Is 24a+16b+8 equivalent to 4(6a+2) +8b+ 2

What is the equation of a line perpendicular to:

Nataly [62]

Step-by-step explanation:

"perpendicular" means it creates a right angle (90°) with the original line.

a key element is the slope (the incline) of the line.

it is the factor of x (here 1/4 for the original line) and is defined as the ratio of "y coordinate change / x coordinate change" when going from one point on the line to another.

the given slope of 1/4 means that for every increase in x by 4 units y increases by 1 unit.

now if you want to draw a few random lines, and then draw lines that cross them with a right angle, you will see very quickly the relationship of the slopes of the crossing lines :

for the slope of the perpendicular line x and y of the original slope trade places (the ratio turns "upside-down") and the sign of the slope flips (if the original line goes up, then the perpendicular line goes down and vice versa. so + turns into -, and - into +).

so, our original slope 1/4 turns into -4/1 = -4.

we still have infinite possibilities to draw such a perpendicular line (more up or more down on the coordinate grid).

to finally "nail" one particular line we need to use the given point and solve for the y-intercept.

the general slope-intercept form is

y = ax + b

a is the slope, b is the y-intercept (the y value for x = 0).

so, using the slope (-4) and the point (2, 5) we have

5 = -4×2 + b = -8 + b

13 = b

so, the full equation is

y = -4x + 13

7 0

2 years ago

Avery and Carmen both have summer jobs. Avery gets paid 360 bucks every 4 weeks, how much money does she make in one week.

artcher [175]

Avery gets paid 90 bucks per week

Step-by-step explanation:

The per month payment is obtained by dividing the whole amount by time.

Given

Avery gets paid 360 for 4 weeks

In order to find her payment for one week, we have to divide the total amount by 4 to get the payment for one week

So,

$One\ week's\ payment = \frac{Total\ payment}{number\ of\ weeks}\\=\frac{360}{4}\\= 90$

Avery gets paid 90 bucks per week

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5 0

3 years ago

Solve the following formula for t. F=J+Jrt

kherson [118]

First, we separate all instances of t by subtracting J from both sides:

F = J + Jrt
F - J = Jrt

Then, we separate the t by dividing both sides by Jr:

$\frac{f - j}{jr} = t$
Therefore, t is equal to (F - J) ÷ Jr

8 0

2 years ago

Isosceles trapezoid ABCD has legs AB and CD, and base BC. If AB = 3y - 4, BC = 2y -3, and CD = 4y - 18, find the value of y.

Kryger [21]

Answer:

(6)

Step-by-step explanation:

Since it is an isosceles trapezoid the length of the two legs (i.e. AB = 5y-10 and CD = 2y+8) are equal. In other words,

5y - 10 = 2 y + 8

Subtract 2y from each side:

5y - 2y - 10 = 8

Now add 10 to each side

5y - 2y - 10 + 10 = 8 + 10 =>

3y + 0 = 18 =>

3y = 18 =>

y = 6

8 0

2 years ago

True or false please answer ASAP <br><br> ( Brainliest )

prisoha [69]

True.

Hope this helps!

8 0

2 years ago

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