y=x2-8x-3 standard to vertex form

Answer:

The maximum height of the ball is 380.25 feet in the air.

Step-by-step explanation:

The quadratic function:

[tex]h(t)=-16t^2+132t+108[/tex]

Models the ball's height h(t), in feet, above the ground t seconds after it was thrown.

We want to determine the maximum height of the ball.

Note that this is a quadratic function. Therefore, the maximum or minimum value will always occur at its vertex point.

Since our leading coefficient is leading, we have a maximum point. So to find the maximum height, we will find the vertex. The vertex of a quadratic equation is given by:

[tex]\displaystyle \left(-\frac{b}{2a},f\left(\frac{b}{2a}\right)\right)[/tex]

In this case, a = -16, b = 132, and c = 108. Find the t-coordinate of the vertex:

[tex]\displaystyle t=-\frac{132}{2(-16)}=-\frac{132}{-32}=\frac{33}{8}=4.125[/tex]

So, the maximum height occurs after 4.125 seconds of the ball being thrown.

To find the maximum height, substitute this value back into the equation. Thus:

[tex]h(4.125)=-16(4.125)^2+132(4.125)+108=380.25\text{ feet}[/tex]

The maximum height of the ball is 380.25 feet in the air.

Answer:

top 8, middle 7, 16, bottom 13

Answer:f(x)=-16(x-1)^2+22

Step-by-step explanation:

The equation for the trajectory of ball in the air is h(t) = -16t² + 32t + 6.

The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) =  lim h --> 0 (f(x + h) - f(x)) /(x + h - x).

It can also be said as the slope of the tangent for the  function at a given point.

Given that,

The maximum height reached by the ball  after 1 sec is 22 ft above ground.

And, the height at which it is thrown is 6 ft above the ground.

Which implies at 0 sec the height is 6 ft.

The quadratic function for the height can be written as,

h(t) = at² + bt + c

Substitute t = 0 to gat,

f(0) = a × 0² + b × 0 + c

=> c = 6

Now, for maximum height,

h'(t) = 0

=> 2at + b = 0

At maximum height t = 1

Then, the above expression becomes,

2a × 1 + b = 0

=> a = -b/2

Substitute t = 1 in h(t) = at² + bt + c to get,

22 = a + b + c

=> 22 = -b/2 + b + 6

=> b/2 = 16

=> b = 32

Then, a = -b/2

            = -32/2

            =-16

Thus substituting the corresponding values the equation can be written as h(t) = -16t² + 32t + 6.

Hence, the required equation for the path of the ball in the air is  h(t) = -16t² + 32t + 6.

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Answer:

a is the answer for this question

Answer:

89m

Step-by-step explanation

area of the triangle 15

area of the rectangle 104

104-15=89m

Answer:

[tex]89[/tex] [tex]m^{2}[/tex]

Step-by-step explanation:

area of a triangle  = [tex]\frac{bh}{2}[/tex]

so [tex]\frac{(5)(6)}{2}[/tex] = 15 [tex]m^{2}[/tex]

area of a rectangle = [tex]\\ bh[/tex]

so [tex]\\ 8[/tex]×[tex]\\ 13[/tex] [tex]\\ = 104[/tex] [tex]m^{2}[/tex]

so the area of the figure is

[tex]\\ 104[/tex] [tex]m^{2}[/tex] -  15 [tex]m^{2}[/tex] = [tex]89[/tex] [tex]m^{2}[/tex]

Answer:

Yep......a lot of notifications on my phone.....lol

thx for points!

Follow me! :)

Answer:

27.7 cm

Step-by-step explanation:

(12,45cm + 2.8cm)=(belinda's shoe+felix added cm)= felix's shoe

12,45cm= belinda shoe

combined lenght = 12,45+ 15,25=27.7 cm

The combined length of the Belinda's shoe which is 12.45 centimeters long and Felix's shoe is 27.7 centimeters.

Length measurement is the measurement of the size of a object. The units of length measurement are meter, feet, yards etc.

In the metric system of length measurement the units are meter, kilometer, centimeter etc.

Belinda's shoe is 12.45 centimeters long.  Felix's shoe is 2.8 centimeters longer than Belinda's shoe. Let suppose the length of Felix's shoe is x meters. Thus,

[tex]x=12.45+2.8\\x=15.25\rm\; cm[/tex]

In centimeters, the combined length of their two shoes is,

[tex]l=15.25+12.45\\l=27.7\rm\; cm[/tex]

Thus, the combined length of the Belinda's shoe which is 12.45 centimeters long and Felix's shoe is 27.7 centimeters.

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Answer:

They donated 6%.

Step-by-step explanation:

The total sales were $9800.

The amount donated is $588.

We want to know what percent of 9800 is 588.

Let's make an equation.

what percent of 9800 is 588

x/100 • 9800 = 588

Divide by 9800.

x/100 = 0.06

Multiply by 100.

x = 6

They donated 6%.

Hope this helps!

Answer:

149500

Step-by-step explanation:

since there's 8 goats, each goat would be 1040000/8, which is 130000 per goat.

marketing at a 15% increase means the new percentage would be 115%, which could be represented by 1.15.

130000 * 1.15 = 149500 / goat

Answer:

72.3

Step-by-step explanation:

So, to find the average you need to add all the numbers together and divide it by the amount of numbers there are, if that makes sense.

so in your question: 100 + 90 + 80 + 89 + 75 + 0= 434

and there are 6 numbers that you had to add together, so you divide 434 by 6, which is 72.3 so that's the answer! It's quite easy once you understand how to do it :)

Answer:

(2x + 1)(x + 5).

Step-by-step explanation:

`y=2x^2+11x+5`

2 * 5 = 10

1 * 10 = 10 and  1 + 10 = 11 so we write:

y = 2^2 + 10x + x + 5

y = 2x(x + 5) + 1(x + 5)

= (2x + 1)(x + 5).

8) is B

9) is also B ([tex]y=2x+3[/tex])

Step-by-step explanation:

12a-9a>-12+6

3a>-6/:3

a>-2

c is the answer

Answer:

Step-by-step explanation:

Welcome to the concept of the maths.

Here, we can see, that Linear equation always have highest power or degree of its variable as '1' ,

thus here, y = 3/x has degree as -1 and y = x^2 +5 has degree 2 ,

hence,

The equations that are NOT linear are

2.) y = 3/x and 5.) y = x^2 + 5

The lateral area of the cone is 20π square centimeters.

Given that a cone with base radius of 4 cm and the height is 3 cm, we need to find the lateral area of the cone,

The lateral area of a cone can be calculated using the formula:

Lateral Area = π r l

where:

π is a mathematical constant approximately equal to 3.14159.

r is the radius of the base of the cone.

l is the slant height of the cone.

To find the slant height, we can use the Pythagorean theorem.

The slant height (l) is the hypotenuse of a right triangle formed by the height (h) and the radius (r) of the cone.

The formula is:

l = √(r² + h²)

Given that the base radius (r) is 4 cm and the height (h) is 3 cm, we can calculate the slant height (l):

l = √(4² + 3²)

= √(16 + 9)

= √(25)

= 5

Now we can substitute the values into the formula for the lateral area:

Lateral Area = π r l

= π × 4 × 5

= 20π

Therefore, the lateral area of the cone is 20π square centimeters.

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Answer:

64 square units

Step-by-step explanation:

if you spilt up the polygon you can find the area of the square and triangle making up the square.

length * width = Area;   6 * 8 = 48 sq units for the square part

1/2 * base * height = Area;   1/2 * 4 * 8 = 16 sq units for the triangle part

then add the two areas together for the area of the entire polygon:

48 + 16 = 64 sq units

Answer:

4.8%

Step-by-step explanation:

Answer:4.8

Step-by-step explanation:

Trust

Answer:

:)

Step-by-step explanation:

  HM    TM    M    HTH    TTH    TH     H     T    O

1.                     2        4         5        8       2     3    6

2.             4     5       3          7        9        2     0   0

3.                              1           5        7       9      0   5

4.  3        7      8       2           6      4        3       3    5

5.                                          6        7        8     9     4

Answer:

The answer is 0.0085 So I'm guessing less than one.

Answer:

Q = (9, 4 )

Step-by-step explanation:

Use the midpoint formula and equate to the coordinates of the midpoint.

M = ([tex]\frac{x_{1}+x_{2} }{2}[/tex] ) , ([tex]\frac{y_{1}+y_{2} }{2}[/tex] )

let the coordinates of Q = (x, y ) , R = (- 7, 0 ) , then

[tex]\frac{x-7}{2}[/tex] = 1 ( multiply both sides by 2 )

x - 7 = 2 ( add 7 to both sides )

x = 9

and

[tex]\frac{y+0}{2}[/tex] = 2 ( multiply both sides by 2 )

y = 4

Thus Q = (9, 4 )

Answer:

The probability that none of the balls selected is red ²⁴/₉₁

Step-by-step explanation:

Given;

number of red balls, R = 5

number of white balls, W = 4

number of blue balls, B = 6

Total number of balls, = 5 + 4 + 6 = 15

Probability of selecting 3 none red balls = P(WWW) or  P(BBB) or P(WWB) or  P(WBW) or P(BWW) or P(BBW) or P(BWB) or P(WBB)

[tex]P = (\frac{4}{15} \times \frac{3}{14} \times \frac{2}{13} ) + (\frac{6}{15} \times \frac{5}{14} \times \frac{4}{13} ) + (\frac{4}{15} \times \frac{3}{14} \times \frac{6}{13} ) + (\frac{4}{15} \times \frac{6}{14} \times \frac{3}{13} ) + \\\\(\frac{6}{15} \times \frac{4}{14} \times \frac{3}{13} ) + (\frac{6}{15} \times \frac{5}{14} \times \frac{4}{13} ) + (\frac{6}{15} \times \frac{4}{14} \times \frac{5}{13} ) + (\frac{4}{15} \times \frac{6}{14} \times \frac{5}{13} )[/tex]

[tex]P = \frac{24}{2730} + \frac{120}{2730} + \frac{72}{2730} +\frac{72}{2730} + \frac{72}{2730} + \frac{120}{2730} + \frac{120}{2730} + \frac{120}{2730} \\\\P = \frac{720}{2730} \\\\P = \frac{24}{91} \\\\[/tex]

Therefore, the probability that none of the balls selected is red ²⁴/₉₁

Answer:

26

Step-by-step explanation:

Answer:

Distribute

Subtract   two from both sides of the equation

Simplify

and that's your solution

which should be t=4

Step-by-step explanation:

Answer:

Bank 3

Step-by-step explanation:

No additional charges for automatic deposit and includes saving account.

Answer:

Step-by-step explanation:

From what I understand, you are trying to solve for a.

So,

d=g+2ac

d-g=2ac

(d-g)/2c=a

So,

a = (d-g) / 2c