Paul and Seth know that one point on a line is (4,2) and the slope of the line is -5. Each student wrote a different equation relating x and y . Do the two equations represent the same line ? Construct a mathematical argument to support your answer .

Paul And Seth Know That One Point On A Line Is (4,2) And The Slope Of The Line Is -5. Each Student Wrote

Answers

Answer 1

Answer:

Step-by-step explanation:

Paul's equation,

Since the given line is passing through a point (4, 2) and slope = -5,

y = mx + b

2 = -5(4) + b

2 = -20 + b

b = 22

Therefore, equation of the line will be,

y = -5x + 22

Seth equation,

Slope of a line passing through two points (x, y) and (4, 2),

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

-5 = [tex]\frac{y-2}{x-4}[/tex]

-5(x - 4) = y - 2

-5x + 20 = y - 2

y = -5x + 22

Therefore, both the equations represent the same line.


Related Questions

A bin at a department store contains blue and red blankets. The ratio of blue blankets to red blankets is 13 to 7. What percent of the blankets in the bin are blue?

Answers

Step-by-step explanation:

13=blue blankets 7=red blankets

First, we need to know how many blankets there are in total.

13+7=20

Now, we don't need the seven anymore. Our ratio is blue blankets to total blankets.

13/20

Now, we need to know how many blue blankets there are in percentage.

13/20 = x/100

Next step: 13 times 100 is divided by 20

x= 13(100)÷20

x=1300÷20

x= 65

Therefore there are 65% of blue blankets.

PLA HELP QUESTION IN PHOTO

Answers

Answer:

Step-by-step explanation:

its the first one

Answer:

C

Step-by-step explanation:

Coconut oil freezes at a high temp, and there for is a greater number.

These two triangles are similar. What are a and b? Note: the two figures are not drawn to scale. Please help with this!!!

Answers

9514 1404 393

Answer:

a = 6b = 22.5

Step-by-step explanation:

The ratio of smallest sides in the two triangles is ...

  smaller / larger = 4/10

To find A and B, we write proportions involving corresponding side lengths.

__

Side A in the smaller triangle is ...

  A/15 = 4/10

  A = (4/10)(15) = 6

__

The ratio of larger to smaller is the inverse of the above ratio, so ...

  B/9 = 10/4

  B = (10/4)(9) = 22.5

646 divided by 9 long division with a reimandeir

Answers

Answer:

71 R. 7

Step-by-step explanation:

Hope this helps!

what is the difference of the fractions? use the number line to help find the answers. 4/7 - 10/7​

Answers

Answer:

This means that the fraction 3/4 is 3 out of 4 equal parts. So, count 3 parts from 0 and you will get 3/4. That's it! You've shown the fractions 1/4 and 3/4 on a number line!

Step-by-step explanation:

It is.

Answer:

This means that the fraction 3/4 is 3 out of 4 equal parts. So, count 3 parts from 0 and you will get 3/4. That's it! You've shown the fractions 1/4 and 3/4 on a number line!

Step-by-step explanation:

The math is just correct

The probability of two events A and B happening simultaneously is 0.17. The probability of only event A happening is 0.34. Find the probability of event B happening, if event A has already happened

Answers

Answer:

because is the probability is 0.17 and 0.34 is fair

You can use the multiplication rule of probability.

The probability of event B happening if event A has already happened is 0.5

What does general multiplication rule of probability says for 2 events A and B?

[tex]P( A \: \rm and \: B) = P(A)P(B|A) = P(B)P(A|B)[/tex]

Since we've to find the probability of B given that A has already happened, we need [tex]P(B|A)[/tex]

Since the probability of both event A and event B happening simultaneously is 0.17, thus:
[tex]P(A \: \rm and \: B) = 0.17\\ [/tex]

Since the probability of only event A happening is 0.34, thus:

[tex]P(A) = 0.34[/tex]

Thus, from the multiplication rule, we have:
[tex]P(A \: \rm and \: B) = P(A)P(B|A)\\ 0.17 = 0.34 \times P(B|A)\\\\ \dfrac{0.17}{0.34} = P(B|A)\\\\ P(B|A) = \dfrac{1}{2} = 0.5[/tex]

Thus, we have the probability of event B happening when A has already happened as 0.5

Learn more about multiplication rule of probability here:

https://brainly.com/question/14450597

Describe the graph of x > 2 and x < 5

Answers

Answer:

y=(x−5)2

The graph of y is the standard parabolic, concave up curve of y=x2 shifted ("transformed") by 5 units right ("positive") on the x−axis,

The graph of y is shown below.

graph{(x-5)^2 [-10, 10, -5, 5]}

Answer:

I'm prettyy sure you already figured this out knowing you, so thanks;)

Step-by-step explanation:

Solve:
5y + 3y +1+1 = 2y + 6y +6 +2

Answers

Answer:

0=6

There are no solutions to this answer.

Step-by-step explanation:

Answer:

There is no solution.

Step-by-step explanation:

i need help with this ^

Answers

Answer:

I think it's 3

Step-by-step explanation:

If 2 is c than subtract  it and it's 3?

There are ten toppings available to make an ice
cream sundae. How many ways can Max choose
two?

Answers

Answer:

There will be 56 possible combinations if he is allowed to choose the same topping twice.

There will be 47 if he is not allowed to choose the same topping twice.

Step-by-step explanation:

Number of ways max choose two are 45

What are combinations?

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of both the selection is irrelevant. You can choose the components of combos in any order;

Permutations and combinations can be mixed up. The sequence in which the chosen components are chosen is crucial in permutations, too. For instance, the configurations ab and ba are distinct in permutations but equivalent in combinations (regarded as one arrangement);

Given;

Toppings available to make an ice cream sundae = 10

The  number of ways can Max choose 2;

= 10C2

=10! / [(10-2)! X 2!]

=45

Therefore, Max can choose toppings is 45 by combination

Learn more about combinations here:

brainly.com/question/295961

#SPJ2

Pls answer and show work!

Answers

Answer:

x represents +50 for every hour. the inequality is y = 4x + 500 or y = x + 500.

they can ride it for 4 hours

Step-by-step explanation:

y(total cost) = x(50 per hour) + 500(y-intercept)

20POINTS WILL MARK BRANLIEST PLSS
The layout of a city park is pictured in the figure above. Park managers would like to find the distance of segment DE, in order to build a walkway across the middle of the park. The park managers look up the distance of segments BC and AB in the city records. If the length of segment AB is determined to be 562 feet, what is the distance of mid-segment DE in feet?

Select one:
A. 220
B. 244
C. 276
D. 281

Answers

244 is the correct answer

What is the first step needed to solve 4 over 7 multiplied by x minus 5 equals negative 13? Subtract 13 from both sides Divide both sides by 7 Add 5 to both sides Multiply both sides by 4

Answers

Answer: C) add 5 to both sides

The given equation is

(4/7)x - 5 = -13

To solve this, we follow PEMDAS in reverse undoing each operation. Normally parenthesis is the first thing we look for, but instead we start with subtraction.

So we'll undo subtraction which means we add 5 to both sides

Answer:

C is your answer

Step-by-step explanation:

11 coommon factor of​

Answers

1? Isn’t it like a prime number

Please helppp
solve for y

Answers

Answer: [tex]y=\frac{-x}{w-3}[/tex]

Step-by-step explanation:

To solve for y, we want to isolate y.

[tex]w=\frac{3y-x}{y}[/tex]             [multiply both sides by y]

[tex]yw=3y-x[/tex]         [subtract both sides by 3y]

[tex]yw-3y=-x[/tex]      [factor out y]

[tex]y(w-3)=-x[/tex]     [divide both sides by (w-3)]

[tex]y=\frac{-x}{w-3}[/tex]

Now, we know that [tex]y=\frac{-x}{w-3}[/tex].

Iwefwegweg weg ewgwewegw egwe gwe gwe weg weg w

Answers

Answer:

gweew gshbx

Step-by-step explanation:

Help i am stuck please be fast

Answers

Answer:

Step-by-step explanation:

They are alike because both involve steps for multiplication and addition but part b uses factoring in its estimation to solve the problem while part c dosesn't.

I NEED HELP! I WILL MARK YOU AS BRAINLIEST IF YOU ANSWER CORRECTLY! :D

Answers

Answer:

1. Train B is faster

Step-by-step explanation:

Train b travels a greater distance in 2 hours than train A.

Train B travels 250 miles in 2 hours, while Train A travels only 120 miles.

A local park is in the shape of a square. A map of the park is made with the scale of 1 inch to 200 feet. If one side of the park on the map is one foot long, how long is the side of the park in real life?

Answers

Answer: The side of the park is 2,400 feet long.

Explanation:
Scale is 1in:200ft
One foot = 12in
The fraction 1/200 = 12/x, which is cross multiplication.
1 times x = 1
12 times 200 = 2400
1 times 2400 = 2400
So that one side equals 2,400ft.
& since it’s a square that means all sides are equal no matter which is talking about.

i need help plzzzzzzzzz

Answers

Answer:

1 2 5 . 6 9

1 2 5 . 6 7 0

125.69 Would be Greater.

Step-by-step explanation:

First number to the right of the decimal is the tenths place 2nd number would be hundredths and you'd increase etc.

I put it at 50 pts because it will take a while plz help me

Answers

Answer:

well i am not that smart sorry i really wish i could help but i know one of the things  

Step-by-step explanation:

3. what causes wind

Gases move from high-pressure areas to low-pressure areas. And the bigger the difference between the pressures, the faster the air will move from the high to the low pressure. That rush of air is the wind we experience.

sorry it took so long for me to type it

hope you have a good day sir/ma'am!!!

A+3/4=7/8. Please help solve equation using subtraction

Answers

1/8
If you can make the bottom numbers (denominator) The same that you can use subtract the top numbers like normally

Solve for x
2x+5 = 32

Answers

Answer:

x=13.5

Step-by-step explanation:

Perform the same operation on each side:

2x+5 = 32

2x     = 27

x       = 13.5

So, x is 13.5

Find the Y intercept of the graph

Answers

Answer:

6

Step-by-step explanation:

The intercept would be 6 because that's the point on the Y line or the line going vertically.    

Answer:

6

Step-by-step explanation:

Hello!

The y-intercept of the graph is when the graph touches the y-axis.

As you can see the graph intersects the y-axis at point (0,6), indicating the y-intercept of the graph to be 6.

y - intercept: 6

The x-intercepts of the graph are when the graph intersects the x-axis. There are three roots for the graph: -1, -3 and 2.

Natalia solved the problem
74
.
4
÷
12
=
6
.
2
. Complete the model with partial products to check Natalia's work using multiplication.

A large rectangle is broken into 4 smaller rectangles The top line is labeled 6 and 0.2. The left side is labeled 10 and 2. The rectangles are divided between those labels. The top left rectangle is labeled A. The top right rectangle is labeled B. The bottom left rectangle is labeled C. The bottom right rectangle is labeled D.

Part A
Drag values to the boxes to complete the partial products. Not all choices will be used.

0.4 1.2 2 4 6 12 20 60


The product for A =
.

The product for B =
.

The product for C =
.

The product for D =
.

Part B
Choose the words to complete the statement.

Natalia's work is
correct
, because the total of the partial products is
Choose...
as the dividend.

Answers

Answer:

The product for A = 60

The product for B = 2  

The product for C = 12

 

The product for D=0.4

Choose......correct, Choose.....the same

Step-by-step explanation:

I had the same question on a test and this is the correct answers. Hope this helped!

The length of the diagonal of a squere is 36 feet. Find the length of the side of the square.
I need help with this pls

Answers

Step-by-step explanation:

by PT,

36^2 = length^2 x length^2

length = 6 feet

Topic: Pythagoras theorem

If you like to venture further, do check out my insta (learntionary) where I regularly post useful math tips! Thank you!

I need help with this question!!!! Plzz

Answers

Answer:

y=-5x+9

Step-by-step explanation:

Answer:

y = -5x + 9

Step-by-step explanation:

Plug each of the x values into this equation and see if you get the corresponding outputs for y, it should work fine.

There are 3.9 milligrams of calcium in a ½ ounce of cooked chicken. How many milligrams are in 6 ounces?

Answers

Answer:

there are 46.80 milligrams in 6 ounces.

Step-by-step explanation:

In AGHI, the measure of

Answers

Answer:

yes

Step-by-step explanation:

Feet thats the answer noooo problem

Find the missing length indicated.
?
12
4
9
28
50
12.

Answers

Answer:

28 probably sorry if wrong

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