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Viefleur [7K]
3 years ago
9

the function f(x) = x2 − 12x 5 written in vertex form is f(x) = (x − 6)2 − 31. what are the coordinates of the vertex? (6, 31) (

−6, 31) (6, −31) (−6, −31)
Mathematics
2 answers:
Elan Coil [88]3 years ago
8 0
F(x)=a(x-h)^2+k
vertex is (h,k)

f(x)=1(x-6)^2-31
f(x)=1(x-(6))^2+(-31)

h=6
k=-31
vertex=(6,-31)
Eduardwww [97]3 years ago
7 0

Answer:

c. -6,31

Step-by-step explanation:

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Which graph represents the function f(x)= 0.2^x + 3
Dennis_Churaev [7]

The third graph or bottom left graph represents f(x) = 0.2^{x} + 3.

Step-by-step explanation:

Step 1:

To determine which of the given graphs represents the equation f(x) = 0.2^{x} + 3, we substitute some values in the place of x.

When x=0, f(x) = 0.2^{x} + 3, f(0) = 0.2^{0} + 3= 4.

Anything with an exponent of 0 will equal 1.

So the graphs on the right side cannot be the answers.

Step 2:

Now we substitute another value to determine which graph represents f(x) = 0.2^{x} + 3.

When x=1, f(x) = 0.2^{x} + 3, f(1) = 0.2^{1} + 3= 4.2.

The value of f(x) when x=1 is lesser than the value of f(x) when x =0.

So the third graph or bottom left graph represents f(x) = 0.2^{x} + 3.

5 0
3 years ago
Which expression below represents "11 more than the difference of b and y?"
gladu [14]
11+b-y
Hope this helps
Have a happy holidays
3 0
2 years ago
Evaluate c (y + 7 sin(x)) dx + (z2 + 9 cos(y)) dy + x3 dz where c is the curve r(t) = sin(t), cos(t), sin(2t) , 0 ≤ t ≤ 2π. (hin
saw5 [17]
Treat \mathcal C as the boundary of the region \mathcal S, where \mathcal S is the part of the surface z=2xy bounded by \mathcal C. We write

\displaystyle\int_{\mathcal C}(y+7\sin x)\,\mathrm dx+(z^2+9\cos y)\,\mathrm dy+x^3\,\mathrm dz=\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r

with \mathbf f=(y+7\sin x,z^2+9\cos y,x^3).

By Stoke's theorem, the line integral is equivalent to the surface integral over \mathcal S of the curl of \mathbf f. We have


\nabla\times\mathbf f=(-2z,-3x^2,-1)

so the line integral is equivalent to

\displaystyle\iint_{\mathcal S}\nabla\times\mathbf f\cdot\mathrm d\mathbf S
=\displaystyle\iint_{\mathcal S}\nabla\times\mathbf f\cdot\left(\dfrac{\partial\mathbf s}{\partial u}\times\dfrac{\partial\mathbf s}{\partial v}\right)\,\mathrm du\,\mathrm dv


where \mathbf s(u,v) is a vector-valued function that parameterizes \mathcal S. In this case, we can take

\mathbf s(u,v)=(u\cos v,u\sin v,2u^2\cos v\sin v)=(u\cos v,u\sin v,u^2\sin2v)

with 0\le u\le1 and 0\le v\le2\pi. Then

\mathrm d\mathbf S=\left(\dfrac{\partial\mathbf s}{\partial u}\times\dfrac{\partial\mathbf s}{\partial v}\right)\,\mathrm du\,\mathrm dv=(2u^2\cos v,2u^2\sin v,-u)\,\mathrm du\,\mathrm dv

and the integral becomes

\displaystyle\iint_{\mathcal S}(-2u^2\sin2v,-3u^2\cos^2v,-1)\cdot(2u^2\cos v,2u^2\sin v,-u)\,\mathrm du\,\mathrm dv
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4 0
3 years ago
What is the geometric mean of 8 and 2?​
Molodets [167]

9514 1404 393

Answer:

  4

Step-by-step explanation:

The geometric mean of two numbers is the square root of their product.

  √(8·2) = √16 = 4

The geometric mean of 8 and 2 is 4.

__

The geometric mean of n numbers is the n-th root of their product.

6 0
3 years ago
Can anyone help me? is it a b c or d
Nataly_w [17]

Answer: choice a

Step-by-step explanation:

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side. Note: This rule must be satisfied for all 3 conditions of the sides.

so it has to be in between 9 and 5

7+2=9

2+x>7

  --> x>5

however, it can't be 5 or 9

Hope this helps! <3

5 0
3 years ago
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