If two triangles are congruent, then they have equal corresponding angles and also the sides.
Therefore, if GHI is congruent to LMN, then GH =LM, HI=MN and GI=LN, and also angle G=angle L, Angle H=angle M, while angle I = angle N, therefore the correct answers is a) ∠M= ∠H, c) ∠L=∠G. and e)IH=NM.
First, calculate for the volume of the cube before each edges are cut.
V = e³
where e is the length of each sides. Substituting the known value,
V = (4/5 cm)³ = 0.512 cm³
Then, calculate for the volume of each of the small cubes cut out from the corners.
V = (1/5 cm)³ = 0.008 cm³
Since there are 8 of these small cube, we multiply the volume by 8.
8V = 8(0.008 cm³) = 0.064 cm³
Then, subtracting the volumes will give us an answer of <em>0.448 cm³</em>
The height of the project becomes zero when it hits the ground which is also the total time at which the projectile stays in the air. Equating the function to zero:
-10(x)(x - 4) = 0
The roots of this quadratic equation are:
x = 0, and x=4
Therefore, the projectile stays in the air for
4 seconds
See attached picture and check solution below.
We are given with the following values:
A = length of transmission line = 96ft
B = length of shadow = 72 feet
C = distance of ladder to base of transmission line = 66 feet
Solve for angle created between the wire and tip of the shadow:
tan x = opposite/ adjacent
tan x = 96 feet / 72 feet
x = 53.13°
Solving for the height of the ladder:
tan x = Ladder length / (72-66)
tan 53.13° * (72-66) = ladder length
ladder length = 8 feet
The answer is letter "B" which is 8 feet.
Let us say that the intersection point of lines
AB and CD is called point E. The lines AB and CD are perpendicular to each
other which also means that the triangle CEB is a right triangle.
Where the line CB is the radius of the circle
while the side lengths are half of the whole line segment:
EB = 0.5 AB = 0.5 (8 ft) = 4 ft
CE = 0.5 CD = 0.5 (6 ft) = 3 ft
Now using the hypotenuse formula since the
triangle is right triangle, we can find for the radius or line CB:
CB^2 = EB^2 + CE^2
CB^2 = (4 ft)^2 + (3 ft)^2
CB^2 = 16 ft^2 + 9 ft^2
CB^2 = 25 ft^2
<span>CB = 5 ft = radius</span>
