Answer:
See attached picture
Step-by-step explanation:
When functions are transformed there are a few simple rules:
• Adding/subtracting inside the parenthesis to the input shifts the function left(+) and right(-).
• Adding/subtracting outside the parenthesis to the output shifts the function up(+) and down(-).
• Multiplying the function by a number less than 1 compresses it towards the x-axis.
• Multiplying the function by a number greater than 1 stretches it away from the x-axis.
The equation for g has been subtracted inside the parenthesis by 2 which will shift the graph 2 units to the right.
The equation for g has also been subtracted outside the parenthesis by 3 which will shift the graph 3 units down.
The graph is shown in black while f(x) is show in purple in the attached picture.
Answer:
4.48
Step-by-step explanation:
Answer: x = 4
y = - 3
Step-by-step explanation:
The given system of simultaneous equations is expressed as
x-3y = 13 ------------------------1
2x+4y=-4--------------------------2
We would apply the method of substitution in solving the equations. From equation 1, we would make x to stand alone by adding 3y to the left hand side and the right hand side of the equation. It becomes
x - 3y + 3y = 13 + 3y
x = 13 + 3y
Substituting x = 13 + 3y into equation 2, it becomes
2(13 + 3y) + 4y = - 4
26 + 6y + 4y = - 4
26 + 10y = - 4
Subtracting 26 from the left hand side and the right hand side of the equation, it becomes
26 - 26 + 10y = - 4 - 26
10y = - 30
Dividing the left hand side and the right hand side of the equation by 10, it becomes
10y/10 = - 30/10
y = - 3
Substituting y = - 3 into x = 13 + 3y, it becomes
x = 13 + 3 × - 3
x = 13 - 9
x = 4
Answer:
x = 4
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtract Property of Equality
Step-by-step explanation:
<u>Step 1: Define</u>
2(x/4 + 8) = 18
<u>Step 2: Solve for </u><em><u>x</u></em>
- Divide 2 on both sides: x/4 + 8 = 9
- Subtract 8 on both sides: x/4 = 1
- Multiply 4 on both sides: x = 4
<u>Step 3: Check</u>
<em>Plug in x into the original equation to verify it's a solution.</em>
- Substitute in <em>x</em>: 2(4/4 + 8) = 18
- (Parenthesis) Divide: 2(1 + 8) = 18
- (Parenthesis) Add: 2(9) = 18
- Multiply: 18 = 18
Here we see that 18 does indeed equal 18.
∴ x = 4 is the solution to the equation.
