Answer:
x = 25%
Step-by-step explanation:
At the first sale of 25% off, the handbag price dropped from $400 to $300. This is because (400 x 0.25 = 100) and (400 - 100 = 300) Therefore, the selling price of the handbag after one sale was $300.
At the second sale of 25% off, the handbag price dropped from $300 to $225. This is because (300 x 0.25 = 75) and (300 - 75 = 225). Therefore, the selling price of the handbag after two sales is $225.
The value of x remained the same for both sales. x = 25% or 0.25
Answer:
19 or √145 ≈ 12.04
Step-by-step explanation:
Use the distance formula to determine the distance between the two points.
Distance = √
(
x
₂ − x
₁
)² + (
y
₂ − y
₁
)
²
Substitute the actual values of the points into the distance formula.
√
(
4 − ( − 5
))
² + (
(
−
5
)
−
3
)
²
Simplify:
√
145
The result can be shown in multiple forms.
Exact Form:
√
145
Decimal Form:
12.04159457 … ≈ 12.04
Step-by-step explanation:
f(x) = -0.01x² + 0.7x + 6.1
a) f(x) is a downward facing parabola, so the maximum height is at the vertex. The vertex of a parabola can be found using x = -b/(2a).
x = -0.7 / (2 × -0.01)
x = 35
f(35) = -0.01(35)² + 0.7(35) + 6.1
f(35) = 18.35
The maximum height is 18.35 feet.
b) The maximum horizontal distance is when the ball lands, or when f(x) = 0.
0 = -0.01x² + 0.7x + 6.1
0 = x² − 70x − 610
Solve with quadratic formula:
x = [ -b ± √(b² − 4ac) ] / 2a
x = [ -(-70) ± √((-70)² − 4(1)(-610)) ] / 2(1)
x = (70 ± √7340) / 2
x = 35 ± √1835
x = -7.84, 77.84
x can't be negative, so x = 77.84. The ball's maximum horizontal distance is 77.84 feet.
c) When the ball is first launched, x = 0. The height at that position is:
f(0) = 6.1
The ball is launched from an initial height of 6.1 feet.
Perform the indicated division ... divide the numerator by the denominator.
The quotient is the decimal form of the ratio.
