Answer:
Y int at
(
0
,
3
2
)
X int at
(
3
,
0
)
Step-by-step explanation:
The line is easier to visualize when the equation is in slope-intercept form:
4
x
+
8
y
=
12
Divide each side by 4:
x
+
2
y
=
3
2
y
=
−
x
+
3
y
=
−
1
2
x
+
3
2
Y-intercept (plug in 0 for x):
y
=
−
1
2
(
0
)
+
3
2
y
=
3
2
X-intercept (plug in 0 for y):
0
=
−
1
2
x
+
3
2
−
3
2
=
−
1
2
x
x
=
3
First, we need to calculate for x. Since,
MP = PN
Thus,
3x-4 = x+4
2x = 8
x = 4
<span>Next, we calculate for MS </span>
MS = 2x + 2 = 10
Since, MS = 2SQ
10 = 2SQ
Then,
SQ = 5 units
Therefore, the correct answer is B.
Answer:
Length of the final sides: 6 cm and 16 cm
Step-by-step explanation:
The lengths of the sides of the original box are

Later, a piece of tin is cut out from each corner; the piece cut out has the shape of the square: we can call the length of its generic side x. Therefore, the dimensions of the box will now be:

We also know that the area is

And the area can be written as product of length and width, therefore:

So we find:

Solving for x,

Which has two solutions:
x = 13 cm (this is larger than the initial length of the width, therefore we discard it)
x = 2 cm
So, the length of the new sides are

The function is equal to (x+2) / (x+2)(x-2), so when you simplify, it would be 1/(x-2). This means that there is a hole in the graph at x=-2, and a vertical asymptote at x=2.