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dybincka [34]
4 years ago
14

The equation of a parabola is given.

Mathematics
1 answer:
Leokris [45]4 years ago
4 0
We have that
y = -5/8 x²- 3x + 4----> multiply by 8----> 8y=-5x²-24x+32
8y-32=-5x²-24x

Factor the leading coefficient

8y-32=-5*(x²+4.8x)

Complete the square  Remember to balance the equation by adding the same constants to each side.

8y-32=-5*(x²+4.8x+5.76-5.76)
8y-32-28.8=-5*(x²+4.8x+5.76)
8y-60.8=-5*(x+2.4)²
8*(y-7.6)=-5*(x+2.4)²
-(8/5)*(y-7.6)=(x+2.4)²
-(1.6)*(y-7.6)=(x+2.4)²

is a vertical parabola-----> open down
The standard form is (x - h)²<span> = 4p (y - k)
</span>
the vertex is the point (-2.4,7.6)
4p=-1.6
p=-1.6/4----> p=-0.40

<span>the directrix is
 y= k - p-------> 7.6-(-0.40)----> y=7.6+0.40----> y=8
</span>
the answer is
y=8
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Step-by-step explanation:

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3 years ago
there is 1 litre of tea in a teapot, alex pours 275ml of the tea into a cup what percentage of the tea has alex poured
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Answer:

27.5%

Step-by-step explanation:

Given:

  • 1 Liter In Teapot
  • Alex poured 275 milliliters of the tea into a cup

Review:

  • 1,000 Milliliters = 1 Liter

Concepts:

  • A liter is a noun meaning a unit of capacity redefined in 1964 by a reduction of 28 parts in a million to be exactly equal to one <em>cubic </em>decimeter. It is equivalent to <em>1.0567</em>  U.S. liquid <u>quarts </u>and is equal to the volume of 1 kilogram of distilled <em>water</em> at 4°C.
  • A millimeter is a noun meaning a unit of capacity <em>equal</em> to one <u>thousandth </u>of a liter, and equivalent to <em>0.033815</em> fluid<u> </u><u>ounce</u>, or<em> 0.061025</em><em> </em>cubic<u> inch</u>.

Formula:

  • The <em>mℓ</em> to <em>ℓ</em> formula is<em> [L] = [mL] / 1000</em>.

Now we must convert <em>275</em> milliliters to liters.

1. Divide the volume by <em>1,000.</em>

275 ÷ 1000 = 0.275

2. Add the Unit Symbol for Liter.

0.275 ⇒ 0.275 L

Now we have to find how much of 1 liter- 0.275 liters as a percentage is.

To convert <em>0.275</em> to percent multiply <em>0.275</em> by <em>100</em>. The result is <em>27.5 </em>percent, or, using the percent sign, <em>27.5 %.</em>

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2 years ago
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Step-by-step explanation:

459( 569 /7 )+997

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837150 /7

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3 years ago
6 students share 4 bagels equally
babunello [35]
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4 years ago
An assembly line produces 2 toasters per minute. It is 2:00pm and the line has finished 560 out of its goal of 900 for the day.
LenaWriter [7]

Answer:

I won't stop the line for a half hour break.

Step-by-step explanation:

<u>Proportions</u>

One quantity A is said to be proportional to other B if A can always be obtained by multiplying or dividing B by any constant number. Numbers {4,8,12} are proportional to {2,4,6} because they can be computed as twice their value

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There is a situation described in the problem where we need to know if there will be enough time to produce the 900 toasters (the goal for the day) when the assembly line is stopped by half an hour.

Actual time: 2:00 pm

Final time: 5:00 pm

Rate of production: 2 toasters/minute

Actual production: 560 toasters

Updated goal: 900-560 = 340 toasters  

Those 340 toasters must be produced in the remaining 3 hours (180 minutes) of work. If the assembly line stops for half an hour (30 minutes), there will be only 150 minutes to finish the goal production. At a rate of 2 toasters/minute, there will be 2*150 = 300 toasters produced. But we need to produce 340 more toasters, so that break cannot be granted or we'll be 40 toasters under goal.

It the line keeps producing for 180 minutes, it would produce 2*180 = 360 toasters, 20 more than the goal.

Note: The maximum break time that can be granted is 20/2 = 10 minutes

4 0
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