Q 1. Is the equation true, false, or open? 3x + 1 = 22
(1 point)
Responses
False; the expressions are never the same.
False; the expressions are never the same.
Not enough information
Not enough information
Open; there is a variable.
Open; there is a variable.
True; the expressions are the same for all values of the variable.
False; the expressions are never the same.
Q 2. Which value is a solution of the equation 4 - 2x = 8?(1 point)
Responses
2
2
- 2
- 2
12
1
2
1 half
−12
−
1
2
negative 1 half
Question 3
- 2
Q 3. Solve the following equation: m - 8 = 14(1 point)
Responses
m = 6
m = 6
m = 20
m = 20
m = 12
m = 12
m = 22
m = 22
Q 4. Which ordered pair is a solution of y = x - 5?(1 point)
Responses
(7, 2)
(7, 2)
(11, 4)
(11, 4)
(2, 7)
(2, 7)
(2, 3)
(7, 2)
Q. 5. Solve the following equation: 10 + x3=1
10
+
x
3
=
1
(1 point)
Responses
x = - 7
x = - 7
x = 33
x = 33
x = -27
x = -27
x = 21
x = 21
Question 2
x = - 9
Q. 5. Solve the following equation: 10 + x3=1
10
+
x
3
=
1
(1 point)
Responses
x = - 7
x = - 7
x = 33
x = 33
x = -27
x = -27
x = 21
x = 21
x = - 9
Q. 6. Solve the following equation: 7 (3x - 4) = 49(1 point)
Responses
x = 1
x = 1
x = 2.5
x = 2.5
x = 311
3
11
x = 3 over 11
x = 113
11
3
x = 11 thirds
x = 3 over 11
Q. 7. Solve the following equation: 1.3 + 0.5x = -3.41(1 point)
Responses
x = -4.22
x = -4.22
x = -9.42
x = -9.42
x = 4.22
x = 4.22
x = 9.42
x = -9.42
Q. 8. Solve the following equation: (413) x = 9
(
4
13
)
x
=
9
(1 point)
Responses
x = 29.25
x = 29.25
x = 2.77
x = 2.77
x = 8.69
x = 8.69
x = 26.15
x = 26.15
Q. 9. Solve the following equation: 4 (2y + 1) = 2(y - 13)(1 point)
Responses
y = −73
−
7
3
y = negative 7 thirds
y = 5
y = 5
y = −176
−
17
6
y = negative 17 sixths
y = - 5
y = - 5
y = -5
Q 10. Which equation is an identity?(1 point)
Responses
x - 3x = 6x + 5 - 8x
x - 3x = 6x + 5 - 8x
2 (a - 4) = 4a - (2a + 4)
2 (a - 4) = 4a - (2a + 4)
-6x + 3 = -3 (2x - 1)
-6x + 3 = -3 (2x - 1)
2 (2a - 1) = 4 (a - 2)
x - 3x = 6x + 5 - 8x
Q. 11.True or False? This equation has no solution: 12 x + 13 (x − 6) = 56 x + 2
1
2
x
+
1
3
(
x
−
6
)
=
5
6
x
+
2
(1 point)
Responses
True
True
False
False
Q 12.
Two college friends rent an apartment. They have to pay the landlord two months rent and a $500 security deposit when they sign the lease. The total amount they pay the landlord is $2800. What is the rent for one month? Remember that they paid for two months plus the security deposit. Click the drop down menu to choose the correct amount.
(1 point)
$900.
it wrong
I apologize for the incorrect response. Let's calculate the rent for one month.
Let's denote the rent for one month as 'x'.
The total amount they pay the landlord is calculated as follows:
2 months rent + $500 security deposit = $2800
2x + $500 = $2800
Subtracting $500 from both sides:
2x = $2800 - $500
2x = $2300
Dividing both sides by 2:
x = $2300 / 2
x = $1150
Therefore, the rent for one month is $1150.
Q. 13. Noah and Kate are shopping for new guitar strings in a music store. They pay a total of $36.00 for their purchases. Noah buys 2 packs of strings. Kate buys 2 packs of strings and a music book. The book costs $16. How much is one pack of strings? Click the drop down menu to choose the correct answer.(1 point)
Let's denote the cost of one pack of strings as 'x'.
Noah buys 2 packs of strings, so his total cost for the strings is 2x.
Kate buys 2 packs of strings and a music book, so her total cost is 2x + $16.
The total cost of their purchases is $36, so we can write the equation:
2x + 2x + $16 = $36
Combining like terms:
4x + $16 = $36
Subtracting $16 from both sides:
4x = $36 - $16
4x = $20
Dividing both sides by 4:
x = $20 / 4
x = $5
Therefore, the cost of one pack of strings is $5.
Q. 14. A hairdresser is deciding to open her own studio. She will pay $1200 per month in rent and will charge $45 per haircut. If rent is her only expense, how many haircuts does she need to do to make a profit? Click on the dropdown menu to choose the correct option. Be careful about rounding correctly!(1 point)
Let's denote the number of haircuts as 'x'.
The total revenue from haircuts is the price per haircut ($45) multiplied by the number of haircuts (x), which is 45x.
The total expense is the monthly rent ($1200).
To make a profit, the revenue needs to be greater than the expenses. So we have the inequality:
45x > 1200
Dividing both sides of the inequality by 45:
x > 1200/45
Calculating the value:
x > 26.67
Since the number of haircuts cannot be fractional, she will need to do at least 27 haircuts to make a profit.
Therefore, the correct option is:
27 (or more) haircuts.