Five students each wrote an expression to represent the perimeter of the given rectangle. Terrell wrote this correct expression: (2x+2x)+(5x+5x)+(1+1). Choose the name of the student who wrote an incorrect expression.
A
Anya: 2�+2�+5�+1+5�+12x+2x+5x+1+5x+12x+2x+5x+1+5x+1
B
Luis: 2(2�)+2(5�+1)2(2x)+2(5x+1)2(2x)+2(5x+1)
C
Steve: 1+1+�(2+2+5+5)1+1+x(2+2+5+5)1+1+x(2+2+5+5)
D
Katrin: 2(5�+1)+2�2(5x+1)+2x2(5x+1)+2x
D
which expression is incorrect? And please explain why it is.
The incorrect expression is D, written by Katrin.
The correct expression for the perimeter of a rectangle is (2x+2x)+(5x+5x)+(1+1). However, in Katrin's expression, she wrote 2(5�+1)+2�2(5x+1)+2x2(5x+1)+2x.
In Katrin's expression, she incorrectly distributed the multiplication for the sides of the rectangle. The correct way to distribute the multiplication would be to have 2(5x+1) for the length and 2(2x) for the width. However, Katrin mistakenly wrote it as 2(5�+1) and 2�2(5x+1).
Therefore, Katrin's expression is incorrect.
A group of friends are going bowling.
The bowling alley charges $2 per person for shoes plus a fee of $15 for the lane.
Write an expression to find the total cost of the bowling trip for (f) friends.
To find the total cost of the bowling trip for (f) friends, we need to consider two expenses: the cost of shoes and the cost of the lane.
The cost of shoes for each person is $2. Since there are (f) friends, the total cost of shoes would be 2f.
The cost of the lane is a flat fee of $15.
Therefore, the expression to find the total cost of the bowling trip for (f) friends would be:
Total cost = 2f + 15
Simplify
−15�+3−25�−6-\frac{1}{5}r+3-\frac{2}{5}r-6−
5
1
r+3−
5
2
r−6
To simplify the given expression:
-15r + 3 - 25r - 6 - \frac{1}{5}r + 3 - \frac{2}{5}r - 6 - \frac{5}{1}r + 3 - \frac{5}{2}r - 6
Next, we can combine like terms:
(-15r - 25r - \frac{1}{5}r - \frac{2}{5}r - \frac{5}{1}r - \frac{5}{2}r) + (3 + 3 + 3 - 6 - 6 - 6)
Simplifying further:
- \frac{23}{5}r + (-3)
Finally, the simplified expression is:
- \frac{23}{5}r - 3
Simplify -1/5r+3-2/5r-6
To simplify the expression:
- \frac{1}{5}r + 3 - \frac{2}{5}r - 6
First, combine the like terms by subtracting the coefficients of the r terms, and then combine the constant terms:
(- \frac{1}{5}r - \frac{2}{5}r) + (3 - 6)
Simplifying further:
- \frac{3}{5}r + (-3)
Finally, the simplified expression is:
- \frac{3}{5}r - 3
Simplify the expression.
3(−12�−4)+103\left(-12x-4\right)+103(−12x−4)+10