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3 years ago

10

The high school varsity basketball team played their rival over the weekend. At the end of the first half, the Bobcats had score

d 36 points. Which situation could describe the points that the Bobcats scored?
A
the players made 18 shots and each shot was worth 2 points

B
14 players scored 22 points

C
2 players made 18 three-point shots

D
the players made 36 shots and each shot was worth 2 points

1 answer:

Leni [432]3 years ago

3 0

Answer: A

Step-by-step explanation: CUZ IF U MULTIPLY 18 TIMES 2 ITS 32

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Calculate the quantity based the percentage given or vice versa.<br> 1)40% of $108

xeze [42]

Answer:

43.2

Step-by-step explanation:

40/100 * 108

4/100*108

43.2

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3 years ago

Parabola Equations - Algebra

mash [69]

Answer:

$h=-\frac{1}{6}x^2+2x$

Step-by-step explanation:

The height of the tunnel is modeled by:

$h=rx^2+tx$

Where r and t are constants.

We know that the maximum height of the tunnel h is 6 meters.

And at ground level, the width is 12 meters.

And we want to determine the equation of the parabola.

First, since this is a quadratic, our maximum height h will occur at the vertex of our equation.

The vertex is given by:

$(-\frac{b}{2a}, f(-\frac{b}{2a}))$

In our case, we have the function:

$h=(r)x^2+(t)x$

Hence, a=r; b=t; and c=0.

Therefore, our vertex is:

$\Rightarrow -\frac{t}{2r}$

Thus, if we substitute this back into our equation, we should get 6 since 6 is the maximum height which is determine by the vertex. In other words:

$(6)=r(-\frac{t}{2r})^2+t(-\frac{t}{2r})$

Simplify:

$6=r(\frac{t^2}{4r^2})-\frac{t^2}{2r}$

Simplify:

$6=\frac{t^2}{4r}-\frac{t^2}{2r}$

Combine fractions:

$6=\frac{t^2}{4r}-\frac{2t^2}{4r}=\frac{-t^2}{4r}$

Multiply both sides by the denominator:

$24r=-t^2$

Let's solve for the constant r. Divide both sides by 24. Hence:

$r=-\frac{t^2}{24}$

Now, we can use our knowledge of the width.

We know that the width is 12 meters at ground level.

Hence, when h=0, the <em>difference of our roots</em> is 12.

So:

$0=rx^2+tx$

We can factor:

$0=x(rx+t)$

By the Zero Product Property:

$x=0\text{ or } rx+t=0$

So, the first zero is 0.

Therefore, the second zero <em>must be 12</em> to ensure that our width is 12.

Let's isolate the second zero. Subtract t from both sides:

$rx=-t$

Divide both sides by r:

$x=-\frac{t}{r}$

We know that this zero must be 12. Thus:

$12=-\frac{t}{r}$

We have previously solved for r. Substitute:

$12=-\frac{t}{\frac{-t^2}{24}}$

Simplify:

$12=\frac{24}{t}$

Take the reciprocal of both sides:

$\frac{t}{24}=\frac{1}{12}$

Multiply both sides by 24. Hence, the value of t is:

$t=2$

Now, we can find r. r is given by:

$r=-\frac{t^2}{24}$

By substituting 2 for t, then, we acquire that:

$r=-\frac{(2)^2}{24}=-\frac{4}{24}=-\frac{1}{6}$

Therefore, for:

$h=rx^2+tx$

Our equation is:

$h=-\frac{1}{6}x^2+2x$

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3 years ago

At a movie theater they sell hotdogs and popcorn. The first hour they sold 15 popcorns and 14 hotdogs for a total of $84. The se

Delicious77 [7]

Answer:

1 hotdog cost $2.25

1 popcorn cost $3.5

Step-by-step explanation:

Let the price of hotdog be and that of popcorn be p

For the first hour;

15p + 14h = 84 •••• (i)

for the second hour;

18p + 16h = 99 •••••(ii)

so we want to solve these two equations simultaneously

In equation 1,

14h = 84-15p

h = (84-15p)/14

Simply insert this into equation ii

18p + 16(84-15p)/14 = 99

Multiply through by 14

252p + 1344 - 240p = 1386

1386-1344 = 252p-240p

12p = 42

p = 42/12

p = $3.5

to get cost of hotdogs;

h = (84-15p)/14

Substitute p = 3.5

h = (84-52.5)/14

h = 31.5/14

h = 2.25

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3 years ago

The Extreme Rock Climbing Club planned a climbing expedition. The total cost was $⁢1800, which was to be divided equally among t

CaHeK987 [17]

Let's say "p" people were going to the expedition initially, and the cost for each was "c", now, we know the total cost is 1800, so for "p", folks that'd be 1800/p how much each one cost, namely, how many times "p" goes into 1800.

well, prior to leaving, 15 dropped out, so that leaves us with " p - 15 ", and the cost "c" bumped up to " c + 27 " for each.

$\bf \begin{cases}
\cfrac{1800}{p}=\boxed{c}\\\\
\cfrac{1800}{p-15}=c+27\\\\
----------\\
\cfrac{1800}{p-15}=\boxed{\cfrac{1800}{p}}+27
\end{cases}\\\\
-------------------------------\\\\
\cfrac{1800}{p-15}={\cfrac{1800}{p}}+27\impliedby 
\begin{array}{llll}
\textit{let's multiply both sides by}\quad p(p-15)\\
\textit{to get rid of the denominators}
\end{array}$

$\bf 1800p=1800(p-15)+27[p(p-15)]
\\\\\\
1800p=1800p-27000+27(p^2-15p)
\\\\\\
0=-27000+27(p^2-15p)\implies 0=-27000+27p^2-405p
\\\\\\
\textit{now, let's take a common factor of }27
\\\\\\
0=p^2-15p-1000\implies 0=(p-40)(p+25)\implies p=
\begin{cases}
\boxed{40}\\
-25
\end{cases}$

well, you can't have a negative value of people... so it has to be 40.

so, 40 folks were initially going, then 15 dropped out, how many went on the expedition? 40 - 15.

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4 years ago

Rewrite the equation in slope-intercept form. Then identify the slope and y-intercept.

ZanzabumX [31]

Answer:

Slope intercept form y= mx+b

y= 3/2x-5

slope= 3/2

y-int= -5

Step-by-step explanation:

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3 years ago