Bev has to cut her grandma's grass this weekend and wants to know exactly how much area she will be cutting. Calculate the area
of the polygon. Be sure to show all your work and explain your answer.
A six-sided polygon that includes two isosceles right triangles, one with height and base of 15 feet, the other height and base of 4 feet, and one rectangle measuring 25 feet by 4 feet.
Please help! whoever gives the right answer and an explanation gets brainliest from ur favorite hope bagel, nagito.
A six-sided polygon that includes two isosceles right triangles, one with height and base of 15 feet, the other height and base of 4 feet, and one rectangle measuring 25 feet by 4 feet.
Please help! whoever gives the right answer and an explanation gets brainliest from ur favorite hope bagel, nagito.
2 answers:
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is the inequality that describes this problem
Given that Travis can spend no more than $125.75 every month
To find: linear inequality that describes the problem
Let the amount spent on movies = x dollars
Given that Travis decided to spend 4.3 times as much money on video games as he spends on movies
Amount spent on video games = 4.3 (amount spent on movies)
Amount spent on video games = 4.3x
Travis can spend no more than $125.75. That is, he can spend less than or equal to $125.75
<em><u>Thus, the inequality representing the situation is:</u></em>
Thus the required inequality is found
Answer:
This statement can be proven by contradiction for (including the case where
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Step-by-step explanation:
Assume that the natural number is a perfect square. Then, (by the definition of perfect squares) there should exist a natural number
(
) such that
.
Assume by contradiction that is indeed a perfect square. Then there should exist another natural number
such that
.
Note, that since ,
. Since
while
, one can conclude that
.
Keep in mind that both and
are natural numbers. The minimum separation between two natural numbers is
. In other words, if
, then it must be true that
.
Take the square of both sides, and the inequality should still be true. (To do so, start by multiplying both sides by and use the fact that
to make the left-hand side
.)
.
Expand the right-hand side using the binomial theorem:
.
.
However, recall that it was assumed that and
. Therefore,
.
.
Subtract from both sides of the inequality:
.
.
Recall that was assumed to be a natural number. In other words,
and
must be an integer. Hence, the only possible value of
would be
.
Since could be equal
, there's not yet a valid contradiction. To produce the contradiction and complete the proof, it would be necessary to show that
just won't work as in the assumption.
If indeed , then
.
, which isn't a perfect square. That contradicts the assumption that if
is a perfect square,
would be a perfect square. Hence, by contradiction, one can conclude that
.
Note that to produce a more well-rounded proof, it would likely be helpful to go back to the beginning of the proof, and show that . Then one can assume without loss of generality that
. In that case, the fact that
is good enough to count as a contradiction.