Answer:
Sorry this is late and I think this is right.
They are both parallel, they have the same slope, and do <em>not </em>intersect. If you were to draw a slope out for it, you would find this to be true.
For example: Say the question called for you to explain why there aren't any solutions to these system of inequalities:
<em>y < - 1/2x -3</em>
<em>y > 1/2x + 2</em>
<em>y= -x/2 -3</em> and <em>y= -x/2 + 2 </em>have the same exact slope, are parallel, and never intersect. The first line is 5 units below the second line when x = 0. Because the lines are parallel, it is always below the second line. The solutions of y < - x/2 -3 are the points in the plane below the first line. The solutions of y > 1/2 + 2 are points above the second line.
I hope this helps you. Good luck on whatever you're working on and stay safe! Please let me know if this helped you or didn't.
Use the quadratic formula to find:
x
=
1
±
√
85
5
Explanation:
5
x
2
−
10
x
−
12
is of the form
a
x
2
+
b
x
+
c
with
a
=
5
,
b
=
−
10
and
c
=
−
12
This has discriminant
Δ
given by the formula:
Δ
=
b
2
−
4
a
c
=
(
−
10
)
2
−
(
4
×
5
×
−
12
)
=
100
+
240
=
340
=
2
2
⋅
85
This is positive, but not a perfect square, so the quadratic equation has a pair of irrational roots, given by the quadratic formula:
x
=
−
b
±
√
b
2
−
4
a
c
2
a
=
−
b
±
√
Δ
2
a
=
10
±
√
340
10
=
10
±
2
√
85
10
=
1
±
√
85
5
Find the least common denominator for all fractions: 12
3/4 = (3*3)/(4*3) = 9/12
1/6 = (1*2)/(6*2)
1/4 = (1*3)/(4*3)
Take the converted fractions to have the honey used taken away from the original total.
Answer:
200 students must agree to attend in order for the school to have the festival.
Step-by-step explanation:
200 is 40% of 500. We can also use fractions to figure this out.
For 100 to become 500 it must be multiplied by 5. And whatever we do to the denominator we have to do to the numerator. So we multiply 40 × 5 = <em>x</em>
<em>x</em> = 200
