Slope of (21, 45) and (84, 87)

The sum of an arithmeit cprogression consisting of 20 positive integer terms with positive common difference is equal to 2020. (

Rufina [12.5K]

Answer:

a) possible progressions are 5

b) the smallest and largest possible values of the first term are 16 and 82

Step-by-step explanation:

Sum of terms:

Sₙ = n/2(a₁ + aₙ) = n/2(2a₁ + (n-1)d)
S₂₀ = 20/2(2a₁ + 19d) = 10(2a₁ + 19d)
2020 = 10(2a₁ + 19d)
202 = 2a₁ + 19d

In order a₁ to be an integer, d must be even number, so d = 2k

202 = 2a₁ + 38k
101 = a₁ + 19k

Possible values of k= 1,2,3,4,5

k = 1 ⇒ a₁ = 101 - 19 = 82
k = 2 ⇒ a₁ = 101 - 38 = 63
k = 3 ⇒ a₁ = 101 - 57 = 44
k = 4 ⇒ a₁ = 101 - 76 = 25
k = 5 ⇒ a₁ = 101 - 95 = 16

As per above,

a) possible progressions are 5
b) the smallest and largest possible values of the first term are 16 and 82

6 0

3 years ago

Which expression is equivalent to (3x^5+8x^3)-(7x^2-6x^3)

inn [45]

Answer: look at the picture that the answer to it

Step-by-step explanation: Hope this help :D

7 0

2 years ago

What is the degree of the polynomial? Can someone please check my work?

worty [1.4K]

Yes I agree with that because you combined the terms in the monomial correctly and the degree of the monomial was greater then the degree of any other mono/binomials in the polynomial

7 0

3 years ago

The function f(x) = 3x + 5,000 represents the amount of money a cell phone screen is being sold for, where x is the number of sc

laila [671]

Explanation:

To answer a question like this, refer to the definitions of the functions:

(f-g)(200) is ...

... the difference between the amount of money a cell phone screen is being sold for and the cost of production, when 200 screens are being manufactured.

__

The numerical value of (f-g)(200) is ...

f(200) -g(200) = (3·200 +5000) -(20·200 -400) = 5600 -3600

(f-g)(200) = 2000

7 0

3 years ago

Read 2 more answers

According to the same report, the 28.5 million passengers in 2018 represented a 6.7% increase in cruise passengers since 2017. h

Alisiya [41]

The number of cruise passengers must there have been in 2017 is 26.7 million.

<h3>What is percentage?</h3>

The term "percentage" comes from the Latin phrase "per centum," meaning "by the hundred." Percentages represent fractions with a denominator of 100. In other terms, it is the relationship between portion and whole in which the value of the whole is always assumed to be 100.

Now according to the question;

Let x represent the total number for cruise passengers during 2017.

In 2018, a 6.7% rise in x results in 28.5 million cruise passengers.

So, 106.7 % of x = 28.5

$\begin{aligned}&\frac{106.7}{100} * x=28.5 \\&\frac{106.7 x}{100}=28.5\end{aligned}$