math

Three trigonometric functions for a given angle are shown below. mc023-1.jpg What are the coordinates of point (x, y) on the terminal ray of angle mc023-2.jpg, assuming that the values above were not simplified?

(-5, 12)

If u(x)=-2x^2+3 and v(x)=1/x, what is the range of (u*v)(x)?

(-infinty,3)

The terminal side of an angle measuring pi/6 radians intersects the unit circle at what point?

(sq root3/2, 1/2

If f(x) = 3 - 2x and g(x)=1/x+5, what is the value of (f/g)(8)?

-169

If f(x) = x2 - 2x and g(x) = 6x + 4, for which value of x does (f + g)(x) = 0?

-2

What is the value of mc005-1.jpg?

-2

A Cepheid star is a type of variable star, which means its brightness is not constant. The relationship between the brightness of a Cepheid star and its period, or length of its pulse, is given by M = -2.78(log P) - 1.35, where M is the absolute magnitude, or brightness, of the star, and P is the number of days required for the star to complete one cycle. What is the absolute magnitude of a star that has a period of 45 days? Use a calculator. Round your answer to the nearest hundredth.

-5.95

If f(x)=sq rt(x)+12 and g(x)=2 sq rt2, what is the value of (f - g)(144)?

0

Kim solved the equation below by graphing a system of equations. mc020-1.jpg What is the approximate solution to the equation?

1.4

What is the value of log 43? Use the calculator. Round your answer to the nearest tenth.

1.6

If f(x) = 16x - 30 and g(x) = 14x - 6, for which value of x does (f - g)(x) = 0?

12

What is 3pi/4 radians converted to degrees? If necessary, round your answer to the nearest degree.

135°

Kalon has $175 and needs to save at least $700 for a new computer. If he can save $35 per week, what is the minimum number of weeks Kalon will need to save to reach his goal?

15 weeks

What is 5pi/6 radians converted to degrees? If necessary, round your answer to the nearest degree.

150°

Angle D has a measure between 0 and 360 and is coterminal with a -920° angle. What is the measure of angle D?

160°

What is the amplitude of the function below? mc007-1.jpg

2

What is the value of mc003-1.jpg?

2

On a unit circle, the vertical distance from the x-axis to a point on the perimeter of the circle is twice the horizontal distance from the y-axis to the same point. What is sinmc013-1.jpg? mc013-2.jpg

2 sq root 0.2

In a right triangle, cosa=0.352 and sina=0.936. What is the approximate value of tana?

2.659

Given that sin0=21/29, what is the value of cos0, for 0<! <90?

20/29

In a right triangle, angle A measures 20°. The side opposite angle A is 10 centimeters long. Approximately how long is the hypotenuse of the triangle?

29.2 centimeters

Which logarithmic equation is equivalent to 32 = 9?

2=log2(9)

If f(x) = 3x + 2 and g(x) = x2 + 1, which expression is equivalent to (f*g)(x)?

3(x 2 + 1) + 2

One leg of a right triangle measures 6 inches. The remaining leg measures mc016-1.jpg inches. What is the measure of the angle opposite the leg that is 6 inches long?

30

The intensity, or loudness, of a sound can be measured in decibels (dB), according to the equation mc026-1.jpg, where I is the intensity of a given sound and I0 is the threshold of hearing intensity. What is the intensity, in decibels, [I(dB)], when mc026-2.jpg? Use a calculator. Round to the nearest whole number.

320

If f(x) = x2 + 1 and g(x) = x - 4, which value is equivalent to (f*g)(10)?

37

What is the approximate degree measure of angle A in the triangle below? mc007-1.jpg

37.9

Which of the following are in the correct order from least to greatest?

38,pi/4,80, 7pi/6, 2pi

What is 270° converted to radians?

3pi/2

If s(x) = x - 7 and t(x) = 4x2 - x + 3, which expression is equivalent to (t*s)(x)?

4(x - 7)2 - (x - 7) + 3

Which of the following represents the measures of all angles coterminal with a 418° angle?

58 + 360n, for any integer n

The length of one leg of an isosceles right triangle is 3 ft. What is the perimeter of the triangle?

6+3sq root 2

What is the approximate length of arc s on the circle below? Use 3.14 for mc024-1.jpg. Round your answer to the nearest tenth. mc024-2.jpg

6.3 in

Manuel has $600 in a savings account at the beginning of the summer. He wants to have at least $300 in the account at the end of the summer. He withdraws $28 each week for food. Which inequality represents w, the number of weeks Manuel can withdraw money while not dropping below a $300 balance?

600-28w>=300

If g(x)=(x+1)/(x-) and h(x) = 4 - x, what is the value of (g*h)(-3)?

8/5

Each side of the regular hexagon below measures 8 cm. What is the area of the hexagon?

96 sq root 3 square centimeters

Keisha and David each found the same value for mc011-1.jpg, as shown below, given mc011-2.jpg.

Both procedures are correct.

Which of the following best explains why cos2pi/3 dont equal cos5pi/3?

Cosine is negative in the second quadrant and positive in the fourth quadrant.

If I=prt, which equation is equivalent to t?

I/pr=t

An angle whose measure is -302° is in standard position. In which quadrant does the terminal side of the angle fall?

Quadrant I

An angle whose measure is 40° is in standard position. In which quadrant does the terminal side of the angle fall?

Quadrant I

An angle whose measure is 92° is in standard position. In which quadrant does the terminal side of the angle fall?

Quadrant II

An angle that shares the same sine value of an angle that measures 5pi/4 radians is located where?

Quadrant IV

Francesca drew point (-2, -10) on the terminal ray of angle mc024-1.jpg, which is in standard position. She found values for the six trigonometric functions using the steps below.

She made her first error in step 3 because the sine, cosine, and tangent ratios are incorrect, which also results in incorrect cosecant, secant, and tangent functions.

Which of the following is true for f(x) = 5cos(x) +1?

The range of the function is the set of real numbers mc018-3.jpg.

The final velocity, V, of an object under constant acceleration can be found using the formula mc009-1.jpg, where v is the initial velocity (in meters per second), a is acceleration (in meters per second), and s is the distance (in meters). What is the formula solved for a?

V^2-v^2/2s=a

Which expression is equivalent to (f + g)(4)?

f(4) + g(4)

Which function is graphed below? mc002-1.jpg

f(x) = cos(x)

Which function is graphed below? mc001-1.jpg

f(x) = sin(x)

For which pairs of functions is (f*g)(x)=x?

f(x)=2/x and g(x)=2x

Grayson charges $35 per hour plus a $35 administration fee for tax preparation. Ian charges $45 per hour plus a $15 administration fee. If h represents the number of hours of tax preparation, for what number of hours does Grayson charge more than Ian?

h<2

Which of the following equations is equivalent to s=pir^2h

h=s/pir^2

Which expression can be used to approximate the expression below, for all positive numbers a, b, and x, where a mc001-1.jpg 1 and b mc001-2.jpg 1? loga(x)

logb(x)/logb(a)

A taxi service charges a flat fee of $1.25 and $0.75 per mile. If Henri has $14.00, which of the following shows the number of miles he can afford to ride in the taxi?

m<=17

What are the values of m and mc012-1.jpg in the diagram below? mc012-2.jpg

m=sq root3/2 0=pi/6

Which of the following is true of the location of an angle, mc025-1.jpg, whose tangent value is -sq root3/3?

mc025-3.jpg has a 30-degree reference angle and is located in Quadrant II or IV

Six times a number is greater than 20 more than that number. What are the possible values of that number?

n>4

Which graph shows the solution set of the inequality 2.9(x+8)<26.1

open circle starting at 1<------

Which expression converts pi/4 radians to degrees?

pi/4*180/pi

Which values for mc017-1.jpg have the same reference angles?

pi/4,3pi/4,7pi/4

A circle has a central angle of 6 radians that intersects an arc of length 14 in. Which equation finds the length of the radius, r, of the circle?

r=14/6

Which set of transformations is needed to graph f(x) = -2sin(x) + 3 from the parent sine function?

reflection across the x-axis, vertical stretching by a factor of 2, vertical translation 3 units up

Which expression is equivalent to (st)(6)?

s(6) × t(6)

Which equation gives the length of an arc, s, intersected by a central angle of 3 radians in a circle with a radius of 4 in.?

s=4*3

Gavin wrote the equation mc004-1.jpg to represent p, the profit he makes from s sales in his lawn-mowing business. Which equation is solved for s?

s=4p-300/3

If cos0=0.3090, which of the following represents approximate values of sin0 and tan0 , for mc008-4.jpg?

sin0=0.9511 tan0=3.0780

Which Pythagorean identity is correct?

tan^2(0)+1=sec^2(0)

Which description best explains the domain of (g*f)(x)?

the elements in the domain of f(x) for which g(f(x)) is defined

What is the domain of f(x) = cos(x)?

the set of all real numbers

What is the range of f(x) = sin(x)?

the set of all real numbers -1<=y<=1

Cary calculated the surface area of a box in the shape of a rectangular prism. She wrote the equation mc023-1.jpg to represent the width and height of the box. She solved for w and got mc023-2.jpg Which of the following is an equivalent equation?

w=(148-12h)/(12+2h)

Paolo wrote the following equation for the perimeter of a rectangle. p=2(1+w) Which equation is equivalent to the equation Paolo wrote?

w=p-2l/2

The point P(x, y) lies on the terminal side of an angle mc014-1.jpg = -60° in standard position. What are the signs of the values of x and y?

x is positive, and y is negative.

Which equation is equivalent to logx(36)=2?

x2=36

Which represents the solution set of 5(x+5)<85

x<12

Which represents the solution set of the inequality 5x-9<=21

x<=6

Remmi wrote the equation of the line mc021-1.jpg He solved for x and got mc021-2.jpg Which of the following is an equivalent equation for x?

x=3(y-2/3)

Which of the following is true of the values of x and y in the diagram below? mc010-1.jpg

y/x=1

Which is the solution set of the inequality 15y-9<36

y<3

Which function describes the graph shown below? mc009-1.jpg

y=1/2sin(x)-2

If (z*z)(x)=(1/16)x, what is z(x)?

z(x)=x/4

What is the range of y = -5sin(x)?

-5<=y<=5

In the triangle below, angle B measures 60° and BC is 18. What is the length of AC?

9 sq root 3

If g(x) = 2x and (f*g)(x)=3/x, what is f(x)?

F(x)=6/x

If c(x)=5/x-2 and d(x) = x + 3, what is the domain of (cd)(x)?

all real values of x except x = 2

The formula mc011-1.jpg gives the partial sum of an arithmetic sequence. What is the formula solved for an?

an=(2s-21n)/n

Which graph represents the solution set of the inequality x+2>=6

closed dot start @4----->

The point (-sq root2/2,sq root2/2) is the point at which the terminal ray of angle mc021-2.jpg intersects the unit circle. What are the values for the cosine and cotangent functions for angle mc021-3.jpg?

cos=-sq root2/2 cot=-1

n the triangle below, which is equivalent to sinA?

cosC

Which equation is equivalent to 4s=t+2

s=t+2/4

Given that tan0=-1, what is the value of sec0, for 3pi/2<0<2pi?

sq root 2