I need help simplifying both of these. thank you!
1 answer:
<h3>Answer:</h3>
- -100x +100; 3
- 5x +81; 162
The distributive property is your friend. It tells you ...
a(b + c) = ab + ac
It can also be used to simplify the product of binomials (or other polynomials).
(a +b)^2 = (a +b)(a +b) = a(a +b) + b(a +b) = a^2 +ab +ab +b^2
(a +b)^2 = a^2 +2ab + b^2 . . . . . . . worth remembering
1. (x -10)^2 -x(x +80) = (x^2 -20x +100) +(-x^2 -80x)
= -100x +100 . . . . . . simplified form
For the purposes of calculation, it can be easier to factor out 100:
= 100 (1 -x)
Then for x = 0.97
= 100(1 -0.97) = 100(0.03) = 3
___
2. (2x +9)^2 -x(4x +31) = (4x^2 +36x +81) -4x^2 -31x = 5x +81
For x = 16.2, this is ...
5(16.2) +81 = 81 +81 = 162
_____
The purpose of the attachment is to show the evaluation is correct.
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Answer:
true.
false
true.
false.
Step-by-step explanation:
1. The domain (x-value) of a function is (-∞, +∞) unless there is some reason for it <u>not </u>to be. No matter what we make x, we do not wind up with something forbidden in the real-number coordinate plane, like a zero denominator or a square root of a negative number, so the domain for x is all real numbers. True.
2. The statement says the range (the y-value) of the function must always be more than zero. There is no particular reason to belive that. If x = -10, then x³ + 6 = -1000 + 6 = -994, which is less that zero. False.
3. We get the y-intercept by making x equal zero. In tha case y = 0³ + 6 = 6. The y-intercept always has an x-coordinate of zero, so the point is (x, y) = (0, 6). True.
4. If a function has symmetry about the origin point, then replacing y with -y and x with -x will get you an equation equivalent to the original. let's try it.
-y = 3(-x)³ + 6 now lets see what happens it we let x = 2
For the original equation: y = 3(2)³ + 6 = 3(8) + 6 = 24 + 6 = 30
Now we try the test equation: -y = 3(-2)³ + 6 = 3(-8) + 6 = -24 + 6 = -18
So -y = -18
So y = 18
The first equation and the test equation are not equivalent, as they do not yield the same results for the same value of x.
Thus, the origin is <u>not </u>a point of symmetry. False.
I am attaching a picture of this function's graph so you can see the actual point of symmetry is (0, 6), which is also the y-intercept. I made it on Desmos dot com, which is free for everyone.
