Algebra 1
Solve for p
3p-7 = 14
Solve the following absolute value equation for x:
|2x-5| = 11
X = 8
X = -3
In a right triangle, sinθ = ⅘. What is the value of tanθ
4/3
A ball’s height is modeled by h(t)=-t2+6t+7 where t is the time in seconds and h is the height in feet.
What is the maximum height of the ball?
16 ft
A rectangle has a width that is 3 inches less than twice its length. If the area of the rectangle is 35 square inches, what is its length?
5 inches
Solve for b:
5(b+2) = 3x-4
Solve the radical equation for x. Be sure to check for extraneous solutions:
√3x+1 = x-3
x=8
A zip wire runs between two posts, 25m apart. The zip wire is at an angle of 10∘ to the horizontal. Calculate the length of the zip wire
25.4m
Solve the compound inequality: (x-2)(x+4)<0
-4<x<2
Points A and B lie on a circle with the center 0. If the measure of the central angle ∠AOB is 120°, what is the measure of the inscribed angle ∠ACB where point C lies on the major arc of the circle?
60
Write the equation of a line in slope-intercept form (y = mx + b) that has a slope of 3 and passes through the point (0,-2)
y=3x-2
Simplify the complex expression and write the answer in standard form
(a+bi)
(4-3i)(2+5i)
23+14i
If cscθ = 13/5 and θ is an acute angle in a right triangle, what is the value of cosθ?
12/13
Multiply and simplify: (x+3)(x2-2x+4)
x^3+x^2-2x+12
A circle in the xy-plane is defined by the equation x^2 + y^2 - 6x + 8y = 11. What is the radius of the circle?
Find the slope of the line that passes through the points (2,5) and (4,11)
m=3
Solve the quadratic equation by completing the square or using the quadratic formula:
2x²-4x+7=0
x= (2(+/-)isqrt(10)/2)
Write 4sin(60) + 3tan(60) in the form a(sqrt k)
5sqrt3
Determine whether the statement is always true, sometimes true, or never true: x2-2x+40. Explain your reasoning.
Can be rewritten as: (x-2)20. Since any # squared is greater than or equal to zero, the statement is always true.
A right circular cylinder has a radius of 3 cm and a height of 10 cm. What is its volume in cm^3?
90pi
Tickets for a local concert cost $5 for active students, and $8 for each adult. A total of 150 tickets were sold bringing in a total revenue of $900. Write and solve a system of equations to find exactly how many student tickets and how many adult tickets were sold.
ST=100
AT=50
An investment of $5000 is placed in an account that earns an annual interest rate of 4.5% compounded continuously. The formula for continuous compounding is A = Peʳᵗ
Write the specific function that models the value of the investment over time t (in years), and calculate the total amount in the account after 8 years. (Round to nearest cent)
(A(t) = 5000e^{0.045t}\).
7,166.65
In the right triangle ABC, angle C is the right angle. If cosA = sqrt3/2 What is the value of sinB?
20sqrt3
Solve for x: x^4-5x^2+4=0
x=1,2
A circle has a center at 2, -3 and passes through point 5,1. Which of the following is the equation of the circle?
(x - 2)^2 + (y + 3)^2 = 25