Heart of Algebra
The graph of y=f(x) is a line in the xy-plane that passes through the point (0,2) and has a slope of 5. Which of the following equations could define the function f?
A. f(x) = -1/2x + 5
B. f(x) = -1/5x + 2
C. f(x) = 2x + 5
D. f(x) = 5x + 2
What is D. f(x) = 5x + 2 ?
Hongbo sold x cell phones in 2013. The number of cell phones he sold in 2014 was 128% greater than in 2013, and the number of cell phones he sold in 2015 was 29% greater than in 2014. Which of the following expressions represents the number of cell phones Hongbo sold in 2015?
A) (0.29)(1.28x)
B) (0.29)(2.28x)
C) (1.29)(1.28x)
D) (1.29)(2.28x)
What is D) (1.29)(2.28x)?
(11x-33)/(x-3)=x.
What is the solution to the equation above?
What is 11?
The two acute angles of a right triangle have degree measures of x and y. If sin x=5/13, what is the value of cos y?
What is 5/13?
In the xy-plane, line m has a slope of 2. If line n is perpendicular to line m, which of the following could be an equation of line k?
A. -10x-5y=20
B. 3x-6y=14
C. 4x-2y=17
D. 6x+12y=36
What is D. 6x+12y=36?
Anita created a batch of green paint by mixing 2 ounces of blue paint with 3 ounces of yellow paint. She must mix a second batch using the same ratio of blue and yellow paint as the first batch. If she uses 5 ounces of blue paint for the second batch, how much yellow paint should Anita use?
A. Exactly 5 ounces
B. 3 ounces more than the amount of yellow paint used in the first batch
C. 1.5 times the amount of yellow paint used in the first batch
D. 1.5 times the amount of blue paint used in the second batch
What is D. 1.5 times the amount of blue paint used in the second batch?
5(x+a) + 3(x2-a) = 3x2+5x+4. In the equation above, a is a constant. If the equation is true for all values of x, what is the value of a?
What is 2?
Triangle ABC and triangle DEF are similar triangles, where AB and DE are corresponding sides. If DE = 2AB and the perimeter of triangle ABC is 20, what is the perimeter of triangle DEF?
What is 40 ?
If ax+a=3, where a is a nonzero constant, which of the following must be equal to x+1?
A. 3
B. a
C. 3a
D. 3/a
What is D. 3/a?
Kelly enlarged the area of a photograph to 250% of its original size. The original domensions of the photograph were 5 inches by 7 inches. What is the area of the enlarged photograph, in square inches?
A. 71.25
B. 87.5
C. 218.75
D. 3000
What is B. 87.5?
y = -16t2+64t+80
The equation above gives the height of an object above the ground, y, in feet, t seconds after it is launched from a platform. How many seconds after it is launches does the object reach the ground?
What is 5 ?
In a right triangle, the tangent of one of the two acute angles is √ 3/3. What is the tangent of the other acute angle?
What is 3/√ 3?
2(x+b) = ax + c
In the equation above, a, b, and c are constants. If the equation has infinitely many solutions, which of the following must be equal to c?
A) a
B) b
C) 2a
D) 2b
What is D) 2b?
If a is the mean and b is the median of nine consecutive integers, what is the value of | a-b | ?
What is 0?
If 4x2+bx+9=0, where b is a constant, has exactly one solution, what is a possible value of b?
A) 72
B) 36
C) 12
D) 6
What is C. 12?
In the xy-plane, the points (2,4) and (-2, -4) are the endpoints of a diameter of a circle. Which of the following is an equation of the circle? (Hint: sketch the circle to make inferences about the center and radius)
A) (x-2)2+(y+4)2=80
B) (x-2)2+(y+4)2=20
C) x2+y2=80
D) x2+y2=20
What is D) x2+y2=20
In the xy-plane, line k intersects the y-axis at the point (0,-6) and passes through the point (2,2). If the point (20,w) lies on line k, what is the value of w?
What is 74?
The number y is 20% greater than the number x. The number z is 20% less than y. The number z is how many times x?
What is 0.96? or What is 24/25?
In the xy-plane, the graph of y=x2+bx+c, where b and c are constants, has x-intercepts at x=-2 and x=-6. What is the value of b?
What is 8?
(x-6)2 + (y-3)2 = 25
The graph in the xy-plane of the equation above is a circle. If the circle is translated downward a units such that the circle is tangent to the x-axis, the equation becomes (x-6)2+(y-3+a)2=25. What is the value of a?
Hint: sketch the circle
What is 8 ?