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padilas [110]
3 years ago
13

determine the vertex and axis of symmetry for the following: f(x) = 2x to the power of 2 - 12x + 24 ?

Mathematics
1 answer:
Vikki [24]3 years ago
7 0

Answer:

vertex = (3,24)  Axis of symmetry = 3

Step-by-step explanation:

Use the vertex formula to find x: x=-b/2(a)

x= 12/2(2) = 3 (this is your axis of symmetry)

Substitute 3 for x in the equation to get y: y = 42

Once you have both x and y you have your vertex.

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Solve the equation to find a positive value of c:<br> 32 + 42 = c2
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Answer:

5

Step-by-step explanation:

7 0
3 years ago
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A model for the density δ of the earth’s atmosphere near its surface isδ=619.09−0.000097pwhere p (the distance from the center o
natta225 [31]

Answer: 3.751*10^18kg

Step-by-step explanation:

δ =619.09−0.000097p....equa1 where p (the distance from the center of the earth) is measured in meters and δ is measured in kilograms per cubic meter.

Calculating the density of air at 5km above earth surface

P = 5000m + 6370000m = 6.375*10^6m

δ = 619.09 -(.000097* 6.375*10^6)

δ = 0.715kg/m^3 = density

Since Mass = density*volume...equ2

To calculate volume of air around the spherical earth at height 5km

V = (4/3 pai R^3) - (4/3pai r^3) ...equation 3 where R =6.375*10^6m, r = 6.37*10^6

Substituting R and r in equation 2 to solve for volume of air

V = 1.085*10^21 - 1.08*10^21

V = 5.25*10^18m^3

Substituting δ and V into equation 2 to solve for mass of air

M = 0.715 * (5.25*10^18)

M = 3.751*10^18kg

8 0
3 years ago
Three postal workers can sort a stack of mail in 20 ​minutes, 30 ​minutes, and 60 ​minutes, respectively. Find how long it takes
Step2247 [10]

Answer: 10 minutes

Step-by-step explanation:

Given : Three postal workers can sort a stack of mail in 20 ​minutes, 30 ​minutes, and 60 ​minutes, respectively.

Let T be the time taken by all of them when they working together.

Then , we have the following equation :-

\dfrac{1}{T}=\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{60}\\\\\Rightarrow\dfrac{1}{T}=\dfrac{3+2+1}{60}\\\\\Rightarrow\dfrac{1}{T}=\dfrac{6}{60}=\dfrac{1}{10}\\\\\Rightarrow T=10

Hence, the time taken by all of them when they working together = 10 minutes.

4 0
3 years ago
Is y = 2 a function?
Serjik [45]

Answer:

No

Step-by-step explanation:

Hope it helps......

8 0
4 years ago
Given that B is between A and C. If AB=x, BC =2x-3, and AC = 30. Find x and bc
Artemon [7]

Answer:

x=11

BC=19

Step-by-step explanation:

AB+AC=AC this is because B is in between A and C. So now we can substitute all of the line segments, so we have

x+2x-3=30          Now you add 2x and x

3x-3=30      Now you add 3 to both sides so you can get 3x alone on one side

3x=33        Now you divide both sides by 3 so you get the x alone on one side

x=11

The next step is to substitute x to find BC.

BC=2x-3       Substitute the x with 11

BC=2(11)-3    Then multiply 2 and 11 because that is the rule with parenthesis

BC=22-3        then subrtact the 3 from 22

BC=19

You can check your work by doing AB+BC=AC

11+19=30        substitute your answers and then add them together

30=30

3 0
3 years ago
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