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3 years ago

the angle of a triangle are given as 6x,(x-3), and (3x+7). find x then find the measures of the angles

Mathematics

1 answer:

kvv77 [185]3 years ago

8 0

Answer:

x =17.6

The three angles are

6x = 105.6

x-3 =14.6

3x+7 = 59.8

Step-by-step explanation:

The three angles of a triangle add to 180 degrees

6x + x-3 + 3x+7 = 180

Combine like terms

10x +4 = 180

Subtract 4 from each side

10x+4-4= 180-4

10x = 176

Divide each side by 10

10x/10 =176/10

x =17.6

The three angles are

6x = 6*17.6= 105.6

x-3 = 17.6-3 =14.6

and 3x+7 = 3(17.6)+7 =52.8+7 = 59.8

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Find exact values for sin θ and tan θ if cos θ = -4/9 and tan θ > 0.

julsineya [31]

Answer:

Part 1) $sin(\theta)=-\frac{\sqrt{65}}{9}$

Part 2) $tan(\theta)=\frac{\sqrt{65}}{4}$

Step-by-step explanation:

we have that

The cosine of angle theta is negative and the tangent of angle theta is positive

That means that the sine of angle theta is negative

step 1

Find $sin(\theta)$

we know that

$sin^{2}(\theta) +cos^{2}(\theta)=1$

we have

$cos(\theta)=-\frac{4}{9}$

substitute

$sin^{2}(\theta) +(-\frac{4}{9})^{2}=1$

$sin^{2}(\theta) +\frac{16}{81}=1$

$sin^{2}(\theta)=1-\frac{16}{81}$

$sin^{2}(\theta)=\frac{65}{81}$

square root both sides

$sin(\theta)=\pm\frac{\sqrt{65}}{9}$

Remember that

In this problem the sine of angle theta is negative

$sin(\theta)=-\frac{\sqrt{65}}{9}$

step 2

Find $tan(\theta)$

we know that

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}$

we have

$sin(\theta)=-\frac{\sqrt{65}}{9}$

$cos(\theta)=-\frac{4}{9}$

substitute the given values

$tan(\theta)=-\frac{\sqrt{65}}{9}:-\frac{4}{9}=\frac{\sqrt{65}}{4}$

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3 years ago

at a local soccer game, 6/7 of the people were fans. one-half of those fans were wearing hats. what fraction of the people was w

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Answer: $\frac{3}{7}$

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3 years ago

Read 2 more answers

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Stells [14]

Answer:

Milk

Step-by-step explanation:

The amount of milk, cottage cheese and strawberries used are given in the attached picture.

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2/6 cup cottage cheese

8/12 cup strawberry

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3 years ago

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blsea [12.9K]

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