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Virty [35]
2 years ago
10

The quadratic function h(t) = -16.1? + 150 models a ball's height, in feet, over time, in seconds,

Mathematics
1 answer:
Sliva [168]2 years ago
5 0
<h2>Hello!</h2>

The answer is: The first graphic representation.

<h2>Why?</h2>

We are given a quadratic equation, meaning that it could be two possible solutions for the exercise, however, we are talking about time, so we have to consider only the obtained positive values.

Let's make the equation equal to 0 in order to find the values of "t"

h(t) = -16.1t^2 + 150

0=-16.1t^2+150

16.1t^2=150

t^2=\frac{150}{16.1} =9.32

t=+-\sqrt{9.32} =+-3.05

t1=3.05

t2=-305

So, discarding the negative value, we can use the possitive value to find the correct graphic representation.

To find the correct graphic representation we must take into consideration the following:

- We must remember that the sign of the coefficient of the quadratic term (t^2) will define if the parabola opens downward or upward.

From the given quadratic (or parabola) equation we have:

a=-1

b=0

c=150

So, since the coefficient of the quadratic term is negative, the parabola opens downward.

- Since we are looking for a graphic that represents the change in height over time, we need to look for a graphic that shows only positive values for the x-axis (time)

- We are looking for a parabola which y-axis intercept is equal to 150.

Therefore, the graphic representation of the quadratic function that models a ball's height over time is the first graphic representation.

Have a nice day!

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DerKrebs [107]
First, you have to set up two equations. X + y = 45 18x + 24y = 1,050 To do this, you have to solve for an exponent by cancelling out the other one. To solve for y, you multiply everything in the first equation by -18. -18x -18y = -810 This cancels out the x and leaves you with 6y = 240. Divide both sides by 6 and you have the number of Yankee hats that were bought. Then, you have to substitute 40 for y in the first equation and solve for x.
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3 years ago
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inessss [21]

Answer:

(17)

Sum of interior angles of a quadrilateral is 360°

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(18)

Sum of interior angles of a hexagon is 180°*(6 - 2) = 720°

  • 2*90° + 2x + 2(x + 22°) = 720°
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Interior angles of a given pentagon are all marked as congruent, so the exterior angles are congruent too.

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8 0
2 years ago
Please help!!!!
valentina_108 [34]
ANSWER

\frac{ {t}^{2}  + 4t - 12}{ {t}^{2} - 4 }  =  \frac{t  + 6}{ t + 2}
where,
t \ne - 2



EXPLANATION

We want to simplify the rational expression

\frac{ {t}^{2}  + 4t - 12}{ {t}^{2} - 4 }


We can observe that the numerator of the given rational expression is a quadratic trinomial and the denominator is a difference of two squares



We need to split the middle term in the numerator and rewrite the denominator as a difference of two squares to obtain,




\frac{ {t}^{2}  + 4t - 12}{ {t}^{2} - 4 }  =  \frac{{t}^{2}  + 6t - 2t - 12}{ {t}^{2}  -  {2}^{2} }



We now factor to obtain,

\frac{ {t}^{2}  + 4t - 12}{ {t}^{2} - 4 }  =  \frac{t (t+ 6) - 2(t  + 6)}{ (t  -  2)(t + 2)}


This implies that,

\frac{ {t}^{2}  + 4t - 12}{ {t}^{2} - 4 }  =  \frac{(t - 2) (t  + 6)}{ (t  -  2)(t + 2)}


We now cancel out common factors to obtain,

\frac{ {t}^{2}  + 4t - 12}{ {t}^{2} - 4 }  =  \frac{(t  + 6)}{ (t + 2)}


The restriction is that, the denominator cannot be zero.

Thus

t + 2 \ne0


This implies that,

t  \ne - 2
6 0
3 years ago
Read 2 more answers
The sum of all digits of some number is 210. The number is always divisible by:
AlekseyPX

Answer:

2

Step-by-step explanation:

so so that you could get both halves, we had to divide by two then I got 105 +105 meaning 210 could be divided by 2

4 0
3 years ago
Whats the equation of a line with slope 3/5 that passes through the point (15,8)
Elden [556K]

Answer:

y=3/5x-1

Step-by-step explanation:

The formula you need to find this would be

(y-y1)=m(x-x1)

The y1 is your y point.

The x1 is your x point.

m is your slope.

Start by plugging in your numbers that they provide you.

(y-8)=3/5(x-15)

Now you need to distribute the slope to the terms inside the parenthesis next to it.

3/5(x)=3/5x

3/5(-15)= -9       Now you put those back into the equation.

(y-8)=3/5x-9

At this point you can get rid of the parenthesis around the y-8 since it is basically saying to take the term times 1.

To get y alone we not need to add 8 to both sides.

y-8=3/5x-9

+8          +8

y=3/5x-1

3 0
3 years ago
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