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3 years ago

Give the equation of the line which is perpendicular to y = 5x + 6 and goes through the point (- 15, 2)

Mathematics

1 answer:

Reptile [31]3 years ago

7 0

Answer:

x+5y+5=0

Step-by-step explanation:

y=5x+6

Therefore the gradient of the line = 5

Now reciprocate the gradient and negate it

i.e -1/5

let (x,y) and (-15,2) be points on the line

y-2/x-(-15)=-⅕

5y-10=-x-15

5y-10+15+x=0

x+5y+5=0

Therefore the equation of the line =

x+5y+5=0

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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

If x:6 as 3:9 then x is equal to<br> pleas help!!

natima [27]

Answer:

Step-by-step explanation:

x/6 = 3/9

cross multiply

9x = 18

divide 9 on both sides

x= 2

7 0

3 years ago

16)<br> (lly-32)<br> (6x + 7)<br> What’s X

Y_Kistochka [10]

This has alot of information missing. Can you please repost this with more detailed information? Thanks.

6 0

3 years ago

Complete the square. Fill in the number that makes the polynomial a perfect-square

FromTheMoon [43]

=s(s-26) is 4 step s^2-26s the polynomial of a must be 4 since the known number we don’t know I guess it’s 4

4 0

3 years ago

The average age of 15 students is 16 years. If teacher’s age is included the average increases by 1. Find teacher’s age. (a) 30

Mrac [35]

Answer:

Age of teacher = 32 years

Step-by-step explanation:

Average age of 15 students = 16 years

Sum of age of 15 students = 16 * 15 = 240 years

Average of age 15 students and a teacher = 17 years

Sum of age 15 students and a teacher = 17 * 16 = 272 years

Age of teacher = 272 - 240 = 32 years

4 0

4 years ago

Read 2 more answers

Give the equation of the line which is perpendicular to y = 5x + 6 and goes through the point (- 15, 2)​

Give the equation of the line which is perpendicular to y = 5x + 6 and goes through the point (- 15, 2)