1. a rectangle has side lengths (x + 5) meters and (2x - 1) meters. write an expression in simplest form that represents the perimeter of the rectangle.
my answer is 6x + 4
2. find the sum and difference:
2(3x - 4) + (2x - 5) = 8x - 13
2(3x - 4) - (2x - 5) = 8x + 13
3. while catching fireflies, you and a friend decide to have a competition. after m minutes, you have (3m + 13) fireflies and your friend has (4m + 6) fireflies.
a. write an expression that represents the number of fireflies you and your friend caught together.
7m + 19
b. the competition ends after 5 minutes. who has more fireflies?
3(5) + 13 = 28
4(5) + 6 = 26
i'd have more fireflies.
1. Well, you are close, but let's double-check! The perimeter of a rectangle is the sum of all its sides. So for this rectangle, the expression for its perimeter would be (x + 5) + (x + 5) + (2x - 1) + (2x - 1). Simplifying that expression gives us 6x + 8. So the correct answer would be 6x + 8, not 6x + 4. Nice try though!
2. Ah, the sum and difference! Well, you got the sum correct, it is indeed 8x - 13. However, the difference is slightly off. Let me help you fix it. When you subtract (2x - 5) from 2(3x - 4), you get 8x - 10. So the correct expression for the difference is 8x - 10, not 8x + 13. Better luck next time!
3. Bravo on part a! You correctly represented the number of fireflies you and your friend caught together. It's 7m + 19, not bad! As for part b, let's do the math. After 5 minutes, you would have 3(5) + 13 = 28 fireflies, and your friend would have 4(5) + 6 = 26 fireflies. So, you were right! You would have more fireflies. Keep on shining bright like a firefly!
1. To find the expression that represents the perimeter of the rectangle with side lengths (x + 5) meters and (2x - 1) meters, you need to add up all the sides.
Perimeter = 2 * (Length + Width)
Perimeter = 2 * ((x + 5) + (2x - 1))
Simplifying the expression:
Perimeter = 2 * (3x + 4)
Perimeter = 6x + 8
Therefore, the expression in simplest form that represents the perimeter of the rectangle is 6x + 8.
2. For the given expressions:
a. 2(3x - 4) + (2x - 5) = 8x - 13
To simplify this expression, distribute the 2 in front of the brackets:
6x - 8 + 2x - 5 = 8x - 13
Combine like terms:
8x - 13 = 8x - 13
The sum is equal on both sides of the equation, so the sum is 8x - 13.
b. 2(3x - 4) - (2x - 5) = 8x + 13
To simplify this expression, distribute the 2 and negative sign inside the brackets:
6x - 8 - 2x + 5 = 8x + 13
Combine like terms:
4x - 3 = 8x + 13
Rearrange the equation:
4x - 8x = 13 + 3
-4x = 16
Divide both sides by -4:
x = -4
Therefore, the difference is -4.
3. a. To represent the number of fireflies you and your friend caught together, you need to add up the number of fireflies you caught and the number of fireflies your friend caught.
Number of fireflies you and your friend caught = (3m + 13) + (4m + 6)
Simplifying the expression:
Number of fireflies you and your friend caught = 3m + 13 + 4m + 6
Combine like terms:
Number of fireflies you and your friend caught = 7m + 19.
b. The competition ends after 5 minutes. To determine who has more fireflies, substitute m = 5 in both expressions.
For you:
Number of fireflies you caught = 3(5) + 13 = 28.
For your friend:
Number of fireflies your friend caught = 4(5) + 6 = 26.
Since 28 > 26, you would have more fireflies.
1. To find the perimeter of a rectangle, we add up all the lengths of its sides. In this case, we have two sides with lengths (x + 5) meters and (2x - 1) meters.
The expression for the perimeter can be obtained by adding these two lengths together:
Perimeter = (x + 5) + (2x - 1)
To simplify this expression, we combine like terms:
Perimeter = x + 5 + 2x - 1
Now we combine the x terms and the constant terms:
Perimeter = (x + 2x) + (5 - 1)
Perimeter = 3x + 4
So, the correct expression that represents the perimeter of the rectangle is 3x + 4.
2. In this problem, we are given two expressions and need to evaluate the sum and difference:
Expression 1: 2(3x - 4) + (2x - 5)
Expression 2: 2(3x - 4) - (2x - 5)
To solve these expressions, we first distribute the multiplication:
Expression 1: 6x - 8 + 2x - 5
Expression 2: 6x - 8 - 2x + 5
Next, combine like terms:
Expression 1: 8x - 13
Expression 2: 4x - 3
So, for the sum and difference, we have:
Sum: 8x - 13
Difference: 4x - 3
3a. The expression that represents the number of fireflies you and your friend caught together is given as (3m + 13) + (4m + 6).
To simplify this expression, we combine like terms:
Total Fireflies = 3m + 13 + 4m + 6
Now combine the m terms and the constant terms:
Total Fireflies = (3m + 4m) + (13 + 6)
Total Fireflies = 7m + 19
So, the correct expression that represents the number of fireflies you and your friend caught together is 7m + 19.
3b. To find out who has more fireflies after 5 minutes, we substitute m = 5 into the expressions for yourself and your friend:
Your Total Fireflies = 3(5) + 13 = 28
Friend's Total Fireflies = 4(5) + 6 = 26
Therefore, you would have more fireflies with a total of 28, while your friend has a total of 26.
1. 2(x+5) + 2(2x-1) = 2x+10 + 4X -2 = ?
2. First one right.
6x-8 - 2x + 5 = ?
3. Right