Answer:
a linear equation in x and y
Step-by-step explanation:
The given equation is a linear equation (all variables to the first power) relating the variables x and y. There are an infinite number of values of x and y that will satisfy this equation.
When graphed on an x-y plane, those solution values will fall on a straight line with a slope of 2. It will cross the y-axis at y=32, and the x-axis at x=-16.
Answer:
x = 1
Step-by-step explanation:
Given in the question the equation
y = -x² + 2x - 1
To find the x-intercept, substitute in 0 for y
0 = -x² + 2x - 1
To find value of x use quadratic equation
x = -b ± √b²-4ac / 2a
here a = -1
b = 2
c = -1
x1 = -2 + √2²-4(-1)(-1) / 2(-1)
= -2 + 0 / -2
= -2 / -2
= 1
x2 = -2 - √2²-4(-1)(-1) / 2(-1)
= -2 - 0 / -2
= -2 / -2
= 1
Because I see a graph in the picture, I am assuming you need to graph the equations. The two equations are in slope-intercept form. They are in the form
y = mx + b
Where m is the slope and b is the y-intercept. That is why it is called the slope-intercept form.
If you want to graph a slope-intercept form equation, first plug in a value for x then compute it to get the y-coordinate.
First, let's get some points with the equation y = 4x + 3
We will plug in three values for x. 0, 1, and 2.
When x = 0
y = 4(0) + 3
y = 3
When x = 1
y = 4(1) + 3
y = 7
When x = 2
y = 4(2) + 3
y = 11
Now we have the points (0, 3), (1, 7), and (2, 11)
These points are called ordered pairs. Where the first number is the x-coordinate and the second number is the y-coordinate.
The ordered pairs tell you how many times you move your point away from the origin. The origin is (0, 0).
The first number of an ordered pair tells you how many times to move in the x direction and the second number how many times in the y direction.
Now graph the second equation. y = -x - 2
Just plug in some values for x.
I picked 0, 1, and 2.
When x = 0
y = 0 - 2
y = -2
When x = 1
y = -1 - 2
y = -3
When x = 2
y = -2 - 2
y = -4
Now we have the points (0, -2), (1, -3), and (2, -4)
Now plot those points and draw a line through them.
If you need to find the intersection of the equations y = 4x + 3 and y = -x - 2 you need to find where they intersect. Or in other words, share a common point.
After playing around with the numbers, I got the intersection point for the both of the equations.
It is the ordered pair (-1, -1). This the solution to both of the equations. If you plug in the ordered pairs into both of the equations, they will show it belongs to their graphs.
Plug in the values for y = 4x + 3
-1 = 4(-1) + 3
-1 = -4 + 3
-1 = -1
Plug in the values for y = -x - 2
-1 = -(-1) - 2
-1 = 1 - 2
-1 = -1
So, this ordered pair is on both equations!
Answer: he collected 22 quarters and 8 fifty-cent pieces
Step-by-step explanation:
Given;
The total amount of money he is to collect is;
A = 20 - 10.50 = $9.50
Let x represent the number of quarter he collected.
Then the number of fifty-cent pieces he collected will be; 30-x
Therefore we can represent it with the equation below;
0.25x + 0.50(30-x) = 9.50
0.25x + 15 - 0.50x = 9.50
0.25x = 15-9.50
x = (15-9.50)/0.25
x = 5.50/0.25
x = 22
The number of fifty-cent is equal to;
30-x = 30-22 = 8
Therefore, he collected 22 quarters and 8 fifty-cent pieces
Step-by-step explanation:
Let's subtitute 
for the above equation:
