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
To simplify the given expression:
3(-12x - 4) + 10
First, we can distribute the 3 to each term inside the parentheses:
3 * -12x + 3 * -4 + 10
Simplifying further:
-36x - 12 + 10
-36x - 2
So, the simplified expression is:
-36x - 2
Find the GCF of 20� − 420x\ -\ 420x − 4
To find the greatest common factor (GCF) of the given expression:
20x - 420x - 420x - 4
First, we can look for common factors in each term. The common factor in the first two terms is 20x, and the common factor in the last two terms is -4.
Now, we can factor out the common factors:
20x - 420x - 420x - 4 = 20x(1 - 21) - 4(1 + 105)
Further simplifying:
20x(-20) - 4(106)
Now, we can see that the GCF is 4. Therefore, the GCF of 20x - 420x - 420x - 4 is 4.
Factor 8� − 288a\ -\ 288a − 28 using the GCF
To factor the given expression using the greatest common factor (GCF), we need to identify the common factors in each term.
The common factor in the first two terms is 8a, and the common factor in the last two terms is -4.
Factoring out the common factors, we have:
8a(1 - 36) - 4(1 + 7)
Simplifying further:
8a(-35) - 4(8)
-280a - 32
Therefore, factoring the expression by the GCF gives us:
8a(1 - 35) - 4(1 + 7)
-280a - 32
Factor 8a-28 using the GCF
To factor the expression 8a - 28 using the greatest common factor (GCF), we need to find the common factor in both terms.
The common factor in 8a and 28 is 4.
So, factoring out 4 from the expression, we have:
4(2a - 7)
Therefore, the factored form of 8a - 28 using the GCF is 4(2a - 7).
(a)
To go horseback riding, you pay $40 per hour and a saddle fee of $15. Write an expression, where h is the number of hours, to represent the total amount you would spend.
The expression to represent the total amount you would spend for horseback riding, where h is the number of hours, is:
40h + 15
This accounts for the cost per hour ($40) multiplied by the number of hours (h), and adds the saddle fee of $15.
How much will you pay for a 6 hour ride
To calculate the total amount you would pay for a 6-hour horseback ride, you can substitute h = 6 into the expression:
40h + 15
Plugging in h = 6:
40(6) + 15
Simplifying the expression, we have:
240 + 15
Combining like terms:
255
Therefore, you would pay a total of $255 for a 6-hour horseback ride.
A student claims that
is equivalent to
. The student's steps are shown below.
Expression:
Step 1:
Step 2:
Step 3:
Step 4: 3x
Describe ALL errors in the student's work. (There is more than one error.)
Based on the information provided, it's difficult to identify the exact errors in the student's work without the expressions shown in each step. However, I can make some assumptions based on the given steps:
Expression:
Step 1:
Step 2:
Step 3:
Step 4: 3x
From Step 4, it seems that the student arrived at the expression 3x as the equivalent of a previous expression, but without the previous steps or complete information, it's not possible to identify the errors made in the student's work.
If you could provide more information or the complete expressions shown in each step, I would be able to analyze the errors made by the student more accurately.
Step 1: 8x-2(4+3x)
Step: 8x-8+3x
Step 3: 11x-8
Step 4: 3x
Based on the given steps, there are a couple of errors in the student's work:
1. In Step 2, when distributing the -2 to the terms inside the parentheses, the sign of the 3x term should change. The correct distribution should be: 8x - 8 - 2(3x), which simplifies to 8x - 8 - 6x.
2. In Step 3, the student simplified 8x - 8 - 6x to 11x - 8. However, the correct simplification should be 2x - 8.
So, the correct final expression should be 2x - 8, not 3x as claimed by the student.
Simplify the expression 8x-2(4+3x)
To simplify the expression 8x - 2(4 + 3x), we need to apply the distributive property by multiplying -2 to both terms inside the parentheses:
8x - 2(4) - 2(3x)
Simplifying further:
8x - 8 - 6x
Combining like terms:
(8x - 6x) - 8
Simplifying again:
2x - 8
The simplified expression is 2x - 8.
Which expressions are equivalent to 6m + 18? Select all that apply.
A
6(m + 18)
B
2(3m + 9)
C
6 + m + 18
D
5m + 10 + 8 + m
E
6(m + 3)
The expressions that are equivalent to 6m + 18 are:
A) 6(m + 18)
B) 2(3m + 9)
E) 6(m + 3)
These three expressions involve distributing 6 to the terms inside the parentheses, resulting in the same equivalent expression of 6m + 18.