Answer:
A. "an arithmetic sequence with a common difference (d) of -6."
B. 33 hours
C. ![a_n=a_1+(n-1)d](https://tex.z-dn.net/?f=a_n%3Da_1%2B%28n-1%29d)
D. See below
Step-by-step explanation:
A.
Since the sequence lessens by 6, this is an arithmetic sequence with a common difference (d) of -6.
B.
The formula for term of arithmetic sequence is:
![a_n=a_1+d(n-1)](https://tex.z-dn.net/?f=a_n%3Da_1%2Bd%28n-1%29)
Wher a_1 is the first term and d is the common difference. Since we want to find after 33 weeks, we plug in 33 into n:
![a_{33}=225 + (-6)(33-1)\\a_{33}=33](https://tex.z-dn.net/?f=a_%7B33%7D%3D225%20%2B%20%28-6%29%2833-1%29%5C%5Ca_%7B33%7D%3D33)
She will have left 33 hours
C.
We will use the arithmetic sequence term formula written above, that is:
![a_n=a_1+(n-1)d](https://tex.z-dn.net/?f=a_n%3Da_1%2B%28n-1%29d)
THis gives us the amount of hours left after a certain number of weeks.
D.
We plug in 40 into n and find the hours left:
![a_{40}=225+(40-1)(-6)\\a_{40}=225-234\\a_{40}=-9](https://tex.z-dn.net/?f=a_%7B40%7D%3D225%2B%2840-1%29%28-6%29%5C%5Ca_%7B40%7D%3D225-234%5C%5Ca_%7B40%7D%3D-9)
THis term is NEGATIVE, which means that Greta will not have to work 40 weeks to fulfill the target of 225 hours. She needs to work less.
Answer:
0.5x - y = 1.5
Step-by-step explanation:
First, put the equation in point slope form:
y - y1 = m(x - x1)
y + 2 = 1/2(x + 1)
Distribute the 1/2:
y + 2 = 1/2x + 1/2
Change the fractions to decimals:
y + 2 = 0.5x + 0.5
Subtract y from both sides:
2 = 0.5x - y + 0.5
Subtract 0.5 from both sides:
1.5 = 0.5x - y
Rearrange the equation:
0.5x - y = 1.5
So, the equation of the line in standard form is 0.5x - y = 1.5
The range is the y values so your answer is.
Range = 3, 7, 11
Answer: 1,509.52 meters
Step-by-step explanation:
Hi, since the situation forms a right triangle (see attachment) we have to apply the next trigonometric function.
Tan α = opposite side / adjacent side
Where α is the angle of depression from one mountain to another, the opposite side is the difference between heights, and the adjacent side (x) is the horizontal distance between the two summits.
Replacing with the values given:
Tan 15.9 = 430/x
Solving for x:
x = 430/ (tan 15.9)
x= 1,509.52 meters
Feel free to ask for more if needed or if you did not understand something.
Answer:
(x + 3)(x + 2)
Step-by-step explanation:
Given
x² + 5x + 6
Consider the factors of the constant term (+ 6) which sum to give the coefficient of the x- term (+ 5)
The factors are + 3 and + 2 , since
3 × 2 = + 6 and + 3 + 2 = + 5 , then
x² + 5x + 6 = (x + 3)(x + 2) ← in factored form