Find the value of the indicated trigonometric function of the angle \theta in the figure. Give an exact answer with a rational denominator.
Find \sin(\theta).
\sin(\theta) =\frac{6\sqrt{85}}{85}
\sin(\theta) =\frac{\sqrt{85}}{6}
\sin(\theta) =\frac{\sqrt{85}}{7}
\sin(\theta) =\frac{7\sqrt{85}}{85}
Find the value of the indicated trigonometric function of the angle \theta in the figure. Give an exact answer with a rational denominator.
Find \cos(\theta).
\cos(\theta) =\frac{\sqrt{130}}{9}
\cos(\theta) =\frac{\sqrt{130}}{7}
\cos(\theta) =\frac{7\sqrt{130}}{130}
\cos(\theta) =\frac{9\sqrt{130}}{130}
Find the value of the indicated trigonometric function of the angle \theta in the figure. Give an exact answer with a rational denominator.
Find \tan(\theta).
\tan(\theta) =\frac{8\sqrt{39}}{39}
\tan(\theta) =\frac{5\sqrt{39}}{39}
tan(\theta) =\frac{\sqrt{39}}{8}
\tan(\theta) =\frac{5}{8}
In a right triangle with one of the acute angle's equal to \theta, if \sin(\theta)=\frac{\sqrt{5}}{3} and \cos(\theta)=\frac{2}{3}, find \tan(\theta).
\frac{\sqrt{5}}{2}
\frac{3\sqrt{5}}{5}
\frac{3}{2}
\frac{2\sqrt{5}}{5}
A building 230 feet tall casts a 80 foot long shadow. If a person is standing at the top of the building and looking down at the end of the shadow of the building, what is the angle made by the line of sight and the side of the building (to the nearest degree)? (Assume the person's eyes are level with the top of the building.)
71^{\degree}
19^{\degree}
70^{\degree}
20^{\degree}
A photographer points a camera at a window in a nearby building forming an angle of 42^{\degree} with the camera platform. If the camera is 52m from the building, how high above the platform is the window, to the nearest hundreth of a meter?
0.9m
46.82m
1.11m
57.75 m
A tree casts a shadow of 26 meters when the angle of elevation of the sun is 23^{\degree}. Find the height of the tree to the nearest meter.
13m
11m
10m
12m
A twenty-five foot ladder just reaches the top of a house and forms an angle of 41.5^{\degree} with the wall of the house. How tall is the house? Round your answer to the nearest 0.1 foot.
18.8 ft
19 ft
18.6 ft
18.7 ft
The perimeter of an equilateral triangle is 39 cm. Find the length of the altitude (height).
12\sqrt{2}
12
13
6.5\sqrt{3}
The length of an altitude (the height) of an equilateral triangle is 12 ft. Find the length of a side of the triangle.
12
16
64
8\sqrt{3}
Using your knowledge of special right triangles, find the length of y.
y=6
y=2\sqrt{6}
y=6\sqrt{2}
y=3\sqrt{2}
A rectangular garage has a volume of 480 m^3, a length of 12m and a width of 8m. What is the height of the garage?
6m
7m
4m
5m
Which set of dimensions belongs to a right rectangular prism with a volume of 440 cm^3?
6cm \times 12cm \times 5cm
7cm \times 9cm \times 6cm
8cm \times 5cm \times 11cm
12cm \times 2cm \times 5cm
A juice container shaped like a cylinder has a base area of 100 cm^2and can hold 1500cm^3 of juice. The height of the juice container is,
15cm
10cm
1.5cm
150cm
A compound solid is shown. You may assume any consecutive sides or faces are perpendicular. Using the provided measures, find the total surface area of the solid.
147 cm^2
98 cm^2
198 cm^2
206cm^2
The volume of a cone with a radius of 6cm and slant height of 10cm is:
96\pi cm^3
288\pi cm^3
360\pi cm^3
120\pi cm^3
The volume of a sphere with a radius of 3cm is:
9\pi cm^3
36\pi cm^3
72\pi cm^3
12\pi cm^3
The volume of this composite solid is:
1200 cm^3
1680 cm^3
1350 cm^3
960 cm^3
The area of this shape is closest to:
13.41 m^2
5.85 m^2
14.8 m^2
9.02 m^2
Find the area of the base of the pyramid. The base is a regular hexagon. Round to the nearest tenth.
249.4 in^2
432.0 in^2
374.1 in^2
187.1 in^2
Use the diagram to solve for x and y when the surface ares is 138.23 m^2.
x=10.8m, y=10.6 m
x=8m, y=7.7 m
x=9.8m, y=10m
x=20m, y=19.9 m
Find the surface area of the solid. The cylinder and cones are right. Round to the nearest tenth.
942.5 m^2
867.1 m^2
1168.7 m^2
1055.6 m^2
Find the circumference of the great circle if the volume of the sphere is 179.6 m^3. Round to the nearest tenth.
22 m
23.8m
26.6m
11m
Use the diagram of the solids to choose the statement below that is true about the given values.
The two values are equal
The value in column B is greater
The relationship cannot be determined from the given information
The value in column A is greater
Use the diagram of the solids to choose the statement below that is true about the given values.
The relationship cannot be determined from the given information
The two values are equal
The value in column B is greater
The value in column A is greater
Refer to the figure shown. What is the m\angle ABC?
80^{\degree}
240^{\degree}
100^{\degree}
120^{\degree}
Refer to the figure shown.
Given: \overline{CT} is a diameter of the cirlce shown; m \overset{\Large\frown}{AC}=50^{\degree}
Find the measure of \angle TCA
65^{\degree}
90^{\degree}
60^{\degree}
130^{\degree}
Refer to the figure shown. Circle \bigodot Ohas a radius of 6. RQ=9 and QT=12 (yes, \overline{QT} and \overline{QP} are tangent to \bigodot O). Find the exact value of segment \overline{OR}.
8
3\sqrt{3}
9\sqrt{5}
3\sqrt{5}
A ferris wheel has a diameter of 50 ft. How far will a rider travel during a 5-min. ride if the wheel rotates once every 30 seconds?
500\pi ft
400\pi ft
30\pi ft
5000\pi ft
What is the approximate sector area of a sector defined by minor arc \overset{\Large\frown}{BA}?
Givens:
- The center of the circle is point G
- m\angle AHB=61^{\degree}
- GB is 8 inches
8.5 in^2
68.1 in^2
34.1 in^2
17.0 in^2
If a clock's face measure 14 inches across, how much area is between the minute and hour hands at 5 o' clock? (Approximate pi to 3.14)
64.11 in^2
153.86 in^2
49.00 in^2
156.83 in^2
Area of a sector of a circle of radius 36 cm is 54\pi cm^2. The length of the corresponding arc of the sector is:
4\pi cm
2\pi cm
3\pi cm
5\pi cm
Use the below diagram to compare the two sectors shown (not drawn to scale). Based on the measures provided in the diagram which shaded region is larger?
There is not enough information to compare the 2 regions
Both regions have the same area
Region B is larger
Region A is larger
Convert the angle in degrees to radians. Express answer as a multiple of \pi.
144^{\degree}
\frac{3\pi}{4} radians
\frac{5\pi}{6} radians
\frac{4\pi}{5} radians
\frac{3\pi}{5} radians
Convert the angle in radians to degrees.
\frac{55\pi}{18}
550^{\degree}
1100\pi^{\degree}
10^{\degree}
275^{\degree}
Describe how an angle measure can be converted from degrees to radians,
Multiply the degree measure by \frac{\pi}{180^{\degree}}
Multiply the degree meausre by \frac{90^{\degree}}{\pi}
Multiply the degree measure by \frac{180^{\degree}}{\pi}
Multiply the degree measure by \frac{\pi}{360^{\degree}}
Write the equation of an ellipse with center (3,-3), and vertical major axis of length 12, and minor axis of length 6. Graph the ellipse.
Given a parabola has a focus at (-2,-2) and a directrix at y=-4, determine which of the below is a possible equation of the parabola described by these givens.
\frac{1}{4}(y-3)=(x-2)^{2}
4(y+3)=(x+2)^{2}
4(y-2)=(x-3)^{2}
\frac{1}{4}(x+2)=(y+3)^{2}
Identify the conic. If it is a parabola, give the vertex. If it is a circle, give the center and radius. If it is an ellipse or a hyperbola, give the center and foci.
11x^{2}-3y^2-88x+18y+116=0
hyperbola with center (4,-3) and foci at (-3\pm \sqrt{14},-4)
ellipse with center (4,3) and foci at (4,-3\pm \sqrt{14})
hyperbola with center (4,3) and foci at (4 \pm \sqrt{14},3)
ellipse with center (4,-3) and foci at (-4,3\pm \sqrt{14})
In a factory, a parabolic mirror to be used in a searchlight was placed on the floor. It measures 50 centimeters tall and 90 centimaters wide. Where should the filament be placed in the searchlight to acheive the brightest beam?
5 cm from the vertex
10.125 cm from the vertex
at the vertex
20.25 cm from the vertex
Express 8\sqrt{-84} in terms of i
16i\sqrt{21}
16\sqrt{21}
-16i\sqrt{21}
\sqrt{-5376}
Solve the equation 2x^{2}+18=0
x=\pm3i
x=\pm3+i
x=3\pm i
x=\pm3
Find the zeros of the function f(x)=x^{2}+6x+18
x=-3+3i or -3-3i
x=-6+3i or -6-3i
x=3i or -3i
x=-3+3i
Find the zeros of g(x)=4x^{2}-x+5 by using the Quadratic Formula
x=\frac{1}{8} \pm \frac{\sqrt{91}}{8}i
x=\frac{1}{8} \pm \frac{\sqrt{79}}{8}i
x=\frac{1}{2} \pm \frac{\sqrt{79}}{2}i
x=\frac{1}{8} \pm \frac{79}{8}i
Find the number and type of soltuions for x^{2}-9x=-8
Cannot determine without graphing
The equation has two real solutions
The equation has two nonreal complex solutions
The equation has one real solution
Subtract. Wirte the result in the form a+bi
(5 – 2i) – (6 + 8i)
7-2i
-3-8i
11+6i
-1-10i
Multiply 6i(4-6i). Write the result in the form a+bi.
-36+24i
36-24i
36+24i
-36-24i
Simplify -8i^20
-8
8
-8i
8i
Simplify 13i^{29}
-13
-13i
13
13i
Simplify \frac{-2+2i}{5+3i}
-\frac{2}{17}-\frac{8}{17}i
-\frac{2}{17}+\frac{8}{17}i
-\frac{2}{5}-\frac{8}{3}i
-\frac{2}{5}+\frac{2}{3}i
What expression is equivalent to (3-2i)^2
13-12i
13
9+4i
5-12i
Simplify the expression \sqrt[4]{256z^{16}}. Assume that all variables are positive.
4z^4
4z^11
z^{11}\sqrt[4]{256}
z^{4}\sqrt[4]{256}
Simplify the expression \sqrt[5]{32z^{15}}. Assume that all variables are positive.
z^{9}\sqrt[5]{256}
z^{3}\sqrt[5]{32}
2z^9
2z^3
Write the expression 8^{\frac{5}{3}} in radical form, and simplify.
(\sqrt[3]{8})^{5};32
(\sqrt[5]{8})^{3};3
\sqrt[5/3]{8};32
\frac{8^{5}}{8^{3}}; 64
Write the expression \sqrt[11]{10^{8}} by using rational exponents.
10^{\frac{8}{11}}
10^{-3}
10^{\frac{11}{8}}
10^3
Simplify the expression (27)^{\frac{1}{3}}\cdot(27)^{\frac{2}{3}}