Rewrite the quadratic equation y=x2-8x+19 in vertex form

Any help would be appreciated. Thank you!

trapecia [35]

Answer:

Area $=62.5\sqrt{6}$ square units

$AB=5\sqrt{15}$ units

$BC=5\sqrt{10}$ units

Step-by-step explanation:

In a right triangle the altitude drawn to the hypotenuse is the geometric mean of the segments at which this altitude divides the hypotenuse.

So,

$BD^2=15\cdot 10\\ \\BD^2=150\\ \\BD=\sqrt{150}=5\sqrt{6}\ units$

a. The area of the triangle ABC is

$A_{ABC}=\dfrac{1}{2}\cdot BD\cdot AC=\dfrac{1}{2}\cdot 5\sqrt{6}\cdot (15+10)=\dfrac{125\sqrt{6}}{2}=62.5\sqrt{6}\ un^2.$

b. The legs of the right triangle are geometric means of the segment adjacent to this leg and the hypotenuse, so

$AB^2=AD\cdot AC=15\cdot 25\Rightarrow AB=5\sqrt{15}\ units\\ \\BC^2=CD\cdot AC=10\cdot 25\Rightarrow BC=5\sqrt{10}\ units$

5 0

3 years ago

Please help fast will give brainliest

MrRa [10]

Answer:

MN = 160

Step-by-step explanation:

We know that arc MN = arc NO

17g - 10 = 14g+ 20

Subtract 14g from each side

3g -10 = 14g-14g+20

3g -10 =20

Add 10 to each side

3g = 20+10

3g = 30

Divide by 3

3g/3= 30/3

g= 10

We want the arc MN

17g - 10

17(10) - 10

170 -10

160

5 0

3 years ago

Patrick’s luck had changed over night – but not his skill at mathematical reasoning. The day after graduating from college he us

Verdich [7]

Answer:

I assume Josh and Peyton are his friends and both gave him advice on what to do with half of the money from the big lottery win.

Let's say Josh said "save it or invest it for your retirement" and Peyton said "use it to keep playing the lottery.

We will now look at the sense in each piece of advice!

Step-by-step explanation:

JOSH

By investing the $250,000 (half of the money won), Patrick will be sure that the money is available for him anytime and would even have gotten interest, by the time he's ready to use it.

PEYTON

By playing the lottery continuously, Patrick could get lucky once in a while and win big again. How big though?

Analyzing with the figures given,

$20 gets Patrick a lottery ticket.

$250,000 will get him 12,500 lottery tickets!

Whether he's buying the tickets at once or he'll play the lottery once in a while, I'll say he has good chances of winning big again.

So if the probability of winning big after purchasing up to 12,500 tickets is close to 1, Patrick should play the lottery with the $250,000

If the probability of winning big after purchasing 12,500 lottery tickets is close to 0 (closer to 0 than it is to 1) then Patrick should invest the $250,000 in retirement.

5 0

3 years ago

What is the point-slope form of a line that has a slope of –4 and passes through point (–3, 1)?

ivolga24 [154]

Answer:

y-1= -4(x-(-3))

y minus 1 = negative 4 left-bracket x minus (negative 3) right-bracket

Step-by-step explanation:

The formula for point slope form is written: $y-y_{1} = m(x-x_{1})$ . Now we fill in our know information. m=-4 (because that is the slope), $y_{1}$ =1 (It is the y value in the ordered pair), $x_{1}$ = -3 (It is the x value in the ordered pair).

y-1=-4(x- (-3))

4 0

3 years ago

after riding the stationary bike for just 8 minutes, betty had burned 50 calories. how long must she ride if she wants to burn 3

Lyrx [107]

Answer:

52 minutes.

Step-by-step explanation:

4 0

3 years ago