A student wants to prove that she can solve a system of a system of equations by replacing one of the equations with two times t
hat equation and adding the other equation. The original system was 12x +2y =30 and 10x+y = 26. The student claims that her first step is to add the two linear equations. Select the option that refutes the student claim
1 answer:
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I know you didn't want an explanation, but I'll give you one anyway.
So, for a function, when you have f(5) = , then you'll put that 5 in for all of the x's in the function.
The first batch of problems gave you the equation f(x) =
+ 3. Now, plug in the numbers given for s and solve.
1. f(5) = <span> + 3 Plug in 5 for x
</span> =
+ 3 Make three into a fraction over 2
= + <span>
Add
= </span><span><span>
</span>2. f(-4) = </span><span> + 3 Plug in -4 for x
= </span><span>
+ 3 Divide -4 by 2
= -2 + 3 Add
= 1
For the next set, you have g(x) = x</span>² + 1.
3. Let's split this up. Solve the first equation, then the second, and then put the answers together to solve it.
g(4) = x² + 1 Plug in 4 for x
= 4² + 1 Square
= 16 + 1 Add
= 17
g(3) = x² + 1 Plug in 3 for x
= 3² + 1 Square
= 9 + 1 Add
= 10
Now, put the two together.
g(4) + g(3) = Substitute in the answers you just got.
17 + 10 = Add
= 27
4. g(-1) = x² + 1 Substitute in -1 for x
= (-1)² + 1 Square
= 1 + 1 Add
= 2
5. g(-6) = x² + 1 Plug in -6 for x
= (-6)² + 1 Square
= 36 + 1 Add
= 37
For the last set, we have h(x) = x² + 7 and k(x) = 4x - 5. We'll have to pay close attention to the starting variables here.
6. h(-6) = x² + 7 Plug in -6 for x
= (-6)² + 7 Square
= 36 + 7 Add
= 43
k(4) = 4x - 5 Plug in 4 for x
= 4(4) - 5 Multiply
= 16 - 5 Subtract
= 11
Put the two answers into the final equation.
h(-6) + k(4) = Substitute in the answers you got
43 + 11 = Add
= 54
7. k(10) = 4x - 5 Plug in 10 for x
= 4(10) - 5 Multiply
= 40 - 5 Subtract
= 35
h(2) = x² + 7 Plug in 2 for x
= 2² + 7 Square
= 4 + 7 Add
= 11
Now, put those into the equation.
k(10) - h(2) = Plug in the answers you got
35 - 11 = Subtract
= 24
8. For this one, it wants you to add h(x) and k(x). We don't need to plug anything into the equations this time because they're both already solved for x! So, you can just set this up like a standard find-x equation.
(x² + 7) + (4x - 5) =
x² + 7 + 4x - 5 = Combine like terms (7 and -5)
x² + 2 + 4x = Reorder so the variables come first
= x² + 4x + 2
So, for a function, when you have f(5) = , then you'll put that 5 in for all of the x's in the function.
The first batch of problems gave you the equation f(x) =
1. f(5) = <span>
</span> =
=
= </span><span><span>
</span>2. f(-4) = </span><span>
= </span><span>
= -2 + 3 Add
= 1
For the next set, you have g(x) = x</span>² + 1.
3. Let's split this up. Solve the first equation, then the second, and then put the answers together to solve it.
g(4) = x² + 1 Plug in 4 for x
= 4² + 1 Square
= 16 + 1 Add
= 17
g(3) = x² + 1 Plug in 3 for x
= 3² + 1 Square
= 9 + 1 Add
= 10
Now, put the two together.
g(4) + g(3) = Substitute in the answers you just got.
17 + 10 = Add
= 27
4. g(-1) = x² + 1 Substitute in -1 for x
= (-1)² + 1 Square
= 1 + 1 Add
= 2
5. g(-6) = x² + 1 Plug in -6 for x
= (-6)² + 1 Square
= 36 + 1 Add
= 37
For the last set, we have h(x) = x² + 7 and k(x) = 4x - 5. We'll have to pay close attention to the starting variables here.
6. h(-6) = x² + 7 Plug in -6 for x
= (-6)² + 7 Square
= 36 + 7 Add
= 43
k(4) = 4x - 5 Plug in 4 for x
= 4(4) - 5 Multiply
= 16 - 5 Subtract
= 11
Put the two answers into the final equation.
h(-6) + k(4) = Substitute in the answers you got
43 + 11 = Add
= 54
7. k(10) = 4x - 5 Plug in 10 for x
= 4(10) - 5 Multiply
= 40 - 5 Subtract
= 35
h(2) = x² + 7 Plug in 2 for x
= 2² + 7 Square
= 4 + 7 Add
= 11
Now, put those into the equation.
k(10) - h(2) = Plug in the answers you got
35 - 11 = Subtract
= 24
8. For this one, it wants you to add h(x) and k(x). We don't need to plug anything into the equations this time because they're both already solved for x! So, you can just set this up like a standard find-x equation.
(x² + 7) + (4x - 5) =
x² + 7 + 4x - 5 = Combine like terms (7 and -5)
x² + 2 + 4x = Reorder so the variables come first
= x² + 4x + 2