Math

An inscribed angle in a circle intercepts an arc that measures 78 degrees. What is the measure of the inscribed angle?

39 degrees

A circle's equation is x2 + 8x - 10y + y2 = - 6. By how many units right or left, and up or down has this circle been transformed compared to the parent function x2 + y2 = 35?

4 left and 5 up

If the diagonals of a rhombus are of lengths 12 cm and 16cm, what is the perimeter of the rhombus?

40 cm

Angle CBA is inscribed in circle O, and segment BC is a diameter. If the measure of angle CBA is 70 degrees, what is the measure of arc AB?

40 degrees

The acute angles of a right triangle measure 2x - 4 degrees and 2x - 2 degrees. What is the measure of the smaller of these two angles?

44 degrees

Line AB is tangent to circle O at point A. If segment AB = 10 and segment AO = 5, find the length of segment OB.

5 5

If Jamal can chop the weeks' firewood in 3 hours, and working together with Christa they can complete the job in 2 hours, how long will it take Christa to do the job if she works alone?

6 hours

If 4a/9b = 2x/5y, in simplest form, what is the ratio of y to x?

9b/10a

(Math Calculation): Express the range of the following function using specific interval notation: f(x) = x 1+ 3

(-∞, 0 ) ∪ (0, ∞)

Find the points where the line y = x - 3 intersects the circle whose equation is x2 + y2 = 9.

(3, 0) and (0, -3)

The expression │2X - 1 │≤ 9 is equivalent to which mathematical conjunction?

- 4 ≤ X ≤ 5

Find the exact value of tan (-13π/4).

-1

What is the value of "k" such that a line containing the points (-3, k) and (4, 8) is parallel to a line containing the points (5, 3) and (1, -6)?

-7.75 or -31/4 or -73/4

How many solutions will triangle ABC have under the following conditions? Measure of angle A is 60 degrees, side length a = 10 3 , and side length b = 20

1

The lengths of the sides of a triangle are 5, 6, and x. Between which two integers must x lie?

1 and 11

For what value of "k" will the trinomial x2 - 8x + k be transformed into a perfect square trinomial?

16

What value must be added to the following quadratic equation in order to complete the square? 4x2 - 14 = x

1/64

Points A and B lie on a circle with a center at point C. Angle ACB measures 120 degrees and the length of segment BC is 6 centimeters. What is the area of sector ABC?

12π square cm

For planting new flowering shrubs, a gardener uses a special mixture of soil,that contains sand, peat moss, and humus in the ratio of 2:5:3. How many pounds of humus will she need to add if she uses 3 ten pound bags of peat moss?

18 pounds

Determine the number of roots, and describe as real or complex, for the quadratic equation 2x2 - 4x = -3.

2 complex (roots

In Triangle ABC, the length of side b is 10 cm, the length of side c is 8 cm, and the sine of angle A is 0.5. Find the area of triangle ABC.

20 square units [From 1⁄2 (8)(10)(0.5)]

If a profit function is expressed by the equation P(x) = - 1500 + 80 x - 0.2x2, where x is the number of items sold, what is the number of items the company needs to sell in order to maximize profit?

200

For 0° ≤ θ ≤ 360°, for what value of θ [Read: theta] is sin θ = 32- , and cos θ ≤ 0?

240 degrees

The wheel of a truck is turning at 6 rps (revolutions per second), and the wheel is 4 feet in diameter. In terms of π what is the linear velocity V, in feet per second, of a point on the rim of the wheel?

24π feet per second

In a polygon of nine sides, how many distinct diagonals can be drawn?

27

Find the first derivative of y = sinx 2 + sin2x [Read: y = sine of x squared plus sine squared x.]

2x Cosine x2 + 2 Sine x Cosine x

For the polynomial function f(x) = x3 + 2x2 + 5x + 2, what is the maximum number of negative real zeros possible according to Descartes Rule of Signs?

3

If the logarithm of 1.51 is 0.1761, what is the value of the logarithm of 1,510?

3.1761

For the rational function r(x) = 3 x5 x 1 7 -- what is the limit as x approaches positive infinity?

3/5 or y = 3/5

The perimeter of a triangle is 120 cm and the sides are in the ratio of 5:6:9. Find the length of each side.

30 cm, 36 cm, and 54 cm

In square units, what is the area of an equilateral triangle, with a side length of 6 units

9 3 (square units)

The obtuse vertex angle of an isosceles triangle measures 4 more than 2 times the measure of each base angle. What is the measure of the vertex angle of this triangle?

92 degrees

For the following data set, identify the first and third quartiles: 8, 1, 3, 7, 5, 2, 16

First quartile: 2; Third quartile 8

Data is collected at a regional university that relates the number of hours of video games played per day, x, to a college student's semester GPA, y. Based on the data, the linear regression equation or line of best fit ŷ = -0.34x + 2.97 [Read "y hat"] is obtained. Interpret the slope of this linear regression line.

For each additional hour of video games played per day, the semester GPA drops 0.34 points.

Which ratio, equal to the quantity 51+ 2 is sometimes referred to as the "divine proportion", and provides an aesthetically pleasing outcome when applied in art and architecture?

Golden (ratio)

Identify the 1st century Mathematician who devised a method of calculating the area of a triangle using the known side lengths and semi-perimeter of the triangle.

Heron (Also accept Hero.)

Among mathematicians, which one who lived circa 190 - 120 BCE is considered the "Father of Trigonometry" because of his calculations of distances between the stars using triangles?

Hipparchus

This Greek scholar and teacher of the 4th century is revered as the first female Mathematician, but met a violent death in a city-wide uprising at Alexandria in 415 CE. Who was this Mathematician and head of the Neoplatonic School at Alexandria?

Hypatia

n which two quadrants will cot θ [Read: cotangent theta] and sec θ [Read: secant theta] have opposite signs?

III, IV

Given that f(x) = x 3 is a function, determine if it is one-to-one, and if it is "onto" (or surjective).

It is one to one; it is "onto"

With what type of concurrent lines in a triangle is the circumcenter associated?

Perpendicular Bisectors

French mathematician Jules Henri Poincaré was the first to define this branch of mathematics that describes different families of equivalent figures such as a coffee cup, a donut, and the numeral zero. Identify this branch of mathematics that focuses on figures that can be stretched, bent, or molded into similar shapes.

Topology

For the polar equation r = 4 + 4 cos θ, what is the most descriptive name for this graph?

cardioid (Prompt on "limacon.")

While a lemma precedes a mathematical proof, what type of statement that can be easily proven follows a theorem to which it is closely related?

corollary

Identify the type of Mathematical processes that focus on modeling the behavior of non-continuous phenomena, such as algorithms, or other countable systems, including those used in Computer Science andterm-0 Statistical Analysis.

discrete

For the vectors (a,b) and (c,d), what quantity is represented by the number " ac + bd"?

dot product

How many sides are found in a regular polygon if one of its exterior angles measures 108 degrees?

five (pentagon)

What adjective is used in Geometry to describe a circle on the surface of a sphere that lies in a plane passing through the sphere's center?

great (circle

Which conic section is defined as the locus of points in a plane whose distances to two fixed points in a plane have a constant difference? The axes of this graph bisect the angles between the asymptotes.

hyperbole

Re-state the following expression as a single logarithm: log48 + log43 - log42.

log412

If the three sides of a triangle measure 5 meters, 6 meters, and 8 meters, classify this triangle according to its angle measure.

obtuse

The path of a comet has the equation r = 2 1 sinθ - . What is the shape of the curve this comet will trace out in space?

parabola

In a regular dodecahedron, what polygon forms each face?

pentagon

When writing a mathematical proof of a bi-conditional statement, the proof must include two parts: one proof for the original statement, and one for which other conditional?

the converse

If 10 + 5iy = 2 x + 20i what are the values of x and y?

x = 5 and y = 4

Identify both solutions of the following equation: |3x - 2| = 19 [Read: the absolute value of the quantity 3x minus 2 equals 19].

x = 7 and x = -17/3 (or -5 2/3)

Solve the following equation for x: 4x = 128. Express your answer as an improper fraction in simplest form.

x = 7/2

Multiply and simplify the product of the three binomials (x - 5) (x + 6) (x + 5), and express your answer in descending powers.

x3 + 6x2 - 25x - 150

Give the equation(s) of and identify the type (s) of asymptotes associated with the exponential function y = 2-x .

y = 0 is a horizontal asymptote

The lengths of the sides of a triangle are z, z + 3, and z + 6. Express the value of z as an inequality.

z > 3