MATHEMATICS MIDDLE SCHOOL

The height of a ball in feet is modeled by $y = - 16x {}^(2) + 72x$
where X is the time in seconds after the ball is hit. How long is the ball in the air?

(May I also get steps on how to solve these kind of questions please?)

Answers

Answer 1

Answer:

The value of time of the ball in the air is,

⇒ 4.5 seconds

What is Quadratic equation?

An algebraic equation with the second degree of the variable is called an Quadratic equation.

We have to given that;

The height of a ball in feet is modeled by the equation,

y = - 16x² + 72x

where, x is the time in seconds after the ball is hit.

Hence, For time of the ball in the air, we can plug y = 0 in above equation.

y = - 16x² + 72x

0 = - 16x² + 72x

Solve for x;

- 16x² + 72x = 0

- 4x (4x - 18) = 0

This gives,

4x = 18

x = 18/4

x = 4.5 seconds

Thus, The value of time of the ball in the air is,

⇒ 4.5 seconds

Learn more about the quadratic equation visit:

brainly.com/question/1214333

#SPJ2

Answer 2

Answer: The answer to this question is 4.5 seconds. You can see from the graph that the ball is above the ground in the interval 0 < t < 4.5. It is at t = 4.5 where the graph touches the t-axis. When it touches the t-axis, then the height is 0 and therefore on the ground.

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What is 9/10 take away 4/10

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Suppose y is a positive integer.If x-(-y)=z will z be greater than x ?

Answers

Integers are all numbers without decimal point.

z will always be greater than x

Given that:

$x - (-y)=z$

Open the bracket

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From the question, we understand that y is positive.

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Answers

Answer:

Figure 1's surface area: 550 $feet^2$

Figure 2's surface area: 530 $feet^2$

Figure 3's surface area: 790 $feet^2$

So, the order of the figures' surface areas is: Figure 2 < Figure 1 < Figure 3.

Step-by-step explanation:

Bearing in mind that the surface area of a 3D object is the total area of its surface (that is the sum of the areas of its faces), we can count the number of distinct shapes in each figure, calculate their areas and add them up. Be careful not to add the faces that are "inside".

Figure 1

Its surface area consists of 13 squares of 5x5 $feet^2$ and 3 rectangles of 15x5 $feet^2$ . So, its surface area is (13x25 + 3x75) $feet^2 = 550feet^2$

Figure 2

Its surface area consists of 6 squares of 5x5 $feet^2$ , 3 rectangles of 17x5 $feet^2$ , 1 rectangle of 13x5 $feet^2$ and 2 triangles of base 12 feet and height 5 feet. So, its surface area is (17x5x3+6x5x5+13x5+12x5x2:2) $feet^2 = 530feet^2$

Figure 3

Its surface area consists of 2 rectangles of 12.5x5 $feet^2$ , 1 rectangle of 11x5 $feet^2$ , 2 triangles of base 12 feet and height 5 feet, 1 rectangle of 11x13 $feet^2$ , 2 rectangles of 12.5x11 $feet^2$ and 1 rectangle of 12x11 $feet^2$ .

So, its surface area is (2x12.5x5+11x5+2x12x5:2+11x13+2x12.5x11+12x11) $feet^2 = 790feet^2$

Answer:

Least surface area to greatest surface area:

Blue - Red - Green

Step-by-step explanation:

All the surfaces of the shapes are rectangles, then their surface is computed as:

Surface = Length*Width

Blue figure

Area of the top:

5*5 + 5*5 + 5*5 + 5*5 + 5*5 = 125 ft^2

Area of the sides:

2*(5*10) = 100 ft^2

Area of the bottom:

10*5 = 50 ft^2

Area of the front and the back

2*(5*5 + 15*5) = 200 ft^2

Total: 125 + 100 + 50 + 200 = 475 ft^2

Red figure

Area of the top:

5*5 + 13*5 = 90 ft^2

Area of the left side:

5*10 = 50 ft^2

Area of the right side:

5*5 = 25 ft^2

Area of the bottom:

17*5 = 85 ft^2

Area of the front and the back:

2*(17*5 + 12*5/2 + 5*5) = 280 ft^2

Total: 90 + 50 + 25 + 85 + 280 = 530 ft^2

Green figure

Area of the top:

12.5*11 + 13*11 = 280.5 ft^2

Area of the left side:

11*5 = 55 ft^2

Area of the bottom:

(12.5+12)*11 = 269.5 ft^2

Area of the front and the back:

2*(12.5*5 + 12*5/2) = 185 ft^2

Total: 280.5 + 55 + 269.5 + 185 = 790 ft^2

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The height of a ball in feet is modeled by where X is the time in seconds after the ball is hit. How long is the ball in the air?(May I also get steps on how to solve these kind of questions please?)

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What is Quadratic equation?

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The height of a ball in feet is modeled by $y = - 16x {}^(2) + 72x$
where X is the time in seconds after the ball is hit. How long is the ball in the air?

(May I also get steps on how to solve these kind of questions please?)