ABCD is a square . if the coordinates of three of its vertices are A(-1,2a), B(a,2a), C(a,0), find the coordinates of D. BC is obviously 2a (it's a vertical line) then AB must be 2a (notice AB is horizontal) so BC = AC because it is a square 2a = a+1 a=1
Step-by-step explanation:
1.
![- 2(3x + 7) = 32 - 4x \\ distribute \\ - 2 \times 3x = - 6x \\ - 2 \times 7 = - 14 \\ - 6x - 14 = 32 - 4x \\ add \: 4x \: to \: both \: sides \\ - 6x + 4x = 32 - 4x + 4x \\ - 2x = 32 \\ divide \: by \: - 2 \\ \frac{ - 2x}{ - 2} = \frac{32}{ - 2} \\ \\ x = - 16](https://tex.z-dn.net/?f=%20-%202%283x%20%2B%207%29%20%3D%2032%20-%204x%20%5C%5C%20distribute%20%5C%5C%20%20-%202%20%5Ctimes%203x%20%3D%20%20-%206x%20%5C%5C%20%20-%202%20%5Ctimes%207%20%3D%20%20-%2014%20%5C%5C%20%20-%206x%20-%2014%20%3D%2032%20-%204x%20%5C%5C%20add%20%5C%3A%204x%20%5C%3A%20to%20%5C%3A%20both%20%5C%3A%20sides%20%5C%5C%20%20-%206x%20%2B%204x%20%3D%2032%20-%204x%20%2B%204x%20%5C%5C%20%20-%202x%20%3D%2032%20%5C%5C%20divide%20%5C%3A%20by%20%5C%3A%20%20-%202%20%5C%5C%20%20%20%5Cfrac%7B%20-%202x%7D%7B%20-%202%7D%20%20%3D%20%20%5Cfrac%7B32%7D%7B%20-%202%7D%20%20%5C%5C%20%20%5C%5C%20x%20%3D%20%20-%2016)
2.
![4x + y = 3 \\ y = - 4x + 3 \\ using \: point \: slope \: form \\ y - y1 = m(x - x1) \\ y + 6 = - 4(x + 4) \\ y + 6 = - 4x - 16 \\ y = - 4x - 22](https://tex.z-dn.net/?f=4x%20%2B%20y%20%3D%203%20%5C%5C%20%20y%20%3D%20%20-%204x%20%2B%203%20%5C%5C%20using%20%5C%3A%20point%20%5C%3A%20slope%20%5C%3A%20form%20%5C%5C%20y%20-%20y1%20%3D%20m%28x%20-%20x1%29%20%5C%5C%20y%20%2B%206%20%3D%20%20-%204%28x%20%2B%204%29%20%5C%5C%20y%20%2B%206%20%3D%20%20-%204x%20-%2016%20%5C%5C%20y%20%3D%20%20-%204x%20-%2022)
First equation: Your equation is given.
Second equation: Distribute by multiplying every number in the parentheses by the number outside it.
3rd equation: Combine like terms by adding 4x to both sides.
4th equation: Combine like terms by subtracting 14 from both sides.
5th equation: Divide both sides by -2, the coefficient of x.
Answer:
Width = 5 inches
Length = 9 inches
Step-by-step explanation:
The paper;
Length = (x + 4) inches
Width = x inches
The area is close as possible to 50 square inches.
Since this paper is rectangular in shape; the area of a rectangle is given by:
Area = Length × Width
∴ (x + 4) * x = 50 square inches
x² + 4x = 50
Let the area be equal to 45 square inches;
Applying the quadratic formula, x = 5 or -9
But since we are dealing with length measurements, the value of x = 5 inches.
So the width = 5 inches and;
length = 5 + 4 = 9 inches.
Answer:
The answer to your question is:
Step-by-step explanation:
1.- y = 4x + 2
y = x - 3
x - 3 = 4x + 2
4x - x = -3 - 2
3x = -5
x = -5/3
y = -5/3 - 3
y = (-5 - 9) / 3
y = -14/3
2.- 7x + 2y = 18
6x (+) 6y = 0 There is no sign in the second
equation
Answer:
C. $80
Step-by-step explanation:
A. $70
B. $65
C. $80
D. $75
When he pays $70 monthly
Number of months = $2330 / $70
= 33.3 months
When he pays $65 monthly
Number of months = $2330 / $65
= 35.9 months
When he pays $80 monthly
Number of months = $2330 / $80
= 29.1 months
When he pays $75 monthly
Number of months = $2330 / $75
= 31.1 months
The monthly amounts that will allow Arthur to pay off his balance the fastest is $80 per month