Hello there!
The factorization for x³ + 343 is (x + 7)(x² - 7x + 49)
I hope that helps!
The result is a line perpendicular to y=3x-2
This line has the following equation: y =mx + b, where m = slope
Remember that the product of the slopes of two perpendicular lines is always = -1 (or in other term one is the reciprocal inverse of the other) so the
first slope = 3 and the sope perpendicular to 3 will be - 1/3.
Then the new equation is y = - 1/3(x) + b
How to calculate b? This line passes through (6, 8), that
means (x=6 and y=8) . Plug these values in y = -1/3 (x)+b:3
8=(-1/3)(6) + b;
8= - 2 + b and b = 10
Te final equation is y = - 1/3.x+10 (answer A)
Well 40 times 6 is 240 which means that you don't have to round.
There is 1 gram is a milliliter and grams to milligrams is 16,000
so 16,000 is your answer
Answer:
29037.036 miles
Step-by-step explanation
There are two possible ways to solve this problem.
The first option starts with the $2800 dollars for the years. You first want to divide this by $2.70, because it will give you the amount of gallons of gas you can buy with that money.
2800/2.70 = 1037.037
This means you can buy 1037.037 gallons of gas in the year. Now you need to convert this to miles by multiplying by the amount of miles per gallon.
1037.037 x 28 = 29037.036 gallons
The second way to look at this is dimensional analysis. If you have learned this, then continue on reading this, but if you haven't I might only confuse you. I only suggest this because it can make it a little easier.
For the dimensional analysis, you need to start with what you are given and move to what you need to know, so you will start with the $2800 dollars and move to gallons. $2.70 per gallon and 28 miles per gallon are your conversion factors.
Set it up like this:

This allows the equation to be more organized, and you can check your work by canceling the units.
Hope this helps.