Match the reasons with the statements in the proof.

Mathematics

1 answer:

andriy [413]2 years ago

8 0

Answer:

Step-by-step explanation:

You might be interested in

Find the slope of the line whose equation is 5y = x - 3. -3 -3/5 1/5 5

irina1246 [14]

The slope of the line whose equation follows the point-slope form (y=mx + b) is m. Transforming the equation 5y = x - 3 into the point-slope form by dividing the whole equation by 5 results to $y = \frac{1}{5} (x) - \frac{3}{5}$ . The slope, m, is 1/5.

5 0

3 years ago

How many fourths are in 7/8

Nutka1998 [239]

$\dfrac{7}{8} \div \dfrac{1}{4}=\dfrac{7}{8}\cdot4=\dfrac{7}{2}=3.5$

5 0

3 years ago

John and Tim are looking at the equation the square root of the quantity of 3 times x minus 4 equals square root of x . John say

IgorC [24]

The equation is
3x - 4 = sqrt(x)
where 'sqrt' is shorthand for 'square root'

Let's solve the equation. To do so, we square both sides. Then we get everything to one side
3x - 4 = sqrt(x)
(3x - 4)^2 = (sqrt(x))^2
9x^2 - 24x + 16 = x
9x^2 - 24x + 16-x = x-x
9x^2 - 25x + 16 = 0

Now use the quadratic formula. See the attached image for those steps.

After using the quadratic formula the two possible solutions are x = 1 or x = 16/9

We need to check each possible solution to see if it is extraneous or not.

----------------------------

Checking x = 1

3x - 4 = sqrt(x)
3*1 - 4 = sqrt(1)
3 - 4 = 1
-1 = 1

The final equation is false, so x = 1 is not a true solution

x = 1 is extraneous.

So far, John is correct; however, we need to see the nature of the possible solution x = 16/9

So let's check it
----------------------------

Checking x = 16/9

3x - 4 = sqrt(x)
3*(16/9) - 4 = sqrt(16/9)
48/9 - 4 = 4/3
16/3 - 4 = 4/3
16/3 - 12/3 = 4/3
(16 - 12)/3 = 4/3
4/3 = 4/3

The last equation is true, so x = 16/9 is a proper solution.

This solution is considered non-extraneous. So Tim is also correct
----------------------------

They are both correct because there are two possible solutions. One of which is extraneous (x = 1) and the other is non-extraneous (the fraction x = 16/9)