A DVD player that regularly sells for $325 is marked down to $225.75. What is the discount rate?

Using a directrix of y = −3 and a focus of (2, 1), what quadratic function is created?

Lelechka [254]

Answer:

$y=\dfrac{1}{8}(x-2)^2-1$

Step-by-step explanation:

The distance between the focus and the directrix is the vertical distance from the point to the line:

1 -(-3) = 4

The vertex is half that distance between the point and the line, so is at x=2 and ...

y = (-3 +1)/2 = -1

The vertical scale factor of the quadratic is 1/(4p) where p is the distance from vertex to focus. Here, that distance is 2, so the equation in vertex form is ...

y = (1/(4·2))(x -2)² -1

y = (1/8)(x -2)² -1

_____

<em>Check</em>

Any point on the parabola is equidistant from the focus and directrix. This is easily checked at the vertex, which is halfway between focus and directrix, and at the points having the same y-value as the focus. Those two points are (-2, 1) and (6, 1), both of which are 4 units from the focus and 4 units from the directrix.

5 0

3 years ago

Need help with this answer plz help

jeyben [28]

It would be H because 13 has no factors other than 1, and 13.

Hope this helps!

6 0

3 years ago

Read 2 more answers

4 3/4 divided by 1 1/6

ozzi

Answer:

$2\frac{13}{22}$

Step-by-step explanation:

$=\frac{19}{4}\div \frac{11}{6}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}$

$=\frac{19}{4}\times \frac{6}{11}$

$=\frac{19}{2}\times \frac{3}{11}$

$\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}$

$=\frac{19\times \:3}{2\times \:11}$

$\mathrm{Multiply\:the\:numbers:}\:19\times \:3=57$

$=\frac{57}{2\times \:11}$

$\mathrm{Multiply\:the\:numbers:}\:2\times \:11=22$

$=\frac{57}{22}$

$=2\frac{13}{22}$

5 0

3 years ago

A truck that is 10 ft. by 12 ft. by 8 ft. carries cube shaped boxes that have a

dedylja [7]

Answer:

284.4

Step-by-step explanation:

Divide all numbers by 1.5. example: (10)1.5(12)1.5(81.5= 284.444444 but I rounded it to 284. You're welcome

4 0

3 years ago

An object has been thrown straight up into the air. The formula h = vt - 16t^2 gives the height of the object above the ground a

Oxana [17]

Answer:

8 seconds.

Step-by-step explanation:

To solve this question, we need to find the time, $t$ , when $h = 0$ , that is, when the height of the object above the ground is 0 feet.

Substituting $v = 128$ feet per second and $h = 0$ gives the quadratic:

$0 = 128t - 16t^{2}$

Since 128 is divisible by 16, it can be reduced to $0 = 16(8t - t^{2})$ .

We must now solve for $t$ .

We can easily see that one answer to the equation is 0,

$8(0) - (0)^{2} = 0$ (we need not concern ourselves with the 16 outside of the parenthesis as in the equation above, since 16 multiplied by 0 is 0). However this is the time the object is released into the air.

The second answer, $t = 8$ is also easy to see by inspection:

$8(8) - (8)^{2} = 0$ .

Therefore the object lands 8 seconds after it is thrown.

6 0

3 years ago