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docker41 [41]
2 years ago
13

Find the equation of a line perpendicular to y= 3x + 7 that passes through the point (9,-7).

Mathematics
2 answers:
liraira [26]2 years ago
7 0
Okay so the gradient of the perpendicular line is -1/3 and then from there u have to solve for the y intercept. Substitute in 9 and -7 where -7 is y and 9 is x. The equation is y=-1/3x-4 :)
levacccp [35]2 years ago
7 0

Answer:

y=-\frac{1}{3}x-4

Step-by-step explanation:

To find the slope perpendicular to this, take the negative reciprocal of the slope. Basically, invert both the fraction and the negative/positive so that 3 becomes -1/3.

Now, using the new slope and the given point, we can find the y-intercept. Plug the 3 known variables into the equation:

y=mx+b\\-7=(-\frac{1}{3})(9)+b

Then, solve for b:

-7=-3+b\\-4=b\\b=-4\\

Finally, with both the slope and the y-intercept, you can write the equation of the line:

y=-\frac{1}{3}x-4

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Use the identity tan(theta) = sin(theta) / cos(theta) to show that tan(???? + ????) = tan(????)+tan(????) / 1−tan(????) tan(????
VMariaS [17]

Answer:

See the proof below.

Step-by-step explanation:

For this case we need to proof the following indentity:

tan(x+y) = \frac{tan (x) + tan(y)}{1- tan(x) tan(y)}

So we need to begin with the definition of tangent, we know that tan (x) =\frac{sin(x)}{cos(x)} and we can do this:

tan (x+y) = \frac{sin (x+y)}{cos(x+y)}   (1)

We also have the following identities:

sin (a+b) = sin (a) cos(b) + sin (b) cos(a)

cos(a+b)= cos(a) cos(b) - sin(a) sin(b)

Now we can apply those identities into equation (1) like this:

tan (x+y) =\frac{sin (x) cos(y) + sin (y) cos(x)}{cos(x) cos(y) - sin(x) sin(y)}   (2)

We can divide numerator and denominator from expression (2) by \frac{1}{cos(x) cos(y)} we got this:

tan (x+y) = \frac{\frac{sin (x) cos(y)}{cos (x) cos(y)} + \frac{sin(y) cos(x)}{cos(x) cos(y)}}{\frac{cos(x) cos(y)}{cos(x) cos(y)} -\frac{sin(x)sin(y)}{cos(x) cos(y)}}

And simplifying we got:

tan (x+y) = \frac{tan(x) + tan(y)}{1-tan(x) tan(y)}

And that complete the proof.

8 0
3 years ago
The crew worked 2 1/5 days. If they built 3 3/4 kilometers of road each day, what is the length of the road
nordsb [41]
The answer to the question is: The road is 8 1/4
6 0
3 years ago
Read 2 more answers
12 less than a number is the same as 6, deceased by 8 times the number. Find the number
EastWind [94]
12-x•8 if this helps
4 0
3 years ago
Answer for brainlest
antiseptic1488 [7]

A disjunction is a compound statement formed by joining two statements with the connector OR. The disjunction "p or q" is symbolized by p q. A disjunction is false if and only if both statements are false; otherwise it is true. The truth values of p q are listed in the truth table below.

7 0
3 years ago
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omeli [17]

Answer:

Step-by-step explanation:

First order from smallest to largest.

70.8, 71.9, 72.1, 82.4, 85.3, 98.1.

Median is the middle number/s.

72.1+82.4/2 so The median is 77.25

Range is the largest number minus the smallest number.

85.3-70.8=14.5

Mode is the most repeated number.

Since there are no repeated numbers there is no mode.

Second question:

Again rearrage: 6, 9, 11, 14, 17

In order to make the median 10 you would have to add another 9 becasue

11+9/2 = 10

Third: remove 6 to make 12 the middle number

Fourth: add all numbers 90+x/6=20 so x has to be 30

8 0
3 years ago
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