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allochka39001 [22]
3 years ago
15

80% of blank games is 32 games

Mathematics
2 answers:
sergejj [24]3 years ago
8 0
80% of how many games = 32
0.80x = 32
x = 32/0.80
x = 40......so 80% of 40 is 32 games
Svetach [21]3 years ago
6 0
32 is 80% of x games
32=.8*x games
32/.8=x games
40=x games
x=40
80% of 40 games is 32 games.

Hope this helps!
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\textsf{A)} \quad x=-2, \:\:x=\dfrac{5}{2}

\textsf{B)} \quad \left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)

C)  See attachment.

Step-by-step explanation:

Given function:

f(x)=2x^2-x-10

<h3><u>Part A</u></h3>

To factor a <u>quadratic</u> in the form  ax^2+bx+c<em> , </em>find two numbers that multiply to ac and sum to b :

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\implies b=-1

Therefore, the two numbers are -5 and 4.

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Factor the first two terms and the last two terms separately:

\implies f(x)=x(2x-5)+2(2x-5)

Factor out the common term  (2x - 5):

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The x-intercepts are when the curve crosses the x-axis, so when y = 0:

\implies (x+2)(2x-5)=0

Therefore:

\implies (x+2)=0 \implies x=-2

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So the x-intercepts are:

x=-2, \:\:x=\dfrac{5}{2}

<h3><u>Part B</u></h3>

The x-value of the vertex is:

\implies x=\dfrac{-b}{2a}

Therefore, the x-value of the vertex of the given function is:

\implies x=\dfrac{-(-1)}{2(2)}=\dfrac{1}{4}

To find the y-value of the vertex, substitute the found value of x into the function:

\implies f\left(\dfrac{1}{4}\right)=2\left(\dfrac{1}{4}\right)^2-\left(\dfrac{1}{4}\right)-10=-\dfrac{81}{8}

Therefore, the vertex of the function is:

\left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)

<h3><u>Part C</u></h3>

Plot the x-intercepts found in Part A.

Plot the vertex found in Part B.

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Draw a upwards opening parabola that has a minimum point at the vertex and that passes through the x-intercepts (see attachment).

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