Random 1
True or False ?
Is a triangle with sides of length 10 cm, 24 cm, and 27 cm a right triangle?
is not a right triangle bc 676 is not equal to 729
Which expression is always equivalent to sin(x) when 0°<x<90°?
A) cos(45°-x)
B) cos (90° -x)
C) Cos(y)+sin(x)=180°
D)Cos(y)-sin(x)=90°
B) cos (90° -x)
A right triangle has side lengths 8, 15, and 17. What is the tangent of the smallest angle in the triangle?
The tangent of the smallest angle is 8/15.
Square MATH has a side length of 7 inches. Which three-dimensional object will be formed by continuously rotating square MATH around side AT?
1) a right cone with a base diameter of 7 inches
2) a right cylinder with a diameter of 7 inches
3) a right cone with a base radius of 7 inches
4) a right cylinder with a radius of 7 inches
4) a right cylinder with a radius of 7 inches
For the acute angles in a right triangle, sin(4x)° = cos(3x + 13)°. What is the number of degrees in the measure of the smaller angle?
44°
A rectangular prism has a width of 10 cm, a height of 8 cm and a depth of 8 cm. What is the volume of the prism?
Jennifer is standing on a beach, gazing at the top of a lighthouse. Using her smartphone, she measures the angle of elevation to the top of the lighthouse as 34 degrees.
After some online research, she discovers that the lighthouse stands at a height of approximately 90 feet.
What is the horizontal distance from Jennifer to the base of the lighthouse? Round your answer to the nearest foot. Show all work and reasoning.
The horizontal distance from Jennifer to the base of the lighthouse is approximately 133 feet.
David is comparing two cones. The radius of the base of cone A is twice as large as the radius of the base of cone B. The height of cone B is twice the height of cone A. The volume of Cone A is
A) equal to half the volume of cone B
B) twice to volume of cone B
C) four times the volume of cone B
D) equal to the volume of cone B
B) twice to volume of cone B
The cross section of a regular pyramid contains the altitude of the pyramid. The shape of this cross section is a
1) circle 2) square 3) triangle 4) rectangle
3) triangle
Which statement about parallelograms is always true?
1) The diagonals are congruent.
2) The diagonals bisect each other.
3) The diagonals are perpendicular.
4) The diagonals bisect their respective angles.
2) The diagonals bisect each other.
Izzy is making homemade clay pendants in the shape of a solid hemisphere, as modeled below. Each pendant has a radius of 2.8 cm.
How much clay, to the nearest cubic centimeter, does Izzy need to make 100 pendants?
Izzy needs approximately 4594 cubic centimeters of clay to make 100 pendants.
When triangle ABC is dilated by a scale factor of 4, its image image is triangle A'B'C'. Which statement is NOT true. Explain your reasoning.
a) m<A=m<A'
b) AB/A'B' = CB/C'B'
c) 4(m<A)=m<A'
d) AB= 1/4 (A'B')
c) 4(m<A)=m<A' because dilation preserves angle measurement
A 15-foot ladder leans against a wall and makes an angle of 65° with the ground. What is the horizontal distance from the wall to the base of the ladder, to the nearest tenth of a foot?
The horizontal distance from the wall to the base of the ladder is approximately 6.3 feet.
Tom has a solid cement brick in the shape of a rectangular prism with a length of 6 inches, a width of 3.5 inches, and a height of 2.25 inches. If the cement weights 1.055 oz/in, how much does Dwight’s brick 4 weigh, to the nearest ounce?
50 ounce
A regular hexagon is rotated about its center. Which degree measure will carry the regular hexagon onto itself?
1) 45°
2) 90°
3) 120°
4) 135°
3) 120°
Which transformation does NOT always preserve distance?
A) (x, y) → (x + 2,y)
B) (x, y) → (−y,−x)
C) (x, y) → (2x, y − 1)
D) (x, y) → (3 − x,2 − y)
C) (x, y)→(2x, y−1)
Because Dilation does not always preserve distance
.
Rectangle RECT is dilated with a scale factor of 2 to produce image R'E'C'T'. What is the ratio of the area of RECT to the area of R'E'C'T'?
1/4
Right triangle TMR is a scalene triangle with the right angle at M. Which equation is true?
A) sinM = cos T
B) sinR = cosR
C) sinT = cosR
D) sinT = cos M
C) sinT = cosR
The expression cos 27° is equal to cos 63°.
TRUE OR FALSE?
False. cos 27° = sin 63°
A tent is in the shape of a right pyramid with a square floor. The square floor has side lengths of 8 feet. If the height of the tent at its center is 6 feet, what is the volume of the tent, in cubic feet?
The volume of the tent is 128 cubic feet.
Which regular polygon has a minimum rotation of 36° about its center that carries the polygon onto itself?
1) pentagon 2) octagon 3) nonagon 4) decagon
The regular polygon with a minimum rotation of 36° is a decagon.
A cone has a volume of 106π and a base diameter of 8. What is the height of the cone? round nearest degree.
height is 20
A quadrilateral must be a parallelogram if
1) one pair of sides is parallel and one pair of angles is congruent
2) one pair of sides is congruent and one pair of angles is congruent
3) one pair of sides is both parallel and congruent
4) the diagonals are congruent
3) one pair of sides is both parallel and congruent