Answer:
(a) 
(b) It takes <u>26 seconds</u> to completely fill the balloon.
Step-by-step explanation:
Let the time for which balloon is filled be 't' seconds.
(a)
Given:
Rate of filling (r) = 0.5 ft³/s
Initial volume of hydrogen in the balloon (V₀) = 2 ft³
The filling of hydrogen is a linear function of time.
So, Volume of hydrogen filled in the balloon at any time 't' is given as:
Volume = Initial volume + Rate of fill × time taken
⇒ 
⇒
Therefore, the linear function 'V' that models the volume of hydrogen in the balloon at any time 't' is
(b)
Given:
Balloon has a capacity of 15 ft³. This means the total volume of hydrogen that can be filled is 15 ft³.
So, 
Plugging 'V' value in the above equation and solving for 't', we have:
Therefore, it takes 26 seconds to completely fill the balloon.
Answer:
the slope of the given line = 2
Step-by-step explanation:
here's the solution :-
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Answer:
x = - 
, x = 
Step-by-step explanation:
Given
x² - x - 
= 0
Multiply through by 4 to clear the fraction
4x² - 4x - 3 = 0
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 4 × - 3 = - 12 and sum = - 4
The factors are + 2 and - 6
Use these factors to split the x- term
4x² + 2x - 6x - 3 = 0 ( factor the first/second and third/fourth terms )
2x(2x + 1) - 3(2x + 1) = 0 ← factor out (2x + 1) from each term
(2x + 1)(2x - 3) = 0
Equate each factor to zero and solve for x
2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = -
2x - 3 = 0 ⇒ 2x = 3 ⇒ x =
Answer:
B. The student incorrectly calculated the scale factor to be –2
Step-by-step explanation:
Given that :
After a dilation with a center of (0, 0), a point was mapped as (4, –6) → (12, y).
The student determined y to be -2
If a figure dilated with a center of (0, 0) and scale factor k, then
(x , y) → (kx , ky)
(4, -6) → (12, y)
k = 3
Thus; the scale factor is 3
Now; the y-coordinate can now be calculated as;
ky = (3 × -6)
ky = -18
Therefore; the value of y = -18 and the student incorrectly calculated the scale factor to be -2.
