Answer:
1) The vertex form of 
is 
, 2) The stone reaches its maximum height 2 seconds after being thrown.
Step-by-step explanation:
1) Given that height of the stone is represented by a second-order polynomial, which depicts a parabola as graph. The best approach to determine the instant when stone reaches its highest is by vertex form, whose form is:
Where:
, 
- Instant and maximum height of the stone, measured in seconds and meters.
- Vertex constant, which must be negative as there is an absolute maximum, measured in meters per square second.
Let be , which is transformed into vertex form:
i) 
Given
ii) 
Distributive property/
iii) ![h = -5\cdot [(t^{2}-4\cdot t +4)+(-36)]](https://tex.z-dn.net/?f=h%20%3D%20-5%5Ccdot%20%5B%28t%5E%7B2%7D-4%5Ccdot%20t%20%2B4%29%2B%28-36%29%5D)
Existence of additive inverse/Definitions of addition and subtraction
iv) 
Distributive property/
/Perfect square binomial
v) Compatibility with addition/Existence of additive inverse/Modulative property/Definition of subtraction/Result
The vertex form of is .
2) The time can be extracted from previous results, which indicates that stone reaches its maximum height 2 seconds after being thrown.
Answer: -2.145
Step-by-step explanation:
(3.2+4x)+(18.25+6x)=
Simplifying
(3.2 + 4x) + (18.25 + 6x) = 0
Remove parenthesis around (3.2 + 4x)
3.2 + 4x + (18.25 + 6x) = 0
Remove parenthesis around (18.25 + 6x)
3.2 + 4x + 18.25 + 6x = 0
Reorder the terms:
3.2 + 18.25 + 4x + 6x = 0
Combine like terms: 3.2 + 18.25 = 21.45
21.45 + 4x + 6x = 0
Combine like terms: 4x + 6x = 10x
21.45 + 10x = 0
Solving
21.45 + 10x = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-21.45' to each side of the equation.
21.45 + -21.45 + 10x = 0 + -21.45
Combine like terms: 21.45 + -21.45 = 0
0 + 10x = 0 + -21.45
10x = 0 + -21.45
Combine like terms: 0 + -21.45 = -21.45
10x = -21.45
Divide each side by '10'.
x = -2.145
Simplifying
x = -2.145
It’s a machine that works easy and simple..?.?
9514 1404 393
Answer:
(b) 0 ≤ t ≤ 7
Step-by-step explanation:
The appropriate domain is the set of values of the independent variable (t) for which the function reasonably makes sense. We are told the model is of <em>prices over a week</em>, and that t represents the number of days since the beginning of the week.
It seems reasonable that the model is intended to apply to a period between t=0 (the beginning of the week) and t=7 (the end of the week). Thus the appropriate domain is ...
0 ≤ t ≤ 7
Answer and Step-by-step explanation:
There are 3 cases we need to consider:
1. x > -7
2. x = -7
3. x < -7
<u>Case 1: x > -7</u>
If x is greater than -7, then we know that any number x + 7 will be a positive number. This is because -7 is the smallest negative number possible that will produce a non-positive number; any number greater than -7 will give a positive number in x + 7. So, the simplified expression of |x + 7| is just x + 7.
<u>Case 2: x = -7</u>
If x = -7, we know that -7 + 7 = 0, so |x + 7| when x = -7 is simply 0.
<u>Case 3: x < -7</u>
If x is less than -7, then from the argument in Case 1, we know that all numbers x + 7 will be negative. This means that when simplifying the absolute value expression, we have to switch the two terms. So, the simplified expression of |x + 7| when x < -7 is 7 + x. (Note that this isn't the same as x + 7 because here, x is <em>always </em>a negative number)
Hope this helps!
