A student solved the equation: x + 2 (x + 1) = 17
Line 1: x + 2x + 1 =17
Line 2: 3x + 1 = 17
Line 3: 3x = 16
Line 4: x = 16/3 (3 points)
Identify the Property used to go from Line 2 to Line 3:
Which line has a mistake?
What should have been the correct answer for the equation?
Distributive Property
Combine like terms
Subtraction Property of Equality
Multiplication Property of Equality
Line 1
Line 2
Line 3
Line 4
No solution
x = 5
x = 45
x = 15
The Property used to go from Line 2 to Line 3 is the Subtraction Property of Equality.
The mistake is in Line 4. The correct answer for the equation should be x = 5.
What is the missing exponent that would make this equation true? k^5 ⋅ k^2/k^x = (k^2)^−2 (1 point)
x = 6
x = 3
x = 9
x = 1
x = 0
x = 11
To solve this, we simplify both sides of the equation:
On the left side:
k^5 * k^2 / k^x = k^(5+2-x) = k^(7-x)
On the right side:
(k^2)^-2 = k^(-4)
So, we have k^(7-x) = k^(-4)
Now, since the bases on both sides are equal, the exponents must be equal. Therefore, we get:
7 - x = -4
Solving for x:
x = 7 + 4
x = 11
Therefore, the missing exponent that would make the equation true is x = 11.
Two students have bank accounts:
Sama: $ 5^8⋅5^4/(5^3)^2
Jimena: $ 2^9⋅(2^−2)^−3/ 2(4 points)
Who has more money in their account? Response area
What is the difference in the amount of money that they have? Response area
$523
0 difference in the accounts
$759
$1000
They both have the same amount of money.
Jimena
Sama
7 times more money
Let's simplify the expressions for both students' bank accounts:
For Sama:
$ 5^8 * 5^4 / (5^3)^2 = 5^(8+4) / 5^6 = 5^12 / 5^6 = 5^(12-6) = 5^6 = 15625
Therefore, Sama has $15,625 in her account.
For Jimena:
$ 2^9 * (2^(-2))^(-3) = 2^9 * 2^6 = 2^(9+6) = 2^15 = 32,768
Therefore, Jimena has $32,768 in her account.
Now, we can see that Jimena has more money in her account compared to Sama.
The difference in the amount of money they have is $32,768 - $15,625 = $17,143.
Therefore, the correct responses are:
Jimena
$17,143
are you sure
I apologize for the mistake in my previous response. Let's correct that.
For Sama:
$ 5^8 * 5^4 / (5^3)^2 = 5^(8+4) / 5^6 = 5^12 / 5^6 = 5^(12-6) = 5^6 = 15,625
For Jimena:
$ 2^9 * (2^(-2))^(-3) = 2^9 * 2^6 = 2^(9+6) = 2^15 = 32,768
Jimena indeed has more money in her account: $32,768.
The difference in the amount of money they have is $32,768 - $15,625 = $17,143.
Therefore, the correct responses are:
Jimena
$17,143
choose from the answers provided
$17,143
Jimena