Answer: X = 27
Step-by-step explanation: If we observe very closely, we have two similar triangles in the diagram. The first one is ABC and the other triangle is EDC. Also take note that angle ACB in the first triangle is equal in measurement to angle ECD (45 degrees) in the other triangle, (Opposite angles).
Hence in triangle ECD, we have identified two angles so far which are angle 2x + 10 and angle 45. Same applies to triangle ABC, we already have two angles which are, 3x - 10 and 45.
However angle D in the second triangle is equal in measurement to angle B in the first triangle
(Alternate angles).
Hence we have a third angle in triangle ABC which is
Angle B = 2x + 10.
Therefore 3x - 10 + (2x + 10) + 45 = 180
(Sum of angles in a triangle)
3x - 10 + 2x + 10 + 45 = 180
By collecting like terms we now have
3x + 2x = 180 + 10 - 10 - 45
5x = 135
Divide both sides by 5,
x = 27
Answer:
The percent for 3 out of 12 is 25%
If the total number of games was 100, the win amount would need to be 25.
Step-by-step explanation:
3 out of 12 is a fraction - 3/12
3/12 = 0.25 which means 25% because 0.25 is 25% of 1.
Using the same percentage for 100 total games, you just multiply 100 by 0.25, the decimal version of the percentage.
Answer:
96
Step-by-step explanation:
Answer:
m<CDE=66 degrees.
Step-by-step explanation:
(1) Extend the segment DC so it intersects with line BA. Call the intersection F.
(2) Consider triangle BCF. In here, we are given m<ABC=24 deg. Since m<BCD = 90 deg, we known that m<BCF = 90 deg. Knowing two angles in the triangle BCF lets us determine the rhird angle m<BFC = 180-90-24 = 66 deg.
(3) Because of the fact that AB || DE and the fact that line DF intersects AB and DE, the angles <BFC and <CDE are congruent. Therefore m<CDE=66 deg.
Answer:
33.5 cubic inches.
Step-by-step explanation:
If the softball fits perfectly inside the cubical box, the softball is a sphere with diameter of 4 inches (radius os 2 inches).
The volume of a sphere is given by:
For r = 2 inches:
The volume of the softball is 33.5 cubic inches.
