Factoring
Factor completely: x2 + 10x + 25
x2 +10x +25
(x + 5)(x + 5)
(x+5)2
if three apples equal 15, and one pineapple plus one apple equal 8, and one cookie plus two pineapples equals 18, what is one apple plus two pineapples plus four cookies?
15 ÷ 3 = 5
8 - 5 = 3
18 - (3 x 2) = 12
5 + (3 x 2) + (12 x 4) = 59
Simplify : 23 x 24 x 22 x 25
Same base means exponents can be added
23 + 4 + 2 + 5 = 214
Answer = 214
What is the vertex for this function?
y = 3 (x + 18)2 - 8
(-18, - 8)
Factor completely: x2 - 7 + 10x
x2 - 7 + 10x
x2 + 10x - 7
(x - 5)(x - 2)
$16 apples costs $64
2 apples + 40 cucumbers costs $128
17 cucumbers + 24 apples + 18 cookies costs $435
how much does each food item cost
apples: 64/16 = 4
cucumbers: 128 - 8 = 120, 120/4 = 3
cookies: 17 x 3 = 51, 24 x 4 = 96, 435 - 96 - 51 = 288, 288/18 = 16
apple = 4, cucumbers = 3, cookies = 16
Solve: 163/4
163/4 = (161/4)3
(∜16)3 = 23 = 8
Answer = 8
Complete the square.
y = 5x2 + 30x + 41
y = 5x2 + 30x + 41
y= 5(x2 +6x) + 41
y= 5(x2 +6x +9 - 9) + 41
y= 5[(x2 +6x +9) - 9] + 41
y= 5[(x+3)2 - 9] + 41
y= 5(x+3)2 - 45 + 41
y= 5(x+3)2 - 4
Factor completely: 5x2 + 35x + 60
5x2 + 35x +60
5(x2 + 7x + 12)
5(x + 3)(x + 4)
if a car is going at 200 miles per hour and a bus is going at 400 miles per hour in the opposite direction and they are going towards each other and they start from 300 miles apart how long will it take for them to cross paths
find the combined speed: 200mph + 400mph = 600mph
use the formula time = distance over speed: t = 300/600, t = 1/2hours
it would take half an hour for them to cross paths
simplify: (a2/3)5/3
(a2/3)5/3
multiply exponents: a 2/3 x 5/3
answer: a10/9
Write a function to represent the area of a rectangle where the width is "x + 2" and the length is "20 - 2x"
( In terms of X)
L x W = A
(20 - 2x)(x + 2) = A
20x + 40 - 2x2 - 4x = A
-2x2 + 16x + 40 = A
Factor completley: 2x2 + 13x + 15
2x2 + 13x + 15
x2 + 13x + 30
(x + 10)(x + 3)
(x + 10/2)(x + 3/2)
(x + 5)(2x +3)
if the the width of my backyard is 400 meters and the area of my backyard is 240,000 meters how much fencing would i need to fence half of my backyard?
A = L x W
L = A/W
L = 240,000/400 = 600
P = 2L + 2W
P = 2000
Simplify: 3x-3/5 / 2x2/3
3x-3/5 / 2x2/3
3/2 . 1 / x3/5 . x2/3
(3/5 + 2/3 = 9/15 + 10/15 = 19/15)
answer: 3 / 2x19/15
A ball is thrown upward with an initial velocity of 18m/s from a height of 3m.
the height h (in meters) after t seconds is:
h(t)= -5t2 + 18t + 3
How long does it take for the ball to hit the ground?
h(t)= -5t2 + 18t + 3
-5t + 18t +3 = 0
using the quadratic formula with:
a = -5, b = 18, c = 3
t ~ 3.76 seconds
Factor completely: (x2 + 6x +9) - 4y2
(x2 + 6x +9) - 4y2
(x + 3) (x + 3) - 4y2
(x + 3 - 2y) (x + 3 + 2y)
100 farmers go to a fruit stand. There are bulk bags of apples selling for $75 dollars and bulk bags of oranges selling for $50 dollars and each farmer gets one bag. In the end the fruit stand makes a total of 6000 dollars, how many of each type of fruit bag was sold?
let a be the number of apples sold and o be the number of oranges sold. a + o = 100 cause each farmer gets one bag so that means o = 100 - a.
the total revenue is 75a + 50o = 6000. we can express this equation as 75a + 50(100 - a) = 6000
then solve for a: 75a + 5000 - 50a = 6000
25a = 1000
a = 40
that means there were 40 apples bags and 60 orange bags sold
x3/2 y-1 / x-5/3 y
x3/2 y-1 / x-5/3 y
x3/2 - (- 5/3) y -1-1
x9/6 -(-10/6) y -1 -1
answer: x19/6 y-2
a theater charges $12 per ticket and sells 150 tickets per show. For every 1$ increase, 5 fewer tickets are sold.
What ticket price will give the maximum revenue?
What is the maximum revenue possible?
Draw a table or:
R = revenue
x = the number of $1 increases
R(x) = (12 + x)(150 - 5x)
R(x) = -5x2 + 90x + 1800
R(x) = -5(x2 - 18x) + 1800
R(x) = -5(x2 - 18x + 81 - 81) + 1800
R(x) = -5(x - 9)2 - 81) + 1800
R(x) = -5(x-9)2 + 2205
p = 9 (increase price by $9)
12 + 9 = $21
Tickets cost = $21
Maximum revenue = $2,205