System of Equations
y = 8x -1
4x + y = 8
Use substitution method
y = 8x - 1
4x + 8x -1 = 8
12x - 1 = 8
12x = 9
x = 3/4
y = 8(3/4) - 1
y = 5
(3/4,5)
One leg of a triangle is 9 ft and the hypotenuse is 14 ft, what is the length of the other leg
a2 + b2 = c2
92 + x2 = 142
81 + x2 = 196
x2 = 115
x = +/- 10.72
x = 10.72
√48
√(16x3)
√16 √3
4 √3
Find the distance between the points
(8,6) and (14,-4)
d = √((x2-x1)2 + (y2-y1)2)
= √((14-8)2 +(-4-6)2)
√(62 + (-10)2
√36 + 100
√136
11.66 units
x - 3y = 4
5y = 2x - 10
2 (x - 3y) = 4
2( x - 3y = 4)
-2x + 5y = -10
2x -6y = 8
-2x + 5y = -10
-y = -2
y=2
x-3y = 4
x-3(2) = 4
x-6 = 4
x = 10
(10,2)
Solve for C
a = 16
b = 12
a2 + b2 = c2
162 + 122 = c2
256 + 144 = c2
400 = c2
c = 20
5√125
5 √25 √5
5 · 5 √5
25√5
Find the midpoint between the two points
(-6,-1) and (16, -3)
M = ((x1+x2)/2) , ((y1+y2)/2)
= ((-6+16)/2) , ((-1-3)/2)
= (10/2) , (-4/2)
= (5,-2)
2x - 3y = -16
-4x + y = -8
Use Elimination method
2(2x - 3y = -16)
4x - 6y = -32
-4x + y = -8
-----------------
0. -5y = -40
y = 8
2x - 3(8) = -16
2x - 24 = -16
2x = 8
x = 4
(4,8)
A water slide at a park is 18 yards long. The slide is a straight line and covers a horizontal distance of 8 yards between the bottom of the ladder and the bottom of the slide. How high up is the top of the slide form the ground?
a2 + b2 = c2
x2 + 82 = 182
x2 + 64 = 324
x2 = 260
x = 16.1 yds
√48x3
√(16 · 3x2 ·x)
√16 √3 √x2 √x
4x√3x
Find the distance between these two points
(-13, -8) and (3, 12)
d = √((x2-x1)2 + (y2-y1)2)
= √((3 + 13)2 + (12 + 8)2)
= √162 + 202
= √656
x = 25.61
6x - y = 5
5x + 5y = 35
Use Subsititon method
5x = 35 - 5y
x = -y + 7
6x - y = 5
6(-y + 7) - y = 5
-6y + 42 - y = 5
-7y + 42 = 5
-7y = - 37
y = 37/7
6x - 37/7 = 5
7(6x - 37/7 = 5)
42x - 47 = 35
42x = 72
x = 12/7
(12/7,37/7)
Determine if the given Lengths form a right Triangle
11,18,21
a2 + b2 = c2
112 + 182 = 212
121 + 324 = 441
445 does not equal 441
NO
√28b2
√(4 · 7b2)
√4 √7 √b2
2 √(7) b
2b √7
Find the Midpoint between these two points
(5.5, -2) and (5.5, -12)
M = ((x1+x2)/2) , ((y1+y2)/2)
M = ((5.5 + 5.5)/2) , ((-2 - 12)/2)
M = 11/2 , -14,2
M = (5.5, -7)
2x = 2y - 4
3y = 4x - 9
Use elimination method
2(2x - 2y = -4)
-4x + 3y = -9
4x - 4y = -8
+
- 4x + 3y = -9
-------------------
y =17
2x = 2(17) -4
2x = 30
x= 15
Ellery is building a dog ramp for her elderly dog to get into her car. The actual ramp is 6 feet long and reaches the back of the car at a height of 3 feet. What is the horizontal distance covered by the ramp on the ground?
a2 + b2 = c2
32 + x2 = 62
9 + x2 = 36
x2 = 27
x = 5.2 ft
√63m4
√(9 · 7m2m2)
√9 √7 √m2 √m2
3 · √(7) · m · m
3m2 √7
Find the distance between the two points
(1000,225) (300, 882)
d = √((x2-x1)2 + (y2-y1)2)
√((300-1000)2 + (882-225)2)
√(-700)2 + (657)2
√(490000) + (431649)
√921649
960.03 units