The solution of x in the given expression $\mathbf{\sqrt{(3x-8)}+1 = \sqrt{(x+5)}}$ is 4. However, if it is $\mathbf{\sqrt{(3x-8)+1} = \sqrt{(x+5)}}$ , it is 6.

<h3>What is the solution to algebraic expression?</h3>

The solution to the given algebra expression involving surds can be seen in the steps below.

Given that:

$\mathbf{\sqrt{(3x-8)}+1 = \sqrt{(x+5)}}$

Remove the square roots, we have:

12x - 32 = 4x² - 48x + 144

Solving the quadratic equation at the RHS and equating it to LHS, we have:

x = 11, x = 4

Verifying the solutions by replacing the value of x with the given equation:

x = 11 False
x = 4 True

Therefore, we can conclude that the value of x = 4

NOTE:

Given that:

$\mathbf{\sqrt{(3x-8+1)} = \sqrt{(x+5)}}$

Square both sides

3x - 7 = x +5

Solve for x

3x - x = 5 + 7

2x = 12

x = 6

Learn more about solving to algebraic expressions here:

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5 0

2 years ago

Find the slope intercept (9,5),(7,-11) y=

grin007 [14]

Answer:

y=8x-67

Step-by-step explanation:

So the question is what is the equation for the following two coordinate points?

Well to start off what is the formula? The formula is called the linear equation. Which is y=mx+b. What does these letters or "variables" mean or represent?! Welp, m stands for the slope, which is "Δy over Δx." Some people call say "the change of y over x." I call it the rise over run. So it is saying y over x. The b in the linear equation is the y-intercept. The y-intercept is when the line crosses the y-axis.

With that being said, let's find the slope. But how? Well with the Δy over Δx. The formula is y₂-y₁ over x₂-x₁. With the two coordinate points we can label them.

y₂=5

y₁=(-11)

x₂=9

x₁= 7

Now let set it up into the equation of y over x

Slope = 5- (-11) = 5 + 11 = 16 = 8

9-7 9-7 2

So we now have the slope! Which is 8! So put that into the linear equation!

y=8x+b

Next, we need to find b, the y-intercept! How do we do that well, we can figure it out by one of the coordinate points! Let use the (7, -11) point for example! Remember, x= 7 and y= (-11)

(-11) = 8(7) + b

(-11) = 56 + b

-56 -56

-67 = b

We now have b, which is negative 67! So we need to put all the information we have found into the linear equation!

y=8x-67

6 0

3 years ago

The prefix octa-means what?

yuradex [85]

The prefix means 8.How to remember this is a octagon which has 8 sides.Therefore Octa means eight.I hope this helped.

3 0

2 years ago

Read 2 more answers

What is the inverse of f(x) = -5x - 8?

grin007 [14]

Answer:

y=-1/5x-9/5

Step-by-step explanation:

y=-5x-9

x=-5y-9

-5y=x+9

y=-1/5x+9/-5

y=-1/5x-9/5

8 0

3 years ago