We are interested in the dimensions of a certain square. A rectangle has length twice the side of this square and width three units less than the side of this square. If the two areas are equal, what are the square's dimensions (w x h)?

Answers

Answer 1

Answer:
We don't need the length AND width of the square. One number
will be enough for an answer, because all sides of a square have
the same length. Let's call that number ' M ' (for 'mystery number').

-- The area of the square is M² .

The question says that ...
-- The length of the rectangle is 2M .
-- The width of the rectangle is (M - 3) .

Therefore ...
-- The area of the rectangle is (2M)(M - 3) = 2M² - 6M .

The question also says that ...
-- The areas of the square and the rectangle are equal:

So 2M² - 6M = M²

Subtract M² from each side: M² - 6M = 0

Divide each side by M : M - 6 = 0

Add 6 to each side : M = 6 .

Check:

Assume ... Side of the square = 6

Then ...
Area of the square = 6² = 36 .
Length of the rectangle = (6 x 2) = 12
Width of the rectangle = (6 - 3) = 3
Area of the rectangle = (12 x 3) = 36

36 = 36 yay!

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Simplify the radical expression(8+√11)(8-√11)

A.53
B.75+16√11
C.-57
D.64+√11

Answers

(8 + √11)(8 - √11)
8^2 - √11^2
64 - √11^2
64 - 11
53

The answer is: 53.

(8 + root11)(8 - root11) =
64 - root11 + root11 - 11 =
64 - 11 = 53

Answer A.

To paint a house, two painters are hired. The first painter can paint the house in ten hours. The second painter will need six hours to paint the entire house. If the two painters start painting at 8:00 am, at what time will they finish painting the house?

Answers

so
p1 can paint hours in 10 hours, so 1/10 house per 1 hour

p2 can paint house in 6 hours so 1/6 house per 1 hour

if both start at 8:00, when finish??
find how many hours they take

1 hour=p1+p2=1/10+1/6
just add 1/10 and 1/6 and see how many to get 1/1 house done
1/10+1/6=3/30+5/30=8/30=4/15
xhours times 4/15=1
multiply both sides by 15/4 to clear fraction
xhours =15/4
xhours=3 and 3/4

they take 3 and 3/4 hours aka 3 hours and 45 mins so
8:00+3:45=11:45

they finish at 11:45 AM

Evaluate the expression when a=-4 and x=5.

a-2x

Answers

Answer:

That would be -14.

Step-by-step explanation:

Answer:

it's -14 when u evaluate a-2x

Which equation is y = 3(x – 2)2 – (x – 5)2 rewritten in vertex form?

Answers

expand
y=3(x^2-4x+4)-(x^2-10x+25)
y=3x^2-12x+12-x^2+10x-25
y=3x^2-x^2-12x+10x+12-25
y=2x^2-2x-13
complete the square

y=2(x^2-x)-13
y=2(x^2-x+1/4-1/4)-13
y=2((x-1/2)^2-1/4)-13
y=2(x-1/2)^2-1/2-13
y=2(y-0.5)^2-13.5

Answer: D

y=2(x-1/2)^2 - 27/2

Mr Jones places 3 orders for school t-shirts. Each order has 16 boxes of shirts and each box holds 17 shirts. How many T-shirts dos Mr Jones order. Use partial products to help you

Answers

3x16=180 boxes

17x16=272 shirts (17 shirts per boxes, 16 boxes)

the answer is 272 shirts

Answer:

272 shirts

Step-by-step explanation:

given the following system of equations, identify the type of system.x y = 6y = 3 - xconsistentinconsistentequivalent

Answers

Inconstant as there is no solution

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