8a³ (2 − 4a²) ;
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Note: " 8a³ " is the greatest common factor (GCF).
Answer: 1
Step-by-step explanation:
10 - 5- 4 = 1
<u>Answer</u>
9+√14
<u>Explanation</u>
To Rationalize the denominator of 5-√7/9-√14.
To rationalize this we multiply both the denominator and denominator by the conjugate of the denominator.
The denominator is 9-√14 and its conjugate is (9+√14).
(5-√7)/(9-√14) = (5-√7)(9+√14)/(9-√14)(9+√14)
= (5-√7)(9+√14)/(9²-14)
= (45 + 5√14 - 9√7 - √98)/(81-14)
= (45 + 5√14 - 9√7 - √98)/67
= (45 + 5√14 - 9√7 - 7√2)67
This is the rationalized expression.
The denominator is (9-√14) and its conjugate is (9+√14).
Let's set up some equations.
We know that 7/8 of a liter fills up our bottle 5/6 of the way. Thus 7/8=5/6 * b.
Now, let's divide both sides by 5/6 to get b = 21/20. However, none of the answer choices provided are correct. Let's look at each one to determine why it's not correct.
A. This answer is false because 35/48 < 7/8. If 7/8 of a liter doesn't completely fill up the bottle, there is no way that a value less than 7/8 can fill up the bottle - it's impossible.
B. Same case as answer A, but 11/38 instead of 35/48.
C. Same case as answer A, but 11/20 instead of 35/48.
D. This answer however is more than 35/48, so is it correct? No. 113/35 is just over 3. Since 7/8 of a liter almost fills the bottle but does not quite completely fill it, there is no way that adding 2 more liters can fill up the bottle just the tiny 1/6 of the way. That is disproportional and is thus wrong.
First things first. Solve the equation for y, getting it into y = mx + b form so it's easy to determine the slope. 5x + 2y = 12 so 2y = -5x + 12. Dividing everything by 2 we get
. So the slope is -5/2. Parallel lines have the same slope, so we will have a slope of -5/2 in our new equation, we just have to find out what that equation is. We have an x and a y value from the point, so we will use that, along with the slope, to find b, the y-intercept.
and 4 = 5 + b. So b = -1. Now let's write the equation:
. And there you go!
