Answer:
The simplified expression of is 7² ⇒ C
Step-by-step explanation:
Let us revise some rules of exponent
Let us solve the question
∵ The expression is
→ By using the first rule above add the exponents of 7
∴ =
∴ =
→ By using the second rule above, subtract the exponents of 7
∵ =
∴ = 7²
∴ The simplified expression of is 7²
Volume of square pyramid can be calculated by the formula :
V=
a is the length of base and h is the height of the pyramid.
In the given figure a= x in.and h = in.
Volume of pyramid given V =486 cubic inches.
Substituting these values in volume of pyramid we have:
486= ÷ 3
Or 486=
486=
Multiplying both sides by 12
5832 =
Or x= 18 in.
Answer:
=====================================================
Reason:
Plot the points (0,0) and (r,s). You can place (r,s) anywhere you want.
Connect the two points mentioned and form a right triangle such that the segment from (0,0) to (r,s) is the hypotenuse of said right triangle.
The horizontal leg has a length of r-0 = r units, while the vertical leg will be 's' units.
Check out the diagram below.
We then apply the pythagorean theorem to say where h is the hypotenuse. Solving for h gets us
. We only focus on the positive square root since a negative hypotenuse makes no sense.
Since we made the hypotenuse the segment with endpoints (r,s) and (0,0), this means the hypotenuse length and the distance are the same thing.
Therefore, the distance from (r,s) to (0,0) is
As an alternative, you can use the distance formula to get the same answer. The distance formula is effectively the pythagorean theorem phrased a different way.
It's given in the question,
P, Q, V and K are collinear.
VP = 14x + 4
PK = x + 630
VQ = 17x + 6
KQ = 11x + 5
By segment addition postulate,
KQ + VQ + VP = KP
Substitute the values in the expression,
(11x + 5) + (17x + 6) + (14x + 4) = x + 630
(11x + 17x + 14x) + (5 + 6 + 4) = x + 630
42x + 15 = x + 630
42x - x = 630 - 15
41x = 615
x =
x = 15
Therefore, value of VP = (14x + 4)
= 14(15) + 4
= 214 units
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