determine the standard form of the equation of the line that passes through (6,0) and (2,-7). (-7x-4y=-42) (7x-4y=42) (-7x+4y=42) (4x+7y=-42)​

Answers

Answer 1

Answer:

[tex]7x - 4y = 42[/tex]

Step-by-step explanation:

Given

[tex](x_1,y_1) = (6,0)[/tex]

[tex](x_2,y_2) = (2,-7)[/tex]

Required

Determine the equation in standard form

First, calculate the slope (m) using:

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

This gives:

[tex]m = \frac{-7 -0}{2 - 6}[/tex]

[tex]m = \frac{-7}{-4}[/tex]

[tex]m = \frac{7}{4}[/tex]

The equation in standard form is calculated using:

[tex]y - y_1 = m(x - x_1 )[/tex]

This gives:

[tex]y - 0 = \frac{7}{4}(x - 6)[/tex]

[tex]y = \frac{7}{4}(x - 6)[/tex]

Cross Multiply

[tex]4y = 7(x - 6)[/tex]

Open bracket

[tex]4y = 7x - 42[/tex]

Subtract 7x from both sides

[tex]-7x + 4y = 7x - 7x - 42[/tex]

[tex]-7x + 4y = - 42[/tex]

Multiply through by -1

[tex]-1(-7x + 4y) = - 42*-1[/tex]

[tex]7x - 4y = 42[/tex]


Related Questions

A label is twice as long as it is wide. If the length of the label is 10 cm, find the
area of the label.
O 20 square centimeters
O 50 square centimeters
O 60 square centimeters
O 70 square centimeters

Answers

Answer:

50 square centimeters

Step-by-step explanation:

Long means length, and we know the length of the label, 10 centimeters. That means the width is half of 10 centimeters, or 5 centimeters. Now, we multiply 10 and 5 to get 50. That means the area of the label is 50 square centimeters

What is the value of 15 + x2 when the value of x is 3

Answers

Answer:

21

Step-by-step explanation:

15 + (3)2

15 + 6

21

Answer:

24

Step-by-step explanation:

15+x2

= 15 + (3x3)

= 15 + 9

= 24

PLS EXPLAIN HOW THESE SEQUNCE IS FORMED

ALL ODD NUMBERS

Answers

Answer:

7,21,27,81,87, 261, 267....

Step-by-step explanation:

All odd number series from the given figure is

7, 21, 27, 81 , 87....

We can write this series as

7, 7 x 3 , (7x3)+6, ((7x3)+6)x3, (((7x3)+6)x3)+6....

7, 21, 21+6 , 27 x 3, 81+6...

Now, the next term of the series will be

=((((7x3)+6)x3)+6) x 3

= 87 x 3

= 261

And another term of the series will be

= 261 +6

= 267

7,21,27,81,87, 261, 267....

A growth factor is a value that is greater than 1?

Answers

Answer:

No, it is a value that is greater than 0

Step-by-step explanation:

A growth factor is indeed a value greater than 1 except it can be a decimal below 1 to. Therefore, a growth value is any POSITIVE number.

"HOT PIZZA" is offering a 20% discount on all its pizza
Ali orders a pizza for the reduced price of £5.60
What was the original price of the pizza?

Answers

Answer: the answer is 7

Step-by-step explanation:

first you divide the price by four then add a quarter to the original amount. gl

583.31 divided by 7 minus 7.46 is closest to _____ of 100.

Answers

first, 7 x 10 = 70, you now have 30 left, 7 x 4 = 28. 10 + 4 = 14 with a remainder of 2. That is your answer though many would put “14 2/7” as the answer with the 2 over the 7 because its the remainder over what was getting divided first. thus 100/7 is has the remainder of 2 with the quotient 14.

What is the x-intercept of the following equation? 4x + 2y = 12

Answers

Answer:

3

Step-by-step explanation:

On their most recent 8-mile training run, Pepe averaged a speed of 12 of a mile in 4.5 minutes, while Paula averaged 34 of a mile in 7.5 minutes.


How many minutes did it take the faster runner to finish the 8 mile run

Answers

Answer:

1.78 min

Step-by-step explanation:

so first you have to figure out the fastest runner

pepe 12 miles in 4.5 minutes

and paula ran 34 miles in 7.5 minutes

if you divide miles by minutes you get how many miles they ran in one minute

12/4.5=~2.67

34/7.5=~4.53

So you can see that paula is faster

if she ran ~4.5 miles in a minute then it would take her ~1.78 minutes to run 8 miles

they're both super humans though like woah

What is the equivalent percent? 6/15

Answers

Answer .277

Step-by-step explanation:

because 6/15 is not half but almost is

A house cost $112,000 in 2010. By the year 2015, the house had a value of $132,000. What was the growth rate as a percent for that 5-year period?

Answers

Answer:

I believe its 6.48%

need help pls answer asap!

Answers

It should be 40 or near 40 okay

One yard is equal to 0.9144 meters. One foot is equal to how many meters

Answers

Answer:

0.3048 i think

Step-by-step explanation:

X
Betsie tried to solve an equation step by step.
7a =28
7a/a=28/7 Step 1
7=4 Step 2
Find Carly's mistake.
Choose 1 answer:
A .Step 1
B. Step 2 C. Carly did make a mistake

Answers

Answer:

Step 1

Step-by-step explanation:

Carly divided 7a by a when she should have divided 7a by 7

Answer:

she divided 7a by a instead of 7

Most dogs fail to become service dogs. In a recent training class, only 7 of the 15 dogs were certified as service dogs. What percent of dogs became certified service dogs, rounded to the nearest percent?

Answers

Answer:

46.667%

Step-by-step explanation:

Percentage of certified service dogs = 7/15 × 100%

Percentage of certified service dogs = 700/15 %

Percentage of certified service dogs = 46.667%

47%(to the nearest percent)

Sarah has three more than four times the money that Jessica has. Together they have $72. How
much does each person have?

Answers

Answer:

Jessica has x amount of dollars.

Sarah has 4x + 3

Together they have $72

We can combine Jessica and Sara's money to equal $72.

x + (4x + 3) = 72

Combime like terms

5x + 3 = 72

Subtract 3 from both sides to isolate the variable.

5x = 69

Divide both sides by 5

x = 69/5 or 13 4/5 or 13.80

Jessica has $13.80 and

Sarah has 4(13.80) + 3

55.20 + 3 = 58.20

Hawall is 6 hours behind Cincinnati. If it is 5 AM in Hawall, what time is it in Cincinnati?

Answers

Answer:

11 AM

Step-by-step explanation:

5 + 6 = 11

6/12 + 5/6 + 2/4 + 1/2

Answers

Answer:

7/3

Step-by-step explanation:

L.C.M of all of the denominators is 12

We get,

[tex] \frac{6 + 10 + 6 + 6}{12} = \frac{28}{12} \\ \\ = \frac{7}{3} [/tex]

In mixed fraction it becomes 2 1/3

And here is your answer hope it helps :)

Answer pls will
Give brailiest or show how to do it

Answers

Answer:

bro i do not know how to do that stuff im only in Middle school my guy

Step-by-step explanation:

I don't know

Qualitative" variables are measured on either ordinal or nominal scales

Answers

Answer:

I don't get it. Is that the full question?

Plz help me I only have 5 minutes will mark brainliest

Answers

Answer:

THE ANSWER IS B explanation:

The answer is be by isolating the variable and by using the key words in the question to find out what it is.

A large fish tank is having its water drained while being weighed. After 20 gallons have been drained, the tank weighs 1,909 pounds. After 50 gallons have been drained, it weighs 1,660 pounds. Let w be the weight of the tank and let g be the number of gallons drained. Write a linear equation for w in the terms of g.

Answers

Answer:

[tex]w=-8.3g+2075[/tex]

Step-by-step explanation:

Let the x axis represent the gallons g

and y axis represent the weight of the tank w.

So, the first point on the plane will be [tex](20,1909)[/tex]

and the second point will be [tex](50,1660)[/tex]

The line between these points will be

[tex]w-1909=\dfrac{1660-1909}{50-20}(g-20)\\\Rightarrow w-1909=-\dfrac{249}{30}(g-20)\\\Rightarrow w-1909=-\dfrac{83}{10}(g-20)\\\Rightarrow w=-\dfrac{83}{10}g+\dfrac{83}{10}\times 20+1909\\\Rightarrow w=-\dfrac{83}{10}g+2075\\\Rightarrow w=-8.3g+2075[/tex]

The relationship between the weight and gallons of the tank is [tex]w=-8.3g+2075[/tex]

How far is `75\%` of a `2,000`-kilometer trip?

Answers

Answer:

1,500 kilometers

Step-by-step explanation:

To find 75% of 2,000, multiply 2,000 by .75. That gets us 1,500. That means 75% of a 2,000 kilometer trip is 1,500 kilometers.

Answer:

1,500 kilometers

Step-by-step explanation:

If Triangle PQR ~ Triangle SQT, Find the value of x.

Answers

Answer:

x = 15

Step-by-step explanation:

Given that ∆PQR ~ ∆SQT, therefore their side lengths are proportional to each other.

Thus:

[tex] \frac{PQ}{SQ} = \frac{PR}{ST} [/tex]

PQ = (x + 5) + 8 = x + 13

SQ = 8

PR = 21

ST = x - 9

Plug in the values

[tex] \frac{x + 13}{8} = \frac{21}{x - 9} [/tex]

Cross multiply

[tex] (x + 13)(x - 9) = 8*21 [/tex]

[tex] x(x - 9) +13(x - 9) = 168 [/tex]

[tex] x^2 - 9x + 13x - 117 = 168 [/tex]

[tex] x^2 + 4x - 117 = 168 [/tex]

Subtract 168 from both sides

[tex] x^2 + 4x - 117 - 168 = 0 [/tex]

[tex] x^2 + 4x - 285 = 0 [/tex]

Factorize

[tex] x^2 + 19x - 15x - 285 = 0 [/tex]

[tex] x(x + 19) - 15(x + 19) = 0 [/tex]

(x + 19)(x - 15) = 0

x = -19 or x = 15

Answer:

x = 15

Step-by-step explanation:

x+13/9 = 21/x-9

x^2+4x−117=168

x^2+4x−285=0

(x−15)(x+19)=0

x=15

it cannot be a negative number so x cannot be -19

The height of a doorway is 8 yards. What is the height of the doorway in inches?
The height of the doorway is
inches.

Answers

Answer:

288 inches

Step-by-step explanation:

1 yard= 36 inches.

36x8=288

Answer:

It would be 288 inches

Step-by-step explanation:

8 divided by ? inches

1 yard = 36 inches

36 inches times 8 yards = 288 inches

make me brainiest

What is the perpendicular and parallel slope of -2 (PLEASE SHOW HOW YOU GOT IT)

Answers

Answer:

Parallel slope of -2 is -2.Perpendicular slope of -2 is 1/2.

in a class 60% of the students are girls there are are 24 girls in the class how many boys are in the class

Answers

Answer:

16

Step-by-step explanation:

Let s represent all students in the class

.60(s) = 24 This equation means that 60% of students are the 24 girls in class.

Solve for s: s = 24/.60 = 40 There are 40 students in the class

Now to find how many boys are in the class, subtract 24 from 40

40 - 24 = 16

There are 16 boys in the class

Girls=60% of x

so girls 60/100

so left 40%which are boys and girls are given which is 24

students are girls and given they are 24

So total students X= total girls+ total boys

X = (60/100)*X+24

X - (60/100)*X = 24

(40/100)*X = 24

X = (24*100)/40.

X = 60

so there are 60 boys

Subtract

28 1/27 - 2/9=

Answers

Answer:

1759. or 27 58/63

63

hope it helps

Daryl measures the angle of elevation to be 62 degrees. Frances measures the angle of elevation to be 54 degrees. if the two enthusiasts are 28m apart, how far off the ground is the helicopter.

Answers

Answer:

The helicopter is 27.38 m far off the ground

Step-by-step explanation:

The drawing shown in the image below has all the measures and variables needed to solve the problem.

We need to find R, the height of the helicopter. We'll use the law of sines to find the length of side a.

[tex]\displaystyle \frac{28}{\sin X}=\frac{a}{\sin 54^\circ}[/tex]

The angle X is the measure needed to complete 180°:

X = 180° - 54° - 62° = 64°

Solving for a:

[tex]\displaystyle a=\frac{28}{\sin 64^\circ}\cdot \sin 54^\circ[/tex]

Calculating:

a = 31.11 m

Now using the sine ratio in the right triangle to the left side:

[tex]\displaystyle \sin 62^\circ=\frac{R}{a}[/tex]

Solving for R:

[tex]R=a\sin 62^\circ[/tex]

R=31.11*0.88

R = 27.38 m

The helicopter is 27.38 m far off the ground

Bader gave away 24 of his toy cars. Which integer shows the change in the number of toy cars he has?​

Answers

Answer:

The integer that shows the change in the number of toy cars Bader has is -24.

Explanation:

Think of it like a math problem, when you take away from your own amount, (in this case, his cars) you're subtracting from the original amount of things you had. The symbol for subtraction is also "-", so with that information it's a bit self explanatory to know which answer is correct.

3x – 2y = 3
8x – 4y=4
elimination method

Answers

First equation:

Solving for X.

[tex]x = 1 + \frac{2y}{3} [/tex]

Solving for Y.

[tex]y = - \frac{3(1 - x)}{2} [/tex]

Second equation:

Solving for X.

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

Solving for Y.

[tex]y = 2x - 1[/tex]

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