Mathematics, 22.07.2019 10:00 puffley

Look at the rectangle and the square: a rectangle pqrs and square lmno are drawn side by side. the length sr of the rectangle is labeled as 12 inches, and the width qr is labeled as 6 inches. the side lm of the square is labeled as 6 inches. sam says that the length of diagonal sq is two times the length of diagonal om. is sam correct? justify your answer and show all your work. your work should state the theorem you used to find the lengths of the diagonals

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Rectangle has height of 6", and a length of 12".you can make a right triangle by cutting it along the diagonal, thus you are able to use the pythagorean theorem to calculate the diagonal: $a^2 + b^2 = c^2$ $c^2 = 6^2 + 12^2$ $c^2 = 36 + 144 = 180$ $c = \sqrt{180} = \sqrt{4} \sqrt{45} = 2 \sqrt{45}$ , which is the length of the diagonal.now, since the length is double the square root of 45, for the statement to be correct, the length of the squares diagonal must be $\sqrt{45}$ the square has sides of 6", and you can, again, cut it diagonally to make a right triangle.then you would use the pythagorean theorem again to find the diagonal: $6^2 + 6^2 = c^2$ $36+36 = c^2$ $72 = c^2$ $c = \sqrt{72}$ since the square root of 72 is not equal to the square root of 45, you can deduce that the statement is false.

Answer from: Quest

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

Answer from: Quest

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204

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