onsider the line y=-5+6.
find the equation of the line perpendicular to this line and passes through the point (-2,-3)
find the equation of the is parallel to this line and passes through the point (-2,-3)​

Answers

Answer 1

Answer:

The equation of the line perpendicular to the given line is

[tex]y=\frac 1 5 x + \frac {-13}{5}[/tex].

The equation of the line perpendicular to the given line is

[tex]y=-5 x -13[/tex].

Step-by-step explanation:

The given line is y=-5x+6

The slope of the given line, [tex]m_1=-5[/tex]

Let [tex]y= m_2 x + C_2[/tex] be the slope of the line perpendicular to y=-5x+6,

where [tex]C_2[/tex] is constant.

As multiplication of slopes of two perpendicular lines equal to -1, so

[tex]m_1m_2=-1 \\\\\Rightarrow -5\times m_2= -1 \\\\\Rightarrow m_2= \frac {-1}{-5}= \frac 1 5[/tex]

So, the equation of the line perpendicular to the given line is

[tex]y=\frac 1 5 x +C_2[/tex] which passes through the point (-2,-3), so

[tex]-3=\frac 1 5 (-2) +C_2 \\\\\Rightarrow C_2 = -3 +\frac 2 5= \frac {-13}{5}[/tex]

Hence, the equation of the line perpendicular to the given line is

[tex]y=\frac 1 5 x + \frac {-13}{5}[/tex].

Now, let [tex]y=m_3 x +C_3[/tex] be the equation of the parallel line to y=-5x+6.

As the slopes of two parallel lines are the same, so [tex]m_3=-5[/tex].

So, the equation of the parallel line becomes

[tex]y=-5 x +C_3[/tex] which passes through the point (-2,-3), so

[tex]-3=-5 (-2) +C_3 \\\\\Rightarrow C_2 = -3 - 10 = -13[/tex]

Hence, the equation of the line perpendicular to the given line is

[tex]y=-5 x -13[/tex].


Related Questions

Which table shows y as a function of x

Answers

the answer should be C :) in order for there to be a function, first rule is the x number cannot repeat

20 points
A car drove 10.8 miles in 0.4 hours. a.) How fast was the car traveling in miles per hour? b.) At that rate, how long did it take the car to travel 256.5 miles?

Answers

Answer:Miles Per Hour Definition. Our Miles Per Hour Calculator can tell you how many miles you drive in a single stretch. On long road trips, knowing how many miles you are averaging per hour can give you an idea of how long it will take to get to your destination.It is also a good indicator if you are taking too many breaks or if traffic has caused delays in your journey.

Step-by-step explanation:and what you say is 20 points is only 10 points or 13

24) IF area of quadrant of a circle is
38.5 sq.cm then diameter is *
O 7cm
O 14 cm
0 21 cm
O None of these

Answers

Answer:

none of these

Step-by-step explanation:

Jenny, Keith, and Joanna participated in a mini-
marathon. At the end of the marathon, Keith ran 3 miles
more than Jenny. Joanna ran two times more miles
than Keith. The three runners covered a total distance
of 16 miles. How many miles did each person run?
M

Answers

Answer:

Jenny 1.75 miles, Keith 4.75 miles, Jonna 9.5 miles

Step-by-step explanation:

Distance per person:

Jenny - x, Keith - y, Joanna - z

Equation as per given:

y = x + 3z = 2y = 2(x + 3)x + y + z = 16

Substitute and solve for x:

x + (x + 3) + 2(x + 3) = 162x + 3 + 2x + 6 = 164x = 7x = 7/4 = 1.75

Then

y = 1.75 + 3 = 4.75z = 4.75*2 = 9.5

14. Profits at Steven's Pastry shop increased by $1,645 in one 7-day week. By how much did
profits increase each day?

Answers

To find the answer, all we need to do is divide his additional profits ( $1,645 ) by the number of days he made the profit ( 7 days in the week )

$1,645 ÷ 7 = $235

Steven's Shop profits increased by $235 each day!

Hope I helped! If you more explanation, just comment ! :)

plz helps me i need help on dis question

Answers

Answer: 24oz - $2.59

Step-by-step explanation: 3.29/32= 0.1028

2.59/24= 0.1079

Unit rate for

Heinz - 0.102$
Hunts - 0.107$

Pantene - 0.396$
Clairol - 0.342$

Kleenex - 0.019$
Puff - 0.029$

Heinz, Clairol, Kleenex are the best brands

The diagram below shows part of the graph of the equation y= the graph intersects the x-axis at the points. Find the value of a and the value of b. I'm not allowed to use the calculator and I need the process

Answers

The value of a and b are 11 and 14.

What is an equation on a graph?

The equation on a graph shows the point where the equation intersects

on the x-axis and the y-axis.

We have,

The function as y = 2x² + ax + b

Where it intersects on the x-axis at the points (-7/2, 0) and (2, 0).

Now we can write it as:

At point (-7/2, 0).

0 = 2 (-7/2)² + a(-7/2) + b

0 = 49 / 2 - 7a/2 + b

7a/2 - b = 49/2 _____(1)

At point (2, 0)

0 = 2(2)² + 2a + b

0 = 8 + 2a + b

2a + b = -8 _____(2)

From (1) and (2) we can find a and b.

From (1)

7a/2 - 49/2 = b

b = (7a - 49) / 2 ______(3)

putting in (2)

2a + (7a - 49) / 2 = -8

4a + 7a - 49 = -16

3a - 49 = -16

3a = -16 + 49

3a = 33

a = 11

putting in (3)

b = (7x11 - 49) / 2

b = (77 - 49) / 2

b = 28 / 2 = 14

Thus the value of a and b are 11 and 14.

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The value of a and b for the given equation is 3 and -14 respectively.

The given equation is y=2x²+ax+b, (-7/2, 0) and (2, 0).

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Now put (-7/2, 0) and (2, 0) in the given equation and find a and b value.

That is, 0=2 (-7/2)²+a(-7/2)+b

⇒ 49/2 -7a/2+b=0 ----(I)

0=2(2)²+a(2)+b

⇒ 8+2a+b=0

⇒ b=-2a-8 -----(II)

Put b=-2a-8 in equation (I) and simplify.

That is, 49/2 - 7a/2 -2a-8=0

⇒ 49/2 - 11a/2 - 8 =0

⇒ 49 - 11a=16

⇒ 11a=33

⇒ a=3

Put a=3 in equation (II) and simplify.

That is, b=-2(3)-8=-14

Therefore, the value of a and b for the given equation is 3 and -14 respectively.

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The math teacher gives each student a map of the amusement park that uses a coordinate plane. The meeting location is at (0, 0) on the map. Each unit is 100 feet. The first ride that you want to try is located at the coordinates (0, 4). The next ride is located at (3, 0). If you walked in a straight line from the first ride to the second ride, how many feet would you travel?

Answers

Answer:

500 ft

Step-by-step explanation:

use this formula

The actual distance between first and second ride is 500 ft.

What is Distance Formula?

The distance between two point P(a, b) and Q(c, d).

so, the distance PQ = √(c-a)² + (d- b)²

Given:

Starting point = (0,0)

First ride = (0,4)

Second ride = (3,0)

In map, each unit = 100 ft

Using the distance formula

d =  √( 3-0)² + (0-4)²

d = √9+ 16

d= √25

d = 5 units

So, the distance between first ride and second ride in the map is 5 units.

and,1 units  = 100 ft

5 units = 500 ft

Hence, the actual distance between first and second ride is 500 ft.

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Elsa and two of her closest friends went out to dinner to celebrate Elsaś birthday. The bill for dinner totaled $74.80. If they decided to leave a 20% tip, what was the amount paid by each person in Elsaś party before taxes?

Answers

Answer:

$29.92

Step-by-step explanation:

Step one:

given data

The bill for dinner totaled $74.80

Then the tip is 20%

Required

The amount paid by each person after the tip was added to the cost of the dinner

Step two:'

the amount of the tip is

=20/100*74.80

= 0.2*74.80

=$14.96

The total is 14.96+74.80

=$89.76

The number of persons including the celebrant is = 3

so each person will pay

=89.76/3

=$29.92

PLEASE HELP FAST!
Solve for X
3x + 4y = -16
X = 4y

Answers

Answer:

x = -4

Step-by-step explanation:

3x + 4y = -16

X = 4y

3(4y) +4y = -16

=> 12y + 4y = -16

=> 16y = -16

=> y = -1

3x + 4(-1) = -16

=> 3x -4 = -16

=> 3x = -12

=> x = -4

Hope this helps!      :3

plz mark as brainliest!

Answer: It is indeed -4.

Step-by-step explanation: Refer to the answer above me, they have everything exactly right.

PLSS HELP WITH NUMBER 6

Answers

100oz=6.25 lb hope this helps!

Answer: 100oz=6.25 lb

Step-by-step explanation:

Ani sells 527 dollars worth of sodas as part of a school club fundraiser. If the sodas cost 310 dollars, what equation can we make to find out how much money ani raised as the variable ?

Answers

The total money Ani raised was  217 dollars.

Cost price of soda = 310 dollars

money raised = selling price - cost price

What is selling price?

The cost at which something is sold. Calculate the total cost of all the items you bought. To calculate the cost price, divide the total cost by the quantity of units purchased. Use the selling price formula to calculate the final price: Cost price plus profit margin equals selling price.

What is cost price ?

Cost price is the complete sum of money that a manufacturer must spend to create a specific good or render a specific service. Cost is equal to Selling price plus Loss ( when selling price and loss is given ) Cost price = 100 Selling Price + 100 + Profit (where the Selling Price and Profit Percentage are supplied)

Hence

x = 527 - 310

=217 dollars

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The computer has rendered 960 kpx of a garden scene and renders 60 kpx more pixels each
minute.
After how many more minuted will the scenes have the same amounts rendered?

Answers

I will think it be about 960 at the end of the whole thing is done

h(x) = square root of x-10

Answers

Answer:

B

Step-by-step explanation:

solve all for brainliest

Answers

hope this helps!!!!!

Perry's school is selling tickets to a choral performance. On the first day of ticket sales the school sold 12 adult tickets and 7 child tickets for a total of $57. The school took in $63 on the second day by selling 7 adult tickets and 14 child tickets. What is the price of one adult ticket and one child ticket?

Answers

Answer:

$6

Step-by-step explanation:

Answer:

both cost 3 dollars

Step-by-step explanation:

x=adult ticket

y=child ticket

12x+7y=57

7x+14y=63

24x+14y=114

-7x-14y=-63

17x=51

x=3

7(3)+14y=63

21+14y=63

14y=42

y=3

I need help with my working ​

Answers

Answer:

15^2 = 225

7^3 = 343

Step-by-step explanation:

answer
i think this one will be C!

Explanation
The answer is right when i checked DD

Write a function to solve the following word problem

Huey purchases a helicopter for $576,001. The helicopter decreases in value at an 11% rate each year. What will be the value of the helicopter after 12 years? Round to the nearest dollar.​

Answers

The required function is: 576,001 - ( 0.11 * 576,001 * x )

The value of the helicopter after 12 years, to nearest dollar is -$184320

How to find the value of the helicopter after 12 years

Given data

price of a helicopter $576,001

rate of value decrease is 11%

The decrease in value will result to

= 576,001 - 0.11 * 576,001 * x

let x represent the number of years

the required function is: 576,001 - 0.11 * 576,001 * x

plugging in 12 and solving results to

= 576,001 - 0.11 * 576,001 * x

= 576,001 - 0.11 * 576,001 * 12

= 576,001 - 760321.32

= -184320.32

The value of the helicopter after 12 years, to nearest dollar is -$184320

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I need help which one is it?

Answers

Answer:

B. 3

Step-by-step explanation:

What is the axis of symmetry of a quadratic and how is it related to its vertex?

Answers

Answer:

It goes through the vertex

Step-by-step explanation:

The axis of symmetry is an imaginary line that runs vertically or horizontally through the vertex depending on which way the parabola or hyperbola is facing.

Brainliest please.

y = –x + 5
y = –2x + 7

Answers

Answer:

x = 2, y = -3

Step-by-step explanation:

Since both equations are set equal to y,

[tex]-x+5=-2x+7 \\ \\ x=2 \\ \\ \implies y=-2+5= - 3[/tex]

Which expression is equivalent to - 1/3 (3x - 1/2)?

Answers

Answer:

-x+1/6

Step-by-step explanation:

Multiply -1/3 x 3x=-1x or -x

Multiply -1/3 x -1/2= 1/6

Can help with this please,
A phone shop sells iPhones and Samsung phones in a ratio of 7:5.
Last week the shop sold 42 iPhones.

How many Samsung phones did it sell?

Answers

Answer:

30

Step-by-step explanation:

Given the ratio 7 : 5

The 42 iPhones sold relates to the 7 part of the ratio.

Divide 42 by 7 to find the value of one part of the ratio.

42 ÷ 7 = 6 ← value of 1 part of the ratio, thus

5 parts = 5 × 6 = 30 ← number of Samsung phones sold

Answer:
They sold 30 Samsung’s

Step-by-step:explanation:
If they sold 42 iPhones then skip count 7,14,21,28,35,42 and as you can see we skipped count 6 times so then just do 5 times 6 which will give u 30

Hope this helps!!

Games-R-Us offers a video game rental program with a monthly fee of $10 plus $2 per game rental. Games2Go charges a $2 monthly fee plus $4 per game. Given the same to stores Games-R-Us and Games2Go, how many games would you have to rent from each company to have your total cost be the same amount?

Answers

Answer:

4 games

Step-by-step explanation:

Let the number of games rented from both be represented by: g

For Games - R - Us

Games-R-Us offers a video game rental program with a monthly fee of $10 plus $2 per game rental.

$10 + $2 × g

= 10 + 2g

For Games2Go

Games2Go charges a $2 monthly fee plus $4 per game.

$2 + $4 × g

= 2 + 4g

Hence,

Games-R-Us = Games2Go

10 + 2g = 2 + 4g

Collect like terms

10 - 2 = 4g - 2g

8 = 2g

g = 8/2

g = 4 games

Therefore, number of games you would have to rent from each company to have your total cost be the same amount is 4 games

Write an equation in point-slope form of the line that passes through the point (1, 6) and has a slope of −1/2

Answers

Answer:

y-6 = -1/2 * (x-1)

Step-by-step explanation:

Point slope form is y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope. Plug in (1,6) for (x1, y1) and -1/2 for m.

Hey step brroooooooo

A laptop is on sale for 18% off the original price of $450. What is the sale price?

Answers

Answer: 369

Step-by-step explanation:

This is becuase 18% of 450 is 81, and 18% off means you subract the 81 leaving 369.

What is f(4) for the function f(x) = 7x + 6?
Please help asap

Answers

Answer:

f(4) for the function [tex]f(x) = 7x + 6[/tex] is [tex]\mathbf{f(4)=34}[/tex]

Step-by-step explanation:

We need to find f(4) for the function [tex]f(x) = 7x + 6[/tex]

For finding f(4) we will put x= 4 in the given function

[tex]f(x) = 7x + 6[/tex]

Put x = 4

[tex]f(4)=7(4)+6\\f(4)=28+6\\f(4)=34[/tex]

SO, f(4) for the function [tex]f(x) = 7x + 6[/tex] is [tex]\mathbf{f(4)=34}[/tex]

What is the area of a circle if the diameter is 27?

Answers

Answer:

Step-by-step explanation

A = (3.14)(r^2)

r^2 = (1/2 d) = 13.5^2 = 182.25

A = 3.14 x 182.25 = 572.265 unit sq.

Identify the x-intercept and y-intercept

Answers

Answer:

x: -6, y: -2

Step-by-step explanation:

look at the graph, I hope this is the x and y of the lines. It says the answers, but just identify it.

Answer:

(- 6, 0 ) and (0, - 2 )

Step-by-step explanation:

The x- intercept is the value of x on the x- axis where the line crosses.

Here x = - 6 ← x- intercept or (- 6, 0) in coordinate form

The y- intercept is the value of y on the y- axis where the line crosses.

Here y = - 2 ← y- intercept or (0, - 2 ) in coordinate form

For what value of k is the expression [tex]x^{4}[/tex]+k[tex]x^{2}[/tex]+49 a perfect square?


a. 7

b. 14

c. 49

d. 98

Answers

Answer:

k = 14

Step-by-step explanation:

Given:

x⁴ + kx² + 49

Find:

Value of k

Computation:

x⁴ + kx² + 49

(x²)² + (k)(x²) + 7²

we know that;

a² + 2ab + b²

On compare;

k = 2 x 7

k = 14

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