WORD PROBLEMS
Mr. Jackson had a rectangular shaped garden where the Length was less than twice the width. If the area of the garden was 420 square feet, find the dimensions of the garden.
L=28 W=15
Mo's farm stand sold a total of 165 pounds of apples and peaches. She sold apples for $1.75 per pound and peaches for $2.50 per pound. If she made $337.50, how many pounds of peaches did she sell?
65 lbs of Peaches
If a function f is defined as f=(1,2),(2,3),(3,1),(4,4) whats f(2)?
3
Which trinomial is equivalent to 3(x−2)2 −2(x−1)?
3x^2-14x+14
x^2+2x-3
x=-3
x=1
The length of a rectangular sign is 6 inches more than half its width. The area of this sign is 432 square inches. Write an equation in one variable that could be used to find the number of inches in the dimensions of this sign. Solve this equation algebraically to determine the dimensions of this sign, in inches.
W=24
−5x+2y=9
y=7x
x=1
y=7
If fx = 4x + 5, what is the value of f(−3)?
-7
When (2x − 3) 2 is subtracted from 5x^ 2 , the result is…
x^2-12x+9
The height of a ball Doreen tossed into the air can the time elapsed in seconds, and h(x) is the height f(x) = 1250(1.2)x f(x) = 1250(0.8)x
be modeled by the function h(x) = −4.9x 2 + 6x + 5, where x is in meters. The number 5 in the function represents...
the initial height of the ball
The math department needs to buy new textbooks and laptops for the computer science classroom. The textbooks cost $116.00 each, and the laptops cost $439.00 each. If the math department has $6500 to spend and purchases
30 textbooks, how many laptops can they buy?
6 Laptops
y = 2x + 8
3(−2x + y) = 12
No Solution
If g(x) = −4x^2 − 3x + 2, determine g(−2).
-8
Subtract 5x2 + 2x − 11 from 3x2 + 8x − 7. Express the result as a trinomial.
-2x^2+6x+4
Solve using the Quadratic Formula
3x^2-5x-8
x=-1
x=2 2/3
Marilyn collects old dolls. She purchases a doll for $450. Research shows this doll's value will increase by 2.5% each year. Write an equation that determines the value, V, of the doll t years after purchase. Assuming the doll's rate of appreciation remains the same, will the doll's value be doubled in 20 years? Justify your reasoning.
450(1.025)^t
Last week, a candle store received $355.60 for selling 20 candles. Small candles sell for $10.98 and large candles sell for $27.98. How many large candles did the store sell?
8 Large Candles
What is the domain of the relation shown below?
{(4, 2), (1, 1), (0, 0), (1, −1), (4, −2)}
{0, 1, 4}
C = 2a 2 − 5 and D = 3 − a , then C − 2D equals
2a^2+2a-11
Solve by completing the square
x^2+6x=−2
x=-√7 -3
x=+√7 -3
A rectangle is 3 times as long as it is wide. If the width is increased by 6 feet and the length is decreased by 3 feet, the area is doubled. Find the dimensions of the old rectangle.
Original Dimensions: W=2 L=6
−9y+4x−20=0
−7y+16x−80=0
x=5
y=0
Michael has $10 in his savings account. Option 1 will add $100 to his account each week. Option 2 will double the amount in his account at the end of each week. Write a function in terms of x to model each option of saving. Michael wants to have at least $700 in his account at the end of 7 weeks to buy a mountain bike. Determine which option(s) will enable him to reach his goal. Justify your answer.
option 1= 100x+10=710
option 2= 10(2)^7=1280
Both options will help him reach his goal
What are the zeros of the function f(x)=x2 −13x−30?
-2 and 15
500. Mrs. Farber has a snowball fight with Charlie.
The function h(t) = 5 + 25t ─16t
2 gives the height in feet, h(t), of a snowball after t seconds.
a) When does the snowball hit the ground? Show work algebraically.
(Hint: When the snowball hits the ground, the height of the snowball will be 0.)
b) What is the maximum height of the snowball? Show work algebraically.
(Remember: x = −b/21)
c) State the domain for this example. (t represents TIME here...)
d) State the range for this example.
a.1.74 sec
b.945/64 ft
c. t≥0
d. 0≤y≤945/64