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Law Incorporation [45]
2 years ago
7

What is the difference of the fractions? Use the number line and equivalent fractions to help find the answer.

Mathematics
1 answer:
bearhunter [10]2 years ago
4 0

Answer:

-29/4 or -7.25

Explanation:

1/2 = 2/4

2/2 · (-21/2) - (-13/4)

= -42/4 + 13/4 (subtracting a negative = addition)

= -29/4

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The slope of this line is -1 you find this by using the slip formula of y-y over x-x find two points on the line so I used points (-2,2) and (-1,1) plug them into the formula to get the slope of -1 hope this helps:)
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2 years ago
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Find the area of a circle with a diameter of 4.
Oliga [24]

area of circle =22/7×4=12.56

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2 years ago
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[10 points] A manufacturer wants to design an open box having a square base and a surface area of 108 square inches. What dimens
MissTica

Answer:

  6 inches square by 3 inches high

Step-by-step explanation:

For a given surface area, the volume of an open-top box is maximized when it has the shape of half a cube. If the area were than of the whole cube, it would be 216 in² = 6×36 in².

That is, the bottom is 6 inches square, and the sides are 3 inches high.

_____

Let x and h represent the base edge length and box height, respectively. Then we have ...

  x² +4xh = 108 . . . . box surface area

Solving for height, we get ...

  h = (108 -x²)/(4x) = 27/x -x/4

The volume is the product of base area and height, so is ...

  V = x²h = x²(27/x -x/4) = 27x -x³/4

We want to maximize the volume, so we want to set its derivative to zero.

  dV/dx = 0 = 27 -(3/4)x²

  x² = (4/3)(27) = 36

  x = 6

  h = 108/x² = 3

The box is 6 inches square and 3 inches high.

_____

<em>Comment on maximum volume, minimum area</em>

In the general case of<em> an open-top box</em>, the volume is maximized when the cost of the bottom and the cost of each pair of opposite sides is the same. Here, the "cost" is simply the area, so the area of the bottom is 1/3 the total area, 36 in².

If the box has a <em>closed top</em>, then each pair of opposite sides will have the same cost for a maximum-volume box. If costs are uniform, the box is a cube.

7 0
2 years ago
Question 6 (1 point) (01.03 LC) What is the value of 5 to the power of 4 over 5 to the power of 6? (1 point) a 1 over 25 b 1 ove
Vlad [161]

Answer:

a 1 over 25

Step-by-step explanation:

Problem Statement:

     What is the value of  \frac{5^{4} }{5 ^{6} } ?

To solve this problem, we must familiarize ourselves with the concept of exponents and rules that guides them.

Exponents are used by scientists to report higher orders of a number.

Such large and often recurring expression is usually made up of a base and an exponent value.

The exponent value is the power of the base;   for example, 4³ has 4 as its base and 3 as the exponent.

Several rules guides solving an exponent, to this problem, the most applicable one is :

                            \frac{x^{a} }{x^{b} }  =  x^{(a-b)}

                           \frac{5^{4} }{5 ^{6} }   =  5^{4-6}  

                                 = 5^{-2}

                                 = \frac{1}{25}                                  

Therefore the solution is 1 over 25

7 0
2 years ago
Henry sells apples. The graph shows the relationship
Eddi Din [679]

Answer:

Henry does not make money if he does not sell any apples.

Step-by-step explanation:

Henry sells apples. The graph of the relationship between the price of apples and their total weight passes through the point (0,0) or origin.

Now, we have to clarify the meaning of the point (0,0) on the graph.

We choose from the options that Henry does not make money if he does not sell any apples.  

Therefore, option D will be the correct one. (Answer)

8 0
3 years ago
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