Question 1 :
If a = 5√2 and 2a = √(2x), what is the value of x?
Answer :
2a = √(2x)
Substitute a = 5√2.
2(5√2) = √(2x)
10√2 = √(2x)
Square both sides.
(10√2)^{2} = [√(2x)]^{2}
10^{2}(√2)^{2} = 2x
100(2) = 2x
200 = 2x
Divide each side by 2.
100 = x
Question 2 :
Wyatt can husk at least 12 dozen ears of corn per hour and at most 18 dozen ears of corn per hour. Based on this information, what is a possible amount of time, in hours, that it could take Wyatt to husk 72 dozen ears of corn?
Answer :
Wyatt can husk at least 12 dozen ears of corn per hour.
Maximum time required to husk 72 dozen of ears :
= 72/12
= 6 hours
He can husk at most 18 dozen ears of corn per hour.
Minimum time required to husk 72 dozen of ears :
= 72/18
= 4 hours
Therefore, the possible times it could take Wyatt to husk 72 dozen ears of corn are 4 hours to 6 hours, inclusive.
Question 3 :
A landscaping company estimates the price of a job, in dollars, using the expression 60 + 12nh, where n is the number of landscapers who will be working and h is the total number of hours the job will take using n landscapers. Which of the following is the best interpretation of the number 12 in the expression?
A) The company charges $12 per hour for each landscaper.
B) A minimum of 12 landscapers will work on each job.
C) The price of every job increases by $12 every hour.
D) Each landscaper works 12 hours a day.
Answer :
The price of the job, in dollars, is calculated using the expression 60 + 12nh, where 60 is a fixed price and 12nh is a variable price which depends on the number of landscapers and number of hours each landscaper works.
nh ----> number of landscaper times number of hours each landscaper
nh
=
number of landscaper
x
number of hours each landscaper
nh ----> total number of hours works done by n landscapers.
Because 'nh' is multiplied by 12 in the given expression, 12 is the money paid for each hour of work done.
The correct option is (A).
Question 4 :
9a^{4} + 12a^{2}b^{2} + 4b^{4}
Which of the following is equivalent to the expression shown above?
A) (3a^{2 }+ 2b^{2})^{2}
B) (3a^{ }+ 2b)^{4}
C) (9a^{2 }+ 4b^{2})^{2}
D) (9a^{ }+ 4b)^{4}
Answer :
9a^{4} + 12a^{2}b^{2} + 4b^{4} :
= 3^{2}(a^{2})^{2} + 12a^{2}b^{2} + 2^{2}(b^{2})^{2}
= (3a^{2})^{2} + 2(3a^{2})(2b^{2}) + (2b^{2})^{2}
Let x = 3a^{2}, y = 2b^{2}.
= x^{2} + 2xy + y^{2}
Use algebraic identity (a + b)^{2} = a^{2} + 2ab + b^{2}.
= (x + y)^{2}
Substitute 3a^{2 }for x and 2b^{2}for y.
= (3a^{2} + 2b^{2})^{2}
The correct option is (A).
Question 5 :
nA = 360
The measure A, in degrees, of an exterior angle of a regular polygon is related to the number of sides, n, of the polygon by the formula above. If the measure of an exterior angle of a regular polygon is greater than 50°, what is the greatest number of sides it can have?
A) 5
B) 6
C) 7
D) 8
Answer :
nA = 360
Divide each side by n.
A = 360/n
It is given that the measure of A is greater than 50°.
A > 50
Substitute 360/n for a.
360/n > 50
Multiply each side by n.
360 > 50n
50n < 360
Divide each side by 50.
n < 72
n has to be less than 7.2 and also n is an integer.
n = 7
The correct option is (C).
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