Adding and subtracting big polynomials like these are pretty easy. You just need to combine like terms. For example:
1.)
2.)
(The 3x^2 and the 2 stay intact while the 5xy and 7xy combine together)
All you have to do is combine the numbers that have the same powers of x and y with each other. x^2 will combine with x^2 and xy^2 wil combine with xy^2 exc. If there is no other number with the same x and y's, then you just leave it as it is in the answer.
Now with the original question, I see a -9xy^3, and thats gonna combine with the 3xy^3 in the second polynomial and the 2xy^3 in the third one.
So far we have -4xy^3, the next term is going to be a -9x^4y^3, and that's gonna combine with the 3x^4y^3 in the third one.
We now finished adding the like terms that were in the first polynomial, we will move onto the second polynomial. The first term in this one is 3xy^3, in which we already added in the first step. At this point, it doesn't look like there are any other terms that have the same x and y behind them. So we can move on and write the final answer:
(All on the same line of course)
Also, for your second question, the order does not matter in which you write the terms. I could write the 7y^4 behind the -8x^4y^4 and it would still be the same answer.
If you have any other questions let me know :) while I double check my work.
Answer:
1. push 2. machine 3. gravity 4. balance 5. energy. 6 force 7. pull 8. friction 9. newtons 10. inertia
Step-by-step explanation:
Answer:
last option bottom right
x can be equal or greater than -2
Answer:
-y = -2x - 3
Option 3
Step-by-step explanation:
When equations are equivalent, they will have infinitely many solutions.
If you want to find an equivalent equation, you can <u>multiply/divide every</u> term in the equation by the same number. You can also <u>rearrange</u> the equation.
Since the options mostly have "y" by itself, start by <u>rearranging</u> to isolate "y" in the given equation.
Move all the other numbers to the right of the equal sign except for "y". To move a number, apply its reverse operation to the entire equation.
Do reverse operations in reverse BEDMAS order.
2y - 4x = 6 Move "-4x" first. It's reverse is +4x.
2y - 4x + 4x = 6 + 4x
2y = 6 + 4x Move the "2" in 2y. Divide the whole equation by 2.
2y/2 = 6/2 + 4x/2
y = 3 + 2x Rearrange to look like the answer choices.
y = 2x + 3
This equation looks like option 3 except every term has a different negative/positive.
y = 2x + 3 -y = -2x - 3
We can <u>multiply every term</u> by -1.
y = 2x + 3
y*-1 = 2x*-1 + 3*-1
-y = -2x + (-3) Negative and positive make a negative
-y = -2x - 3 Same as option 3
Supplementary angles add up to 180 degrees-
Let x = "the angle"
supplement angle = 2x + 12 // 12 more than twice the measurement of "the angle"
Supplement angle + "the angle" = 180 degrees
(2x + 12) + x = 180 degrees // 2x + 12 is the supplement angle
3x + 12 = 180 // Simplify
3x = 168 // Subtract 12 from both sides
x = 56 degrees // Divide both sides by 3
The measure of the angle is 56° and its supplement is 124°
