1. (9m + 6) + (-5m - 6)
2. (3r^2 + 7r + 1) + (4r^2 - 8r - 2)
3. (h + 1) - (9h + 4)
4. (-7w^2 -2w - 1) - (-5w^2 + 3w - 2)
5. Look at the given rectangle. Write a polynomial expression in simplest form for the perimeter of the rectangle.
5x + 5
_______________________
2x| |2x
- | |-
1 | |1
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5x + 5
Please help ty!
Dang
for 5 it is a rectangle with a length of 5x+5 and a width of 2x-1
2. (3r^2 + 7r + 1) + (4r^2 - 8r - 2)
pretend there is a 1 in front
= 1(3r^2 + 7r + 1) + 1(4r^2 - 8r - 2)
= 3r^2 + 7r + 1 + 4r^2 - 8r - 2
= 7r^2 - r - 1
3. (h + 1) - (9h + 4)
pretend there is a -1 in front of the second bracket
= 1(h+1) - 1(9h + 4)
= h + 1 - 9h - 4
= -8h - 3
do #1 and #4 the same way
#5, can't make out what that is, but will guess the sides of the
rectangle are 5x+5 and 2x-1
perimeter = 2(5x+5) + 2(2x-1)
= 10x + 10 + 4x - 2
= 14x + 8
Thank youuu!!
Sure, I'd be happy to help you with these problems.
1. To simplify the expression (9m + 6) + (-5m - 6), you can first combine like terms. In this case, the like terms are the ones with the variable 'm'. So you can add the coefficients of 'm' together: 9m - 5m = 4m. Next, add the constants together: 6 - 6 = 0. Therefore, the simplified expression is 4m + 0, which can be further simplified as just 4m.
2. Similarly, to simplify the expression (3r^2 + 7r + 1) + (4r^2 - 8r - 2), you need to combine like terms. For the terms with 'r^2', you can add the coefficients: 3r^2 + 4r^2 = 7r^2. Then, for the terms with 'r', you can combine them: 7r - 8r = -r. Lastly, combine the constants: 1 - 2 = -1. The simplified expression is then 7r^2 - r - 1.
3. To simplify (h + 1) - (9h + 4), you can distribute the negative sign (-) to every term inside the parentheses, which changes the signs of each term. This becomes h + 1 - 9h - 4. Then, combine the like terms: h - 9h + 1 - 4 = -8h - 3. Thus, the simplified expression is -8h - 3.
4. For (-7w^2 - 2w - 1) - (-5w^2 + 3w - 2), you need to distribute the negative sign to each term inside the second set of parentheses. This changes the sign of each term: -7w^2 - 2w - 1 + 5w^2 - 3w + 2. Then, combine the terms with 'w^2': -7w^2 + 5w^2 = -2w^2. Next, combine the terms with 'w': -2w - 3w = -5w. Finally, combine the constants: -1 + 2 = 1. The simplified expression is -2w^2 - 5w + 1.
5. To find the perimeter of the given rectangle, you can add up the lengths of all four sides. Looking at the diagram, we see that the lengths of the horizontal sides are given as 5x + 5, and the lengths of the vertical sides are given as 2x. Therefore, the perimeter is calculated by adding all four sides: (5x + 5) + 2x + (5x + 5) + 2x. Simplifying the expression, we get 14x + 10.
I hope that helps! Let me know if you have any further questions.