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Ymorist [56]
3 years ago
8

if the area of a square is 144 feet and the perimeter of the triangle is 28 feet, what is the perimeter of the room's floor?

Mathematics
1 answer:
FinnZ [79.3K]3 years ago
4 0

Answer:

52+12\pi

Step-by-step explanation:

The diagram for the question is attached below

perimeter of the triangle is 28 feet

area of a square is 144 feet

Area of the square is side^2

side ^2= 144

take square root on both sides

side = 12

side of the square = 12

side is the diameter of the semicircle

Diameter = 12 , so radius = 12 divide 2 = 6

circumference of semicircle = 2\pi r=2\pi (6)=12\pi

one side of the rectangle is calculated in the perimeter of triangle and other side is calculated using circumference

perimeter of other two side = 2(12)= 24

Total perimeter = 28+24+12\pi =52+12\pi

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Last year there were 20 girls on the volleyball team. This year the number of girls decreased by 10%. How many girls are on the
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If y= 3x + 6, what is the minimum value of (x^3)(y)?
Rainbow [258]

Answer:

Given the statement: if y =3x+6.

Find the minimum value of (x^3)(y)

Let f(x) = (x^3)(y)

Substitute the value of y ;

f(x)=(x^3)(3x+6)

Distribute the terms;

f(x)= 3x^4 + 6x^3

The derivative value of f(x) with respect to x.

\frac{df}{dx} =\frac{d}{dx}(3x^4+6x^3)

Using \frac{d}{dx}(x^n) = nx^{n-1}

we have;

\frac{df}{dx} =(12x^3+18x^2)

Set \frac{df}{dx} = 0

then;

(12x^3+18x^2) =0

6x^2(2x + 3) = 0

By zero product property;

6x^2=0   and 2x + 3 = 0

⇒ x=0 and x = -\frac{3}{2} = -1.5

then;

at x = 0

f(0) = 0

and  

x = -1.5

f(-1.5) = 3(-1.5)^4 + 6(-1.5)^3 = 15.1875-20.25 = -5.0625


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3 0
3 years ago
Solve:<br><br> a.x3+x2-8x - 12x+2<br> b. x3-4x2-3x + 18x-3<br> c. x2 + 4x + 4<br> d. x2 - 6x + 9
NeTakaya
<h2>Steps:</h2>

So firstly, this function is asking us to divide f(x) by g(x) so let's set that up as such:

(\frac{f}{g})(x)=\frac{x^2-x-6}{1}\div \frac{x-3}{x+2}

Next, remember that <u>dividing by a number is the same as multiplying by its reciprocal.</u> To find the reciprocal of a number, flip the numerator and denominator around. With this info, flip the second fraction to it's reciprocal and change the sign to multiplication:

(\frac{f}{g})(x)=\frac{x^2-x-6}{1}\times \frac{x+2}{x-3}

Next, we are going to factor x² - x - 6. Firstly, what two terms have a product of -6x² and a sum of -x? That would be -3x and 2x. Replace -x with 2x - 3x:

(\frac{f}{g})(x)=\frac{x^2+2x-3x-6}{1}\times \frac{x+2}{x-3}

Next, factor x² + 2x and -3x - 6 separately. Make sure that they have the same quantity on the inside of the parentheses:

(\frac{f}{g})(x)=\frac{x(x+2)-3(x+2)}{1}\times \frac{x+2}{x-3}

Now you can rewrite it as:

(\frac{f}{g})(x)=\frac{(x-3)(x+2)}{1}\times \frac{x+2}{x-3}

Next, multiply:

(\frac{f}{g})(x)=\frac{(x-3)(x+2)^2}{x-3}

Next, divide:

(\frac{f}{g})(x)=(x+2)^2

And lastly, simplify:

  • A good tip: (x+y)^2=x^2+2xy+y^2

(\frac{f}{g})(x)=x^2+4x+4

<h2>Answer:</h2>

<u>The correct option is C. x² + 4x + 4.</u>

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