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3 years ago

What is the solution of x=2+\sqrt(x-2) x = 2 x = 3 x = 2 or x = 3 no solution

2 answers:

5 0

$D:x\geq2\\\\
x=2+\sqrt{x-2}\\
\sqrt{x-2}=x-2\\
x-2=x^2-4x+4\\
x^2-5x+6=0\\
x^2+x-6x+6=0\\
x^2-2x-3x+6=0\\
x(x-2)-3(x-2)=0\\
(x-3)(x-2)=0\\
x=3 \vee x=2$

natta225 [31]3 years ago

4 0

Answer:

The solution is x = 2 or x = 3

Step-by-step explanation:

we have to find the solution of the equation

$x=2+\sqrt{(x-2)}$

$x=2+\sqrt{(x-2)}\\ \\x-2=\sqrt{x-2}\\\\\text{Squaring on both sides }\\\\(x-2)^2=x-2\\\\x^2+4-4x=x-2\\\\x^2-5x+6=0\\\\x^2-2x-3x+6=0\\\\x(x-2)-3(x-2)=0\\\\(x-2)(x-3)=0\\\\x=2\text{ or }x=3$

Hence, correct option is x = 2 or x = 3

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Find the inverse of the following function.

Naddik [55]

For this case we must find the inverse of the following function:

$f (x) = 8 \sqrt {x}$

For this, we follow the steps below:

We change f (x) to y:

$y = 8 \sqrt {x}$

We exchange the variables:

$x = 8 \sqrt {y}$

We solve for y:

$8 \sqrt {y} = x$

We divide between 8 on both sides of the equation:

$\sqrt {y} = \frac {x} {8}$

We raise both sides of the equation to the square to remove the root:

$y = (\frac {x} {8}) ^ 2\\y = \frac {x ^ 2} {64}$

So, the inverse is: $f ^ {- 1} (x) = \frac {x ^ 2} {64}$

ANswer:

Option C

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3 years ago

The length of a rectangle is 4 cm longer than its width. If the perimeter of the rectangle is 44 cm, find its area.

adell [148]

Length: w+4
Width:w
Perimeter:44
Area: L times w
P=44
44=2(w)+2(w+4)
44=2w+2w+8
44=4w+8
36=4w
w=9
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L=9+4
L=13
Area should equal 117 cm squared

5 0

3 years ago

Let f(x) = 1/x . Find the number b such that the average rate of change of f on the interval [2, b] is − 1/8

vekshin1

Answer:

b=4

Step-by-step explanation:

So, we have the function $f(x)=1/x$ . We need to find b such that the average rate of change or the slope is -1/8 between the intervel [2, b]. First, let's find f(2).

f(2) = 1/(2) = 1/2

So, we have the point (2, 1/2)

At point b, f(b) = 1/b.

Let's plug this into the slope formula:

$\frac{y_2-y_1}{x_2-x_1}=\frac{.5-\frac{1}{b} }{2-b} =-1/8$

Now, we just need to solve for b. First, let's multiply both the numerator and denominator by b (to get rid of the annoying fraction in the numerator).

$\frac{.5b-1}{2b-b^2} =\frac{-1}{8}$

Now, cross multiply.

$4b-8=b^2-2b$

$b^2-6b+8=0$

Solve for b. Factor using the numbers -4 and -2.

$=(b-4)(b-2)=0$

Thus, b=4 or b=2.

However, b=2 is not a possible solution since the interval [2,2] means nothing. Thus, b=4.

4 0

3 years ago

A bag contains 4 red marbles, 2 blue marbles, 1 purple marble, and 3 green marbles.If a single marble is pulled out of the bag,

faust18 [17]

Answer:

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Step-by-step explanation:

I don't think it is specific enough for a definite answer.

5 0

3 years ago

Read 2 more answers

Solve the inequality shown below. -2(q-22)+q+12>0

Andru [333]

−2(q−22)+q+12>0
Step 1: Simplify both sides of the inequality.
−q+56>0
Step 2: Subtract 56 from both sides.
−q+56−56>0−56
−q>−56
Step 3: Divide both sides by -1.
−q−1>−56−1
q<56
Answer: q<56

4 0

3 years ago