Triangle ABC is defined by the points A(2,9), B(8,4), and C(-3,-2).
?

Complete the following equation for a line passing through point C and perpendicular AB.?

Answers

Answer 1

Answer:

5y - 6x = 8 or y = 6x/5 + 8/5

Step-by-step explanation:

let M1= gradient of line AB and M2= gradient of the second line

When two lines are perpendicular, the product of their gradients is -1

i.e, M1M2= -1

M2= -1/M1

A(2,9) and B(8,4)

gradient= (y2-y1)/(x2-x1)

M1= (4-9)/(8-2)

= -5/6

M2= -1÷ -5/6

-1 × -6/5= 6/5

Equation of the line passing through C(-3,-2)

[y-(-2)]/[x-(-3)= 6/5

(y+2)/(x+3)= 6/5

5(y+2)= 6(x+3)

5y+10=6x+18

5y= 6x + 8

y= 6x/5 + 8/5

Answer 2

As per the slope-intercept form of a straight line, the equation of the required line is 5y = 6x + 8.

What is the slope-intercept form of a straight line?

The slope-intercept form of a straight line is: y = mx + c

Here, m = slope of the line , c = y-intercept

What is the relation between the slope of a line perpendicular to another line?

If the slope of a line is 'a', then the slope of the line that is perpendicular to the given line is (- 1/a).

The given coordinates of the points A, B, C are (2, 9); (8, 4); and C(- 3, - 2) respectively.

Therefore, the slope of the line AB is (m)

= (y₂ - y₁)/(x₂ - x₁)

= (4 - 9)/(8 - 2)

= (- 5)/6

Slope of the required line is perpendicular to AB.

Therefore, the slope of the required line is

= - 1/(- 5/6)

= 6/5

This line passes through point C(- 3, - 2).

- 2 = - 3(6/5) + c

⇒ c = -2 + 18/5

⇒ c = 8/5

The equation of the required line is

y = (6/5) x + (8/5)

⇒ 5y = 6x + 8

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Related Questions

Which number line correctly shows 4.5 – 2.5?
a) A number line going from 0 to 4.5 in increments of 0.5. An arrow goes from 0 to 4.5 and then backwards from 4.5 to 2.
b) A number line going from negative 4.5 to 0 in increments of 0.5. An arrow goes from negative 4.5 to negative 2 and then backwards from 0 to negative 4.5.
c) A number line going from negative 2.5 to positive 4.5 in increments of 0.5. An arrow goes from negative 2.5 to 0 and also from 0 to 4.5.
d) A number line going from negative 4.5 to positive 2.5 in increments of 0.5. An arrow goes from 2.5 to 0 and from 0 to negative 4.5.

Answers

Answer:

its A i think

Step-by-step explanation:

Hope this helps!

Each box of candy canes has 12 candy canes. How much does each candy cane cost?

Answers

Based on the information given, the cost of each candy cane will be $3.00.

This is an incomplete information as you didn't provide the cost of the box. Let's assume that the cost of the box is $36.

From the information given, we are told that each box of candy canes has 12 candy canes. Therefore, the cost of each candy cane will be:

= $36 / 12

= $3.

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Basket A had 7 times as many plums as Basket B at first. Zoe put 58 more plums in each basket. Now Basket A has thrice as many plums as Basket B. How many more plums are there in Basket A than Basket B now?

Answers

Answer:

174 plums

Step-by-step explanation:

a=7b

a+58=3b

7b+58=3b

4b=58

b=14.5

29,203 earlier

87,261 now

261-87=174

What is an equation of the line that passes through the points (2, -1) and (3,-4)

Answers

Answer:

Step-by-step explanation:

Given:

x1 = 2

x2 = 3

y1 = -1

y2 = -4

Solution:

m = ( y2 - y1 ) / ( x2 - x1 )

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

m = -3 / 1

m = -3

Then,

y - y1 = m ( x - x1 )

y - (-1) = -3 ( x - 2 )

y + 1 = -3x + 6

y = -3x + 6 - 1

y = -3x + 5

Let f be a differentiable function. If h (x) = (2+ f (sin x))", which of the following gives a correct process for finding h' (x) ?

Answers

Answer:

[tex]\displaystyle h'(x) = \cos (x) f'(\sin x)[2 + f(\sin x)]'''[/tex]

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Derivative Property [Addition/Subtraction]:                                                         [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Derivative Rule [Basic Power Rule]:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify.

[tex]\displaystyle h(x) = [2 + f(\sin x)]''[/tex]

Step 2: Differentiate

Derivative Rule [Chain Rule]:                                                                       [tex]\displaystyle h'(x) = [2 + f(\sin x)]''' [2 + f(\sin x)]'[/tex]Rewrite [Derivative Property - Addition/Subtraction]:                                 [tex]\displaystyle h'(x) = [2 + f(\sin x)]''' \bigg[(2)' + [f(\sin x)]' \bigg][/tex]Derivative Rule [Basic Power Rule]:                                                             [tex]\displaystyle h'(x) = [2 + f(\sin x)]''' [f(\sin x)]'[/tex]Derivative Rule [Chain Rule]:                                                                       [tex]\displaystyle h'(x) = [2 + f(\sin x)]''' f'(\sin x)(\sin x)'[/tex]Trigonometric Differentiation:                                                                       [tex]\displaystyle h'(x) = \cos (x) f'(\sin x)[2 + f(\sin x)]'''[/tex]

From here, if you would like, you can take the 3rd derivative of the last piece.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

What is an equivalent expression to 7x - 3y + 8x ?



Pls look at the image that I uploaded

Answers

Answer:

15x - 3y

Explaination:

Adding 7x and 8x will give you 15x and the -3y doesn't need to be added up.

I hope this helps you.

inverse of
f(x)=6x+5

Answers

Attached image is the answer

Please Help Question In Picture

Answers

Answer:

A

Step-by-step explanation:

Since Angle XYZ is equal to Angle YZX,

XY=XZ

The two triangles are congruent.So,

VW=YZ

XY=UV

XZ=UW

Thus;

XY=UV

XZ=UW

XZ=XY=UV=UW

So the permieter is 5.7 + 5.7 + 3.7 = 15.1 cm





Find the measure of the missing angles. 99° e f d​

Answers

Answer:

e = 99 , d = 90 , f = 81

Step-by-step explanation:

Answer:

81º

Step-by-step explanation:

Notice that angle f and 99º form a straight line. A straight line is 180º, so angle f = 180º - 99º = 81º.

If ALMN = AXYZ, which congruences are true by CPCTC? Check all that
apply.

Answers

Answer:

A C E

Step-by-step explanation:

these triangles can be mapped onto eachother. its basically asking which parts of the triangle would line up with eachother.

The required congruences that are true by CPCTC are LN ≅ XZ, ∠M ≅ ∠Y, and ML ≅ XY. Options A, C, and E are correct.

What is CPCTC?

CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent." It is a theorem in geometry that states that if two triangles are congruent, then their corresponding parts (sides and angles) are also congruent.

More formally, if two triangles are congruent, then the three pairs of corresponding sides are congruent, and the three pairs of corresponding angles are congruent.

Here,
Since the triangle LMN ≅ triangle XYZ,
By CPCTC, we can say that,
∠L ≅ ∠X
∠N≅ ∠Z
∠M ≅ ∠Y
ML ≅ XY
MN ≅ YZ
LN ≅ XZ

Thus, the required congruences that are true by CPCTC are LN ≅ XZ, ∠M ≅ ∠Y, and ML ≅ XY. Options A, C, and E are correct.

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Which inequality is graphed below

Answers

The answer would be C

Which of these actions would decrease heat transfer between two objects?

increasing the temperature of the warmer object
increasing the area of their contact
reducing the thermal energy of the cooler object
reducing the time of their contact
(Fr ran out of free answers)

Answers

Answer:

increasing the area of their contact

find the output (y) of the function y= - 4/15 x +24 if the input (x) is 120

Answers

[tex]\text{Given that,}\\\\y = -\dfrac 4{15} x + 24\\\\\text{When x = 120,}\\\\y = -\dfrac 4{15} (120) + 24\\\\\implies y = - \dfrac{480}{15} +24\\\\\implies y=-32+24 \\\\\implies y = -8[/tex]

A parallelogram and some of its
dimensions are shown below.
2
15 in.
T
hin.
The area of the parallelogram is
90 square inches. What is h, the height
in inches of the parallelogram?
A.
6
B.
8
C. 10
D. 12
Which of the following expressions
3

Answers

Answer:

8?

Step-by-step explanation:

i am not sure

A.6
90➗15=6
so that A is the correct answer

An item is regularly priced at $55. Miguel bought it on sale for 40% off the regular price. How much did miguel pay?

Answers

Answer: so Miguel payed $33

steps:

1. first find what 40% of $55 which gives us $22

2. Final Price = Original Price - Discount

Final Price = 55 - 22

Final Price = $33.00

They are similar or not similar and why?

Answers

Answer:

Yes its similar because if you look at all the numbers they are all the same but the shape is just turned around

please consider brainliest <3

Answer:

Step-by-step explanation:

Yes its similar because if you look at all the numbers they are all the same but the shape is just turned around

love ELVIS

solve the equation 5x+x-7=4x-2-x

Answers

Answer:

[tex]x=\frac{5}{3}[/tex]

Step-by-step explanation:

Brainliest pls?

Investors buy a studio apartment for $180,000. Of this​ amount, they have a down payment of $18,000. Their down payment is what percent of the purchase​ price? What percent of the purchase price would a ​$9,000 down payment​ be? Their down payment is enter your response here​% of the purchase price. ​(Type a whole​ number.) A ​$9,000 down payment would be enter your response here​% of the purchase price. ​(Type a whole​ number.)

Answers

Answer:

$180,000 is 10% $9,000 is 5%

Step-by-step explanation:

To solve for this, you would set up a ratio and cross-multiply.

$18,000/$180,000 = x%/100%

(18,000)(100) = 180,000x

1,800,000 = 180,000x

10 = x

9,000/180,000 = x/100

900,000 = 180,000x

5 = x

OR

$18,000 ÷ 2 = $9,000

10% ÷ 2 = 5%

HELP THIS IS URGENT!!!!!!!!!!!!!1Fill in the blank so that the equation has the solution x=3
3x+ =5

Answers

That makes noooo sense booooyyyy

Answer:

y = 3x + 5

Step-by-step explanation:

Since this is a linear function, its graph is a straight line stretching from - infinity to infinity on both x and y axes, hence domain and range is all real numbers from - infinity to infinity.

lowest common factor of 6 and 12

Answers

Answer:

36

Step-by-step explanation:

It's so obvious lollllll

Answer:

36

Step-by-step explanation:

3x+12-6x less than or equal to -9

Answers

Answer:

less than, it is the answer

Trevor paid a total of $1.08 in fines for an overdue library book. If the penalty for overdue books is $0.09 per day, how many days late was the book?
2 days
8 days
12 days
20 days

Answers

Answer:

12

Step-by-step explanation:

You have to divide the total by the number per day to solve this problem.

1.08/0.09=12

the state of California keeps track of how many millions of students are learning English as a second language each year: English Learners are shown in millions in the table.
find an equation for the median fit line

Answers

There is no table too be seen, this data can’t be calculated by itself for viewers

If the distance between A(0, 4) and B(3,a) is 5 units then find the value of a.​

Answers

Answer:

Step-by-step explanation:

a = 0

So that AOB makes a right triangle with sides 3-4-5

Answer:

a = 8

Step-by-step explanation:

Calculate AB using the distance formula and equate to 5

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = A (0, 4 ) and (x₂, y₂ ) = B (3, a )

d = [tex]\sqrt{(3-0)^2+(a-4)^2}[/tex]

  = [tex]\sqrt{3^2+(a-4)^2}[/tex]

  = [tex]\sqrt{9+(a-4)^2}[/tex] , then

[tex]\sqrt{9+(a-4)^2}[/tex] = 5 ( square both sides )

9 + (a - 4)² = 5² = 25 ( subtract 9 from both sides )

(a - 4)² = 16 ( take square root of both sides )

a - 4 = 4 ( add 4 to both sides )

a = 8

Please HELP!!!

What are the first 4 terms of the arithmetic sequence in the graph?

Enter your answers in the boxes.

_,_,_, and _


Answers

Answer:

- 3, 1, 5, 9

Step-by-step explanation:

The first 4 terms are the values of y corresponding to x = 1, 2, 3, 4 , that is

(1, - 3 ) , (2, 1 ) , (3, 5 ) , (4, 9 )

first 4 terms are - 3, 1, 5, 9

Find the slope of the line below. Enter your answer as a fraction or decimal.
Use a slash mark ( 1 ) as the fraction bar if necessary.
10
(-4,8).
(-6,-4)
Answer here

Answers

Answer:

slope = 6

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (-6, - 4) and (x₂, y₂ ) = (- 4, 8) ← 2 points on the line

m = [tex]\frac{8-(-4)}{-4-(-6)}[/tex] = [tex]\frac{8+4}{-4+6}[/tex] = [tex]\frac{12}{2}[/tex] = 6

The slope of the line given in the task content is; m = 6.

What is the slope of the line?

The slope of the line is the rate of change of the dependent variable with respect to the independent variable.

On this note, the slope of the equation is;

Slope, m = (-4-8)/(-6-(-4))

m = -12/-2

m = 6.

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An astronomical unit (AU) is the average distance between Earth and the sun. One AU is equal to approximately 150,000,000 km. Astronomers also use light years to measure distance. A light year is approximately 9.5×10^12
km.

Use scientific notation to rewrite the measure of one astronomical unit (1 AU) in kilometers

Answers

Using scientific notation, it is found that the measure of one astronomical unit in kilometers is [tex]1.5 \times 10^8[/tex]

A number in scientific notation is given by:

[tex]a \times 10^b[/tex]

In which [tex]a \in [1, 10)[/tex]To realize the conversion from decimal to scientific notation, b is the number of decimal places the comma moves, being positive if to the left, negative if to the right.  

In this problem, 1 AU = 150,000,000 km.

The comma has to move 8 places to the right, hence [tex]b = 8[/tex]

Then, the measure is: [tex]1.5 \times 10^8[/tex]

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2=2m​−7 SOLVE FOR M PLS AND THANK YOU

Answers

Answer:

m = 4.5

Step-by-step explanation:

2 = 2m - 7

add 7 to both sides

9 = 2m

divide by 2 on each side

4.5 = m

CHECK:

2 = 2(4.5) -7 (TRUE)

2 · 4.5 = 9

9 - 7 = 2

I hope this helps!

Answer:

m=4.5

Step-by-step explanation: First, add 7 to each  side and you get 9=2m. divide each side by 2 and you get m=4.5

At the end of the day, a bakery had 6/7 of a pie left over. Louie, Duey and Huey split the pie, with each taking home the same amount of leftover pie. How much pie did Louie take home?

Answers

6/7 : 3 = 2/7
because 2/7 * 3 = 6/7

Answer:

2/7 of the pie

Step-by-step explanation:

6/7 / 3 = 2/7

PLEASE HELP TEST DUE SOON⚠️
What is the equation for the line in slope intercept form

Answers

Answer:

The answer should be [tex]y=mx+b[/tex]

Step-by-step explanation:

[tex]y=mx+b[/tex] is the only thing I can think of when your talking about the equation of the line in intercept form, but I'm 85% sure this is correct.

Hope this helps!

Can you mark me brainliest?

Have a great day/night/afternoon!

- ❤ 7272033Alt ❤

The answer is: y=mx+b
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