Algebra Unit 2 WA
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University of the People *
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Course
1101
Subject
Mathematics
Date
Jan 9, 2024
Type
docx
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3
Uploaded by DeaconFieldMagpie39
1.
a. The graphs are parallel, meaning there is no algebraic solution because the
graphs don't cross.
b. The graphs are neither parallel nor perpendicular.
3y+x = 12
-y = 8x-1
Change -y to positive y = -8x-1
Solve for x = 3(-8x-1)+x= 12
-24x-3+x= 12
-24x+x = 12+3
-23x = 15
X = -15/23 = -0.652
Solve for y = -8(-15/23)-1
Y = 120/23-23/23 (changed one to 23/23 to be able to solve the function)
Y = 97/23 = 4.217
c. These graphs are perpendicular. They meet at a right angle.
4x-7y = 10
7x-4y = 1
Get x on one side
4x-7y = 10
| + 7y
4x = 10 + 7y
| : 4
X = 2.5 + 1.75 y
Solve for y
7(2.5+1.75y) + 4y = 1
17.5 + 16.5y = 1
| -17.5
16.5y = -16.5
| : 16.5
Y = -1
Solve for x
X = 2.5 + 1.75(-1)
X = 2.5 - 1.75
X = 0.75
2. Y = -4.9x2 + 24x + 8 | plug 0 into x, because the time starts at 0
Y = 0 + 0 + 8
Y = 8
The building is 8 high.
To find the time for the ball to reach the highest point, I am using the vertex
formula:
H = -b/2a
A = 4.9, b = 24 c = 8
-24/2*4.9
-24/9.8
=
2.449
time
To find the highest point, the ball reaches, I am going to plug the vertex formula into
the function given to us.
Y = -4.9(-24/9.8)^2*2 + 24(-24/9.8) + 8
Y = -4.9(2.449)^2 + 24(2.449) + 8
Y = -4.9 (5.998) + 24(2.449) + 8
Y = (-29.391) + 58.776 + 8
Y = 37.385 Highest point of the ball
3. First, I want to see if more or fewer shops make more revenue.
N = 100
R = 100*200 = 20,000
N = 101
R = 101*195 = 19,695
N = 99
R = 99*205 = 20,295
Fewer shops make more revenue.
Because it's a linear function, I am going to use the equation of a line.
N * (a*N+b)
When N = 100
Then 100a+b = 200
When N = 99
Then 99a+b = 205
Solving for a
When I subtract 99a+b from 100a+b = 200, I get a+0 = -5
This means that a= -5
When I solve for b
100* (-5) + b = 200
B = 200 + (-100) * (-5)
B = 200 + 500
B = 700
R = N*(-5*N+700)
R = -5N^2+700N
To find the perfect number of shops for the revenue, I will use the vertex formula
again, because the highest amount of revenue is the vertex of the parabola.
N =-b/2a
N = -700/(2*-5)
N = 700/10
N = 70
The perfect number of shops for the highest revenue is 70.
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