There are `11` dancers in a performance. Their ages (in years) are:  `5. 5`, `6`, `6`, `6. 5`, `7`, `7. 5`, `8`, `8`, `8. 5`, `9`, `9` What is the median age of the dancers?

(a) The vertical motion equation for the ball is h = 8 + 48t - 16t².

(b) The time for the ball to hit the ground is 3.15 s.

(c) The time for the ball to travel 56 ft above the ground is 0.79 s.

The vertical motion equation for the ball is calculated as follows;

h = h₀ + vt - ¹/₂gt²

h = 8 + 48t - ¹/₂(32)t²

h = 8 + 48t - 16t²

0 = 8 + 48t - 16t²

solve the above quadratic equation with formula method;

a = -16, b = 48, c = 8

t = 3.15 s

h = 8 + 48t + 16t²

56 = 8 + 48t + 16t²

0 = -48 + 48t + 16t²

solve the above quadratic equation with formula method;

a = 16, b = 48, c = -48

t = 0.79 s

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Answer:

I think the answer is no

Step-by-step explanation:

It's been awhile but if I remember correctly a function cannot be a parabola (this graph) because it does not pass the vertical line test. If there are two points on a vertical line it is not a function. Hope this helps!

Step-by-step explanation:

How to solve your problem

(x+5)=x

Solve

1

Subtract

5

from both sides

x+5=x

x+5

2

Simplify

Subtract the numbers

x=x-5

3

Subtract

x

from both sides

x=x-5

Simplify

Combine like terms

Combine like terms

0=-5

Result

0=-5

The input is a contradiction: it has no solutions

Answer:

x=x-5 or 0=-5

Step-by-step explanation:

subtract 5 from both sides

Answer:

x^2 + 9x + 30 = 0

Step-by-step explanation:

Given: f(x) = x² – 10x + 24

g(x) = x – 6

f(- x) = g(x) :

(-x)² - 10(- x) + 24 = x - 6

x² + 10x + 24 - x + 6 = 0

Result: x² + 9x + 30 = 0

Answer:

Y = (x - 11/2)^2 -1/4

Step-by-step explanation:

subtract g(x) to f(x)

f (x) - g (x) = x^2 -10x +24 -x + 6

f (x) - g (x) = x^2 -11x +30

Let's call Y

Y = x^2 -11x +30

The standard form is by definition as Y = a (x-b)^2 + h

In this specific case:

Y = (x - 11/2)^2 -121/4 + 30

Y = (x - 11/2)^2 -1/4

All are technically squares, but if you are referring to just squares, then C and D are squares.

Answer:

40%

Step-by-step explanation:

The original is $20. It is now 12/20 is ?/100

12*100=1,200/20=60     100-60=40%

Answer:

D. 40%

Step-by-step explanation:

Percent change refers to how much, as a percentage, a quantity increases or decreases. The formula for percent change is [tex]\frac{FV-IV}{IV} * 100 = PC[/tex]. Keep in mind percent change is not negative, but can be written as 40% decrease or 40% increase.

We are being asked to find the percent change, or the change in the price of the sweater from $20 to $12. Thus, we will have to use the aforementioned formula. $20 is the initial value and $12 is the final value.

Solving for Percent Change

Step 1: Plug in values.

Step 2: Simplify.

Therefore, the answer is D. 40%.

Answer:

1.15

2.1

3.3

45

5.3

6.8

7.4

8.5

9. 24

Step-by-step explanation:

Answer:

1. 15

2. 1

3. 3

4.  2.5

5. 3

6. 8

7. 4

8. 5

9. 24

10. 6

11. 3

12. 52

13. 44

14. 38

15. 24

16. 12

17. 2

18. 12

Step-by-step explanation:

Answer:

~Senpi boi here~

Step-by-step explanation:

Multiply all terms by x and cancel:

x+2x+1=1x

3x+1=x(Simplify both sides of the equation)

3x+1−x=x−x(Subtract x from both sides)

2x+1=0

2x+1−1=0−1(Subtract 1 from both sides)

2x=−1

2x

2

=

−1

2

(Divide both sides by 2)

x=

−1

2

Check answers. (Plug them in to make sure they work.)

x=

−1

2

(Works in original equation)

Answer:

x= −1/2

(Hope this helps!)

Answer: 32 m^2

Step-by-step explanation:

first set up your equation; A=A rectange - 2(A square). The you plug in your numbers A = 40-2(4). The you do 40-8 = 32

Answer:

B

Step-by-step explanation:

sorry if im wrong

Answer:

See below ~

Step-by-step explanation:

(a)

(b)

Fractions are written as the ratio of two integers. 8.4km^2 of her property are covered in trees

Fractions are written as the ratio of two integers

Given the following parameters

total area of open field = 21km^2

If 2/5 of Joys cottage property is covered with trees, the amount covered in trees is expressed as:

Amount covered in trees = 2/5 * 21

Amount covered in trees = 42/5

Amount covered in trees  = 8.4km^2

Hence 8.4km^2 of her property are covered in trees

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Answer:

14

increase

Step-by-step explanation:

Answer:

14, increase

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The function sine of 'x' repeats its value after a full rotation of π radians. In degrees, that would be 180 degrees. On a unit circle, the sine is the y-component at any point along the circumference of the circle. In the first two quadrants, the y-component is the exact same until you exceed a rotation of 180 degrees. The degree of a circle is 360 degrees, therefore the answer would be C.

The two angles given are vertical angles, which mean they are equal to each other.

2x + 2 = 3x -52

Add 52 to both sides:

2x + 54 = 3x

Subtract 2x from both sides:

54 = x

Rewrite as x = 54

Answer: x = 54

Answer: z _> -10

Step-by-step explanation:

The exact values are;sin -7π/6 = 0.5; cos -7π/6 = -√3/2; tan -7π/6 = -1/√3; sec -7π/6 = -2/√3; csc -7π/6 =2; cot -7π/6 = -√3

We want to find the six trigonometric functions for  -7π/6 radians.

It should be noted that;

7π/6 radians = -210° degree = -210 +360 = 150° = 5π/6

From the definition of unit circle and applying to what we have here, we can express them as;

sin -7π/6 = 0.5

cos -7π/6 = -√3/2

tan -7π/6 = -1/√3

sec -7π/6 = -2/√3

csc -7π/6 =2

cot -7π/6 = -√3

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Therefore, the surface area of the rectangular prism is 2600 square inches.

In geometry, surface area is the total area that the surface of a 3-dimensional object covers. It is the sum of the areas of all the faces or surfaces that make up the object. Surface area is often used to determine the amount of material needed to cover an object or to calculate the heat transfer between an object and its surroundings.

Here,

To find the surface area of the rectangular prism, we need to find the area of each of its faces and add them together. Looking at the net, we see that there are three pairs of identical rectangles: the top and bottom faces, the front and back faces, and the left and right faces. Each of these rectangles has dimensions of 23 inches by 8 inches.

Therefore, the surface area of the rectangular prism is:

=2 * (23 in. * 8 in.) (top and bottom faces)

=2 * (36 in. * 8 in.) (front and back faces)

=2 * (23 in. * 36 in.) (left and right faces)

= 368 + 576 + 1656

= 2600 square inches

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Answer:

the width is 1.5meters

Step-by-step explanation:

the perimeter of the fence is 120m

the perimeter= 3w+w+3w+w

120= 3w+w+3w+w

120= 8w

w=1.5m

Answer:

15m

Step-by-step explanation:

Well, she needs 120 meters, which means we already know the circumference (P). P is the sum of all sides.

The lenght (a) is 3 times the width(b).

a = 3b.

Which means if a is x then b is equal to 3x

Since P is the sum of all sides, P is equal to 2a + 2b or 2x + 2*3x = 2x + 6x = 8x

120 = 8x. We are now left with an equation that has one variable only, all we need to do is to divide 120 by 8 to find what x is equal to.

8x = 120

x = 120 / 8

x = 15

We know that width(a) is equal to x, so that's the answer.

Here's a solution you can write:

P = 120m

w = x

l = 3w = 3x

P = 2w + 2l

P = 2*x + 2*3x

P = 2x + 6x

P = 8x

8x = 120

x = 120 / 8

x = 15

w = x -> w = 15m

Answer:

Step-by-step explanation:

Compounding interest :

Future value of money = Present value * (1+ r)^N

r - interest rate

n - number of period

In our example, Present value = 325.76, FV = 400, r = 2%, and we need to find N

by solving that we can find it that N is equal to 10.3675

Simple interest :

400 - 325.76 = 74.26$ we need to increase

325.76*2% = 6.5152$ each year

74.26 / 6.5152 = 11.3949

as a whole year = 12years

Answer:

B

Step-by-step explanation:

Answer:

2 units!

Step-by-step explanation:

Answer: 2 units

Answer:

The answer is 9

Because the 4 meters short than bank and ban is 13 meters

So subtract 13 - 4=9

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

For both tree A and tree B calculated slope is less than 0.06. Then it does not satisfy the slope constraint.

The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.

To use the treehouse as the start of the zip line, the cable needs to be attached to the starting tree at a height of 18 feet above the ground.

To meet the slope constraint, Esteban wants to change the height to 7 feet and end the zip line at a height of 11 feet above the ground.

He claims this vertical change meets the slope constraint.

The slope for tree A will be

[tex]\rm Slope \ A = \dfrac{7}{120}\\\\Slope \ A = 0.0583[/tex]

The slope for tree B will be

[tex]\rm Slope \ B = \dfrac{7}{160}\\\\Slope \ B = 0.043[/tex]

For both tree A and tree B calculated slope is less than 0.06. Then it does not satisfy the slope constraint.

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Answer:

(-8,-10)

Step-by-step explanation:

Rewrite (x+8)2(x+8)² as (x+8)(x+8).

f(x)=3((x+8)(x+8))−10

Expand (x+8) (x+8) using the FOIL Method.

Apply the distributive property.

f(x)=3(x(x+8)+8(x+8))−10

Apply the distributive property.

f(x)=3(x⋅x+x⋅8+8(x+8))−10
Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

Multiply x by x.

f(x)=3(x2+x⋅8+8x+8⋅8)−10

Move 8 to the left of x.

f(x)=3(x2+8⋅x+8x+8⋅8)−10

Multiply 8 by 8.

f(x)=3(x2+8x+8x+64)−10

Add 8x and 8x.

f(x)=3(x2+16x+64)−10

Apply the distributive property.

f(x)=3x2+3(16x)+3⋅64−10

Simplify.

Multiply 16 by 3.

f(x)=3x2+48x+3⋅64−10

Multiply 3 by 64.

f(x)=3x2+48x+192−10

Subtract 10 from 192.

f(x)=3x2+48x+182

The minimum of a quadratic function occurs at x=[tex]-\frac{b}{2a}[/tex] If a is positive, the minimum value of the function is f ([tex]-\frac{b}{2a}[/tex]).

Substitute in the values of aa and b.

x=−[tex]\frac{48}{2(3)}[/tex]

x=-8

Replace the variable x with −8 in the expression.

f(−8)=3(−8)2+48(−8)+182

Y=-10

Therefore, the minimum value is (-8,-10) but if it is asking for just the y-value it would be -10.

Answer:

Given:

A set of functions,

A. y = -(x-4)^2  

B. y=3(x- 4)^2

C. y = [x] + 4

D. y = -5x + 4.  

To Find:

The function whose range is (-infinity, 4].

Solution:

1. The function y = -(x-4)^2 has a minimum value of 0 and it is an increasing function. Hence the maximum value tends towards infinite. Hence the range is [0, infinite).

2. The function y = 3(x-4)^2 has a minimum value of 0 and it is an increasing function. Hence the maximum value tends towards infinite. Hence the range is [0, infinite).

3. y = [x] + 4 (where [x] = greatest integer function). This function is an increasing function with a minimum value towards negative infinity and the maximum value tends towards the positive side of infinity.  

=> Range of y = [x]  + 4 is (-infinite, infinite).

4. y = -5x+4 is a continuous increasing function without any exceptions.  

=> Range of y = -5x+4 is (-infinite,infinite)

Therefore, none of the functions has their range from (-infinity,4].

Step-by-step explanation: