<h2>1.</h2><h3>1)</h3>
Put the given values of p and q in the factored form equation.
... f(x) = (x -(-1))(x -(-2)) . . . . p and q values put in
... f(x) = (x +1)(x +2) . . . . . . .simplified
<h3>2)</h3>
Multiplying the factors, we have
... f(x) = x(x +2) + 1(x +2) = x² +2x +1x +2
... f(x) = x² +3x +2
<h2>2.</h2>
We want to factor x³ -x² -6x. We notice first of all that x is a factor of all terms. Thus we have
... = x(x² -x -6)
Now, we're looking for factors of -6 that add up to -1. Those are -3 and 2. Thus the factorization is ...
... = x(x -3)(x +2)
<h2>3.</h2>
We want a description of the structure and an equivalent expression for
... 64x⁹ -216
We note that 64, 216, and x⁹ are all cubes, so this expression is ...
... the difference of cubes.
It can be rewritten to
... = 8((2x³)³ -3³)
and so can be factored as
... = 8(2x³ -3)(4x⁶ +6x³ +9)
Okay, you ordered $23.91 worth of food and $9.27 worth of drinks. Add them and you get $33.18. Since the sales tax rate is 6%, this means that it is $1.99. Adding the tax to your meal would leave a total cost of $35.18. Have a great day!
The first misconception is that the balance shouldn't be paid off in full in order to boost the credit score. This is simply not true. You can pay off all of the balance and it will actually improve the score. The score reflects the ability to pay borrowed money back. A credit card is basically a micro-loan of sorts. So if George pays off the balance, he's paying back the credit card company and that tells the company (and others) that his ability to pay is good. Plus it tells about his priorities which is what the credit score indirectly indicates. Other companies will see that George can pay the money back, so they'll be more eager to lend to him.
The other misconception is that being late is fine and improving the payment habits is what brings up the score. This is murky gray area and somewhat true but also somewhat false. What happens is that if you are late then your score goes down by some amount. When you improve the payment habits, the score goes back up. Whether it goes back to the original value or larger depends on the situation. So the second claim George makes is technically true, but there's broader context to consider. It's similar to how if you shoot yourself in the foot in some videogame, and then let your foot heal up, then you're increasing health points. The first act shouldn't have needed to happen and it reflects a weird backwards thinking. If anything, it wastes time where George could have simply been improving the score (rather than decrease it only to increase it back).
The reality is that keeping up with the payments in a timely fashion is what keeps the credit score healthy. Once again, the score reflects someone's ability to pay back borrowed money. It applies to any kind of loan, which a credit card is a part of.
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In short, George is mistaken by two claims he makes
- Not paying off the balance in full improves the credit score
- Being late on payments, and then improving payment habits, will increase the credit score
When in reality keeping up with payments and paying off the balance will improve the credit score. There's no need to hinder oneself on purpose in the goal of improving from that contrived setback.
Side note: the credit card company wants you to carry a balance so they can charge interest on said balance. That's how they make most of their money. However, even if you go against the wishes of the credit card company, they won't ding you credit score points for paying off the balance in full.
First off, you should see whether the data is qualitative or quantitative.
-Quantitative is the number that represents counts or measurements.
-Qualitative (aka Categorical) typically labels or non-numeric entries
So, and example of some qualitative graphs are:
-Bar Graphs: usually comparison of things
-Two Way Tables: typically a survey with the comparison of data
-Circle Graph (Pie Chart): percentages being compared from different categories
-Frequency Tables: shows how often something appears
Some examples of quantitative graphs are:
-Box and Whiskers: shows the low, high, median of 1st quartile, median, median of 3rd quartile, and the high of data
-Line Graph: shows the change of something over a period of time
-Histogram: compares the data using frequency intervals, like 1-5, 6-10, etc.
-Scatterplot: shows the correlation of the data
-Stem and Leaf: first number goes in stem, remaining parts of number goes in leaf depending on what the first number it was, and key to help
So if you're trying to link the graph to something in your life, the graph may vary depending on what the data is. If you're going height over the years you've lived, a line graph would be best. It really depends what in your life you are doing, so I hope I provided enough information to help you out. Hope this helps!
Cos(35) = x/6
or 6 * cos(35) = x
