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3 years ago

Write the slope-intercept form of the glven line. Include your work in your final answer. Type your answer in the box

Mathematics

1 answer:

mrs_skeptik [129]3 years ago

6 0

Answer:

-1/3

Step-by-step explanation:

the line rises 1 and runs back 3

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let sin(θ) =3/5 and tan(y) =12/5 both angels comes from 2 different right trianglesa)find the third side of the two tringles b)

statuscvo [17]

In a right triangle, we haev some trigonometric relationships between the sides and angles. Given an angle, the ratio between the opposite side to the angle by the hypotenuse is the sine of this angle, therefore, the following statement

$\sin (\theta)=\frac{3}{5}$

Describes the following triangle

To find the missing length x, we could use the Pythagorean Theorem. The sum of the squares of the legs is equal to the square of the hypotenuse. From this, we have the following equation

$x^2+3^2=5^2$

Solving for x, we have

$\begin{gathered} x^2+3^2=5^2 \\ x^2+9=25 \\ x^2=25-9 \\ x^2=16 \\ x=\sqrt[]{16} \\ x=4 \end{gathered}$

The missing length of the first triangle is equal to 4.

For the other triangle, instead of a sine we have a tangent relation. Given an angle in a right triangle, its tanget is equal to the ratio between the opposite side and adjacent side.The following expression

$\tan (y)=\frac{12}{5}$

Describes the following triangle

Using the Pythagorean Theorem again, we have

$5^2+12^2=h^2$

Solving for h, we have

$\begin{gathered} 5^2+12^2=h^2 \\ 25+144=h^2 \\ 169=h^2 \\ h=\sqrt[]{169} \\ h=13 \end{gathered}$

The missing side measure is equal to 13.

Now that we have all sides of both triangles, we can construct any trigonometric relation for those angles.

The sine is the ratio between the opposite side and the hypotenuse, and the cosine is the ratio between the adjacent side and the hypotenuse, therefore, we have the following relations for our angles

$\begin{gathered} \sin (\theta)=\frac{3}{5} \\ \cos (\theta)=\frac{4}{5} \\ \sin (y)=\frac{12}{13} \\ \cos (y)=\frac{5}{13} \end{gathered}$

To calculate the sine and cosine of the sum

$\begin{gathered} \sin (\theta+y) \\ \cos (\theta+y) \end{gathered}$

We can use the following identities

$\begin{gathered} \sin (A+B)=\sin A\cos B+\cos A\sin B \\ \cos (A+B)=\cos A\cos B-\sin A\sin B \end{gathered}$

Using those identities in our problem, we're going to have

$\begin{gathered} \sin (\theta+y)=\sin \theta\cos y+\cos \theta\sin y=\frac{3}{5}\cdot\frac{5}{13}+\frac{4}{5}\cdot\frac{12}{13}=\frac{63}{65} \\ \cos (\theta+y)=\cos \theta\cos y-\sin \theta\sin y=\frac{4}{5}\cdot\frac{5}{13}-\frac{3}{5}\cdot\frac{12}{13}=-\frac{16}{65} \end{gathered}$

4 0

1 year ago

What is equivalent to (4xy-3z)^2 and<br> what type of special product is it?

sergey [27]

Answer:

the answer on edgenuty is option D

Step-by-step explanation:

i just took the quiz

3 0

3 years ago

(-3/4m)-(1/2)=2+(1/4,)

Aleks [24]

(-3/4m) -(1/2)=2+(1/4m)
-(1/2)=2+m
m= -3/2

5 0

3 years ago

as you did during the lesson, label and represents the product or quotient by drawing disks on the place value chart 10 x 4 thio

Naily [24]

Answer : 40,000

Explanation : when multiplying 10 with 4,000 we get

4000 X 10 = 40,000.

As we multiply, using the chart there are 4 thousand present in the row of thousand column. When we multiply that with 10 it gets shifted to left and becomes 40,000.

6 0

3 years ago

A sports ball has a diameter of 27 cm. Find the volume of the ball. cm.) Round your answer to the nearest tenth if necessary.

Anestetic [448]

To calculate the volume of a sphere you must use the formula
v=4/3pir^3

The radius (r) is half of the diameter
r=13.5

v=4/3pi13.5^3
v=10305.99

Therefore the volume of the sports ball is 10306cm^3 (to the nearest tenth)

8 0

3 years ago