The line L is a tangent to the circle x2 + y2 = 45 at the point (-3, 6).
The line L crosses the x-axis at the point P.
Work out the coordinates of P.

Answers

Answer 1

Answer:

The point P is (-15,0).

Step-by-step explanation:

We need to find the slope of the line L to get the coordinates of P.

We know that L is tangent to the circle at point (-3, 6), which means L is perpendicular to the radius of the circle (a line between the origin (0,0) and the tangent point (-3,6))

So let's find the slope or the radius.

[tex]m_{R}=\frac{6-0}{-3-0}[/tex]    

[tex]m_{R}=-2[/tex]

Now, we know that if two lines are perpendiculars their slopes follow the rule:

[tex]m_{L}=-\frac{1}{m_{R}}[/tex]  

[tex]m_{L}=\frac{1}{2}[/tex]  

Knowing the slope of L we can find the equation of this line. The slope-intercept equation of a line is:

[tex]y=mx+b[/tex]

[tex]y=\frac{1}{2}x+b[/tex]

Using the point (-3,6) we can find b.

[tex]6=\frac{1}{2}(-3)+b[/tex]

[tex]b=\frac{15}{2}[/tex]

The line equation will be:

[tex]y=\frac{1}{2}x+\frac{15}{2}[/tex]

The point P has only an x-coordinate value (x,0)

So we have:

[tex]0=\frac{1}{2}x+\frac{15}{2}[/tex]

[tex]x=-15[/tex]

Therefore, the point P is (-15,0).

I hope it helps you!


Related Questions

How do you find the square root of a number? For example: the square root of 64 or something.

Answers

using a calculator hit 2nd then x^2 and the number you want then enter

Is (4, 2) is the solution to the system below?
Explain how you know by recording an audio response or by showing your work.
y=2x-6
x+y=8

Answers

It is not a solution because when it is plugged into the second equation x+y=8, making it 4+2=8, it is not true.

HELP HELP HELP HELP FAST

Answers

Answer:

[I didn't do it right]

Step-by-step explanation:

[Deleted since it has been said to be wrong and I would not like to spread misinformation]

CAN SOMEONE PLZ HELP ME

The price of a visit to the dentist is $50. If the dentist fills any cavities, an additional charge of $100 per cavity gets added to the bill.

If the dentist fills n cavities, what will be the cost of the visit to the dentist?

Write your answer as an expression.

Answers

Answer:

The expression for the total cost of the visit to dentist is T = 50 + 100n .

Step-by-step explanation:

As given

The price of a visit to the dentist is $50.

If the dentist fills any cavities, an additional charge of $100 per cavity gets added to the bill.

If the dentist n cavities .

Let us assume that the total cost of the visit to dentist be T.

Than the expression becomes

T = 50 + 100n

Therefore the expression for the total cost of the visit to dentist is T = 50 + 100n .

What is 4.89 + ? = 11.26

Answers

Answer:

The answer is 6.37.

Step-by-step explanation:

Please pick me as brainlest answer

Answer:

6.37

Step-by-step explanation:

11.26 - 4.89 = 6.37

Hope this help ;)

What is the Algebraic Notation for this reflection?

A (x,y) ---> (y,x)
B (x,y) ---> (-x,y)
C (x,y) ---> (-y,-x)
D (x,y) ---> (x,-y)

Answers

B

Your y coordinates do not change, but your x coordinates are opposites

What is m<1?
A.39
B. 47
C. 51
D. 129

Answers

Oops i accidentally deleted it, but the angle would be 39 degrees :)

5 - 3(7 - 2r)
How do I simplify the expression

Answers

5-3(7-2r) rearrange the terms: 5-3(-2r+7)
distribute: 5-3(-2r+7) to 5+6r-21
Subtract the numbers: 5+6r-21 becomes -16+6r
Rearrange the terms: 6r-16

Hope this helped!

A line includes the points (-1,0) and (-2,-9). What is its equation in slope-intercept form?​

Answers

Answer:

y = -7x -7

Step-by-step explanation:

If (-1, 0) and (-2, -9) are on the same line then that means their slope is the same. We can find slope with (y1 - y2)/(x1 - x2)

(-2 - (-9)) / (-1 - 0) = 7 / -1 = -7

then we can use the formula y = mx + b

we know that forthe first instance y = 0 and x = -1 and m(slope) = -7

0 = -7*-1 + b

0 = 7 + b

b = -7

our formula then becomes y = -7x -7

Please help me!!!!!!!!

Answers

$5.95 is the answer for the problem

HELP ANSWER FAST!!!!!

Answers

Answer:

i don't know i am sososososo sosososososososo sorry

Step-by-step explanation:

(9x + 7) + (x + 3)

I really don't know.​

Answers

Answer:

10x + 10

Step-by-step explanation:

Thank me later

(9x + 7)
(16x) + (x + 3)
(4)
16x + 4
20x
I think 20x is the answer but I’m probably wrong

3,6,12,24,_,_


What’s the number pattern

Answers

Answer:

48 and 96...,.................

Answer:

3,6,12,24,48,96

Step-by-step explanation:

multiply by 2.

A cell phone is originally priced at $120. The online retailer gives a discount and the cell phone is now priced at $90. Enter the percentage discount for the cost of the cell phone.

Answers

Answer:

25% discount

Step-by-step explanation:

The base charge of a cab in new york is $2.50 as soon as you enter the cab. There is an additional charge of $2.50 per mile traveled. Calculate how many miles you can travel on $20 without giving any tip.

Answers

I HOPE MY ANSWERS HELPS YOU:)

Answer:

7 miles

Step-by-step explanation:

A bag contains 21 coins consisting of nickles and dimes. The total value of the coins is $1.70.
Write a system of equations that models this situation. How many nickels are in the bag?

Answers

Answer:

8

Step-by-step explanation:

x = nickles

y = dimes

0.05x + 0.10y = 1.70

x + y = 21

y = 21 - x

0.05x + 0.10 (21 - x) = 1.70

0.05x - 0.10x + 2.10 = 1.70

-0.05x + 2.10 = 1.70

-0.05x = -0.40

x = 8

HELP I NEED HELP ASAP

Answers

15 hope this helps you

I NEED HELP WITH THIS!!!!

Answers

Answer:

-6r+6

Step-by-step explanation:

1) Remove parentheses

8-6r-2

2) Collect like terms

-6r+(8-2)

3) Simplify

-6r+6

Find the length of BC. (Decimal Answer)

Answers

Answer:

the answer is 9 1/3 i think the decimal would be 3 repeating

Step-by-step explanation:

Factor the expression.
3x + 6
The factored expression is

Answers

Answer:

3(x+2)

3x+6

hope it's helpful ❤❤❤❤

THANK YOU.

#

3x+6 hopes this helps you

Ava takes care of 6 horses Each horse eats about 85 pounds of feed per year. How many pounds of feed will all the horses eat in 18 months?
A. 114lb
B. 30lb
C. 108lb
D. 765lb

Answers

Answer:

The answer is A

Explanation:

If a horse eats 85 pounds of horse feed a year that adds up to about 7 pounds a month so if you add it up it equals 114

Dakari makes 2 dozen jars of jam. The total
weight of all of the filled jars is 211.2 ounces.
When empty, each jar weighs 1.2 ounces. The
equation
can be used to calculate the weight, j, of jam in
one jar. The weight of jam in one jar is

Answers

Answer:

a and c for the blanks.

Write an equation
1)y=3x
2)y=3
3)x=3
4)y=3x+3

Answers

The answer to your question is y = 3

On a coordinate plane, what is the distance between the point at (7, 6) and the point at (7, 9)?

Answers

Answer:

-12

Step-by-step explanation:

6+-9 =-12


7y - 9 = 3y + 19
a. 7
b. -4
C.
-7
d. 4

Answers

The answer is A. 7
so y=7

help me plz due soon

Answers

It's exponential decay by 10%

Pweeze help and i will give brainliest UwU <3

Answers

Answer:

See below for answers

Step-by-step explanation:

1st blank: 2*2*2*2*2*2*2

2nd blank: 2

3rd blank: 7*7

4th blank: 7

5th blank: no

6th blank: doesn't equal

Neeeeeeeeeeeedddddddd hellllllllppppppppppp

Answers

Answer:

0.8333333 which goes on forever

Step-by-step explanation:

Z-Grand Shipping Company manufactures boxes in the shape of a cube.
The formula for the surface area of a cube is 6s, where s is the length of one side.
Z-Grand Shipping Company manufactures large boxes with a side length of 6 feet. The surface area of each large box is
square feet
The company also manufactures small boxes with a side length of 3 feet. The surface area of each small box is
square feet
The surface area of the large box is times larger than the small box.

Answers

Answer:

Z-Grand Shipping Company manufactures boxes in the shape of a cube.

The formula for the surface area of a cube is 6s, where s is the length of one side.

Z-Grand Shipping Company manufactures large boxes with a side length of 6 feet. The surface area of each large box is 216

square feet

The company also manufactures small boxes with a side length of 3 feet. The surface area of each small box is 54

square feet

The surface area of the large box is 4 times larger than the small box.

{So for the first line which is The surface area of each large box is

square feet.}

Ans;216

{The second line which is The surface area of each small box is

square feet.]

Ans;54

{The Third line which is The surface area of the large box is times larger than the small box.}

Ans;4

Thank you So much Hope this helps you! Please Mark Brainleast looking forward to help everyone ty!

The surface area of each small box is 54 square feet and each large box is 216 square feet.

What is the area of cube?

The formula for the surface area of a cube is 6s, where s is the length of one side.

We are given that Z-Grand Shipping Company manufactures large boxes with a side length of 6 feet.

The surface area of each large box is 216 square feet

The company also manufactures small boxes with a side length of 3 feet. The surface area of each small box is 54 square feet

The surface area of the large box is 4 times larger than the small box.

The surface area of each large box = 216 square feet.}

The second line which is The surface area of each small box is

= 54 square feet.

The Third line which is surface area of the large box is times larger than the small box is;

4

Learn more about the area;

https://brainly.com/question/1658516

#SPJ2

What is the simplest form of 12/54

Answers

Answer:

2/9

Step-by-step explanation:

Answer:

reduce it

six goes into both evenly

2/9

Other Questions
Grace wants to participate in a dance recital. She cannot miss more than 15% of the 40 classes before the recital. What is the minimum number of classes Grace must go to in order to be in this recital?(BUT DON'T SAY 6 I PUT IT AND IT WAS WRONG!) Please help me to complete the impact on equity Please answer helppppp!!!!!!!!!!!plz anyone know what this is? what will the equation be for this "Ryan is saving money to buy a skateboard that costs $85. He has already saved $40. He plans to save the same amount each week for three weeks. Let "x" represent the amount he saves each week. Write and solve an equation to represent this situation." hi, pls help.Why do Jews consider the Western Wall in Jerusalem a sacred place? *1. It was built by King Solomon.2. It was all that was left of the Second Temple after the Romans destroyed it.3. It was the place where Abraham settled.4. It was constructed with the stones that held the Ten Commandments. PLZ HELP ITS VERY VERY VERY DUE Classic civilizations developed ____,where is early river valley civilizations did not how do you graph x+ 4 Find the value of x in the triangle shown below. Explicit bias can be stated obviously. True or False?Help please Order these numbers from least to greatest.2.2, 2.1021, 2.104, 2.12 I give up someone help If 27 = 500 rubles, how many are in 1,144 rubles? Give your answer to 2 dp. Flowers and chocolates are popular gifts, but they are impractical. Simple, compound or complex? A bag contains 5 red marbles, 3 blue marbles, 7 yellow marbles, and 2 green marbles. Which ratio can be used to compare the redmarbles to the blue marbles?A) 3/5B) 3/8C) 5/3D) 5/8 HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPP PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEE BRAINLIEST TO RIGHT ANSWER FIND X What does root mean and What is the synonym of it?? Mrs. Avery is going to randomly select one student from her class to read a poem out loud. There are 15 boys and 13 girls in her class.What is the P{boy}? Anyone know this answer