3 years ago

Which function has a range of {y|y<_5}?

Mathematics

1 answer:

Sveta_85 [38]3 years ago

8 0

Answer:

f(x) = -(x-4)² + 5

Step-by-step explanation:

f(x) = -(x-4)² + 5

Has a maximum vertex at (4,5)

Which means the function has a greatest value of 5 at x = 4

Therefore the range is:

y《5

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A private club was reduced by 15 members in 3 weeks. It’s size changed by the same number of members each week. What was the cha

dimulka [17.4K]

Answer:

5 members

Step-by-step explanation:

15/3 = 5

5 members left each week

15 members divided by 3 weeks is 5 members per week

the rate of members who left per week is 15/3 or, simplifying this fraction, 5/1.

4 0

3 years ago

Read 2 more answers

18. Determine the common difference, the fifth term, and the sum of the first 100 terms of the following sequence:

Ksenya-84 [330]

$a_1=1,\ a_2=2.5,\ a_3=4,\ a_4=5.5,\ ...\\\\a_2-a_1=2.5-1=1.5\\a_3-a_2=4-2.5=1.5\\a_4-a_3=5.5-4=1.5\\a_{n+1}-a_n=1.5=constans\\\\\text{It's an arithmetic sequence with}\\a_1=1,\ \boxed{d=1.5}\\\\a_n=a_1+(n-1)d\to a_n=1+(n-1)(1.5)=1+1.5n-1.5\\\\a_n=1.5n-0.5\\\\a_5=1.5(5)-0.5=7.5-0.5=7\\\boxed{a_5=7}\\\\\text{The formula of a Sum of the First n Terms of an Arithmetric Sequence:}\\\\S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n\\\\\text{We have:}\\a_1=1,\ d=1.5,\ n=100\\\\\text{Substitute}$

$S_{100}=\dfrac{(2)(1)+(100-1)(1.5)}{2}\cdot100=\dfrac{2+(99)(1.5)}{1}\cdot50\\\\=(2+148.5)\cdot50=150.5\cdot50=7,525\\\\\boxed{S_{100}=7,525}\\\\Answer:\\the\ common\ difference:\ d=1.5\\the\ fifth\ term:\ a_5=7\\the\ sum\ of\ first\ 100\ terms:\ S_{100}=7,525$