math b

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 I=prt, which equation is equivalent to t?

I/pr=t

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)

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

Quadrant II

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

n>4

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

Which function is graphed below? mc002-1.jpg

f(x) = cos(x)

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

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

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

h=s/pir^2

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)

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

-2

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

0

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°

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

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

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

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

F(x)=6/x

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

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----->

n the triangle below, which is equivalent to sinA?

cosC

Which function is graphed below? mc001-1.jpg

f(x) = sin(x)

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 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

Which equation is equivalent to 4s=t+2

s=t+2/4

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

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.

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)

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

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

-5<=y<=5

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

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

160°

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

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

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

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

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

9 sq root 3

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

96 sq root 3 square centimeters

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.

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

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

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

f(4) + g(4)

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

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

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

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 value of mc005-1.jpg?

-2

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.

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

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

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

x2=36

What is 270° converted to radians?

3pi/2

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

sq root 2