1answer.
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
Allushta [10]
3 years ago
8

In an AP the seventh term is 38 and the twelfth term is 63. What is the sum of the first twenty terms?

Mathematics
1 answer:
lorasvet [3.4K]3 years ago
3 0

Answer: 1110

Step-by-step explanation:

For an arithmetic progression, the nth term is gotten by using the formula:

= a + (n-1)d

Therefore,

7th term = a + 6d = 38 ..... equation i

12 term = a + 11d = 63 ...... equation ii

Subtract equation i from ii

(a + 6d) - (a + 11d) = 38 - 63

-5d = -25

d = 25/5

d = 5

Since d = 5

From a + 6d = 38

a = 38 - 6d

a = 38 - (6×5)

a = 38 - 30

a = 8

The sum of the first 20 terms will be:

= n/2[2a + (n-1)d]

= 20/2[(2×8) + (20-1)5]

= 10[16+(19 × 5)]

= 10(16+95)

= 10(111)

= 1110

You might be interested in
there are 36 pupils in mr. castro mathematics class mr. castro wants to seperate the class into equal group for doing an activit
posledela

Answer:

He can use the factors of 36 to determine the number of groups he can divide the class into such that they are equal.

The Factors (excluding 1) are;

2, 3, 4, 6, 9, 12, 18

Using these therefore he can divide them;

  1. Into 3 groups each with 12 people.
  2. Into 4 groups each with 9 people.
  3. Into 6 groups each with 6 people.
  4. Into 9 groups each with 4 people.
  5. Into 12 groups each with 3 people.
3 0
3 years ago
Select ALL ordered pairs that are located in the first quadrant of the coordinate plane.
SpyIntel [72]

Answer:

C, D

Step-by-step explanation:

in the first coordinate plane, both numbers in a coordinate must be positive

6 0
3 years ago
A bank offers 2.12 interest compounded annually for investing money in a savings account, you open an account with $300. How muc
Tresset [83]

Answer:

\large \boxed{\$70.02}

Step-by-step explanation:

The compound interest formula is

A = P\left(1 + \dfrac{r}{n}\right)^{nt}

Data:

P = 300

r = 2.12 % = 0.0212

t = 10 yr

n = 1 calculation per year

1. Accrued amount:  

A = 300(1+ 0.0212)¹⁰

  = 300 × 1.0212¹⁰

  = 300 × 1.233 41

  = 370.02

2. Interest

I = A - P = 370.02 - 300.00 = 70.02

\text{The interest is $\large \boxed{\mathbf{\$70.02}}$}

7 0
3 years ago
SURFACE AREA PLEASE HELP
disa [49]

Answer:

486 yd^2

Step-by-step explanation:

Surface area is just finding the area of each face in a figure and adding it all up.

For the surface area of a cube, use this formula:

(a^2) 6

(a is the side length) a^2 is the area of one face of a cube, then multiply it by 6 since there are 6 faces on a cube.

Use formula with given dimensions:

(9^2) 6 = 486

Surface area is measured in square yards

(yards in this case)

Therefore, the surface area of the cube is 486 yd^2

Hope this helps!

6 0
3 years ago
Four less than a number q is at least -16.
Natali5045456 [20]

Answer:

q > -12

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtract Property of Equality

Step-by-step explanation:

<u>Step 1: Translate</u>

q - 4 > -16

<u>Step 2: Solve for </u><em><u>q</u></em>

  1. Add 4 to both sides:                    q > -12

Here we see that any number <em>q</em> greater than -12 would work as a solution to the inequality.

7 0
3 years ago
Other questions:
  • A baseball coach gives half his players an energy drink to consume before each game; the other half does not receive the energy
    6·1 answer
  • Find the compound interest of $100 for 2 years at 5%
    7·1 answer
  • Mario draws two cards, one from each of two shuffled decks. Each deck has 12 cards labeled 1-12. What is the
    7·1 answer
  • Jimmy can run 3.5 miles in 20 minutes. How far can he run in one hour and ten minutes?
    5·1 answer
  • Which ordered pair would you remove to make this
    11·1 answer
  • A school produced a comedy show to raise money for a field trip. Every
    8·1 answer
  • which type of account is more suitable for saving money :a savings account! a debt card or a fixed deposit account​
    7·1 answer
  • Jada was using square stickers with a side length of 3/434 inch to decorate the spine of a photo album. The spine is 10 1/21012
    5·1 answer
  • 1. A line goes through the points (4, 5) and (2, -6). Write the equation of the line in point-slope form. Show your work for ful
    6·1 answer
  • Willow owns 225 books. Of these, 5/9 are mysteries. How many of Willows books are mysteries?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!