The sum of two numbers is 80<br> their difference is 38.<br> The product of these 2 numbers is _

Your friend Alex was solving the equation 2x^2+3x=20 and the work below. Tragically, she made an error in her work. First, expla

earnstyle [38]

Answer:

Her error is that For solving by Completing the square method.

She has not made the Coefficient of x² as 1.

Therefore,

$x=\dfrac{-3+13}{4}=\dfrac{10}{4}=2.5\ OR\ x=\dfrac{-3-13}{4}=\dfrac{-16}{4}=-4$

Step-by-step explanation:

Alex was solving the equation

$2x^{2}+3x=20$

She is solving for x by Completing the square method

Her error is that For solving by Completing the square method

First step is to make Coefficient of x² as 1 ( one )

She has not made the Coefficient of x² as 1

The Require steps for the equation by Completing the square method are

Step 1 : Given

$2x^{2}+3x-20=0$

Step 2: Divide the whole by 2 we get

$x^{2}+\dfrac{3}{2}x-10=0$

Step 3 : Add 10 to both side

$x^{2}+\dfrac{3}{2}x-10+10=0+10\\\\x^{2}+\dfrac{3}{2}x=10$

Step 4 : Add $(\dfrac{1}{2}coefficient\ of\ x)^{2}=\dfrac{9}{16}$ to both the side.

$x^{2}+\dfrac{3}{2}x+\dfrac{9}{16}=10+\dfrac{9}{16}\\\\x^{2}+2\times \dfrac{3}{4}x+(\dfrac{3}{4})^{2}=\dfrac{169}{16}$

Step 5 : We have A² + 2AB + B² = (A+B)²

$(x+\dfrac{3}{4})^{2}=\dfrac{169}{16}$

Step 6 : Taking Square root

$(x+\dfrac{3}{4})=\pm \sqrt{\dfrac{169}{16}}=\pm \dfrac{13}{4}$

Step 7 : Subtract $\dfrac{3}{4}$ both side

$x+\dfrac{3}{4}-\dfrac{3}{4}=-\dfrac{3}{4}\pm \sqrt{\dfrac{169}{16}}=\pm \dfrac{13}{4}\\\\x=-\dfrac{3}{4} \pm \dfrac{13}{4}$

Step 8 : Finally we get

$x=\dfrac{-3+13}{4}=\dfrac{10}{4}=2.5\ OR\ x=\dfrac{-3-13}{4}=\dfrac{-16}{4}=-4$

Therefore,

$x=\dfrac{-3+13}{4}=\dfrac{10}{4}=2.5\ OR\ x=\dfrac{-3-13}{4}=\dfrac{-16}{4}=-4$

5 0

3 years ago

I’ll pay another & give extra points!

faltersainse [42]

Answer:

Step-by-step explanation:

A baseball team played 75 games and lost 20% of them. How many games did the team lose?

8 0

3 years ago

Please help:) i need a answer quickkk 10 pointsss

Lady_Fox [76]

Answer:

simplify

Step-by-step explanation:

7 0

3 years ago

12. How many solutions does the following system have? Explain. x + 4y = 0 1y = -Ax

nexus9112 [7]

Ax is the answer if not wrong please brainlies

6 0

3 years ago

The following chart shows "living wage" jobs in Rochester per 1000 working age adults over a 5 year period.

Stella [2.4K]

1. The average rate of change in the number of living wage jobs from 2016 to 2018 is <u>7.35%.</u>

2. The average rate of change in the number of living wage jobs from 2018 to 2020 is <u>4.45%</u>.

<h3>What is the average rate of change?</h3>

The average rate of change shows how much the function or value has changed per unit, on average, over the stated interval.

To calculate the average rate of change, divide the change rate in y-values by the x-values, where y-values refer to the latest dates and x-values refer to the past dates.

<h3>Data and Calculations:</h3>

Living Wage Jobs in Rochester

Year: 2016 2017 2018 2019 2020

Jobs: 625 675 720 760 785

Change from 2016 to 2017 = 8% (675 - 625)/625

Change from 2017 to 2018 = 6.7% (720 - 675)/675

Average rate of change = 7.35% (8% + 6.7%)/2

Change from 2018 to 2019 = 5.6% (760 - 720)/720

Change from 2019 t0 2020 = 3.3% (785- 760)/760

Average rate of change = 4.45% (5.6% + 3.3%)/2

Thus, the average rate of change in the number of living wage jobs from 2016 to 2018 is <u>7.35%</u> and <u>4.45%</u> from 2018 to 2020.

Learn more about the average rate of change at brainly.com/question/5026569

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4 0

2 years ago

The sum of two numbers is 80 their difference is 38. The product of these 2 numbers is __?