Problem 1 :
Which graph shows the solution for the system of inequalities below?
y ≤ 2x + 2
y > -3x - 1
a)
b)
c)
Solution:
In general the overlapping region of the inequalities given can be considered as solution region.
From option A, choosing one of the points :
(5, 5)
y ≤ 2x + 2 5 ≤ 2(5) + 2 5 ≤ 12 True |
y > -3x - 1 5 > -3(5) - 1 5 > -16 True |
So, option A is correct.
Problem 2 :
The amount of medicine in Elizabeth's blood is modeled by the function
M(t) = -t^{2} + 10t
where t is the number of hours after she takes the medicine. How many hours after Elizabeth takes her medicine is the amount of medicine in her blood the highest?
A. 5 hours B. 10 hours C. 25 hours
Solution:
M(t) = -t^{2} + 10t
x = -b/2a
Here a = -1 and b = 10
x = -10/2(-1)
= -10/-2
x = 5 hours
So, option (A) is correct.
Problem 3 :
What is the smallest positive integer for x, so that the value of f(x) = 200(2)^{x} is greater than the value of g(x) = 500x + 400?
Solution:
f(x) = 200(2)^{x }------(1)
g(x) = 500x + 400^{ }------(2)
(1) = (2)
200(2)^{x }= 500x + 400
Dividing by 100
2(2)^{x }= 5x + 4
2^{x+1 }= 5x + 4
Let us apply x = 5
2^{5+1 }= 5(5) + 4
2^{6 }= 25 + 4
64 > 29 (true)
Let us apply x = 4
2^{4+1 }= 5(4) + 4
2^{5 }= 20 + 4
32 > 24 (Ture)
Let us apply x = 3
2^{3+1 }= 5(3) + 4
2^{4 }= 15 + 4
16 > 19 (false)
So, the smallest integer is 4.
Problem 4 :
What is the y-intercept of the function f(x) = 1/2(2x - 4)?
A. (0, -4) B. (0, -2) C. (0, 1)
Solution :
f(x) = 1/2(2x - 4)
f(x) = x - 2
y-intercept = (0, -2)
So, option (B) is correct.
Problem 5 :
A girl drops a ball from a height of 10 feet. Each time the ball hits the ground, it bounches to 2/3 its previous height. Which equation gives y, the height of the ball after x bounches?
Solution:
Given, initial height = 10 feet
Rate of decrease = 2/3
y = ab^{x}
y = 10(2/3)^{x}
So, option (B) is correct.
Problem 6 :
Which expression is equivalent to 3(x - 4)^{2}?
A. 3x^{2} + 48 B. 3x^{2} - 24x + 48 C. 9x^{2} - 72x + 144
Solution:
= 3(x - 4)^{2}
= 3(x - 4)(x - 4)
= 3(x^{2} - 8x + 16)
= 3x^{2} - 24x + 48
So, option (B) is correct.
Problem 7 :
Jane owns x comic books. Derrek owns y comic books.
How many comic books does Derrek own?
Solution:
j = 2d - 1 ---> (1)
j + d = 11 ---> (2)
j = 11 - d
Substitute j = 11 - d in (1),
11 - d = 2d - 1
-3d = -12
d = 4
4 comic books does Derrek own.
Problem 8 :
James is at a gift sale where everything costs $4 (tax included).
What is the greatest number of gifts James can buy?
Solution:
x = number of items
4x ≤ 50 - 28
4x ≤ 22
x ≤ 5.5
5 gifts James can buy.
Problem 9 :
The expression -5t^{2} + 40t predicts the height, in meters, of an object t seconds after a person launches it into the air. Using this expression, how many seconds will it take the object to hit the ground?
Solution:
-5t^{2} + 40t = 0
-5t(t - 8) = 0
-5t = 0 or t - 8 = 0
t = 0 or t = 8
t = 8
8 seconds will it take the object to hit the ground.
Problem 10 :
Solution:
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM