To solve two-step equations, it is useful to use reverse ________________ as a guide to isolate the variable efficiently. *

Ok, so you are given an equation in standard form, 5x+4y=2, and a point, (7, 5). You are being asked to write the equation for a line that is parallel to the equation in standard from, and that includes the point (7, 5).  

First, let's start by finding the slope of your new line. We know that it needs to have the same slope as 5x+4y=2, because parallel lines have the same slopes. To do that, we need to put the equation into slope-intercept form (y=mx+b), which means we need to isolate the "y."  

 5x+4y=2

-5x     -5x  (subtract 5x from both sides to move it to the right side of your equation)

4y = 2 - 5x

/4  /4  /4 (divide all the terms by 4 to get "y" by itself)

y = (1/2) - (5/4)x  ... I suggest leaving your slope as a fraction.

Now, we know that our slope, m , is going to be -(5/4).  

Next, we are going to use our slope, -(5/4), and point, (7, 5), to find the b-value (y-intercept) of your new line. Let's plug in what we know:

y = 5

m = -(5/4)

x = 7

y=mx+b

5=(-5/4)(7) + b  -> I plugged in what we knew for y, m, and x.  

5 = -(35/4) + b  -> I multiplied the numbers in the numerator (5 x 7) to get 35/4

20/4 = -(35/4) + b -> I converted 5 into a faction with a denominator of 4 by multiplying by (4/4)

+(35/4) +(35/4)  -> I add (35/4) to both sides to isolate b

55/4 = b ... or b = 13.74

Answer:  

m = -(5/4)

b = 13.75

The equation perpendicular to the line going through the points (5, -1) and (7, -5) is [tex]y=\frac{1}{2} x-\frac{7}{2}[/tex]

The line passes through the points (5, -1) and (7, -5)

That is [tex]x_1=5, y_1=-1, x_2=7, y_2=-5[/tex]

Calculate the slope(m) using the formula below:

[tex]m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{-5-(-1)}{7-5} \\\\m=\frac{-4}{2}\\\\m=-2[/tex]

The equation of the new line perpendicular to the line above will be given as:

[tex]y-y_1=\frac{-1}{m} (x-x_1)\\\\y-(-1)=\frac{-1}{-2} (x-5)\\\\y+1=\frac{1}{2}(x-5)\\\\y=\frac{1}{2} x-\frac{5}{2} -1\\\\y=\frac{1}{2} x-\frac{7}{2}[/tex]

The equation perpendicular to the line going through the points (5, -1) and (7, -5) is [tex]y=\frac{1}{2} x-\frac{7}{2}[/tex]

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Answer:

3:10

Step-by-step explanation:

Disposal time=1:15PM

Choir ending time:-

[tex]\\ \sf\longmapsto 1:15-0:40=12:35PM[/tex]

Answer:

1)36

2)1/36

Step-by-step explanation:

Hope it can help you lovelots

Answer:

52.6?

Step-by-step explanation:

Step-by-step explanation:

[tex] \\ 994.14 \div 18.9[/tex]

[tex] \\ = \frac{99414}{100} \div \frac{189}{10} [/tex]

[tex] \\ = \frac{49707}{50} \div \frac{189}{10} [/tex]

[tex] \\ = \frac{49707}{50} \times \frac{10}{189} [/tex]

[tex] \\ = \frac{263}{5} [/tex]

[tex] \\ = 52.6[/tex]

Answer:

All of the equations seem to have infinitely many solutions.

Step-by-step explanation:

Since the same equations are equal to each other, whatever you replace x with, it will be equal to the other equation's solution since all answers have equations equal to each other.

Answer:

The answer is 8!

Step-by-step explanation:

I took the quiz. Have a great day, hope this helps!

Answer: 4k^2 - 9k - 9 = 0

Step-by-step explanation:

lmk if i was right please and ty

Yes it is possible.

- BRAINLIEST answerer

Answer:

252.21m

Step-by-step explanation:

Times it by 3 and that should give you the answer you are looking for. Please mark it as brainliest

Answer:

Step-by-step explanation:

Time in travel:

Average speed is 5 mph

Distance travelled:

Correct choice is A

Total time taken

Distance

Option A

Answer:

a+b+2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

3,-3

Step-by-step explanation:

The coordinates are 3 and -3. x is 3 and y is -3.

Answer:

(3,-3)

Step-by-step explanation:

as the answer is at down of x axis

Answer:

4.2

Step-by-step explanation:

All sides are proportional, so choose a pair and find the proportion

Ex: AB and JK = 7/5=1.4

so each side is multiplied by 1.4 to get the larger figure

So 3*1.4=4.2

Answer:

1.

Step-by-step explanation:

Answer:

The graphs that could be this function are the third one and the last one.

C and E

Hope this helps!

Step-by-step explanation:

Other than C and E, all of the other functions start out by decreasing starting from -5.

They both also have the straight part from -3 - 0 where the function neither increases nor decreases.

They also have the part where from 2 increases to 5.

Answer:

The amount of sparkling water that would be needed to mix with 9 quarts of grape juice is 18 quarts.

Ratio expresses the relationship between two or more numbers. It shows the frequency with which one value is contained in another value. According to the question, the ratio of sparkling water to grape juice is .

In order to determine the amount of sparkling water that would be needed with 9 quarts of grape juice, this equation would be used:

( × 9) ÷  

( × 9) ×  = 18 quarts

To learn more about ratios, please check: brainly.com/question/17995727

Step-by-step explanation:

18 quarts of sparkling water would you need to mix with 9 quarts of grape juice.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that recipe for sparkling grape juice calls for [tex]1\frac{1}{2}[/tex] quarts of sparkling water and 3/4 quart of grape juice

Let us convert  [tex]1\frac{1}{2}[/tex] to improper fraction as 3/2

We need to find the amount of sparkling water would you need to mix with 9 quarts of grape juice

Let x be the sparkling water would you need to mix with 9 quarts of grape juice

Let us form a proportional equation.

3/2/(3/4)=x/9

3/2×4/3=x/9

2=x/9

18=x

Hence, 18 quarts of sparkling water would you need to mix with 9 quarts of grape juice.

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2: c

Step-by-step explanation:

3: a

by Supplementing each answer Into the equation

Step-by-step explanation:

what don't you understand about this ? did you never solve 2 equations with 2 variables ?

it is really easy. there are 2 main approaches :

1. substitution. you use one of the two equations to express one variable by an expression purely in the other variable. then you use that in the other equation (resulting in one equation with one variable) and solve it. with that result you go back to the other equation and calculate the other variable.

2. equation arithmetic. when the terms of at least one of the variables are similar in both equations, you can multiply (if needed) one or both equations (left and right side !) by a fitting number and then add it subtract one equation from the other, so that you are left with one equation in one variable, which you solve. with that result you go back to any of the original equations and calculate the other variable.

there would be a third option for questions like this :

3. trial and error. simply put the point coordinates as x and y into both equations, and see for what point(s) both remain true.

but in order to show you the methodical approaches, we will use substitution for question 2 and equation arithmetic for question 3.

2)

2x + y = 5

-x + 2y = 5

I use the first equation to transform. and I get

y = 5 - 2x

with that I go into the second equation :

-x + 2(5 - 2x) = 5

-x + 10 - 4x = 5

-5x = -5

x = 1

and with that I get

y = 5 - 2×1 = 5 - 2 = 3

so, C (1, 3) is the right answer.

3)

2x + y = 7

-x + y = 1

let's subtract the second equation from the first :

2x + y = 7

- -x + y = 1

------------------

3x + 0 = 6

3x = 6

x = 2

with that I go into one of the original equations :

-2 + y = 1

y = 3

so, A (2, 3) is the right answer.

Answer:

[tex]\frac{400}{(10\sqrt{2} + 14\sqrt{3}) }= h[/tex]   or  10.42 = h

Step-by-step explanation:

The area of a trapezoid is [tex]A = \frac{1}{2}h(b_{1} + b_{2} )[/tex].

[tex]200 = \frac{1}{2}h(10\sqrt{2} + 14\sqrt{3})[/tex]

[tex]400 = { h(10\sqrt{2} + 14\sqrt{3} )[/tex]             Multiply both sides by 2

[tex]\frac{400}{(10\sqrt{2} + 14\sqrt{3}) }= h[/tex]

 [tex]\frac{400}{38.39} = h[/tex]

10.42 = h  

Answer:

Answer is 2,000 option (B)

Answer:

2

Step-by-step explanation:

4-2=2

55-55=0

so:

2:00

Answer:

John: $80

Mary: $120

Step 1: Add the ratios (3 and 2).

=> 3 + 2 = 5

Step 2: Divide 200 by 5.

=> 200 ÷ 5

= 40

Step 3: Multiply.

=> Mary total: 40 x 3 = $120

=> John total: 40 x 2 = $80

Hoped this helped

2.5 is the scale dilation.

Kinda Logic

Answer:

1/3 is less than 1

Step-by-step explanation:

3/3=1

1/3<1

I think you have to put all the fractions on one side of the equation and the x-terms on the other side. But I don't see an option for that...

Answer:

x = - [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

[tex]\frac{2}{3}[/tex] - 4x + [tex]\frac{7}{2}[/tex] = - 9x + [tex]\frac{5}{6}[/tex]

Multiply through by 6 ( the LCM of 3, 2 and 6 ) to clear the fractions

4 - 24x + 21 = - 54x + 5 , that is

25 - 24x = - 54x + 5 ( add 54x to both sides )

25 + 30x = 5 ( subtract 25 from both sides )

30x = - 20 ( divide both sides by 30 )

x = [tex]\frac{-20}{30}[/tex] = - [tex]\frac{2}{3}[/tex]

Answer:

Step-by-step explanation:

Answer:

"X: 3: 9/2 =15/4: 9/2 :Yask" is difficult for me to understand.

The best I can find is x = 11 1/4 or 11.25

I'll assume:

X: 3: 9/2 means X/3/(9/2) and that is equal to 15/4/(9/2)

Step-by-step explanation:

X/3/(9/2) = 15/4/(9/2)

X/3/(9/2) = 15/4/(9/2)   [Multiply both sides by (1/(9/2)

X/3 = 15/4

4x = 45

x = 11 1/4 or 11.25