A line in point-slope form has the equation
y = mx + b
where m=slope (increase in y for unit increase in x), and
b=y-intercept (value of y where line cuts y-axis)
The original line is
y=(-1/2)x + 11
so
slope = m = -1/2
Any line perpendicular to a line with slope m has a slope of m1=-1/m
So the slope m1 of the required line
m1 = -1 / (-1/2) = +2
and the required line therefore has an equation of
y=2x+b
Knowing that the line passes through P1=(x1, y1)=(4,-8), we can find b using the point slope form of a line with slope m : (y-y1) = m(x-x1)
where m=+2 as found above.
Substituting values, m=+2, x1=4, y1= -8
y-(-8) = +2(x--4)
simplify
y+8 = 2x-8
=>
y=2x-16 (in point slope form)
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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Answer:
The expected payoff for Ann is that she loses the game
Step-by-step explanation:
The expected payoff for Ann is that she loses the game, this is because only 5 out of the 20 sections allow Ann to win money, this is only 25% of the spinner. Meaning that 75% of the spinner will cause Ann to lose the game. Rolling two times increases the odds that she will lose the game. Since the greatest probability is that Ann will land on a section that causes her to lose the game, then this is the expected payoff.
Answer:
Point C
Step-by-step explanation:
Answer:
These reflected points represent the inverse function
Step-by-step explanation:
This is just one of the rules that are true.