What is the value of the x variable in the solution to the following system of equations? 2x

Line DE contains the points D (–1, –4) and E (3, 3). Line FG contains the point F (–3, 3). Which set of coordinates for point G

Bond [772]

Answer:

The set of coordinates for point G that make the two lines perpendicular are given through the relation

7y = -4x + 9

Step-by-step explanation:

The condition for perpendicularly of two lines is that the products of the slope of the two lines, m₁ and m₂ must be equal to -1.

For a line whose two points (x₁, y₁) and (x₂, y₂)

on the line are known, the slope of the line, m, is given as

m = (Δy/Δx) = (y₁ - y₂) ÷ (x₁ - x₂)

points D (–1, –4) and E (3, 3).

Let the slope of DE be m₁ and the slope of FG be m₂

Since the two lines are perpendicular,

m₁m₂ = -1

m₁ = (Δy/Δx) = (-4 - 3) ÷ (-1 -3) = (7/4) = 1.75

Since, m₁m₂ = -1, this means that,

m₂ = (-1/m₁) = (-1/1.75) = -(4/7)

Let the coordinates of point G be (x, y)

m₂ = (3 - y) ÷ (-3 - x)

(-4/7) = [(3-y)/(-3-x)]

-4(-3-x) = 7(3-y)

12 + 4x = 21 - 7y

7y = -4x + 9

Hope this Helps!!!

8 0

2 years ago

Mathematical word describes both 27x and 6x in the expression 27x+6x?

Maslowich

The mathematical word describing both $27x$ and $6x$ in the expression $27x+6x$ is "<u><em>addition</em></u>"

<h3>How to form mathematical expression from the given description?</h3>

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

For the given case, the terms were $27x$ and $6x$ and the expression formed from them is $27x+6x$

This means both the terms were added together, as denoted by '+' (called 'plus') sign.

When two terms are written with 'plus' sign in between, then that means they're added to each other and the result will be addition of both of their's values.

Thus, the mathematical word describing both $27x$ and $6x$ in the expression $27x+6x$ is <u><em>addition</em></u>"

Learn more about addition here:

brainly.com/question/14148883

7 0

2 years ago

How much of a stick of butter is 1/2 cup?

V125BC [204]

1 stick of butter :))))))))))))))

4 0

2 years ago

Find the area of a circle with a diameter of four

Elis [28]

Answer:

12.57

Step-by-step explanation:

the formula for the area of a circle is $\pi r^{2}$

the diameter is 2 times the radius, so dividing it by 2 gives you a radius of 2

substitute the 2 for the r in the formula and solve

$\pi 2^{2}$

4 $\pi$

≈12.57

7 0

3 years ago

Read 2 more answers

In this fulcrum, for the weights to be balance, what do the distances d1 and d2 have to be if the overall length is 12 feet?

mel-nik [20]

For the fulcrum to balance, the product of weight and distance on both sides of the fulcrum must be the same.

Let d1= x. since total distance is 12, we can write d2 = 12 - x

for the fulcrum to balance:

60x = 50(12 - x)

60x = 600 - 50x

110x = 600

x = 5.45

Thus, d1= 5.45
and
d2= 12 - d1 = 12 - 5.45 = 6.55

d1 = 5.45
d2 = 6.55

5 0

3 years ago

Read 2 more answers

What is the value of the x variable in the solution to the following system of equations? 2x - 3y = 3