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)
2 (a - 4) = 4a - (2a + 4) is an identity.
Q. 11.True or False? This equation has no solution: 12 x + 13 (x − 6) = 56 x + 212 x + 13 (x − 6) = 56 x + 2 (1 point) Responses True True False
The correct response is: false.
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)
The rent for one month can be determined by subtracting the security deposit from the total amount they paid and then dividing by 2 (since they paid for two months).
So, the rent for one month would be:
($2800 - $500) / 2 = $1150
Therefore, the correct amount to choose from the drop down menu 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 assume the cost of one pack of strings is "x".
Noah buys 2 packs of strings, so the cost of his strings is 2x.
Kate buys 2 packs of strings and a music book, so the cost of her strings is 2x + $16.
The total cost of their purchases is $36.
Therefore, the equation is: 2x + 2x + $16 = $36.
Simplifying the equation, we get: 4x + $16 = $36.
Subtracting $16 from both sides, we get: 4x = $20.
Dividing both sides by 4, we get: x = $5.
Therefore, one pack of strings costs $5. The correct answer to choose from the drop-down menu 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)
To calculate the number of haircuts the hairdresser needs to do to make a profit, we need to determine the breakeven point where her total revenue equals her total expenses.
Let's assume the number of haircuts she needs to do is "x".
Her total monthly expenses, in this case, is just the rent, which is $1200.
Her total monthly revenue is the price per haircut multiplied by the number of haircuts, which is $45 * x.
To make a profit, her total revenue should be greater than her total expenses. So, we have the inequality:
45x > 1200
Dividing both sides by 45, we get:
x > 26.67
Since we can't do a fraction of a haircut, we need to round up to the nearest whole number. Therefore, she needs to do at least 27 haircuts to make a profit.
The correct option to choose from the dropdown menu is "27".
To determine which equation is an identity, we need to simplify each equation and see if it holds true regardless of the value of the variable(s) involved.
Let's analyze each equation:
1) x - 3x = 6x + 5 - 8x
To simplify this equation, combine like terms on both sides:
-2x = -2x + 5
Notice how the variable "x" cancels out on both sides of the equation. Therefore, this equation is an identity.
2) 2(a - 4) = 4a - (2a + 4)
Begin by distributing the multiplication on the left side:
2a - 8 = 4a - 2a - 4
Combine like terms:
2a - 8 = 2a - 4
In this case, the variable "a" cancels out on both sides of the equation, resulting in -8 = -4. Since this statement is false, the equation is not an identity.
3) -6x + 3 = -3(2x - 1)
Start by distributing the multiplication on the right side:
-6x + 3 = -6x + 3
In this equation, notice how both sides are already identical. Therefore, this equation is an identity.
4) 2(2a - 1) = 4(a - 2)
Begin by distributing the multiplication on both sides:
4a - 2 = 4a - 8
Simplify the equation by combining like terms:
4a - 2 = 4a - 8
Even though both sides of the equation are technically the same, notice how there is an inconsistency with the variables. This means that the equation is not an identity.
Based on our analysis, the equations that are identities are:
1) x - 3x = 6x + 5 - 8x
This equation holds true for any value of "x."
2) -6x + 3 = -3(2x - 1)
This equation also holds true for any value of "x."