Linear Equations
5x+ 4y= -7
-5x- 2y= 1
(1,-3)
work: 2y= -6 -> y= -3
5x+ 4(-3)= -7 -> 5x=5 -> x=1
What is 20% as a fraction (completely reduced)?
1/5
x2+ 6x+ 9= 0
x= -3
(x+3) (x+3)
x+3= 0
x=-3
what is the perimeter of a rectangle whose length and width are 7 units and 2 units, respectively?
18units
work:
7+7+2+2= 18
if 4m-3 is greater than or equal to 1, what is the least possible value of 4m+3
7
4m-3> or = 1
4m> or =4 -> m> or = 1
y= 2x-10
y= 4x- 8
(-1, -12)
work: 2x- 10= 4x- 8
-2= 2x -> x=-1
y= 2(-1)-10 -> y= -12
What is 1.35 as a percentage?
135%
x2+ 5x+ 6= 0
(-2,-3)
work: (x+2) (x+3)
x+2=0 -> x=-2
x+3=0 -> x=-3
if the area of a square in 49 square units, what is the squares perimeter?
28 units
work:
square root of 49 = 7
7+7+7+7= 28
the equation x2= 4x-3 has how many distinct real solutions?
2
y= 3x-2
x-y= 4
(-1,-5)
work: x-(3x-2)=4 -> -2x= 2 -> x=-1
y= 3(-1) -2 -> y= -5
If x % of 15 is 60, than what is 40% of X?
160
work: 15x=60 -> x=4
x% = 400%
0.4(400)= 160
6n2-18n-18=6
(4,-1)
work: 6n2-18n-24=0
6(n2-3n-4=0)
(n-4) (n+1)
n-4=0 n=4 n+1=0 n=-1
if the radius of a circle is 2, then what is the area of the circle?
4 time pi
if y = mx+2 where m is a constant, and when x=6, y=14, what is the value of y when x= 10?
22
4x+3y= -5
-2x+2y=6
(-2, -1)
work: 2(-2x+2y=6) -> 4x+3y= -5
-4x+4y=12
y=1
4x+ 3(1)= -5 -> 4x= -8 -> x=-2
126 is 150% of what number?
84
work: 126= 1.5x
b2+5b-35=3b
(-7,5)
work:
b2+2b-35= 0
(b-5)(b+7)
b-5=0 --> b=5
b+7 =0 --> b=-7
if the base of a paralellogram is equal to 14cm and the area is 70cm2 , then find its height.
5cm
5x14= 70
If f(x)=2x2+4 for all real numbers, x, what is equal to f(3) f(5)
f(6)
f(3)=2(32)+4
f(5)=2(52)+4
f(3)+f(5)
-2x+2y=6
4x+2y= -5
(-11/6, 7/6)
work: -1 (2x-2y= -6)
4x+2y= -5
6x= -11
x= -11/6
-2(-11/6)+ 2y= 6 -> 22/6+ 2y= 36/6 -> 2y=14/6
y= 7/6
Three saleswomen, Julie, Cecilia, and Sophia, competed to sell the highest number of sweaters in the month of October. A total of 575 were sold! Cecilia sold 158 sweaters, Julie sold approximately 41% of the remaining sweaters, and Sophia sold the rest. How many sweaters did Sophia sell?
Sophia sold 246 sweaters
work: 575-158= 417 (Cecilia)
417(0.41)= 171 (Julie)
575-158-171= 246 (Sophia)
(2m+3) (4m+3)=0
-3/2, -3/4
work:
2m+3 = 0
2m= -3 --> m= -3/2
4m+3 = 0
4m= -3--> -3/4
if the area of an equaliterial triangle is square root of 3cm2 then the side is...
2cm
If line L is translated up 5 units and right 7 units, then what is the slope of the new line?
-3/2