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noname [10]
3 years ago
8

Which phrase should be inserted on the line to make a true statement

Mathematics
2 answers:
Murljashka [212]3 years ago
8 0

Answer:

\frac{8}{12} equal to \frac{8}{12}

Step-by-step explanation:

\frac{2}{3} -------------------------  \frac{8}{12}

Lets compare both the fractions

To compare both the fractions the denominators should be same

Lets make the denominators same

WE try to get 12 in the denominator of first fraction, so we multiply top and bottom by 4

\frac{2*4}{3*4}=\frac{8}{12}

\frac{8}{12} -------------------------  \frac{8}{12}

Both fractions are equal

So \frac{8}{12} equal to \frac{8}{12}

Oxana [17]3 years ago
4 0
They’re equal. 8 is 2/3 of 12.
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What is the value of x?
dlinn [17]

Answer:

X= O.8 or 10 over 12.5

Step-by-step explanation: Hope this helps darling

5 0
3 years ago
Compare the two figures. How many times bigger or smaller is the cone to
Gemiola [76]

Answer:

The proportion of the volume of the cone to the volume of the pyramid is: 3.14 times bigger.

Step-by-step explanation:

<u>Given the information of the cone: </u>

  • The height: 12 inches
  • The radius of the base is : 10/2= 5 inches

=> the volume of the cone

= 1/3πr^{2} *h

= 1/3*3.14*5^{2} *12

= 314 cubic inches

<u>Given the information of the pyramid: </u>

  • the height: 12 inches
  • The base is a suqare with a side lengh = 5 inches  

=> the volume of the pyramid:

= 1/3*Bh            (where B is the area of the base)

= 1/3*5*5*12

= 100 cubic inches

<u>The proportion of the volume of the cone to the volume of the pyramid is: </u>

= 314 /100

= 3.14 times bigger.

Hope it will find you well

3 0
3 years ago
What are the coordinates for the center of the circle and the length of the radius ?
Vadim26 [7]

the answer to your question is D

5 0
3 years ago
Read 2 more answers
Gabriella is x years old. Her sister, Felicia, is six years older than she is. Their mother is twice as old as Felicia. Their au
Snowcat [4.5K]

x(x+6)=

x^2+6x

4 0
3 years ago
You have asked to design a rectangle box with a square base and an open top. The volume of the box must be620 cm to the 3rd powe
hammer [34]

Answer:

$69.21

Step-by-step explanation:

Since the box has a square base the length and breadth of the box will be equal. Let it be x

Let h be the height of the box

V = Volume of the box = 620\ \text{cm}^3

x^2h=620\\\Rightarrow h=\dfrac{620}{x^2}

Now surface area of the box with an open top is given

s=x^2+4xh\\\Rightarrow s=x^2+4x\dfrac{620}{x^2}\\\Rightarrow s=x^2+\dfrac{2480}{x}

Differentiating with respect to x we get

\dfrac{ds}{dx}=2x-\dfrac{2480}{x^2}

Equating with zero

0=2x-\dfrac{2480}{x^2}\\\Rightarrow 2x^3-2480=0\\\Rightarrow x^3=\dfrac{2480}{2}\\\Rightarrow x=(1240)^{\dfrac{1}{3}}\\\Rightarrow x=10.74

Double derivative of the function

\dfrac{d^2s}{ds^2}=2+\dfrac{4960}{x^3}=2+\dfrac{4960}{1240}\\\Rightarrow \dfrac{d^2s}{ds^2}=6>0

So, x at 10.74 is the minimum value of the function.

h=\dfrac{620}{x^2}\\\Rightarrow h=\dfrac{620}{10.74^2}\\\Rightarrow h=5.37

So, minimum length and breadth of the box is 10.74 cm while the height of the box is 5.37 cm.

The total area of the sides is 4xh=4\times 10.74\times 5.37=230.7\ \text{cm}^2

The area of the base is x^2=10.74^2=115.35\ \text{cm}^2

Cost of the base is $0.40 per square cm

Cost of the side is  $0.10 per square cm

Minimum cost would be

230.7\times 0.1+0.4\times 115.34=\$69.21

The minimum cost of the box is 69.21 dollars.

8 0
3 years ago
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