Work out Sarah's total pay for the last week

2. Solve the equation by completing the square. Show your work.

scoundrel [369]

Answer:

x = 5 or 25

Step-by-step explanation:

I think the method I am about to explain is slightly quicker and easier than the method in your question. This works for any 'complete the square' question.

We begin with x² - 30x = - 125.

First, we are going to factorise the left-hand side of the equation by dividing the 'b' value (-30) by 2 (you'll see why this works in a minute):

(x - 15)²

We want these brackets to multiply out to give x² - 30x, so that they equal the left-hand side of the equation. Unfortunately, if we multiply them out, we get:

(x - 15)(x - 15) =

x² - 30x + 225

There is an unwanted term (the + 225, from 15²)! We only want x² - 30x, so we have to remove this term by subtracting it from the left side of the equation. To do this, let's set up the original equation again:

(x² - 30x + 225) - 225 = - 125

Note: The reason why we don't have to subtract it from both sides is because the original equation is x² - 30x = - 125, and so we must make sure the left hand side is still equal to x² - 30x.

So now we know that (x - 15)² multiplies out to give x² - 30x +225, we can write this as (x - 15)² in our equation:

(x² - 30x + 225) - 225 = - 125

is the same as:

(x - 15)² - 225 = - 125

Now add 225 to both sides of the equation:

(x - 15)² = - 125 + 225 = 100

(x -15)² = 100

The next step is to square root both sides. Be careful here, and remember that √100 can either be 10 or -10, as (-10)² = 100. To indicate both results, write ±10 ("plus or minus 10").

√(x - 15)² = √100

x - 15 = ±10

Because, there are two possible values for the right-hand side of the equation, we need to separate our equation into two equations:

1. x - 15 = 10

and

2. x - 15 = -10

Now we solve these two simple linear equations for x:

1. x = 10 + 15 <- add 15 to both sides

x = 25 This is our first solution.

2. x = -10 + 15 <- add 15 to both sides again

x = 5 This is our other solution.

So our two solutions are x = 5 and x = 25!

I have attached the quick version of the working out for this question - that is what you would be expected to write down in a test.

5 0

4 years ago

Gina worked 32 hours at a rate of $24.50 per hour . which in the table will help her caculate her income tax for this week ?

shusha [124]

Alright, to start the problem, we need to know what Gina makes! If Gina worked 32 hours for $24.50 per hour, all we need to do is multiply 24.50 by 32 to get 748, which means that this week, Gina made $748!

Next, we need to look at the chart to see where he falls on income tax. Because Gina made more than $218, she makes too much for line 1. Because Gina made more than $758, she makes too much for line 2.
Because Gina made less than $1762, and more than 753, it looks like Gina will fall into line 3, so your answer should be C!

6 0

4 years ago

If trapezoid JKLM is translated according to the rule (x, y) → (x + 8, y − 3), what are the coordinates of point L'?

olga nikolaevna [1]

Another answer: According to the figure, the coordinates of JKLM are, J(-7,-2), K(-4,-2), L(-2,-5) and M(-9,-5) JKLM is translated to J'K'L'M' by means of the rule (x+8, y-3), we should know that (x, y) are coordinates of the pre image, to find the coordinates of each image we have (x', y') such that x' =x+8, and y' =y-3. Therefore, the coordinates of L' can be found by L'(-2+8, -5-3)=(6, -8) the final answer is L'(6, -8).

5 0

4 years ago

Read 2 more answers

What best describes the number 5 ?write prime or composite or both prime and composite

Salsk061 [2.6K]

It is prime because nothing equals it other than 5x1

8 0

4 years ago

Simplify a) a^5 divided by a^3

Ymorist [56]

The value simplified is a²

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