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3 years ago

The measure of the supplement of an angle is three times the measure of the

Mathematics

1 answer:

gtnhenbr [62]3 years ago

5 0

<h2>Answer:</h2>

<h3><em>x=45degrees</em></h3>

<h2>Step-by-step explanation:</h2>

Let the angle to be solved be x

Let the supplement/compliment by y

x+y=90 Complimentary angles add up to 90 degrees.

x+3y=180 Supplementary angles add up to 180 degrees, the other angle is thrice the other compliment.

Evaluating this as a system:

x+y=90 Isolate x:

x=90−y Input into the other equation:

(90−y)+3y=180 Combine like terms, isolate y and its coefficients:

2y=90 Isolate y

y=45 Input into the first equation:

x+45=90 Isolate x:

x=45degrees

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Solve the inequality -5(d-2)>35

chubhunter [2.5K]

Answer:

d < -5

Step-by-step explanation:

Okay, so the equation is -5(d-2)>35

First we have to use distributive property to get rid of the parenthesis.

we do -5(d) --> -5d

then, -5(-2) --> 10

So now we just redo the equation---

-5d + 10 > 35

now you have to isolate d, the variable

First, to isolate you have to get rid of 10. Subtract 10 on both sides.

-5d + 10 > 35

- 10 -10

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

-5d > 25

Then you have -5d > 25. You have to do the opposite operation again to make the d by itself, so you divide -5 on each side.

-5d > 25

----- -----

-5 -5

-5d/-5 is d because the -5's cancel out. 25/-5 is -5. Now, you have to flip the equation because when working with inequalities, you have to flip the symbol.

SO,,, the answer is

d < -5

Hope this helps!!

-Ketifa

8 0

3 years ago

In the diagram, ΔGEF and ΔHEF are congruent. What is the value of x?

mojhsa [17]

Similar triangles are triangles that has all sides and angles to be equal. The value of x if , ΔGEF and ΔHEF are congruent is 28

<h3>Similar triangles</h3>

Similar triangles are triangles that has all sides and angles to be equal. From the given diagram;

<GFE = <EFH

Given

<GFE = 60 degrees

<EFH = 2(x+2)

Substitute

2(x+2) = 60
2x + 4 = 60

2x = 60 - 4

2x = 56

x = 28

Hence the value of x if , ΔGEF and ΔHEF are congruent is 28

Learn more on congruent shapes here: brainly.com/question/2644832

#SPJ1

8 0

2 years ago

Solve the system by submission -5y-10=x<br> x+9y=-2

Sonbull [250]

Answer: =−20

y=2

Step-by-step explanation:

Solve for xx in -5y-10=x−5y−10=x.

x=-5y-10

x=−5y−10

2 Substitute x=-5y-10x=−5y−10 into x+9y=-2x+9y=−2.

4y-10=-2

4y−10=−2

3 Solve for yy in 4y-10=-24y−10=−2.

y=2

4 Substitute y=2y=2 into x=-5y-10x=−5y−10.

x=-20

x=−20

5 Therefore,

\begin{aligned}&x=-20\\&y=2\end{aligned}

x=−20

y=2

8 0

3 years ago

Please show work for both problems

sukhopar [10]

(1) The value of x is 25

(2) The measure of ∠CBD is 60°

Explanation:

(1) The given two angles are vertical angles. Since, vertical angles are equal, we can add the two angles to determine the value of x.

Thus, we have,

$5x+15=6x-10$

Subtracting 5x from both sides, we have

$15=x-10$

Adding 10 to both sides , we have,

$25=x$

Thus, the value of x is 25.

(2) It is given that the measure of ∠ABC = (x+7)° and ∠CBD = (2x+14)°

Since, these two angles are supplementary angles and supplementary angles add upto 90°

Thus, we have,

$2x+14+x+7=90$

Simplifying, we get,

$3x+21=90$

$3x=69$

$x=23$

Thus, substituting the value of x in ∠CBD = (2x+14)° to determine its value.

$2x+14=2(23)+14=46+14=60$

Thus, the measure of ∠CBD is 60°

5 0

4 years ago

Find an equation for the nth term of the arithmetic sequence. -3, -5, -7, -9

solniwko [45]

Answer:

Step-by-step explanation:

an=a1+d(n-1)

an=-2n-1

next term a5=-11

hope helps

8 0

3 years ago