Quadratics
x^2 - 5x - 6 = 0.
x = 6
f Triangle A is dilated by a scale factor of $k = 3$ to form Triangle B, how many times larger is the area of Triangle B compared to Triangle A?
9 times larger
In a right triangle, what is the trigonometric ratio for Sine (sin 0)?
opposite/ hypotenuse (SOH)
What is the simplified imaginary value of i^2
-1
What is the center and radius of the circle given by the equation (x - 4)^2 + (y + 2)^2 = 36?
Center: (4, -2), Radius: 6
What is the vertex of the quadratic function given in vertex form: f(x) = (x - 3)^2 + 5?
(3, 5)
Name the three primary triangle similarity theorems used to prove two triangles are similar without checking every side and angle.
AA, SAS,SSS
In a 45^\circ-45^\circ-90^\circ$ special right triangle, if the leg length is $5$, what is the exact length of the hypotenuse?
5/2
Simplify the expression: (3 + 2i) + (5 - 7i).
8 - 5i
Convert an angle of 180^\cir into radians.
pi radians
What formula is used to find the $x$-coordinate of the vertex for a quadratic equation in standard form ax^2 + bx + c = 0?
x = - b/2a
A 6-foot-tall man casts a 4-foot shadow. At the same time, a nearby flagpole casts a 20-foot shadow. How tall is the flagpole?
30 feet tall
In a 30^\circ-60^\circ-90^\circ special right triangle, if the hypotenuse is 12, what are the lengths of the shorter leg and the longer leg?
Shorter leg = $, Longer leg =6 / 3
Multiply and simplify the complex numbers: (2 + 3i)(2 - 3i).
13
If a central angle of a circle measures 60^\circ and the radius is 6 cm, what is the exact arc length intercepted by this angle?
2\pi cm
Use the discriminant (b^2 - 4ac) to determine the number and type of solutions for 2x^2 - 4x + 5 = 0.
(-4)^2 - 4(2)(5) = 16 - 40 = -24. Since it is negative
Line segment DE is parallel to base BC inside triangle ABC, cutting through sides AB and AC. If AD = 4, DB = 2, and AE = 6, what is the length of EC?
3
A ladder is leaning against a wall. The angle the ladder makes with the ground is 60^\circ$. If the ladder is 10feet long, how high up the wall does it reach? (Round to the nearest tenth).
8.7 feet
what is the value of i^3
-i
: What is the area of a sector of a circle with a radius of $4 inches and a central angle of 90^\circ
4\pi square inches
Solve the following equation using the quadratic formula: x^2 + 6x - 2 = 0.
x = -3
If two similar polygons have a scale factor ratio of a:b, what is the ratio of their volumes?
a^3:b^3
If tan^0 = frac{3}{4}$ in a right triangle, what is the value of cos^0
frac 3/4
what is the value of I^1
1
Write the equation of a circle in standard form given its general form equation: x^2 + y^2 - 6x + 8y = 0.
(x - 3)^2 + (y + 4)^2 = 25