1.Isolated of a
, using .
(b3)3
2.Isolated
.
(6m1b2)0
1Zero exponent rule
Any nonzero base raised to the power 0 equals 1.
Answer1
3.IsolatedDifference of cubes
completely.
y3 − 64
1Difference of cubes formula
A3 − B3 = (A − B)(A² + AB + B²)
2Substitute A = y and B = 4
= (y − 4)(y2 + 4y + 42)
Answer(y − 4)(y2 + 4y + 42)
4.Isolated
Find the .
x2 − 6x + 5 = 0
1Use b² − 4ac
b² − 4ac = (-6)² − 4 · 1 · 5
3Interpret
Because the discriminant is 16, the equation has two distinct real roots.
Answer16
5.Isolated with
for the .
x3 − 4 = 1
1Add 4 on both sides
x3 = 5
2Multiply both sides by 3
x = 15
Answerx = 15
6.Hybrid
for 0° ≤ θ ≤ 360°.
4 sin θ = 4√32
1Divide both sides by 4
sin θ = √32
2Find the reference angle
sin θ = √32 → reference angle = 60°.
3Sine is positive in quadrants I and II
θ = 60°, 120°
Answerθ = 60°, 120°
Geometry
7.Isolated in a
Find the missing .
A triangle has angles of 60° and 20°. Find the third angle.
1Angle sum of a triangle
The angles sum to 180°.
2Subtract the known angles
Third angle = 180° − 60° − 20° = 100°
Answer100°
8.Hybrid between two points
Find the .
(3, -1) and (18, 35)
1Change in each coordinate
Δx = 15, Δy = 36
2Pythagorean theorem
d = √((15)² + (36)²) = √1521
Answer39
9.Hybrid between two points
Find the .
(-4, 1) and (2, 9)
1Change in each coordinate
Δx = 6, Δy = 8
2Pythagorean theorem
d = √((6)² + (8)²) = √100
Answer10
10.Hybrid between two points
Find the .
(-1, 1) and (7, -14)
1Change in each coordinate
Δx = 8, Δy = −15
2Pythagorean theorem
d = √((8)² + (-15)²) = √289
Answer17
Answer key
- 1.
- 2.
- 3.
y3 − 64
(y − 4)(y2 + 4y + 42)
- 4.
- 5.
- 6.
4 sin θ = 4√32
θ = 60°, 120°
- 7.
A triangle has angles of 60° and 20°. Find the third angle.
100°
- 8.
- 9.
- 10.