answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
makvit
2 months ago
7

What is a31 of the arithmetic sequence for which a5=12.4 and a9=22.4

Mathematics
1 answer:
PIT_PIT [12.4K]2 months ago
6 0
In an arithmetic sequence
a₁, a₂, a₃,...,
the n-th term is
a_{n}=a_{1}+(n-1)d
where d = the common difference

Given that a₅ = 12.4,
a₁ + 4d = 12.4           (1)
With a₉ = 22.4,
a₁ + 8d = 22.4          (2)

Subtracting (1) from (2) yields:
a₁ + 8d - (a₁ + 4d) = 22.4 - 12.4
4d = 10
Thus, d = 2.5
From (1),
a₁ = 12.4 - 4*2.5 = 2.4

Consequently,
a₃₁ = 2.4 + 30*2.5 = 77.4
Answer:  a₃₁ = 77.4
You might be interested in
Jessica is selling books during the summer to earn money for college. She earns a commission on each sale but has to pay for her
Svet_ta [12734]

Answer:

Her weekly expenses amount to $25.

Detailed reasoning:

Given: Jessica earns commissions for every sale but must cover her own spending costs.

She expresses her income function as E(x) = 7x - 25, where x represents the number of doors she approaches in a week and E(x) denotes her weekly earnings in dollars.

To determine: What are plausible meanings for the y-intercept in Jessica's earnings function?

Working it out:

E(x) = 7x - 25

x symbolizes the doors knocked per week

E(x) reflects her weekly total earnings in dollars.

Calculating the y-intercept:

Set x = 0

y= - 25

Given that E(x) is the net earning after expenses,

the value 25 corresponds to her weekly expenses.

Since she is responsible for covering costs,

if she makes zero sales, these expenses still apply.

Therefore, the y-intercept realistically represents her $25 weekly expenses.

4 0
3 months ago
Read 2 more answers
A recipe for salsa uses 65% tomatoes. If a batch contains 5.2 cups of tomatoes, how large is the batch of salsa.
AnnZ [12381]

The salsa consists of 65% tomatoes, which amounts to 5.2 cups.

Let’s denote the total salsa as "x" cups, representing 100%. Given that 5.2 cups makes up 65%, we have:

\bf \begin{array}{ccll} cups&\%\\ \cline{1-2} 5.2&65\\ x&100 \end{array}\implies \cfrac{5.2}{x}=\cfrac{65}{100}\implies \cfrac{5.2}{x}=\cfrac{13}{20}\implies 104=13x \\\\\\ \cfrac{104}{13}=x\implies 8=x

3 0
2 months ago
Think about the function f(x) = 10 - x3. What is the input, or independent variable? f(x) x y What is the output, or dependent v
Zina [12379]
F(2) denotes function 2 f(2)=f(X))
8 0
2 months ago
Read 3 more answers
A large bag of marbles contains an equal amount of red, orange, yellow, blue, and green marbles. Quinn randomly selects 1 marble
Inessa [12570]
Given there are equal amounts of each color and four colors in total, the probability is calculated out of four. As there's an equal quantity of both red and blue, the chance of drawing either a red or blue marble is 2/4.
8 0
2 months ago
In 2015, in Buffalo, New York, there were 8,625 arrests, 2,678 robberies, 865 assaults, and 20 murders. The population of Buffal
tester [12383]
I believe the simplest form remains 865:2678, although I could be mistaken.
6 0
1 month ago
Read 2 more answers
Other questions:
  • Angie and Becky each completed a separate proof to show that the measures of vertical angles AKG and HKB are equal. Who complete
    9·1 answer
  • Figure 2 was constructed using figure 1. On a coordinate plane, 2 parallelograms are shown. Parallelogram 1 is in quadrant 1 and
    16·3 answers
  • The volume of a prism is the product of its height and area of its base, V = Bh. A rectangular prism has a volume of 16y4 + 16y3
    13·2 answers
  • The circumference of a circle can be found using the formula C = 2r. Which is an equivalent equation solved for r? r = C r = C(2
    12·2 answers
  • V=s^2+1/2sh solve for h
    10·1 answer
  • Pat had 9 flowerpots, and she wants to plant a different type of flower in each one. There are 11 types of flowers available at
    7·2 answers
  • Todd had 6 gallons of gasoline in his motorbike. After driving 150​ miles, he had 3 gallons left. Compute the​ slope, or rate of
    9·2 answers
  • Steve buys 2 lb of grapefruit and 3 lb of oranges for $7.20. Kennedy buys 4 lb of grapefruit and 2 lb of oranges for $8.80. Let
    6·1 answer
  • What is the value of l n e Superscript 4<br> 0<br> 1<br> 2<br> 4
    14·2 answers
  • An animal shelter is feeding 24 dogs. Each dog is fed 8 ounces of dog food twice a day. How many pounds of dog food does the she
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!