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likoan [24]
2 years ago
5

A window is being replaced with tinted glass. The plan below shows the design of the window. Each unit length represents 1 foot.

The glass costs $23 per square foot. How much will it cost to replace the glass? Use 3.14 for π.

Mathematics
2 answers:
Marysya12 [62]2 years ago
7 0

Answer:

748.88

Step-by-step explanation:

Ilia_Sergeevich [38]2 years ago
5 0
Let us solve for the total area. In this problem, we solve area 1 (the rectangle in the middle) and the area 2 ( the two half circle on the sides).

Solve for area 1:
Area rec = L * W = 5units * 4 units = 20 squared units

Solve for area 2:
Area cir = pi *r² = 3.14 * (2 units)² = 12.56 squared units

Total area = 20 + 12.56 = 32.56 foot²
Total cost = 32.56 foot² * ($23/foot²) = $ 748.88

Total cost is $748.88.
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You are designing a rectangular garden. the garden will be enclosed by fencing on three sides and by a house on the fourth side.
RUDIKE [14]
Suppose the dimensions of the rectangle is x by y and let the side enclosed by a house be one of the sides measuring x, then the sides that is to be enclosed are two sides measuring y and one side measuring x.

Thus, the length of fencing needed is given by

P = x + 2y

The area of the rectangle is given by xy,

i.e.

xy = 288  \\  \\  \\  \\ \Rightarrow y= \frac{288}{x}

Substituting for y into the equation for the length of fencing needed, we have

P=x+2\left( \frac{288}{x} \right)=x+ \frac{576}{x}

For the amount of fencing to be minimum, then

\frac{dP}{dx} =0 \\  \\ \Rightarrow1- \frac{576}{x^2} =0 \\  \\ \Rightarrow \frac{576}{x^2} =1 \\  \\ \Rightarrow x^2=576 \\  \\ \Rightarrow x=\sqrt{576}=24

Now, recall that

y= \frac{288}{x} = \frac{288}{24} =12

Thus, the length of fencing needed is given by

P = x + 2y = 24 + 2(12) = 24 + 24 = 48.

Therefore, 48 feets of fencing is needed to enclose the garden.
8 0
3 years ago
Please someone help me out. I beggggg
bezimeni [28]

Answer:

1.  144  2. 16 3. 1   4. 3x-6  

Step-by-step explanation:

So think of this as a function in a function.  So you work from the inside to the outside.  So for problem 1, we start with f(4)) [you read it "f of 4"] so what is the solution when x = 4, since f(x) means the function of x so f(4) means 'the function of 4' inside f(x).  

Since f(x) = 3x then f(4) = 3(4) [notice how you substitute the 4 everywhere you see a letter x]

so f(4) = 12, now you work the next part h(f(4)) since f(4)=12 then h(12)

So take the h(x) function which is h(x) = x^{2} then h(12) = 12^{2} so h(12) = 144

4 0
2 years ago
Can someone please help me with this
Anit [1.1K]

180 = 96 + 2x + x + 12

180 = 96 + 3x + 12

180 = 108 + 3x

-108  -108

72   =  3x

/3       /3

24 = x

7 0
2 years ago
Read 2 more answers
What is the prime factorization of 60
jeka57 [31]

Answer:

2*2*3*5

Step-by-step explanation:

We need to factor 60 until it is prime numbers

60 = 12*5           5 is prime 12 is not

     =3*4   *5       3,5 prime   4 is not

    = 3 *2*2 *5     2,3,5 are prime

Rearranging the order

    =2*2*3*5

                     

5 0
3 years ago
A jeweler is making a triangular pendant. He has two sides of length 23 mm and 31 mm. What are the
denis-greek [22]

Answer:

38.60mm

Step-by-step explanation:

Step one:

Given data

We are given that the dimension of the triangles are length 23 mm and 31 mm

Let us assume that the triangle is a right angle triangle

Step two:

Applying the Pythagoras theorem we can find the third as

z^2= x^2+y^2\\\\z^2= 31^2+23^2\\\\z^2= 961+529\\\\z^2= 1490\\\\

square both sides

z= √ 1490

z= 38.60mm

Hence a possible dimension of the third side is 38.60mm

3 0
3 years ago
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