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
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$193.50
start by multiplying 240 by .25 (25%) to find out how much is 25% of 240. this equals 60.
then, subtract $60 from $240. equals 180.
next, to add the sales tax, multiply 180 by 0.075 (7.5%) this is $13.50.
lastly, add the tax, which is $13.50, to the suit's sale price, which is $180.
180+13.5= $193.50
Solve for x over the real numbers:
x^3 (x^2 - 4) = 0
Split into two equations:
x^3 = 0 or x^2 - 4 = 0
Take cube roots of both sides:
x = 0 or x^2 - 4 = 0
Add 4 to both sides:
x = 0 or x^2 = 4
Take the square root of both sides:
Answer: x = 0 or x = 2 or x = -2
9514 1404 393
Answer:
5. x = 160; y = 20
6. h = 125°; g = i = 55°
Step-by-step explanation:
Vertical angles are found on opposite sides of a point where lines cross. Each angle is formed from rays opposite those of the other angle. Vertical angles are congruent.
5. x° and 160° are vertical angles: x° = 160°
y° and 20° are vertical angles: y° = 20°
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6. h° and 125° are vertical angles: h° = 125°
The angles g° and 125° form a "linear pair" so total 180°.
g° = 180° -125° = 55°
g° and i° are vertical angles: g° = i° = 55°