g(x) = (x - 3)² - 4
given f(x) is shifted a units horizontally to the right → f(x) → f(x - a)
If f(x) is shifted by a units horizontally left → f(x) → f(x + a)
If f(x) is shifted by b units vertically up → f(x) → f(x) + b
If f(x) is shifted by b units vertically down → f(x) → f(x) - b
The vertex (0, 0) of f(x) has shifted to (3, -4)
that is 3 units horizontally to the right and 4 units vertically down
hence g(x) = (x - 3)² - 4
Answer:

Step-by-step explanation:


a. The expression y=5x represent the number of small marbles she has.
b. The expression z=3x+2 represents the number of large marbles she has.
c. Amy has 310 small marbles, 62 medium marbles and 188 large marbles.
Step-by-step explanation:
a. Let x represent the number of medium marbles Amy has. Write an algebraic expression to represent the number of small marbles she has.
Medium marbles = x
Let,
Small marbles = y
According to given statement;
She has five times as many small marbles as medium marbles.
y = 5x Eqn 1
The expression y=5x represent the number of small marbles she has.
b. Write an algebraic expression to represent the number of large marbles she has.
Let,
Large marbles = z
The number of large marbles is two more than three times the number of medium marbles.
z = 3x+2 Eqn 2
The expression z=3x+2 represents the number of large marbles she has.
c. If Amy has a total of 560 marbles, how many of each size does she have?
x+y+z= 560 Eqn 3
Putting value of y and z from Eqn 1 and 2 in Eqn 3

Dividing both sides by 9

Putting x=62 in Eqn 1

Putting x=62 in Eqn 2

Amy has 310 small marbles, 62 medium marbles and 188 large marbles.
Keywords: linear equation, substitution method
Learn more about substitution method at:
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4: (3/4 - 1/2) X 3/5.
You need them all to have the same denominator (bottom number)
The lowest common denominator (LCM) of 2,4 and 5 is 20
4 X 5 = 20
2 X 10 = 20
5 X 4 = 20
Then multiply the top number by the amount you need to multiply the bottom number by to get 20
3 X 5 = 15
1 X 10 = 10
3 X 4 = 12
(3/4 - 1/2) X 3/5. Turns to (15/20 - 10/20) X 12/20.
15 - 10 = 5
5 X 12 = 60
Answer: 60/20
Simplified: Either 3 or 3/1.
If you use the steps above then you should be able to do the rest :D
If you need anymore help, please ask