5x^{2}=-9

÷-5   ÷-5

x^{2} =1.8

\sqrt{x^{2} }= \sqrt{1.8}

x= \sqrt{1.8}

6x^{2} -15=27

+15        +15

6x^{2} =42

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x^{2} =7

\sqrt{x^{2} }= \sqrt{7}

x=\sqrt{7}

4 0
3 years ago
M∠a=(48−x)°m∠b=(9x−38)°m∠c=90°
Fudgin [204]

Answer:

Option C:

  • m∠a = 38°
  • m∠b = 52°
  • m∠c = 90°

Step-by-step explanation:

Hello!

The sum of all angles in a triangle is 180°.

Add up all the angles and solve for x by setting the equation to 180°.

<h3>Solve for x</h3>
  • ∠a + ∠b + ∠c = 180°
  • (48 - x)° + (9x - 38)° + 90° = 180°
  • 10° + 8x + 90° = 180°
  • 8x = 180° - 90° - 10°
  • 8x = 80°
  • x = 10°

Now that we solved for x, we can plug it back into each equation to solve for each angle.

<h3>Angle A</h3>
  • 48° - x
  • 48° - 10°
  • 38°
<h3>Angle B</h3>
  • 9x - 38°
  • 9(10°) - 38°
  • 90° - 38°
  • 52°
<h3>Angle C</h3>
  • 90°

The answer is Option C:

  • m∠a = 38°
  • m∠b = 52°
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4 0
2 years ago
1. Identify your variables using let statements.
Advocard [28]

The number of chicken dish is 131 dishes while the number of lobster dishes is 119 dishes

<h3>How to find the number of each type of dish.</h3>

Let

  • x = number of chicken dish and
  • y = number of lobster dish
<h3>How to determine the equations for the linear system</h3>

Since it cost $40 per dish for chicken dish, the total cost of chicken dish is 40x.

Also, since it cost $70 per dish for lobster dish, the total cost of lobster dish is 70y

So, the total cost of dish is T = 40x + 70y

Also, we know that the total cost of dish is $13,570.

So, 40x + 70y = 13570  (1)

Also, there are going to be 250 guest at the dinner and thus 250 dishes.

So, the total number of dishes is x + y = 250

So, x + y = 250 (2)

So, the equations of the linear system are

40x + 70y = 13570  (1)

x + y = 250 (2)

<h3>How to determine the solution for the linear system</h3>

Since

40x + 70y = 13570  (1)

x + y = 250 (2)

From (2), x = 250 - y

Substituting x into (1), we have

40x + 70y = 13570  (1)

40(250 - y) + 70y = 13570  (1)

10000 - 40y + 70y = 13570  

30y = 13570 - 10000

30y = 3570

y = 3570/30

y = 119

Substituting y = 119 into x, we have

x = 250 - y

x = 250 - 119

x = 131

Therefore, the number of chicken dish is 131 dishes while the number of lobster dishes is 119 dishes

Learn more about equation of linear system here:

brainly.com/question/13729904

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2 years ago
HELP <br> what is the equation of the lines in slope - intercept form
34kurt

Answer:

y=7x

Step-by-step explanation:

slope intercept form is y=mx+b.

m is the slope (rise over run) and b is your y- intercept. you leave y as it is. if the line is going down, you have a negative slope. hope this helped :)

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2 years ago
In the diagram B is the midpoint of a A and C. B is also the midpoint or E and F. C is the midpoint of A and D.
aivan3 [116]

Answer:

AD = 84

Step-by-step explanation:

Since B is the midpoint of AC then AB = BC = 2x - 5

Since C is the midpoint of AD then AC = CD, thus

AB + BC = CD, that is

2x - 5 + 2x - 5 = x + 29

4x - 10 = x + 29 ( subtract x from both sides )

3x - 10 = 29 ( add 10 to both sides )

3x = 39 ( divide both sides by 3 )

x = 13

Hence

AD = AB + BC + CD

     = 2x - 5 + 2x - 5 + x + 29 = 5x + 19, thus

AD = (5 × 13) + 19 = 65 + 19 = 84

6 0
3 years ago
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