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3 years ago

Look at the triangle below which of the following represents two of the angle measures of the triangle

Mathematics

1 answer:

Gelneren [198K]3 years ago

6 0

Answer:

C. 60° and 80°

Step-by-step explanation:

Sum of triangle = 180°

Therefore,

8x + 4 + 6x - 2 + 10x + 10 = 180

Add like terms

8x + 6x + 10x + 4 - 2 + 10 = 180

24x + 12 = 180

24x = 180 - 12

24x = 168

x = 168/24

x = 7

Find each measure of the angles by substitute x = 7 into each expression

8x + 4 = 8(7) + 4 = 60°

6x - 2 = 6(7) - 2 = 40°

10x + 10 = 10(7) + 10 = 80°

The answer is 60° and 80°

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RoseWind [281]

Answer:

$m\angle KLM=53.13^o$

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the measure of angle KOM

In the triangle KOM

we have

$KO=MO=r=5\ units$

$KM=8\ units$

Applying the law of cosines

$8^2=5^2+5^2-2(5)(5)cos(KOM)$

$64=50-50cos(KOM)$

$50cos(KOM)=50-64$

$50cos(KOM)=-14$

$cos(KOM)=-14/50$

$m\angle KOM=cos^{-1}(-14/50)$

$m\angle KOM=106.26^o$

step 2

Find the measure of the arc KM

we know that

$arc\ KM=m\angle KOM$ ----> by central angle

we have

$m\angle KOM=106.26^o$

$arc\ KM=106.26^o$

step 3

Find the measure of angle KLM

we know that

The inscribed angle is half that of the arc comprising

$m\angle KLM=\frac{1}{2}[arc\ KM]$

we have

$arc\ KM=106.26^o$

substitute

$m\angle KLM=\frac{1}{2}[106.26^o]$

$m\angle KLM=53.13^o$

7 0

4 years ago

Two teachers purchase supplies for their classrooms.

inna [77]

Answer:

Cost of One Journal = $3.99

Cost of One pen = $0.59

Step-by-step explanation:

Let

Cost of One Journal = x

Cost of One pen = y

We can make equation from given statements.

Mr. Bowden purchases 18 journals and 40 pencils for $95.42.

$18x+40y=95.42$

Ms. Jacinto purchases 11 journals and 16 pencils for $53.33.

$11x+16y=53.33$

Now solving these equations to find the value of x

$18x+40y=95.42--eq(1)\\11x+16y=53.33--eq(2)$

Multiply eq(1) with 2 and eq(2) with 5

$36x+80y=190.84\\55x+80y=266.65\\-\:\:\:\:-\:\:\:\;\:\:\:\:\:\:\:-\\---------\\-19x=-75.81\\x=\frac{-75.81}{-19}\\x=3.99\\$

We get the value of x is: x=3.99

Now, putting value of x in equation 1 to find value of y.

$18x+40y=95.42\\18(3.99)+40y=95.42\\71.82+40y=95.42\\40y=95.42-71.82\\40y=23.6\\y=\frac{23.6}{40}\\y= 0.59$

So, we get the value of y: y = 0.59

Now, finding the costs:

Cost of One Journal = x = $3.99

Cost of One pen = y = $0.59

7 0

3 years ago

Look at the triangle below which of the following represents two of the angle measures of the triangle￼

Look at the triangle below which of the following represents two of the angle measures of the triangle