Suppose that the height (in centimeters) of a candle is a linear function of
the amount of time (in hours) it has been burning.
Let x be the amount of time in hours
Let y be the heoght of a candle in centimeters
The two points are then as (9,24.5) and (23,17.5).
Now plug in x=21, we get
Thus the height of the candle after 21 hours is 18.5 centimeters.
Answer:
-2y + 3 = 0
Step-by-step explanation:
x - 6y - 9 = 0
-6y - 9 = -x subtract x from both sides
6y + 9 = x divide both sides by -1
x = 8y + 6
6y + 9 = 8y + 6 replace x with 6y + 9
-2y + 9 = 6 subtract 8y from both sides
-2y + 3 = 0 subtract 6 from both sides
Answer:
k = 9
length of chord = 2/3
Step-by-step explanation:
Equation of parabola: 
<u />
<u>Part 1</u>
If the curve passes through point 
, this means that when 
, 
Substitute these values into the equation and solve for 
:
Apply the exponent rule 
:
<u>Part 2</u>
- The chord of a parabola is a line segment whose endpoints are points on the parabola.
We are told that one end of the chord is at and that the chord is horizontal. Therefore, the y-coordinate of the other end of the chord will also be 1. Substitute y = 1 into the equation for the parabola and solve for x:
Therefore, the endpoints of the horizontal chord are: (0, 1) and (2/3, 1)
To calculate the length of the chord, find the difference between the x-coordinates:
**Please see attached diagram for drawn graph. Chord is in red**
Answer:
The factors of given expression are 10+10√2 and 10-10√2.
Step-by-step explanation:
We have given a quadratic expression.
s²-20s-100
We have to find factors of given expression.
We use quadratic formula to find factors.
x = (-b±√b²-4ac) / 2a
From given expression, a = 1 , b = -20 and c = -100
Putting values in above formula, we have
x = (-(-20)±√(-20)²-4(1)(-100) ) / 2(1)
x = (20±√400+400 ) / 2
x = (20±√800) / 2
x = (20± √400×2) / 2
x = (20±20√2) / 2
x = 10±10√2
Hence, the factors of given expression are 10+10√2 and 10-10√2.
