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3 years ago

Ella collects 50 bottles to recycle. Of the bottles she collects, 19 are plastic and the rest are glass.

1 answer:

8 0

QUESTION A

The total number of bottles Ella collected is
$50$

The number of bottles that are plastic is

$19$

The percentage of bottles that are plastic is

$= \frac{number \: of \: plastic \: bottles}{total \: number \: of \: bottes} \times 100\%$

$= \frac{19}{50} \times 100\%$

$= 19 \times 2\%$
$= 38\%$

Therefore 38% of the bottles are plastic.

QUESTION B

The total number of bottles that are glass is
$50 - 19 = 31$

The total number of bottles Ella collected is
$50$

The percentage of bottles that is glass is
$= \frac{number \: of \: glass \: bottles}{total \: number \: of \: bottles} \times 100\%$

$= \frac{31}{50} \times 100\%$

$= 31 \times 2\%$
$= 62\%$

Therefore 62% of the bottles are glass

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3 years ago

(08.07 HC)

andreev551 [17]

Answer:

$\textsf{A)} \quad x=-2, \:\:x=\dfrac{5}{2}$

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

C) See attachment.

Step-by-step explanation:

Given function:

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

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$\implies ac=2 \cdot -10=-20$

$\implies b=-1$

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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):

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

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

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

Therefore:

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

$\implies (2x-5)=0 \implies x=\dfrac{5}{2}$

So the x-intercepts are:

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

The x-value of the vertex is:

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

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

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Therefore, the vertex of the function is:

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

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