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lora16 [44]
3 years ago
8

What is the vertex of the graph of the function f(x) = x^2 + 8x - 2?

Mathematics
1 answer:
notsponge [240]3 years ago
8 0

Answer:

(-4,-18)

Step-by-step explanation:

go to math(way).com to find the answer

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The segment AC is?
Rama09 [41]

Answer:

B

Step-by-step explanation:

the hypotenuse........

6 0
1 year ago
Read 2 more answers
Use trigonometric substitution to evaluate the integral 13 + 12x − x2 dx . First, write the expression under the radical in an a
SCORPION-xisa [38]

I don't see a square root sign anywhere, so I'll assume the integral is

\displaystyle\int\sqrt{13+12x-x^2}\,\mathrm dx

First complete the square:

13+12x-x^2=49-(6-x)^2=7^2-(6-x)^2

Now in the integral, substitute

6-x=7\sin t\implies\mathrm dx=-7\cos t\,\mathrm dt

so that

t=\sin^{-1}\left(\dfrac{6-x}7\right)

Under this change of variables, we have

7^2-(6-x)^2=7^2-7^2\sin^2t=7^2(1-\sin^2t)=7^2\cos^2t

so that

\displaystyle\int\sqrt{13+12x-x^2}\,\mathrm dx=-7\int\sqrt{7^2\cos^2t}\,\cos t\,\mathrm dt=-49\int|\cos t|\cos t\,\mathrm dt

Under the right conditions, namely that cos(<em>t</em>) > 0, we can further reduce the integrand to

|\cos t|\cos t=\cos^2t=\dfrac{1+\cos(2t)}2

\displaystyle-49\int|\cos t|\cos t\,\mathrm dt=-\frac{49}2\int(1+\cos(2t))\,\mathrm dt=-\frac{49}2\left(t+\frac12\sin(2t)\right)+C

Expand the sine term as

\dfrac12\sin(2t)}=\sin t\cos t

Then

t=\sin^{-1}\left(\dfrac{6-x}7\right)\implies \sin t=\dfrac{6-x}7

t=\sin^{-1}\left(\dfrac{6-x}7\right)\implies \cos t=\sqrt{7^2-(6-x)^2}=\sqrt{13+12x-x^2}

So the integral is

\displaystyle-\frac{49}2\left(\sin^{-1}\left(\dfrac{6-x}7\right)+\dfrac{6-x}7\sqrt{13+12x-x^2}\right)+C

3 0
3 years ago
A big-screen TV that previously sold for $2,400 has been marked down to $2,040. What is the percent of decrease?
Hitman42 [59]

[~Answer~] (8.):
Heyyy. I'm Avery, and I'm always here to help!

I believe the percent may be 15% ($2,400 - 15% = $2,040)

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

[~Answer Explanation~}:

The percent of the difference is the rate of the difference * 100%

the percent of the difference = .15 * 100% = 15%

since the new price is less than the old price, that is the percent of the decrease.

(See if it'll work): $2,400- 15% = $2,040

And there's your answer <33

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
[~Last Messages~}:

<em>Hope this helped you <333
Bye!

</em><u><em>[-!AveryIsSomeHowAlive!-]

</em></u><em>"Just call me and I will be there :)"</em>

3 0
2 years ago
There were 36 balloons at the beginning of the party. By the end of the party, d of them popped. Using d, write an expression fo
kap26 [50]

Answer:

b=36-d

Step-by-step explanation:

b=balloons after being popped

d=balloons popped

6 0
2 years ago
Find the inverse function of <img src="https://tex.z-dn.net/?f=y%3D3%5E%7Bx-2%7D" id="TexFormula1" title="y=3^{x-2}" alt="y=3^{x
kirill [66]

Step-by-step explanation:

Inverse of

y

=

x

+

3

x

−

2

is

y

=

2

x

+

3

x

−

1

Explanation:

As

y

=

x

+

3

x

−

2

x

y

−

2

y

=

x

+

3

or

x

y

−

x

=

2

y

+

3

or

x

(

y

−

1

)

=

2

y

+

3

or

x

=

2

y

+

3

y

−

1

Hence inverse of

y

=

x

+

3

x

−

2

is

y

=

2

x

+

3

x

−

1

Observe that each of the function is a reflection of the other in the line

x

=

y

.

graph{(y-(x+3)/(x-2))(y-(2x+3)/(x-1))(x-y)=0 [-10, 10, -5, 5]}

6 0
3 years ago
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