Answer:
24s^2, 54s^2, 96s^2
Step-by-step explanation:
Let s represent the initial side length of the cube. Then the area of each face of the cube is A = 6s^2 (recalling that the area of a square of side length s is s^2).
a) Now suppose we double the side length. The total area of the 6 faces of the cube will now be A = 6(2s)^2, or 24s^2 (a 24 times larger surface area),
b) tripled: A = 6(3s)^2 = 54x^2
c) quadrupled? A = 6(4s)^2 = 96s^2
Answer: She can use 4 gigabyte while remaining in her budget.
Step-by-step explanation:
You would first subtract 54 from 70 which leaves you with 16,
Then you would divide 16 by 4 to find how many gigabytes she could use which gives you 4
So she can use 4 gigabyte while remaining in her budget.
Learn more about basic mathematics operations here
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Answer:
-3.5 ( or -7/2)
Step-by-step explanation:
we can substitute the point into this function to find out the answer
that is:
4 = m*(-2) -3
7 = m*(-2)
m = 7 / (-2)
m = -3.5
5*4 equals 20 so her wall is 20 square meters
Given that one litre can cover 10 square meters, she needs 2 litres of paint to cover the wall
There is a not so well-known theorem that solves this problem.
The theorem is stated as follows:
"Each angle bisector of a triangle divides the opposite side into segments proportional in length to the adjacent sides" (Coxeter & Greitzer)
This means that for a triangle ABC, where angle A has a bisector AD such that D is on the side BC, then
BD/DC=AB/AC
Here either
BD/DC=6/5=AB/AC, where AB=6.9,
then we solve for AC=AB*5/6=5.75,
or
BD/DC=6/5=AB/AC, where AC=6.9,
then we solve for AB=AC*6/5=8.28
Hence, the longest and shortest possible lengths of the third side are
8.28 and 5.75 units respectively.
