The correct option is the last one. h is negative and k is positive.
<h3>
What can we say about h and k?</h3>
For the absolute value function:
g(x) = |x - h| + k
We know that the vertex is on the point (h, k).
On the graph, we can see that the vertex is on the point (-2, 1), then we have:
h = -2
k = 1
So the sign of h is negative and the sign of k is positive. The correct option is the last one.
If you want to learn more about absolute value functions:
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It would be zero because you can’t raise 0 to any positive power.
Answer:
They made 4 forks and 6 spoons last April.
Step-by-step explanation:
Let forks they made in april be x and spoons be y.
To make 1 fork we need $2
To make 1 spoon we need $1
They sell 1 fork for $6 and 1 spoon for the same amount So,
now,
Turning it into two equations :-
(x = number of forks and y = number of spoons)
2x + 1y = 14
6x + 6y = 60
Now,
2x + y = 14
y = 14 - 2x
Now,
6x + 6y = 60
or, 6x + 6(14-2x) = 60
or, 6x + 84 - 12x = 60
or, -6x = -24
so, x = 4
Now,
y = 14 - 2x
or, y = 14 - 2×4
or, y = 14-8
so, y = 6
Answer:
2) x = -4; y = 0; z = -2
4) x = 4; y = 2; z = 0
Step-by-step explanation:
2)
-4x - 5y - z = 18
-2x - 5y - 2z = 12
-2x + 5y + 2z = 4
Add the 2nd and 3rd equations to eliminate y and z.
-4x = 16
x = -4
Substitute x = -4 in first and second equations.
(-4)(-4) - 5y - z = 18
(-2)(-4) - 5y - 2z = 12
-5y - z = 2
-5y - 2z = 4
Multiply first equation by -1 and add to second equation.
5y + z = -2
(+) -5y - 2z = 4
----------------------
-z = 2
z = -2
Substitute x = -4 and z = -2 in first original equation and solve for y.
-4(-4) - 5y - (-2) = 18
16 - 5y + 2 = 18
-5y = 0
y = 0
Answer: x = -4; y = 0; z = -2
4)
4x + 4y + z = 24
2x - 4y + z = 0
5x - 4y - 5z = 12
Add equations 1 and 3 to eliminate y.
9x - 4z = 36 Eq. 1
Add equations 1 and 2 to eliminate y.
6x + 2z = 24 Eq. 2
Multiply Eq. 2 by 2 and add to Eq. 1.
12x + 4z = 48
(+) 9x - 4z = 36
----------------------------
21x = 84
x = 4
Substitute x = 4 into Eq. 1 to solve for z.
9x - 4z = 36
9(4) - 4z = 36
-4z = 0
z = 0
Substitute x = 4 and z = 0 into the first original equation to solve for y.
4x + 4y + z = 24
4(4) + 4y + 0 = 24
4y = 8
y = 2
Answer: x = 4; y = 2; z = 0