Find the length of CD and BF given a square ABCD with straight lines AFD, BFE, and CDE, where DF=6cm and EF=10cm. CD=(6)2+(10)2=100=10cmBF=(6)2−(10)2=4=2cm
Find the surface area of a rectangular-based prism with dimensions x−2, x−2, and x. Expand, simplify, and factor the surface area formula. Determine the surface area when x=10cm.
Yusuf uses a mirror to measure the height of his school building. He walks 13.95 m, places a mirror with an X, steps 2.15 m, and his eye height is 1.35 m. Find the school's height rounded to the nearest hundredth of a meter.
Find the area in square inches of a scale drawing of a classroom floor that is 34 ft long and 36 ft wide, if the scale drawing has a length of 17 inches.
Find the slope of a 120-inch waterslide with a 56-inch height for children's play. Simplified problem statement: What is the slope of a waterslide with a run of 120 inches and a height of 56 inches?
Identify the property that justifies each statement: a) If 2x=y and y=7, then 2x=7. b) If ∠X≅∠P and ∠P≅∠D, then ∠X≅∠D. c) m∠DEF=m∠DEF. d) If ST=XY, then XY=ST.
Find the radius of a sphere with a surface area of 324πcm2, given the formula surface area=4πr2, where r is the radius. Round your answer to 1 decimal place.
Find the total volume of Tyler's two cube-shaped storage spaces, where the small space has volume 12ft3 and the side length of the large space is s (ft).
Find the equation of the line containing side BP in a parallelogram where the opposite sides have the same slope, given the equation of the line containing side DQ is y−7=5(x+4).
Choose 3 true statements: 1) The centroid is the concurrency of a triangle's altitudes. 2) The incenter is the concurrency of a triangle's angle bisectors. 3) The circumcenter is the concurrency of a triangle's perpendicular bisectors and is equidistant from the vertices.
Bestimme die Innenwinkel eines Dreiecks mit gegebenen Winkeln. Gib die längste Seite an.
a) α=43∘;β=65∘
b) α=40∘;β=90∘
d) α=90∘;β=γ
e) β=2α;γ=3α
c) β=γ=60∘
Fill in the table for side length and area of different squares. Is the relationship between side length and area proportional? 3 cm, 100 cm, 25 cm, s cm,
Find the central angle (in degrees) for the Drums sector in a circle graph displaying the number of students playing instruments: Drums 8, Trumpet 11, Guitar 9, Violin 8.
Find the measure of angle D in a parallelogram with m∠B=5x and m∠C=2x+12. Answer: m∠D=180−5x−(2x+12)=180−7x−12. To check, sum the angles of a parallelogram is 360 degrees.
Find the side length of the largest square tile that can cover a 15in. high and 24in. rectangular wall, where the tile side length must divide both height and width.
Determine how many rectangular prism-shaped concrete bricks a company made given the brick dimensions and total concrete volume used. 13 in×5 in×4 in brick dimensions, 11,700in3 concrete volume.
Find the percent of Container A that is full after pumping water into Container B until it is completely full. Container A has radius 13 ft and height 18 ft. Container B has radius 11 ft and height 20 ft.
A rectangular metal piece is 25 in longer than its width. Cutting 5 in squares from the corners and folding the flaps up forms a 1120in3 open box. Find the original width and length.
Find the area of a pizza slice with a central angle of 23∘ from an 18-inch diameter pizza. The area is approximately □ square inches (rounded to two decimal places).
Find the slopes of 3 lines passing through given points, then determine if each pair of lines is parallel, perpendicular, or neither. Slope of Line 1 = 0−(−5)1−(−2)=53
Slope of Line 2 = 5−(−5)−4−0=10−4=−52
Slope of Line 3 = 3−01−6=3−5 Line 1 and Line 2: Perpendicular
Line 1 and Line 3: Neither
Line 2 and Line 3: Perpendicular
Arch is a parabola with 640 ft span and 32 ft max height. Find equation and height 92 ft from center.
y=−0.0003125x2+32∨x2=−3200(y−32)
Height 92 ft from center is 20.58 ft.