What is the distributive property of -4 (10-b)
2 answers:
You might be interested in
Answer:
The ball is at a height of 120 feet after 1.8 and 4.1 seconds.
Step-by-step explanation:
The statement is incomplete. The complete statement is perhaps the following "A ball is thrown vertically in the air with a velocity of 95 ft/s. What time in seconds is the ball at a height of 120ft. Round to the nearest tenth of a second."
Since the ball is launched upwards, gravity decelerates it up to rest and moves downwards. The position of the ball can be determined as a function of time by using this expression:
Where:
- Initial height of the ball, measured in feet.
- Initial speed of the ball, measured in feet per second.
- Gravitational constant, equal to
.
- Time, measured in seconds.
Given that ,
,
and
, the following second-order polynomial is found:
The roots of this polynomial are, respectively:
and
.
Both roots solutions are physically reasonable, since represents the instant when the ball reaches a height of 120 ft before reaching maximum height, whereas
represents the instant when the ball the same height after reaching maximum height.
In nutshell, the ball is at a height of 120 feet after 1.8 and 4.1 seconds.
Answer:
x >= -7 ................(1a)
x >= 3 ...............(2a1)
Step-by-step explanation:
f(x) = .............(0)
find the domain.
To find the (real) domain, we need to ensure that each term remains a real number.
which means the following conditions must be met
x+7 >= 0 .....................(1)
AND
x^2+2x-15 >= 0 ..........(2)
To satisfy (1), x >= -7 .....................(1a) by transposition of (1)
To satisfy (2), we need first to find the roots of (2)
factor (2)
(x+5)(x-3) >= 0
This implis
(x+5) >= 0 AND (x-3) >= 0.....................(2a)
OR
(x+5) <= 0 AND (x-3) <= 0 ...................(2b)
(2a) is satisfied with x >= 3 ...............(2a1)
(2b) is satisfied with x <= -5 ................(2b1)
Combine the conditions (1a), (2a1), and (2b1),
x >= -7 ................(1a)
AND
(
x >= 3 ...............(2a1)
OR
x <= -5 ................(2b1)
)
which expands to
(1a) and (2a1) OR (1a) and (2b1)
( x >= -7 and x >= 3 ) OR ( x >= -7 and x <= -5 )
Simplifying, we have
x >= 3 OR ( -7 <= x <= -5 )
Referring to attached figure, the domain is indicated in dark (purple), the red-brown and white regions satisfiy only one of the two conditions.
Answer:
The answer is below
Step-by-step explanation:
The minimum payment on a credit card is based on the total amount owed. A credit card company uses the following rules: For a bill less than $20 the entire amount is due, for a bill of at least $20 but less than $500, the minimum due is $20. For a bill of at least $500 but less than $1000 the minimum due is $40 and for a bill of at least $1000 but less than $1500 the minimum due is $80 dollars. For a bill of $1500 or more the minimum due is 1/10th of the bill.
a. Write a function to describe the minimum payment due.
b. What is the minimum payment due if the bill is $345?
c. What is the minimum payment due if the bill is $1410?
d. What is the minimum payment due if the bill is $1700?
Solution:
Let B represent the minimum due payment for a bill in dollars and let x represent the bill in dollars. Therefore:
For x < 20, B = x
For 20 ≤ x < 500, B = 20
For 500 ≤ x < 1000, B = 40
For 1000 ≤ x < 1500, B = 80
For x ≥ 1500, B = (1/10)x
a)
b) For 20 ≤ x < 500, B = 20
Therefore if the bill is $345 (x = 345), the minimum payment due would be $20
c) For 1000 ≤ x < 1500, B = 80
Therefore if the bill is $1410 (x = 1410), the minimum payment due would be $80
d) For x ≥ 1500, B = (1/10)x
Therefore if the bill is $1700 (x = 1700), the minimum payment due would be $170 (1/10 * 1700)