Answer:
![\boxed{\text{1. y + 5 = -4(x - 3); \qquad 2. y - 8 = x + 1}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Ctext%7B1.%20y%20%2B%205%20%3D%20-4%28x%20-%203%29%3B%20%5Cqquad%202.%20y%20-%208%20%3D%20x%20%2B%201%7D%7D)
Step-by-step explanation:
Question 1
The point-slope formula for a straight line is
y – y₁ = m(x – x₁)
x₁ = 3; y₁ = -5; m = -4
Substitute the values
![\boxed{\textbf{y + 5 = -4(x - 3)}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Ctextbf%7By%20%2B%205%20%3D%20-4%28x%20-%203%29%7D%7D)
The diagram shows the graph of equation 1 (red) with slope -4 passing through (3,-5).
Question 2
x₁ = -1; y₁ = 8; m = 1
Substitute the values
![\boxed{\textbf{y - 8 = x + 1}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Ctextbf%7By%20-%208%20%3D%20x%20%2B%201%7D%7D)
The diagram shows the graph of equation 2 (green) with slope 1 passing through (-1,8).
Answer: -3 ≤ -2c
Step-by-step explanation:
First multiply C by -2, and make sure it's not less than -3. It can be -3, but it can't be less than.
Answer:
Length
inches
Width
inches
Step-by-step explanation:
Let
= length of rectangle,
= width of rectangle
Given the area and the perimeter of the rectangle, we can write:
![2l+2w=80](https://tex.z-dn.net/?f=2l%2B2w%3D80)
So:
![l+w = 80\div2](https://tex.z-dn.net/?f=l%2Bw%20%3D%2080%5Cdiv2)
![=40](https://tex.z-dn.net/?f=%3D40)
![l=40-w](https://tex.z-dn.net/?f=l%3D40-w)
Now, we can use substitution to find the value of
:
![lw = 375](https://tex.z-dn.net/?f=lw%20%3D%20375)
![(40-w)w = 375](https://tex.z-dn.net/?f=%2840-w%29w%20%3D%20375)
![40w-w^2 = 375](https://tex.z-dn.net/?f=40w-w%5E2%20%3D%20375)
(Quadratic equation)
∴ ![w = 15, 25](https://tex.z-dn.net/?f=w%20%3D%2015%2C%2025)
We can use substitution again to find the value of ![l](https://tex.z-dn.net/?f=l)
![lw = 375](https://tex.z-dn.net/?f=lw%20%3D%20375)
![l=375\div w](https://tex.z-dn.net/?f=l%3D375%5Cdiv%20w)
![=25,15](https://tex.z-dn.net/?f=%3D25%2C15)
∵ Length usually refers to the longer side of a rectangle, ∴ length
inches and width
inches.
Hope this helps :)