Question:
A prism with a base area of 8 cm² and a height of 6 cm is dilated by a factor of 5/4 .
What is the volume of the dilated prism?
Enter your answer, as a decimal, in the box.
Answer:
The volume of the dilated prism is
Explanation:
A prism with a base area of 8 cm² and a height of 6 cm
The volume of the prism can be determined by the formula,
Volume of the prism is given by
Thus, the volume of the prism is
It is also given that the volume of the dilated prism is dilated by a factor of
Hence, the new volume is given by
Thus, the volume of the dilated prism is
Answer:
(a) false
(b) true
(c) true
(d) true
(e) false
(f) true
(g) false
(h) true
(i) true
Step-by-step explanation:
(a) 15 ⊂ A, since 15 is not a set, but an element, we cannot say of an element to be subset of a set. False
(b) {15} ⊂ A The subset {15} is a subset of A, since every element of {15}, that is 15, belongs to A.
15 ∈ {15} and 15 ∈ { x ∈ Z: x is an integer multiple of 3 } 15 is an integer multiple of 3. since 15/3=5. True
(c)∅ ⊂ A
∅ is a subset of any set. True
(d) A ⊆ A
A is a subset of itself. True
(e)∅ ∈ B
∅ is not an element, it is a subset, so it does not belong to any set. False
(f)A is an infinite set.
Yes, there are infinite integers multiple of 3. True
(g)B is a finite set.
No, there are infinite integers that are perfect squares. False
(h)|E| = 3
The number of elements that belong to E are 3. True
(i)|E| = |F|
The number of elements that belong to F are 3. So is the number of elements of E. True
For every loaf of bread there are 4 flour used
Answer:
PQ = 3.58, and RQ = 10.4
Step-by-step explanation:
We are given the hypotenuse of the triangle, and an angle. Use sin and cos to solve.
Hypotenuse = 11,
Opposite side is PQ
Adjacent side is RQ
x = 19
Sin x = (opposite side)/(hypotenuse)
Cos x = (adjacent side)/(hypotenuse)
For PQ, this is the side opposite to the angle, so use sin,
Sin 19 = x/11
11(Sin 19) = x
3.58 = x (rounded to the nearest hundredth)
For RQ, this is the side adjacent to the angle, so use cos,
Cos 19 = x/11
11(Cos 19) = x
10.4 = x (rounded to the nearest hundredth)