Heart of Algebra
2y + 6x = 3
y + 3x = 2
How many solutions (x, y) does the given system of equations have?
A) Zero
B) Exactly one
C) Exactly two
D) Infinitely Many
A) Zero
f(x) = a(x-h)2 + k
Which point (variables) is known as the vertex?
(h, k)
Which expression is equivalent to xy2 + 2xy2 + 3xy?
A) 2xy2 + 3xy
B) 3xy2 + 3xy
C) 6xy4
D) 6xy5
B) 3xy2 + 3xy
Define sin, cosine, and tangent in terms of right triangles.
Sin = opp./hyp.
Cos = Adjacent/hyp.
Tan = opp/adj
Scientists estimate that the Pacific Plate, one of Earth's tectonic plates, has moved about 1,060 kilometers in the past 10.3 million years. About how far, in miles, has the Pacific Plate moved during this same time period?
(1 mile = 1.6 kilometers)
A) 165
B) 398
C) 663
D) 1696
C) 663
A line in the xy-plane passes through the origin and has a slope of 1/7. Which of the following points lies on the line?
A) (0, 7)
B) (1, 7)
C) (7, 7)
D) (14, 2)
D) (14, 2)
On Thursday, 240 adults and children attended a show. The ratio of adults to children was 5 to 1. How many children attended the show?
A) 40
B) 48
C) 192
D) 200
A) 40
Which of the following is equivalent to 16s4 - 4t2?
A) 4(s2 - t)(4s2 + t)
B) 4(4s2 - t)(s2 + t)
C) 4(2s2 - t)(2s2 + t)
D) (8s2 - 2t)(8s2 + 2t)
C) 4(2s2 - t)(2s2 + t)
In a right triangle ABC, sin of < C = 4/5
What is cos of C?
3/5
What is the volume of a right rectangular prism that has a length of 4 cm, a width of 9 cm, and a height of 10 cm?
360
Which of the following numbers is NOT a solution of the inequality 3x - 5 ≥ 4x - 3 ?
A) -1
B) -2
C) -3
D) -5
A) -1
On an architect's drawing of the floor plan for a house, 1 inch represents 3 feet. If a room is represented on the floor plan by a rectangle that has sides of lengths 3.5 inches and 5 inches, what is the actual floor area of the room, in square feet?
A) 17.5
B) 51.0
C) 52.5
D) 157.5
D) 157.5
g(x) = ax² + 24
For the function g defined above, a is a constant and g(4) = 8. What is the value of g(-4)?
A) 8
B) 0
C) -1
D) -8
A) 8
In right triangle ABC, B is the right angle. What is the greatest possible integer measurement of one of the acute angles?
89
The ratio of shirts to shorts to pairs of shoes in Kevin's closet is 5 : 2 : 3. If Kevin owns 10 shirts, how many pairs of shoes does he have to give away so that he ends up having the same number of shorts as he does pairs of shoes?
A) 1
B) 2
C) 4
D) 5
B) 2
b = 2.35 + 0.25x
c = 1.75 + 0.40x
In the equation above, b and c represent the price per pound, in dollars, of beef and chicken, respectively, x weeks after July 1 during last summer. What was the price per pound of beef when it was equal to the price per pound of chicken?
A) $2.60
B) $2.85
C) $2.95
D) $3.35
D) $3.35
A furniture store buys its furniture from a wholesaler. For a particular table, the store usually charges its cost from the wholesaler plus 75%. During a sale, the store charged the wholesale cost plus 15%. If the sale price of the table was $299, what is the usual price of the table?
A) $359
B) $455
C) $479
D) $524
B) $455
10
In a right triangle, sin x = 4/5.
What is cos(90 - x)?
4/5
Ahmad 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 Ahmad to husk 72 dozens ears of corn?
4, 5, or 6 hours
3s - 2t = a
-15s + bt = -7
In the system of equations above, a and b are constants. If the system has infinitely many solutions, what is the value of a?
7/5
County Y consists of two districts. One district has an area of 30 square miles and a population density of 370 people per square mile, and the other district has an area of 50 square miles and a population density of 290 people per square mile. What is the population density, in people per square mile, for all of County Y?
320
What are the solutions to the equation x2 - 3 = x?
A) (−1 ± √11) / 2
B) (−1 ± √13) / 2
C) (1 ± √11) / 2
D) (1 ± √13) / 2
D) (1 ± √13) / 2
30-60-90, and 45-45-90
(Ex: 1 side = x, other = 3x, other = 4x, etc)
30-60-90: Short leg: x Medium Leg: x sqrt 3 Hypotenuse: 2x
45-45-90: Both legs = x, hypotenuse = x sqrt 2
The total number of seats in an auditorium is modeled by f(x) = 2x2 - 6x, where x represents the number of rows of seats. How many rows are there in the auditorium if it has a total of 416 seats?
A) 32
B) 13
C) 20
D) 16
D) 16 (x-16)(x+13) factored form