Answer:
1 hour and 42 minutes
Step-by-step explanation:
Answer:
One form of an equation is given by
y=a(x−h
)
2
+k
y=a(x−h)2+k
where
(h,k)
(h,k)
the coordinates of the vertex and
(h,k+
1
4a
)
The parabola is symmetric with respect to
y=x
y=x
and can be viewed as a standard downward parabola with a rotation of 45 degrees clockwise. So, follow the steps below to obtain its equation.
1) The length between the focus and vertex is
f=
4
2
+
4
2
−
−
−
−
−
−
√
=4
2
–
√
f=42+42=42
. The standard equation is
y=−
1
4f
x
2
y=−14fx2
.
2) Shift the vertex to (-2, -2),
y+2=−
1
16
2
–
√
(x+2
)
2
y+2=−1162(x+2)2
3) Rotate the equation -45-degrees
x→
1
2
√
(x−y)
x→12(x−y)
,
y→−
1
2
√
(x+y)
y→−12(x+y)
to get
−
1
2
–
√
(x+y)+2=−
1
16
2
–
√
(
1
2
–
√
(x−y)+2)
2
Step-by-step explanation:
Answer:
x=21
Step-by-step explanation:
since the triangle is isosceles, the two lower angles are equal.
2(2x+3)=90
4x+6=90
4x=84
x=21
<u>Step-By-Step Solution for Part 1:</u>
- 3(4p + 2) = 12p + 6
- => (3 x 4p) + (3 x 2) = 12p + 6
- => 12p + 6 = 12p + 6
Answer: Equivalent
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<u>Step-By-Step Solution for Part 2:</u>
Answer: Equivalent
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<u>Step-By-Step Solution for Part 3:</u>
- 2y + z² = y x y + z + z
- => 2y + z² = y² + 2z
<u>[Replacing y as 2 and z as 3]</u>
- => 2(2) + (3)² = (2)² + 2(3)
- => 4 + 9 = 4 + 6
- => 13 ≠ 10
Answer: Not Equivalent
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<u>Step-By-Step Solution for Part 4:</u>
15n + 5 = 5(3n + 1)
=> 15n + 5 = (5 x 3n) + (5 x 1)
=> 15n + 5 = 15n + 5
Answer: Equivalent
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