I have included a screenshot of the entire question along with its accompanying diagram.
Answer:∠1 = 163°
Explanation:1- finding angle 2:Given that ∠2 together with 17° creates a straight angle, their total is 180°.
Thus:
180 = 17 + ∠2
Solving for ∠2 gives us:
∠2 = 180 - 17
∠2 = 163°
2- finding angle 1:Since lines a and b are parallel, ∠1 and ∠2 are alternate angles and therefore equal.
We determined that ∠2 = 163°, leading to:
∠1 = 163°
I hope this clarifies things!:)
Answer:
The appropriate expression is 1 Over 5 x Superscript minus 8 Baseline y Superscript minus 13 Baseline EndFraction
Step-by-step explanation:
In order to simplify the expression 
where x ≠ 0, y ≠ 0, we must work through the given expression.
The appropriate expression is 1 Over 5 x Superscript minus 8 Baseline y Superscript minus 13 Baseline EndFraction
Response:
a
f'(t) is negative
b
The unit is degC/min
c
At 35 minutes since the coffee was placed on the counter, the temperature is 68, and it will drop by approximately 0.75 in the next 30 seconds.
Detailed explanation:
According to the question, we are informed that
The temperature of a cup of coffee on a counter is represented by the equation
where t indicates the time in minutes since the coffee was set on the counter.
In general, f(t)' denotes the derivative of f(t), indicating the change in temperature over time for the coffee
As the coffee rests on the counter, its temperature tends to decrease after a few minutes; thus, f(t)' is negative.
The temperature is measured in degrees Celsius while time is expressed in minutes.
Therefore, the change in temperature with respect to time, f(35)', will be given in degrees Celsius per minute (i.e., degC/min).
The question states that
which means the rate of temperature change after 35 minutes is 1.5.
And
indicating that the coffee's temperature after 35 minutes is 67 degrees Celsius.
Subsequently, after another t= 30 seconds = 
the rate at which the coffee's temperature changes is
=> 
=> 
Thus
At 35 minutes since the coffee was placed on the counter, its temperature is 68 and will drop by roughly 0.75 in the next 30 seconds.
1. "The limit on John's credit card is defined by the function f(x)=15,000+1.5x," indicating that if John's monthly income is $5,000, he can spend a maximum of f(5,000)=15,000+1.5*5,000=15,000+ 7,500=22,500 (dollars). As another example, if John's monthly income is $8,000, then he can spend up to f(8,000)=15,000+1.5*8,000=15,000+ 12,000=27,000 (dollars). 2. If we consider the maximum amount John can spend as y, it can be represented as y=15,000+1.5x. To express x, the monthly income, in terms of y, we rearrange this equation: y=15,000+1.5x results in 1.5x = y-15,000. Therefore, in functional notation, x is a function, referred to as g, based upon y, the maximum sum. Generally, we denote the variable of a function by x, so we redefine g as: This tells us that if the maximum amount that John can spend is $50,000, then his monthly income would be $23,333. 3. If John's limit is $60,000, his monthly income equals $30,000. Note: g is deemed as the inverse function of f because it reverses the actions of f.
