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IRINA_888 [86]
3 years ago
7

Which number line shows the solution set for StartAbsoluteValue 8 minus 2 p EndAbsoluteValue = 6?

Mathematics
1 answer:
Illusion [34]3 years ago
5 0

Answer:

A number line going from negative 1 to positive 7. Points are at positive 1 and positive 7.

Step-by-step explanation:

We have the equation:

|8 - 2*p| = 6

Remember that the equation:

|f(x)| = A

with A > 0

means that:

f(x) = A

or

f(x) = -A

Then for our case, we can rewrite:

|8 - 2*p| = 6

as:

(8 - 2*p) = 6

or

(8 - 2*p) = -6

Now we can solve these two equations to find the two possible values of p.

From the first one, we get:

8 - 2*p = 6

8 - 6 = 2*p

2 = 2*p

2/2 = p = 1

so one solution is  p = 1

Now from the other equation, we can get the other solution:

(8 -2*p) = -6

8 - 2*p = -6

8 + 6 = 2*p

14 = 2*p

14/2 = p = 7

So the two solutions are p = 1 and p = 7

Then the correct option is:

"A number line going from negative 1 to positive 7. Points are at positive 1 and positive 7."

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Nesterboy [21]

Answer:

Vertex form: f(x)=(x-1)^2-3

Standard form: f(x)=x^2-2x-2

Step-by-step explanation:

A quadratic function in vertex form is f(x)=a(x-h)^2+k where (h,k) is the vertex.

We are given h=1,k=-3.

Let's plug that in:

f(x)=a(x-1)^2-3.

Now let's find a.

We will use the y-intercept (0,-2) to find a.

f(0)=a(0-1)^2-3

-2=a(0-1)^2-3

-2=a(-1)^2-3

-2=a(1)-3

-2=a-3

1=a

So the function in vertex form is:

f(x)=(x-1)^2-3.

In standard form, we will have to multiply and combine any like terms.

Let's do that:

f(x)=(x-1)(x-1)-3

f(x)=x^2-x-x+1-3

f(x)=x^2-2x-2

5 0
3 years ago
A circle with radius \pink{9}9start color #ff00af, 9, end color #ff00af has a sector with a central angle of \purple{120^\circ}1
GrogVix [38]

Answer:

Area of sector = 84.861

Step-by-step explanation:

Given

The radius of the circle = 9

central angle of sector = 120^{o}

value of pi π = 3.143

To find : the area of sector = ?

We know that the formula to calculate area of sector is given as:

area of sector = (π r^{2}Θ)/ 360^{o}

where, r  is radius and Θ is the central angle of the sector

Substituting the known values in above formula, we get

area of sector = (3.143 x 9^{2} x 120^{o}) / 360^{o}

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Hence area of sector is 84.861

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There are two scales that may be possible for this scale model; one where it's for every foot and one where it's for every meter.
The for every foot would be better to find out since the scale would be easier to use.
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