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3 years ago

Need help with these to its called solving inequalities

Mathematics

2 answers:

grigory [225]3 years ago

5 0

1 would be 4 with an open circle that points to the right
2 would be 6 with a closed circle that points to the left

Y_Kistochka [10]3 years ago

3 0

Both of them are on the incorrect place. The first one the arrow is going the right way but the dot has to be on the 4. On the second one the dot is supposed to be on the 6 and the arrow is supposed to go the other way.
I hope that helps!

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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

3 years ago

The Washer family spent $15.80 each week for milk until the milk prices rose 5% in their town How much do they spend weekly on m

Law Incorporation [45]

15.80 * 1.05 should give you the answer

A method to solve it would be would be:
First converting 5% to a decimal then multiplying that by 15.80 in order the find 5 percent of 15.80...Afterwards you have to add that value to the original 15.80 ..And you should end up with the same answer.

6 0

4 years ago

Read 2 more answers

Taco Tuesday math paper restraint

White raven [17]

May we have details so we know how to answer

8 0

3 years ago

The Chartered Financial Analyst (CFA) designation is fast becoming a requirement for serious investment professionals. Although

Nastasia [14]

Answer: ($141,775, $158,225)

Step-by-step explanation:

Given : Significance level : $\alpha: 1-0.9=0.1$

Critical value : $z_{\alpha/2}=1.645$

Sample size : n= 49

Sample mean : $\overline{x}=150,000$

Standard deviation : $\sigma=35,000$

The confidence interval for population mean is given by :_

$\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

$= 150,000\pm (1.645)\dfrac{35000}{\sqrt{49}}\\\\\approx150,000\pm8225\\\\=(150,000-8225,150,000+8225)=(141,775,158,225)$

Hence,he 90% confidence interval for the average salary of a CFA charter-holder = ($141,775, $158,225)

7 0

3 years ago

The sum of any two consecutive prime numbers is also prime

jek_recluse [69]

Let's consider two prime numbers where each is larger than 2

Say the primes 7 and 11. Adding them gets us 7+11 = 18. This counter example disproves the initial claim since 18 = 9*2 = 6*3 making 18 composite (not prime)

In general, if we let p and q be two primes such that q > p > 2 and q is the next prime after p, then p and q are both odd. If any of them were even then they wouldn't be prime (2 would be a factor)

Adding any two odd numbers together leads to an even number

Proof:
p = 2k+1 where k is some integer
q = 2m+1 where m is some integer
p+q = 2k+1+2m+1 = 2(k+m) + 2 = 2(k+m+1) which is in the form of an even number

That proof above shows us that adding any prime larger than 2 to its next prime up leads to an even number. This further shows us that the claim is false overall. It is only true if you restrict yourself to the primes 2 and 3, which add to 5. Otherwise, the claim is false.

3 0

4 years ago