Answer:
Emily is solving the following system of equations using substitution:
y = 3x - 4
y = 2x + 1
<u>Part</u><u> </u><u>A</u><u>:</u>
After substituting y's values:
3x - 4 = 2x + 1
<em><u>What she did:</u></em>
3x - 4 = 2x + 1
3x + 2x - 4 = 1
5x - 4 = 1
<em><u>What she should have done:</u></em>
3x - 4 = 2x + 1
3x - 2x - 4 = 1
x - 4 = 1
<u>Part</u><u> </u><u>B</u><u>:</u>
This rule has not been followed: Sign changes when numbers shift from left to right of ' = 'sign.
Emily did not changed the sign of the number, 2x from + 2x to - 2x when it was moved from the right side to the left.
So that they have the same denominator you can rewrite 9n as (27/3)n
(27/3)n + (2/3)n = 4
(29/3)n = 4
Multiply both sides by 3/29 to isolate variable n.
n = 4(3/29)
n = 12/29
Alternate exterior means opposite sides of the transversal and outside the parallel lines... angles 1, 2, 5, 6 are all outside the parallel lines.. now you just need to match up the ones that are on opposite sides... 1 and 5 are opposite sides and 2 and 6 are opposite sides.. so those two pairs are the alternate exterior angles.. since 2 and 6 isn't a choice and 1 and 5 is, then there is your answer.
Answer:
Determine the point of intersection by using substitution and solving for the variables.
Explanation:
Solving a system of equations imply we find the point of interception.
To do this, we must use substitution to find one variable, and use that value to determine the exact value of the other.
Here, we'll isolate
x
.
−
2
x
−
2
y
=
−
4
−
2
x
=
2
y
−
4
x
=
−
y
+
2
Now that we have our variable expression, we can sub this into the other equation and solve for
y
.
2
x
+
3
y
=
9
2
(
−
y
+
2
)
+
3
y
=
9
−
2
y
+
4
+
3
y
=
9
4
+
y
=
9
y
=
5
Now that we know our
y
value, we can sub it into any equation to solve for
x
.
x
=
−
y
+
2
x
=
−
(
5
)
+
2
x
=
−
5
+
2
x
=
~
3
Thus, our point of intersection is
(
~
3
,
5
)
.
If we graph the two equations, we can see the point of intersection is in fact
(
~
3
,
5
)
.
graph{(-2x-2y+4)(2x+3y-9)=0 [-8.875, 11.125, -0.36, 9.64]}
Hope this helps :)
Please, use "^" to denote exponentiation. Your 2x2 should be written as 2x^2.
Your relationships are then f(x,y)=2x^2+3y^2-4x-2
and x^2 + y^2 <span>≤ 16
Please note that the 2nd relationship represents a circle of radius 4 whose entire interior has been shaded.
Graph this. Then, rewrite f(x,y) in the form f(x,y) = 2x^2 - 4x + 3y^2 -2. Can you identify the shape of the curve in the xy plane representing this function? You'll need to find the points (x,y) in which the graph of f(x,y) intersects the shaded circle x^2 + y^2 </span><span>≤ 16.
</span>
Think: what do "extreme values of f"
