Answer:
x = - 7 , x = 2 , x = 1
Step-by-step explanation:
note that
p(1) = 1³ + 4(1)² - 19(1) + 14 = 1 + 4 - 19 + 14 = 0
since p(1) = 0 , then x = 1 is a zero
using synthetic division
1 | 1 4 - 19 14
↓ 1 5 - 14
------------------------
1 5 - 14 0
quotient is x² + 5x - 14
equating quotient to zero
x² + 5x - 14 = 0
(x + 7)(x - 2) = 0
equate each factor to zero and solve for x
x + 7 = 0 ⇒ x = - 7
x - 2 = 0 ⇒ x = 2
then zeros are x = - 7, x = 2 , x = 1
Answer:
The coordinate of pre-image is, B(3 , -9).
Step-by-step explanation:
Given an image point has coordinate B'(7, -4).
We have to find the coordinates of its pre-image:
The rule of translation on pre-image (x, y) is given by;

then;
(7, -4) = (x+4, y+5)
on comparison we have;
x+4 = 7 and y + 5 = -4
First solve for x;

Subtract 4 from both sides we have;
x + 4 -4 =7-4
Simplify:
x = 3
To solve for y;
y+5 = -4
Subtract 5 from both sides we get;
y = -9
Therefore, the coordinate of pre-image is, B(3, -9)
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Answer:

Step-by-step explanation:
Given
--- candles melted

--- time to melt
Required
The time since the first was lit
If 1 candle melts in 4 hours, 2 candles will melt in 8 hours.
i.e.



For the 3rd candle that has melted, 4 inches
First, calculate the fraction that melt



The time to melt is:



So, the required time is:


Convert to minutes



Exponential decay is given by the equation
F = P(1 - r)^t
0.5 = 1(1 - 0.092)^t
0.5 = (0.908)^t
log 0.5 = log (0.908)^t
log 0.5 = t * log 0.908
t = (log 0.5)/(log 0.908)
t = 7.18
Answer: 7.2 years