Answer:
a) 1325 frogs b)75.47 hours
Step-by-step explanation:
start = 150 frogs
after 4 hours = 530
1) figure out how many frogs per hour 530/4 = 132.5 frogs per hour
2) 10 hours after initial time * 132.5 frogs = 1325 frogs
3) Time to reach 10000 frogs is => 10000 / 132.5 = 75.47 hours
Answer:
n = 10
Step-by-step explanation:
The sum to n terms of an arithmetic sequence is
= 
[ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Here a₁ = 12 and d = 5 and = 345, thus
[ (2 × 12) + 5(n - 1) ] = 345 ( multiply both sides by 2 )
n( 24 + 5n - 5) = 690 ← distribute and simplify left side
n(19 + 5n) = 690
19n + 5n² = 690 ( subtract 690 from both sides )
5n² + 19n - 690 = 0 ← in standard form
(5n + 69)(n - 10) = 0 ← in factored form
Equate each factor to zero and solve for n
5n + 69 = 0 ⇒ 5n = - 69 ⇒ n = - 
n - 10 = 0 ⇒ n = 10
However, n > 0 , thus n = 10
Answer:
2) 0.3
4) 0.09
6) 0.65
8) 4.45
Step-by-step explanation:
hope this helps ;)
Answer:
x = 6 or x = -3/2
Step-by-step explanation:
Solve for x:
16 x^2 - 72 x + 145 = 289
Hint: | Write the quadratic equation in standard form.
Divide both sides by 16:
x^2 - (9 x)/2 + 145/16 = 289/16
Hint: | Solve the quadratic equation by completing the square.
Subtract 145/16 from both sides:
x^2 - (9 x)/2 = 9
Hint: | Take one half of the coefficient of x and square it, then add it to both sides.
Add 81/16 to both sides:
x^2 - (9 x)/2 + 81/16 = 225/16
Hint: | Factor the left hand side.
Write the left hand side as a square:
(x - 9/4)^2 = 225/16
Hint: | Eliminate the exponent on the left hand side.
Take the square root of both sides:
x - 9/4 = 15/4 or x - 9/4 = -15/4
Hint: | Look at the first equation: Solve for x.
Add 9/4 to both sides:
x = 6 or x - 9/4 = -15/4
Hint: | Look at the second equation: Solve for x.
Add 9/4 to both sides:
Answer: x = 6 or x = -3/2
