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2 years ago

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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<img src="https://tex.z-dn.net/?f=%20%5Csqrt%7Bx%20%5Csqrt%7Bx%20%5Csqrt%7Bx%20%5Csqrt%7Bx....%7D%20%7D%20%7D%20%7D%20%20%3D%20%

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