Solve the proportion x/2=5/15

Answers

Answer 1

Answer: $(x)/(2)= (5)/(15)$

$x= (5)/(15)(2)$

$x= (2)/(3)$

Answer 2

Answer: $(x)/(2)= (5)/(15) \n \n ((2)x)/(2)= ((2)5)/(15) \n \n x= (10)/(15)= ((5)2)/((5)3) \n \n \boxed { x= (2)/(3) }$

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Which expression is equivalent to (3x^2+4x-7)(x-2)A.x(3x^2+4x-7)+2(3x^2+4x-7)B.(3x^2+4x-7)(x)+(3x^2+4x-7)(-2)C.x(3x^2+4x-7)-2D.2x(3x^2+4x-7)

An open box is to be constructed from a square piece of sheet metal by removing a square of side 6 feet from each corner and turning up the edges. If the box is to hold 864 cubic feet, what should be the dimensions of the sheet metal?

Answers

Answer:

24 feet

Step-by-step explanation:

We are given that an open box is to be constructed from a square piece of sheet metal by removing a square side 6 feet from each corner and turning up the edges.

We have to find the dimensions of the sheet metal

Let x feet be the side of square metal sheet

Length of box=x-12 feet (because 6 feet removed from each corner)

Width of box=x-12 feet

Height of box=6 feet

Volume of box=864 cubic feet

We know that volume of cuboid= $l* b* h$

Box is in cuboid shaped

Therefore, volume of box= $6(x-12)(x-12)$

$6(x^2-24x+144)=864$

$x^2-24x+144=(864)/(6)$

$x^2-24x+144=144$

$x^2-24x+144-144=0$

$x(x-24)=0$

Then , $x=0 , x-24=0$

$x=24$

x=0 is not possible because side of square metal sheet can not be zero

Therefore, x=24

All sides of square metal sheet are equal.

Hence, side of square metal sheet =24 feet

Final answer:

The original sheet of metal from which an open box holding 864 cubic feet is constructed by removing 6-foot squares from each corner and folding up the edges should be a square with a side length of 26 feet.

Explanation:

To answer your question about the open box constructed from a square piece of sheet metal, let's assume the original side length of the sheet metal is x feet. When squares of length 6 feet are removed from each corner and the edges are turned up, we're left with a box with length and width of (x - 2*6) feet and height of 6 feet.

Given that the volume of the box is 864 cubic feet, we set up this equation to find x:

(x - 12 feet)(x - 12 feet)*6 feet = 864 cubic feet.

Solving this equation gives us a value for x, which is the side length of the original square piece of sheet metal. Doing the math, we find x = 26 feet. So, the dimensions of the original sheet metal are 26 feet by 26 feet.

Learn more about Open Box Construction here:

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A function f (x)=-8x^2. What is f (-3)?

Answers

f(x) = -8x²

To find the value of f(-3), put -3 in place of 'x' in the definition of the function.

f(-3) = -8(-3)²

f(-3) = -8(9) = -72

f(x)= -8x²

f(-3)= -8* (-3)²

f(-3)= -8 * 9

f(-3)= -72

You have 324 ft^2 of fabric to make a circular play parachute for kids. What is the radius of the largest parachute you can make? Round to the nearest tenth of a foot.

Answers

Area of a circular play parachute:
A = 324 ft²
A = r² π
r² π = 324
r² = 324 : 3.14
r² = 103.1874
r = √103.1874
r = 10.157987 ≈ 10.2 ft

what is the smallest possible whole number length for the third side if the other sides are 15 and 20?

Answers

i believe 5 because you subtract 20 from 15

State a conclusion that seems reasonable.Donald is older than Jeanette; Donald is older than Ethel. Donald is older than Allen.

Conclusion:

Answers

Donald is the oldest of the four of them

Donald Is Older Than Jeanette , Ethel And Allen

Can 24 7ths be equal to another fraction or be simplified in another way

Answers

To check if an improper fraction like like 24/7 can still be simplified, you have to find similar factors that can divide both the numerator (24) and the denominator (7). However in this case, there are no longer any common factors that can divide both of them. However, improper fractions can be represented in a mixed fraction form.

A mixed fraction is made up of a whole number and a fraction. To change an improper fraction to a mixed fraction, divide the numerator by the denominator. The quotient should be a whole number and a remainder. The whole number in the quotient would be the whole number in the mixed fraction, and the remainder would be the numerator.

In the case of 24/7, dividing it would yield us 3 remainder 3. Therefore, the mixed fraction would be:

3 3/7

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