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Zina [86]
3 years ago
15

In Δ A B C, the measure of the largest angle is 32 less than 3 times the smallest angle. The measure of the middle angle is 8 mo

re than half the measure of the largest angle. What is the measure of the middle angle?
Mathematics
1 answer:
AlladinOne [14]3 years ago
5 0

Answer:

52degrees

Step-by-step explanation:

Let the measure of the largest angle be x

middle angle be y

smallest angle be z

Since the sum of angle in a triangle is 180 degrees, hence;

x + y + z = 180 .... 1

If the measure of the largest angle is 32 less than 3 times the smallest angle, then;

x = 3z - 32

3z = x+ 32

z = x+32/3 ..... 2

If he measure of the middle angle is 8 more than half the measure of the largest angle, then;

y = x/2 + 8 .... 3

Substitute 2 and 3 into 1;

x + x/2 + 8 + (x+32)/3 = 180

multiply through by 6

6x + 3x + 48 + 2(x+32) = 1080

9x + 48 + 2x + 64 = 1080

11x + 112 = 1080

11x = 1080-112

11x = 968

x = 968/11

x = 88 degrees

Get the middle angle y;

Since y = x/2 + 8

y = 88/2 + 8

y = 44 + 8

y = 52 degrees

Hence the measure of the middle angle is 52degrees

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Answer:

a) Eva will need 2 bags of clay to make both pieces of pottery.

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Step-by-step explanation:

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a) We have to find the total amount of clay, as she needs \frac{3}{5}pound=P_{1} and \frac{7}{10}pound=P_{2}, so P_{1}+P_{2}= \frac{3}{5} +\frac{7}{10} =\frac{6+7}{10}=\frac{13}{10}pounds, is the total amount of clay. Then as we Know that one bag of clay has \frac{4}{5} =\frac{8}{10} pounds, It isn´t enough, but with two bags 2*\frac{8}{10}=\frac{16}{10}  pounds, It is enough clay.

b) She will have leftover \frac{16}{10} -\frac{13}{10} =\frac{3}{10}pounds of the second bag, then we add the third one, so \frac{3}{10} +\frac{8}{10} =\frac{11}{10}pounds are leftover.

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Answer:

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Step-by-step explanation:

Simple interest is

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Where A is the amount in the account

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Subtract 1 from each side

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Answer:

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Step-by-step explanation:

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Answer:

There are 327,811 doctors.

Step-by-step explanation:

Percentage of female doctors = 16.9%

Number of female doctors = 55,400

Percentage of Male doctors = 100-16.9%

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So if 55,400 doctors are represented by 16.9 how many doctors are represented by 100%?

100% represents total number of doctors.

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Number of doctors has to be a whole number so we rounf off the number to nearest whole number:

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