Answer:
y = 3x - 16
Step-by-step explanation:
We are asked to find the equation of the line perpendicular to 2x + 6y = 30
We can use two formulas for this question, either
y = mx + c. Or
y - y_1 = m(x - x_1)
Step 1: calculate the slope
From the equation given
2x + 6y = 30
Make y the subject of the formula
6y = 30 - 2x
Or
6y = -2x + 30
Divide both sides by 6, to get y
6y/6 = ( -2x + 30)/6
y = (-2x + 30)/6
Separate them in order to get the slope
y = -2x/6 + 30/6
y = -1x/3 + 5
y = -x/3 + 5
Slope = -1/3
Step 2:
Note: if two lines are perpendicular to the other, both are negative reciprocal of each other
Perpendicular slope = 3/1
Substitute the slope into the equation
y = mx + c
y = 3x + c
Step 3: substitute the point into the equation
( 6,2)
x = 6
y = 2
2 = 3(6) + c
2 = 18 + c
Make the c the subject
2 - 18 =c
c = 2 - 18
c = -16
Step 4: sub the value of c into the equation
y = 3x + c
y = 3x - 16
The equation of the line is
y = 3x - 16
If you try out the other formula, u will get the same answer
A function is a constant on a interval and the constant is a interval which is horizontal in the entire interval the way a constant interval can be produce is by putting a interval horizontal
Answer:
f(g(3)) = -7
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Functions
- Function Notation
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
f(x) = -2x + 7
g(x) = x² - 2
<u>Step 2: Find f(g(3))</u>
- Substitute in <em>x</em> [Function g(x)]: g(3) = 3² - 2
- Evaluate exponents: g(3) = 9 - 2
- Subtract: g(3) = 7
- Substitute in g(3) [Function f(x)]: f(g(3)) = -2(7) + 7
- Multiply: f(g(3)) = -14 + 7
- Add: f(g(3)) = -7
<span>x cubed +3x squared - 4x= 0
= x^3 + 3x^2 -4x = 0
=x(x^2 +3x -4) = 0
= x (x+4)(x-1) = 0
x = 0
x+ 4 = 0 then x = -4
x - 1 = 0 then x = 1
answer: x = 0, x = -4 and x = 1</span>
First, we determine the area of the wall before cutting out the door by multiplying the dimensions given.
area of wall = ( 9 ft)(5.25 ft) = 47.25 ft²
Then, we determine the area of the door by subtracting from the total area the area of the remaining wall.
area of door = 47.25 ft² - 26.25 ft² = 21 ft²
The two whole numbers that can be the sides of the door are 7 ft x 3 ft.