Answer:
x can be 3, -3, i, or -i.
Step-by-step explanation:
If you can't find the factoring by looking at this, simplify the equation.
let
x
2
=
y
to make things easier to see
Now we have
y
2
−
8
y
−
9
=
0
See it now?
We can factor into
(
y
−
9
)
(
y
+
1
)
Now substitute back in
x
2
for
y
.
(
x
2
−
9
)
(
x
2
+
1
)
Since
(
x
2
−
9
)
is a difference of two squares,
(
x
−
3
)
(
x
+
3
)
Now we have
(
x
−
3
)
(
x
+
3
)
(
x
2
+
1
)
x can be 3, -3 for the first two parts
x
2
+
1
=
0
can become
x
2
=
−
1
Taking the positive and negative root means
x
=
±
√
−
1
Thus
x
=
±
i
in addition to 3 and -3.
Answer: choice C, y = 0.014x+0.85
==============================
Explanation:
Each column of the table represents an (x,y) pair of values
x = number of pages
y = cost
If we look at the first two columns, we see the two points (50,1.55) and (100,2.25). The x value is listed first. Let's compute the slope of the line through these two points
m = (y2-y1)/(x2-x1)
m = (2.25-1.55)/(100-50)
m = 0.7/50
m = 0.014
So far, we see the answer is between A,B or C as they have the slope of 0.014
Use this slope value, and one of the points -- say (x,y) = (50,1.55) -- to find the y intercept b
y = mx+b
y = 0.014x+b .... plug in the slope found earlier
1.55 = 0.014*50+b ... plug in the point (x,y) = (50,1.55)
1.55 = 0.7+b
1.55-0.7 = 0.7+b-0.7 ... subtract 0.7 from both sides
0.85 = b
b = 0.85
With m = 0.014 as the slope and b = 0.85 as the y intercept, we can say that y = mx+b turns into y = 0.014x+0.85. That narrows the answer down to choice C.
2x + y = 350
x + 2y = 475
3x + 3y = 825
x + y = 275
x = 275 - y
(plug back into first equation)
2(275 - y) + y = 350
550 - 2y + y = 350
550 - y = 350
-y =-200 or y = $200 (dog)
therefore, x = $75 (cats)
Check
2(75) + 200 = 350
75 + 400 = 475
HAPPINESS! :)
