10/3 which is the same as 3 1/3
70, Multiply 5 pieces by 12 friends and you get 60, then add the 10 pieces he originally took out, and you get 70
5(7)5x=60
35*5x=60
175x=60
x=60/175
x= 0.342
Enjoy and your answer is 0.342
Answers:
- Lateral Area = No lateral area (choice D)
- Surface Area = 25.97 square inches (choice E)
- Volume = 12.44 cubic inches (choice A)
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Explanation:
Lateral area only applies to prisms and cylinders. Spheres do not have lateral sides, so there is no lateral area.
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The radius is 1 & 7/16
Let's convert this to decimal form
1 & 7/16 = 1 + (7/16)
1 & 7/16 = 1 + 0.4375
1 & 7/16 = 1.4375
The radius is r = 1.4375 inches.
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SA = Surface area the sphere
SA = 4*pi*r^2
SA = 4*pi*(1.4375)^2
SA = 25.9672267773281
SA = 25.97 square inches (choice E)
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V = Volume of the sphere
V = (4/3)*pi*r^3
V = (4/3)*pi*(1.4375)^3
V = 12.4426294974698
V = 12.44 cubic inches (choice A)
Answer:
1. ΔXYZ is a right Δ with altitude YU.
Given
2. ΔXYZ ~ ΔYUZ
Right Triangle Altitude Similarity Theorem
3. VW || XY
Given
4. ∠VWZ ≅ ∠XYZ
Corresponding angles
5. ∠Z ≅ ∠Z
Reflexive property of congruence
6. ΔXYZ ~ ΔVWZ
AA Similarity postulate
7. ΔYUZ ~ ΔVWZ
Transitive property of similar triangles
Step-by-step explanation:
The first statement is given in the problem. Since we know the altitude of a right triangle, we can use the Right Triangle Altitude Similarity Theorem to say that the triangles formed by the altitude are similar to each other and the original triangle.
Next, we are given in the problem statement that the lines VW and XY are parallel. Therefore, ∠VWZ and ∠XYZ are corresponding angles, which makes them congruent. And since ∠Z is equal to itself (by reflexive property), we can use AA similarity to say ΔXYZ and ΔVWZ are similar.
Finally, combining statements 2 and 6, we can use transitive property to say that ΔYUZ and ΔVWZ are similar.
