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Oduvanchick [21]
3 years ago
10

Which point is the vertex of the quadratic function f(x) = x^2-6+8?

Mathematics
1 answer:
Free_Kalibri [48]3 years ago
7 0

Answer:

Step-by-step explanation:

f(x)= x^2 - 6x + 8

a of s= 6/2 = 3

(3)^2 - 6(3) + 8

9 - 18 + 8

-9 + 8 = -1

(3, -1)

answer is B

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Find the unknown side length. Write your answer in simplest radical form.
Eva8 [605]

Answer: 1. x= 20 units,   2. x= 5\sqrt{3} units    3. x= 4\sqrt{2} units.

Step-by-step explanation:

In a right triangle,

Hypotenuse^2= Perpendicular^2+Base^2  (Pythagoras theorem)

1. Hypotenuse = x , Base = 16, Perpendicular = 12

\Rightarrow\ x^2 =12^2+16^2\\\\ \Rightarrow\ x^2=144+256\\\\ \Rightarrow\ x^2=400\\\\ \Rightarrow\ x=\sqrt{400}=20

2. Hypotenuse = 14 , Base = 11, Perpendicular = x

\Rightarrow\ 14^2=x^2+11^2\\\\\Rightarrow\ 196=x^2+121\\\\\Rightarrow\ x^2=196-121\\\\\Rightarrow\ x^2 = 75\\\\\Rightarrow\ x=\sqrt{75}=\sqrt{25\times3}=5\sqrt{3}

3.  Hypotenuse = 9 , Base = x, Perpendicular =7

\Rightarrow\ 9^2=x^2+7^2\\\\\Rightarrow\ 81= x^2+49\\\\\Rightarrow\ x^2=81-49\\\\\Rightarrow\ x^2=32\\\\\Rightarrow\ x=\sqrt{32}=\sqrt{16\times2}\\\\\Rightarrow\ x=4\sqrt{2}

5 0
3 years ago
Can you graph this equation - Y=3×^2
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So you start at 0 then (1,3) , (2,12) and the other side would be (-1,3) , (-2,12)
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In 2013, the moose population in a park was measured to be 5,100. By 2018, the population was measured again to be 5,200. If the
natka813 [3]

Answer:

P(t) = 5100e^{0.0039t}

Step-by-step explanation:

The exponential model for the population in t years after 2013 is given by:

P(t) = P(0)e^{rt}

In which P(0) is the population in 2013 and r is the growth rate.

In 2013, the moose population in a park was measured to be 5,100

This means that P(0) = 5100

So

P(t) = 5100e^{rt}

By 2018, the population was measured again to be 5,200.

2018 is 2018-2013 = 5 years after 2013.

So this means that P(5) = 5200.

We use this to find r.

P(t) = 5100e^{rt}

5200 = 5100e^{5r}

e^{5r} = \frac{52}{51}

\ln{e^{5r}} = \ln{\frac{52}{51}}

5r = \ln{\frac{52}{51}}

r = \frac{\ln{\frac{52}{51}}}{5}

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So the equation for the moose population is:

P(t) = 5100e^{0.0039t}

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3 years ago
These five frames show a shapes different positions
kipiarov [429]

From the attached image, we can tell that:

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From 4 to 5: There is a 180° rotation in the clockwise direction.

<h3>What is a rotation?</h3>

It is to be noted that a rotation is a sort of transformation that rotates each point in a figure a specific number of degrees around a particular point.

Learn more about rotation in math:
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Full Question:

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Answer is <

Why? 1/4 is smaller than 1/2

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2 slices > 4 slices

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