Exterior angles are on the outside
3, 5, 4
Answer: a) H = h( 0.5 )^n
b) H = 1.125inches
Step-by-step explanation:
Let H = height of the ball
n = number of time the ball bounces
h = initial height.
The exponential function to model the height of the ball will be:
H = h( 1 - 0.5)^n
H = h( 0.5 )^n
It's minus because the height of the ball is decreasing.
h = 36 inches
n = 5
H = 36( 1 - 0.5 ) ^5
H = 36( 0.5 )^5
H = 36 × 0.03125
H = 1.125inches
Given:
Initial value = 400
Interest rate = 5% compounded quarterly.
To find:
The function that gives you the amount of money in dollars, J(t) in t years after the initial deposit.
Solution:
The formula for amount is:
Where, P is principal, r is the rate of interest in decimals, n is the number of times interest compounded in an year and t is the number of years.
The interest rate is 5% compounded quarterly. So, r=0.05 and n=4.
Substituting in the above formula, we get
The required function notation is:
Therefore, the amount of money in dollars, J(t) in t years after the initial deposit is .
Good evening ,
<u><em>Answer:</em></u>
<h2>the regular price of the item is $80.</h2>
<u><em>Step-by-step explanation:</em></u>
Let p represent the regular price of the item.
p - p×(40/100) = 48 ⇌ p×(1 - 40/100) = 48 ⇌ p×(100/100 - 40/100) = 48
⇌ p×(60/100) = 48 ⇌ p = (480×100)/60 = 48 000/60 = 80.
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:)
Answer:
The equation is ( x² / 9 ) - ( y² / 7 ) = 1
Step-by-step explanation:
Given the data in question;
hyperbola is centered at the origin, this means h and k are all equals to 0.
Vertices: (-3,0) and (3,0)
Since y-coordinates are constant, this implies it is a hyperbola with horizontal transverse axis.
h - a = -3
0 - a = -3
a = 3
Foci: (-4,0) and (4,0)
h - c = -4
0 - c = -4
c = 4
we know that, for a hyperbola
c² = a² + b²
so
⇒ ( 4 )² = ( 3 )² + b²
16 = 9 + b²
b² = 16 - 9
b² = 7
So the equation for the hyperbola will be;
⇒ ( (x-h)² / a² ) - ( (y-k)² / b² ) = 1
so we substitute
⇒ ( (x-0)² / 3² ) - ( (y-0)² / 7 ) = 1
⇒ ( x² / 3² ) - ( y² / 7 ) = 1
⇒ ( x² / 9 ) - ( y² / 7 ) = 1
Therefore, The equation is ( x² / 9 ) - ( y² / 7 ) = 1