Answer:
(
2
x
−
6
)
2
+
4
(
2
x
−
6
)
+
3
=
0
Simplify the left side.
Tap for more steps...
(
2
x
−
6
)
2
+
8
x
−
21
=
0
Use the quadratic formula to find the solutions.
−
b
±
√
b
2
−
4
(
a
c
)
2
a
Substitute the values
a
=
4
,
b
=
−
16
, and
c
=
15
into the quadratic formula and solve for
x
.
16
±
√
(
−
16
)
2
−
4
⋅
(
4
⋅
15
)
2
⋅
4
Simplify.
Tap for more steps...
x
=
4
±
1
2
The final answer is the combination of both solutions.
x
=
5
2
,
3
2
Step-by-step explanation:
Making a profit means ending the month with a number above 0, so your inequality will have to be greater than 0.
(sell) t-shirt = 12
(make) t-shirt = 6.50
and a constant of 150
so your current equation will be the cost of making a t-shirt, the money received by selling, and the cost of rent. it'll look like:
12t - 6.50t -150 > 0
but you want to get t alone to know how many t-shirts you have to sell, so solve the inequality:
12t - 6.50t - 150 > 0
12t - 6.50t > 150
5.50t > 150
t > (150/5.50)
and that fraction is roughly 27.27, so you'll round it up to the next whole number because alex can't make/sell a twenty-seventh of a t-shirt.
alex will have to make 28 t shirts to make a profit, and you can plug it back into the equality like so to check it:
12t - 6.50t - 150 > 0
12(28) - 6.50(28) - 150 > 0
336 - 182 - 150 > 0
4 > 0
and that statement is true, measly profit as it is.
The answer can be positive or negative. See picture...
Answer:
translation 2 units left
; reflection across the y-axis
Step-by-step explanation:
The y-coordinates of the points do not change from the pre-image to the image. This means there is no translation down (this would add or subtract to the y-coordinates) and no reflection across the x-axis (this would negate the y-coordinates).
This leaves us with a translation 2 units left and a reflection across the y-axis.
The translation 2 units left adds 2 to the x-coordinates, and the reflection across the y-axis negates the x-coordinates. If we add 2 first, the coordinates would be (-4+2, 6) = (-2, 6); (-2+2, 2) = (0, 2); and (-6+2, 2) = (-4, 2).
Negating each of these would give us (2, 6); (0, 2); and (4, 2). These are the desired image coordinates.