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3 years ago

Solve by completing the square p^2 +10p - 3 = 0

Mathematics

1 answer:

Mrac [35]3 years ago

7 0

Solving $p^2 +10p - 3 = 0$ by completing the square method we get $(p+5)^2-28=0$

Step-by-step explanation:

We need to solve by completing the square method.

We are given: $p^2 +10p - 3 = 0$

The Completing square method is: (a+b)^2 = a^2+2ab+b^2

Solving:

$p^2 +10p - 3 = 0\\For \,\,making\,\,perfect\,\,square\,\,we\,\,add\,\,and\,\,subtract\,\,(5)^2\\p^2+2(p)(5)^2+(5)^2-3-(5)^2=0\\(p+5)^2-3-25=0\\(p+5)^2-28=0$

Solving $p^2 +10p - 3 = 0$ by completing the square method we get $(p+5)^2-28=0$

Keywords: completing the square method.

Learn more about completing the square method at:

#learnwithBrainly

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A shelf has different sizes of bottles of laundry detergent. This line plot shows the number of cups of laundry detergent in eac

salantis [7]

Answer:

2 / 3 loads

Step-by-step explanation:

From. The plot, we can conclude that, the detergent that has the most bottles is that with 5 ; the number of cups in the detergent with 5 bottles is 12 cups

Number of cups used for each load of laundry = 18 cups

The loads of laundry Eric can do is thus :

Number of cups of detergent / number of cups used for each load of laundry

= 12 / 18

= 2 / 3 loads

8 0

3 years ago

The table below shows the number of customers that come eat lunch at a local deli each week.

jek_recluse [69]

The table of the number of customers illustrates two different patterns

Deli should expect 90 customers to serve during week 8

<h3>How to determine the number of customers</h3>

From the table, the even number of week increases by 10, while the odd number of weeks reduces by 5.

At week 6, the number of customers is 80.

So, the number of customers at week 8 is:

Week 8 = Week 6 + 10

This gives

Week 8 = 80 + 10

Week 8 = 90

Hence, deli should expect 90 customers to serve during week 8

Read more about sequence and patterns at:

brainly.com/question/15590116

8 0

3 years ago

Simplify, state all restrictions.

Kipish [7]

The simplified expression is $\frac{1 - x - y}{x + y}$ and the restriction is $y \ne -x$

<h3>How to simplify the expression?</h3>

The expression is given as:

$\frac{x - y}{4x^2 - 8xy + 3y^2} \div \frac{2x + y}{2x - 3y} \times \frac{4x^2 - y^2}{x^2 - y^2} -1$

Express x^2 - y^2 as (x + y)(x - y) and factorize other expressions

$\frac{x - y}{(2x - y)(2x - 3y)} \div \frac{2x + y}{2x - 3y} \times \frac{4x^2 - y^2}{(x - y)(x + y)} -1$

Rewrite the expression as products

$\frac{x - y}{(2x - y)(2x - 3y)} \times \frac{2x - 3y}{2x + y} \times \frac{4x^2 - y^2}{(x - y)(x + y)} -1$

Cancel out the common factors

$\frac{1}{(2x - y)} \times \frac{1}{2x + y} \times \frac{4x^2 - y^2}{(x + y)} -1$

Express 4x^2 - y^2 as (2x - y)(2x + y)

$\frac{1}{(2x - y)} \times \frac{1}{2x + y} \times \frac{(2x - y)(2x + y)}{(x + y)} -1$

Cancel out the common factors

$\frac{1}{x + y} -1$

Take the LCM

$\frac{1 - x - y}{x + y}$

Hence, the simplified expression is $\frac{1 - x - y}{x + y}$ and the restriction is $y \ne -x$