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ololo11 [35]
3 years ago
8

A family is building a rectangular fountain in the backyard. The yard is also rectangular and measures 6x by 7x. The fountain is

going to measure 2x by 4x. Once the fountain is built, what is the area of the remaining yard?
I'm totally stumped. Can you show me how to do this? My mum hasn't come back from work yet, and my older sister is at the cinema...
Mathematics
2 answers:
svetoff [14.1K]3 years ago
6 0

Answer:

34x²

Step-by-step explanation:

The area of a rectangle is given by the formula

A = L*w*h.  This means the area of the backyard is

A = 6x(7x) = 42x²

The fountain will also be rectangular; since its dimensions are 2x by 4x, this makes the area

A = 2x(4x) = 8x²

The remaining area will be given by

A = 42x²-8x² = 34x²

Natasha_Volkova [10]3 years ago
5 0

Answer:

34x²

Step-by-step explanation:

6x * 7x = 42x²

2x * 4x = 8x²

42x² - 8x² = 34x²

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3+3+3x

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Step-by-step explanation:

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3 years ago
Is 10(x-2)=5(2x-4) infinitely many or no solution
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10x-20=10x-20, make your decision on the answer from this which they are all real numbers. Hope this will help you!
7 0
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Differentiate with respect to X <br><img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B%20%5Cfrac%7Bcos2x%7D%7B1%20%2Bsin2x%20%7D%20
Mice21 [21]

Power and chain rule (where the power rule kicks in because \sqrt x=x^{1/2}):

\left(\sqrt{\dfrac{\cos(2x)}{1+\sin(2x)}}\right)'=\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'

Simplify the leading term as

\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}

Quotient rule:

\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'=\dfrac{(1+\sin(2x))(\cos(2x))'-\cos(2x)(1+\sin(2x))'}{(1+\sin(2x))^2}

Chain rule:

(\cos(2x))'=-\sin(2x)(2x)'=-2\sin(2x)

(1+\sin(2x))'=\cos(2x)(2x)'=2\cos(2x)

Put everything together and simplify:

\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{(1+\sin(2x))(-2\sin(2x))-\cos(2x)(2\cos(2x))}{(1+\sin(2x))^2}

=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{-2\sin(2x)-2\sin^2(2x)-2\cos^2(2x)}{(1+\sin(2x))^2}

=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{-2\sin(2x)-2}{(1+\sin(2x))^2}

=-\dfrac{\sqrt{1+\sin(2x)}}{\sqrt{\cos(2x)}}\dfrac{\sin(2x)+1}{(1+\sin(2x))^2}

=-\dfrac{\sqrt{1+\sin(2x)}}{\sqrt{\cos(2x)}}\dfrac1{1+\sin(2x)}

=-\dfrac1{\sqrt{\cos(2x)}}\dfrac1{\sqrt{1+\sin(2x)}}

=\boxed{-\dfrac1{\sqrt{\cos(2x)(1+\sin(2x))}}}

5 0
3 years ago
A local high school has both male and female students.
Kitty [74]

Answer:

a. P(male) = 0.4

b. P(no sport and male) = 0.1

c. Unclear question (isn't it the same as b.?)

Step-by-step explanation:

The data below is what I've worked according to, which isn't very clear from the question so the answers are only correct if this is the correct table of data;

\left[\begin{array}{ccc}&No \ Sports&Sports\\Female&10&32\\Male&7&21\end {array}\right]

a.

P(male) = \frac{7 + 21}{70} \\\\ = \frac{28}{70} \\\\ = \frac{2}{5}

b.

Using the tree diagram in the picture;

P(no \ sport \ and \ male) = \frac{2}{5} * \frac{1}{4} \\\\ = \frac{1}{10}

8 0
2 years ago
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Alchen [17]
Rate x time = distance
25   x  35/60 = distance  (35/60 is 35 minutes out of an hour- 60 minutes)
25/1 x 7/12  = distance (I put the 25 over 1 and reduced 35/60)
175/12 ≈ 14.58 miles

Notice that the time had to be in a fraction of an hour in order to do this.
8 0
2 years ago
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