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3 years ago

What's the answer and how do I work the problem out?!!

Mathematics

1 answer:

Kobotan [32]3 years ago

5 0

If 28% is 42 people
you have to get from 28 to 100 by timsing 28 by '?'
100/28 =3.57142857143
3.57142857143 x42=150 people

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Find the focus and the directrix for the parabola with the given equation.

musickatia [10]

Answer:

$\mathrm{Focus:\;\;} \left(-\frac{5}{3},\:2\right)$

$\mathrm{Directrix:\;\;}x=-\frac{1}{3}$

Step-by-step explanation:

The standard equation for a parabola is

$4p\left(x-h\right)=\left(y-k\right)^2$

with vertex at (h, k) and a focal length of |p|

$\mathrm{Rewrite}\:x=-\frac{3}{8}\left(y-2\right)^2-1\:\mathrm{in\:the\:standard\:form}$ :

$\mathrm{Add\:}1\mathrm{\:to\:both\:sides}$

$x+1=-\frac{3}{8}\left(y-2\right)^2-1+1$ or

$x+1=-\frac{3}{8}\left(y-2\right)^2$

$\mathrm{Divide\:both\:sides\:by\:}-\frac{3}{8}$
$\frac{x+1}{-\frac{3}{8}}=\frac{-\frac{3}{8}\left(y-2\right)^2}{-\frac{3}{8}}$

$\mathrm{Simplify}$
$-\frac{8x}{3}-\frac{8}{3}=\left(y-2\right)^2$

$\mathrm{Factor\:}-\frac{8}{3}$
$\left(-\frac{8}{3}\right)\left(x+\frac{-\frac{8}{3}}{-\frac{8}{3}}\right)=\left(y-2\right)^2$

$\mathrm{Simplify}$
$\left(-\frac{8}{3}\right)\left(x+1\right)=\left(y-2\right)^2$

$\mathrm{Factor\:}4$
$4\cdot \frac{-\frac{8}{3}}{4}\left(x+1\right)=\left(y-2\right)^2$

$\mathrm{Simplify}$
$4\left(-\frac{2}{3}\right)\left(x+1\right)=\left(y-2\right)^2$

$\mathrm{We\; can\; rewrite\:this\;as}$
$4\left(-\frac{2}{3}\right)\left(x-\left(-1\right)\right)=\left(y-2\right)^2$

Comparing this with the standard form we get
$\left(h,\:k\right)=\left(-1,\:2\right)$
$\:p=-\frac{2}{3}$

The parabola is symmetric around the x-axis.

The focus lies a distance $p$ from the center $\left(-1,\:2\right)$ along the x axis

So focus is at
$\left(-1+p,\:2\right)$ $=\left(-1+\left(-\frac{2}{3}\right),\:2\right)$ $=\bold{ \left(-\frac{5}{3},\:2\right)}$

The parabola is symmetric around the x-axis and so the directrix is a line parallel to the y-axis at a distance -p from the center

$x=-1-p$

$x=-1-\left(-\frac{2}{3}\right) = \bold{-\frac{1}{3}}$

3 0

2 years ago

Help me pls need help

alexira [117]

Answer:

9s+11

Step-by-step explanation:

Combine like terms → (7s+2s and 2+9 = 9s and 11) and boom

7 0

3 years ago

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john currently has $50 in savings. he had been saving $8 each week. yesterday he spent $142 of the savings. for how many weeks h

anastassius [24]

Answer:

24 weeks

Step-by-step explanation:

He now has $50.

He just spent $142.

Before spending the $142, he had a total of

$142 + $50 = $192

He had saved a total of $192.

He saves $8 per week.

$192/$8 = 24

He saved for 24 weeks.

3 0

4 years ago

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Find the midpoint of a line segment with given endpoints (4,-5) and (-6,3)

Mashcka [7]

The equation for the midpoint of a line segment is $( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$ . Thus, the midpoint of this segment is $(\frac{4 + (-6)}{2}, \frac{-5 + 3}{2}) = \boxed{(-1, -1)}$ .

3 0

4 years ago

A(t)=400e^-0.032(t) after 3, 8 and 10 yrs

tatyana61 [14]

Answer:

10 yrs

Step-by-step explanation:

3 0

3 years ago

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