sophia is designig a logo with three lines,y, m, and n. Line m passes through point (-2, -1) and is perpendicular to the graoh of y=-2/3 x +6. line n is parallel to line m and passes through the point (4, -3). what is the equation in slope-intercept form of linen?

Answers

Answer 1

Answer:

y = 3/2x - 9

Step-by-step explanation:

Finding equation of line m

⊥ to the line y = -2/3x + 6new slope = -(-3/2) = 3/2Passes through the point (-2, -1)y + 1 = 3/2(x + 2)y + 1 = 3/2x + 3y = 3/2x + 2

Equation of line n

Parallel ⇒ slope is same = 3/2Passes through the point (4, -3)y + 3 = 3/2(x - 4)y + 3 = 3/2x - 6y = 3/2x - 9
Answer 2

Answer:

[tex]\textsf{Equation of line n}:\quad y=\dfrac32x-9[/tex]

Step-by-step explanation:

Equation of line m

If two lines are perpendicular to each other, the product of their slopes will be -1.

The slope of the line [tex]y=-\dfrac23x+6[/tex] is [tex]-\dfrac23[/tex]

Therefore, the slope of the line m is:

[tex]\implies m \times -\dfrac23=-1[/tex]

[tex]\implies m=\dfrac32[/tex]

If line m passes through point (-2, -1), then the equation of line m is:

[tex]\implies y-(-1)=\dfrac32(x-(-2))[/tex]

[tex]\implies y+1=\dfrac32(x+2)[/tex]

[tex]\implies y=\dfrac32x+2[/tex]

Equation of line n

If line n is parallel to line m, then they will have the same slope.

Therefore, slope of line n is [tex]\frac32[/tex]

If line n passes through point (4, -3), then the equation of line n is:

[tex]\implies y-(-3)=\dfrac32(x-4)[/tex]

[tex]\implies y+3=\dfrac32x-6[/tex]

[tex]\implies y=\dfrac32x-9[/tex]

Sophia Is Designig A Logo With Three Lines,y, M, And N. Line M Passes Through Point (-2, -1) And Is Perpendicular

Related Questions

4. Alex wants to measure lengths of rope for a knot-tying activity at camp What is the best customary unit of measurement for Alex to use to measure the rope? Why?

Answers

The best unit of measurement for Alex to use for the ropes he is going to use at camp would be centimeters because it is a measurement that fits the needs of his knot shop.

What is a unit of measure?

A unit of measure is a unit that is used as a reference and international standard on length, weight, height, among others.

In the case of length, there are several units of measurement such as:

KilometresMetersMilesCentimetersMillimeters

For a knot-making workshop in a camp, the ideal would be to have a rope of at least 2 or 3 meters. However, the ideal unit of measurement for teaching about knots is centimeters because knots do not require a large amount of rope to tie.

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In the translation T of the graph below, use the figure to describe the Following transformation.

Answers

Answer:

  (a)  (x -6, y -2)

Step-by-step explanation:

You seem to want to see the inverse of the translation T, applied twice. Your notation seems to mean ...

  For T = (x, y) +(a, b)

  T⁻¹ = (x, y) -(a, b)   ⇒   T⁻² = (x, y) -2(a, b)

__

Your given transformation is ...

  T = (x, y) +(3, 1)

which means ...

  T⁻² = (x, y) -2(a, b) = (x, y) -2(3, 1)

  T ⁻² = (x -6, y -2)

Find the median of the set of numbers below.
15, 16, 15, 7, 21, 18, 19, 20, 11

Answers

Answer :

16

Explanation :

You arrange the numbers from least to greatest. 7,11,15,15,16,18,19,20,21 After you do that you will find the numbers that are in the center and that will be your median.

Mai received and spent money in the following ways last month. For each example, write a signed number to represent the change in money from her perspective.



1. Her grandmother gave her $25 in a birthday card.


2. She earned $14 dollars babysitting.


3. She spent $10 on a ticket to the concert.


4. She donated $3 to a local charity.


5. She got $2 interest on money that was in her savings account.

Answers

The signed numbers that represent a change in money from her perspective is:

+$25

+$14

-$10

-$3

+$2

What are the signs to put in front of the amounts?

When a person receives money, earns interst or his paid wages, the amount of money the person has increases. Thus, the sign to be used is the addition sign(+).

When a person pays for an item, donates to charity or loses money, the amount of money the person has reduces. Thus, the sign to be used is the subtraction sign (-).

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y=x^2+x+5 How many x-intercepts does the graph of this quadratic have?

Answers

Answer:

0

Step-by-step explanation:

Use discramint formula,

[tex] \sqrt{ {b}^{2} - 4ac} [/tex]

Here a and b is 1

c is 5 so we have

[tex] \sqrt{ {1}^{2} - 4(1)(5) } [/tex]

[tex] \sqrt{1 - 20} [/tex]

[tex] \sqrt{ - 19} [/tex]

Since the number is negative, we have zero x intercepts.

The C major key, starting with the middle C, consists of seven notes (white keys on the piano) with the following frequencies.

Note
C
D
E
F
G
A
B
Frequency(Hz)
261.6
293.7
329.6
349.2
392.0
440.0
493.9

Determine the ratio of the note E to middle C.
a.
1.1224
c.
1.434
b.
1.2599
d.
1.3454

Answers

Answer:

  b.  1.2599

Step-by-step explanation:

The ratio of the two frequencies is found by dividing the first by the second.

__

  (Freq of E)/(Freq of C) = 329.6/261.6 = 1.2599

I need help with a math problem

Answers

Answer:

a) meters

b) liters

c) kilograms

Step-by-step explanation:

Hope it helps you in your learning process.

Find the surface area of the pyramid. DO THIS AS QUICK AS POSSIBLE

Answers

Explanation:

How many surface has a pyramid?

5 Faces

It has 5 Faces. The 4 Side Faces are Triangles. The Base is a Square.

The difference between the supplement of an angle and twice its complement is 28°, find the measure of the supplement of the angle.​

Answers

Answer:

152°

Step-by-step explanation:

Supplementary angles are two angles that sum to 180°

Complementary angles are two angles that sum to 90°

Let x° = the angle

⇒ Supplement of the angle = 180° - x°

⇒ Complement of the angle = 90° - x°

The difference between the supplement of an angle and twice its complement is 28°:

⇒ (180 - x)°  - 2(90 - x)° = 28°

⇒ 180 °- x° - 180° + 2x° = 28°

⇒ x = 28°

Therefore, the measure of the supplement of 28° is:

180° - 28° = 152°

In which step was the subtraction property of equality applied?

Answers

Answer:

step 1 is the answer

if you like my answer please like comment and mark me as brilliant

Answer:

D - The subtraction property of equality was not applied to solve this equation

Step-by-step explanation:

I got it right on the test

Explanation - they added 7 to both sides, so there was no subtraction property used

Use the information below to complete the problem: and Perform the operation and show that it results in another rational expression. p(x) * q(x)

Answers

Can you please give me more explanation

What is the answer to the question 6/7 + 3/4

Answers

Answer:

45/28

Step-by-step explanation:

6/7+3/4

The least common multiple of 7 and 4 is 28.

Convert 6/7 and 3/4 to fractions with the denominator of 28

24/28+21/28

Since the denominators are now the same, add the numorators to get 45/28

PLSS HELP.
Simplify the expression. Write the answer using scientific notation (7x10^5)^2

Answers

Answer:

[tex]\sf 4.9 \times 10^{11}[/tex]

Step-by-step explanation:

Given expression: [tex]\sf (7 \times 10^5)^2[/tex]

Apply exponent rule [tex]\sf (ab)^2=a^2 \cdot b^2[/tex] :

[tex]\sf \implies 7^2 \times (10^5)^2[/tex]

[tex]\sf \implies 49 \times (10^5)^2[/tex]

Apply exponent rule  [tex]\sf (a^b)^c=a^{bc}[/tex] :

[tex]\sf \implies 49 \times 10^{5 \cdot 2}[/tex]

[tex]\sf \implies 49 \times 10^{10}[/tex]

Scientific notation:  [tex]\sf a \times 10^n[/tex]

where  [tex]\sf 1\leq a < 10[/tex] and n is an integer

We can write 49 as [tex]\sf 4.9 \times 10=4.9 \times 10^1[/tex]

[tex]\sf \implies 4.9 \times 10^1\times 10^{10}[/tex]

Apply exponent rule [tex]\sf a^ba^c=a^{b+c}[/tex]

[tex]\sf \implies 4.9 \times 10^{11}[/tex]

Which of these graphs has its maximum point on the line x=3

Answers

Answer:

The last graph

Step-by-step explanation:

We are given two tips for finding our graph, it has a max point and the point of the line is x = 3. Meaning that this graph must open down and should not go anything further than 3 on the y graph.

The only one that fits this proposition is the last graph. Making it correct.

Answer:

see below

Step-by-step explanation:

To have a maximum, the parabola must be pointing down.

For the maximum to be at x=3, the vertex must have an x value at 3 and the line of symmetry must be 3

This figure is made up of a rectangle and parallelogram.

What is the area of this figure?

Enter your answer in the box. Do not round any side lengths.

Answers

Step-by-step explanation:

rectangle l = 6 units

b = 3 units

area = 18 units ^ 2

parallelogram l = 6 units

b = 1 unit

area = 6 unit ^2

total area = 24 units ^2

solve for x [tex]\sqrt7x-2=5[/tex]

Answers

Answer:

x=7

Step-by-step explanation:

1, Add 2 to both sides.  This gives us [tex]\sqrt{7x} =7[/tex]

2. Square both sides.  This gives us [tex]7x=49[/tex]

3. Divide both sides by 7.  This gives us [tex]x=7[/tex]

Solve
2(2x + 1) = 3(x - 4)

Answers

Step-by-step explanation:

2(2x + 1) = 3(x - 4)

4x+2=3x-12

4x-3x=--12-2

x=14

MP Justify Conclusions Determine if the circumference of a circle with a
radius of 4 feet will be greater or less than 24 feet. Explain.

Answers

Answer:

less than cause 4 is before 24

Is it possible that someone could help me with this?

(I tried to take the best picture a can)

Answers

Answer:

Below.

Step-by-step explanation:

There are 2 outliers:

234, 880.

All the other values range from 485 to  510.

A small pizza costs $4.50, and a salad costs $3.75. You plan to buy two small pizzas and four salads. Write and solve an inequality to find the additional amounts x you can spend to get free delivery.

Answers

The inequality in the total amount of purchase is the greater than inequality

The inequality to find the additional amounts x you can spend to get free delivery is 24.00 + x > y

How to determine the inequality?

The given parameters are:

Small pizza = $4.50

Salad = $3.75

The cost of two small pizzas and four salads is:

Total = 2 * 4.50 + 4* 3.75

Evaluate

Total = 24.00

Let the amount to get free delivery be y.

So, the inequality would be:

24.00 + x > y

Read more abput inequalities at:

https://brainly.com/question/11234618

PLEASE HELP FOR EACH OF THE FIGURES, WRITE AN ABSOLUTE VALUE EQUATION

Answers

The solution set 0 and 8 are the true values of the absolute value equation

The absolute value equation that has the a solution set of 0 and 6 is |x - 3| = 3

How to determine the absolute value equation?

From the figure, the solution sets of the absolute value equation are given as:

x = {0, 6}

Calculate the mean of the solution set

Mean = 0.5 * (0 + 6)

Mean = 3

Calculate the difference of the solution set divided by 2

Difference = (6 - 0)/2

Difference = 3

The absolute value equation is the represented as:

|x - Mean| = Difference

Substitute known values

|x - 3| = 3

Hence, the absolute value equation that has the a solution set of 0 and 6 is |x - 3| = 3

Read more about absolute value equation at:

brainly.com/question/2166748

Answer:

|x-3|=3

Step-by-step explanation:

Why Is HDL called the "good cholesterol"?
A. It widens the arteries
B. None apply
C. It returns cholesterol to the liver to be broken down
D. It bring cholesterol to the lungs to be broken down

Answers

Answer:

b

Step-by-step explanation:

It helps remove any forms of cholesterol from your blood strem.

Im supper sorry if i do not get it...

Evaluate the expression r3 + 4r2 s for r = – 3 and s = 2.

Answers

Answer:

Sorry if I did wrong..I tried my best

Step-by-step explanation:

-3×3+4×-3×2

-9-12×2

-21×2

-42 ans

PLEASE HELP PLEASE HELP

Answers

Answer:

B

Step-by-step explanation:

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

Write [tex](8a^{-3})^{-2/3}[/tex] in simplest form.

Answers

Answer:

[tex] \frac{1}{64 {a}^{2} } [/tex]

Step-by-step explanation:

[tex](8 {a}^{ - 3} {)}^{ \frac{ - 2}{3} } [/tex]

[tex](8 a {)}^{ - 2} [/tex]

[tex] \frac{1}{ {8}^{2} {a}^{2} } [/tex]

[tex] \frac{1}{64 {a}^{2} } [/tex]

I think its correct

Which value of x from the set 4, 5, 6, 7}, makes this equation true?
4(8 - x) = 8
A. 4
B. 5
c. 6
D. 7

Answers

4(8-x)=8

8-x=8/4

8-x=2

-x= 2-8

-x= -6

x=6

-> c

Find the constant rate of change for each graph.​

Answers

Answer:

i believe the rate of change is 1/1 or just 1.

there is also 1 graph only?

A washer and dryer cost a total of $1014. The cost of the washer is two times the cost of the dryer. Find the cost of each item.
Cost of washers
Cost of dryer:

Answers

Answer:

Washer is $676

Dryer is $338

Step-by-step explanation:

1014 divide by 3 gives you 338.

338 x 2 = $676

676 is twice 338.

676 + 338 = 1014

PLEASE HELP
Type the correct answer in the box. Use numerals instead of words.
What is the value of this expression?
log, 8 + log; (3)

Answers

Answer:

[tex]\log(24)[/tex]

Step-by-step explanation:

[tex]\log(8)+\log(3)=\log(8*3)=\log(24)[/tex]

|-108| divided by |36|+|17|

Answers

108/53 = 2.037 or 2 2/53
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