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VashaNatasha [74]
2 years ago
14

Which set of numbers represents the DOMAIN for the following table below?

Mathematics
1 answer:
ehidna [41]2 years ago
7 0

Answer:

B. (-12,-3,4,6)

Step-by-step explanation:

The above question is asking the domain

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andrey2020 [161]

First observe that if a+b>0,

(a + b)^2 = a^2 + 2ab + b^2 \\\\ \implies a + b = \sqrt{a^2 + 2ab + b^2} = \sqrt{a^2 + ab + b(a + b)} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{\cdots}}}}

Let a=0 and b=x. It follows that

a+b = x = \sqrt{x \sqrt{x \sqrt{x \sqrt{\cdots}}}}

Now let b=1, so a^2+a=4x. Solving for a,

a^2 + a - 4x = 0 \implies a = \dfrac{-1 + \sqrt{1+16x}}2

which means

a+b = \dfrac{1 + \sqrt{1+16x}}2 = \sqrt{4x + \sqrt{4x + \sqrt{4x + \sqrt{\cdots}}}}

Now solve for x.

x = \dfrac{1 + \sqrt{1 + 16x}}2 \\\\ 2x = 1 + \sqrt{1 + 16x} \\\\ 2x - 1 = \sqrt{1 + 16x} \\\\ (2x-1)^2 = \left(\sqrt{1 + 16x}\right)^2

(note that we assume 2x-1\ge0)

4x^2 - 4x + 1 = 1 + 16x \\\\ 4x^2 - 20x = 0 \\\\ 4x (x - 5) = 0 \\\\ 4x = 0 \text{ or } x - 5 = 0 \\\\ \implies x = 0 \text{ or } \boxed{x = 5}

(we omit x=0 since 2\cdot0-1=-1\ge0 is not true)

3 0
1 year ago
Solve - 3 [ ( x + 2 ) ( x - 1 ) - x ^ { 2 } + 1 ] + 3 ( x - 1 ) (and could you please explain it to me?? I really don't get it.
Mazyrski [523]

Answer:

Step-by-step explanation:

(x+2)(x-1)= x^2+2x-x-2= x^2 +x -2\\\\( x + 2 ) ( x - 1 ) - x ^ { 2 } + 1 =x^2+x-2-x^2+1=x-1\\\\- 3 [ ( x + 2 ) ( x - 1 ) - x ^ { 2 } + 1 ] =-3(x-1)=-3x+3\\\\- 3 [ ( x + 2 ) ( x - 1 ) - x ^ { 2 } + 1 ] + 3 ( x - 1 ) =-3x+3+3x-3=6x\\

5 0
3 years ago
OK so I have two questions to answer. So the first picture is question five in the second picture is question six.
Vesnalui [34]

Answer:

The slope is 2.25

The y-intercept is 3

Step-by-step explanation:

Assuming from the cut off picture, that we need to find the slope of ...

y=2.25x +3

y=mx+b form makes it easy to identify the slope and the y-intercept.

m is the slope and b is the y-intercept. Anything number that is in place of m, is the slope; and any nother in place of b is the y-intercept.

In that case, 2.25 is the slope and 3 is the y-intercept

3 0
3 years ago
Drag each tile to the correct box. Amanda, Derrick, and Todd attend the same high school. Each student works as the cashier one
wel

Answer:

Amanda > Todd > Derrick

Step-by-step explanation:

Amanda's IQR- 3.5

Derrick's IQR- 2

Todd's IQR- 3

4 0
2 years ago
Simplify the expression.<br><br> 10 + 3(2v - 3)
Vikentia [17]

Answer:

6v+1

Step-by-step explanation:

7 0
3 years ago
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