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
Delvig [45]
2 years ago
15

The 4th term of an arithmetic sequence is 24 and the 12th term is 56, what is the first term?​

Mathematics
2 answers:
Virty [35]2 years ago
8 0

Answer:

First term = 12

Step-by-step explanation:

A4 = 24

A12 = 56

An = A1 + (n-1)d; this defines the formula of an arithmetic series

A4 = 24 = A1 + (4-1)d

A4 = 24 = A1 + 3d

A12 = 56 = A1 + (12-1)d

A12 = 56 = A1 + 11d

Subtract A4 from A12 to get d (distance)

(56 = A1 + 11d) - (24 = A1 +3d)

32 = 8d

d = 4

Substitute d = 4 into A4

A4 = 24 = A1 + 3(d)

24 = A1 + 3(4)

24 = A1 + 12

24 - 12 = A1

12 = A1

spin [16.1K]2 years ago
4 0
First term = 12
Solution:
A4 = 24
A12 = 56
An = A1 + (n-1)d; this defines the formula of an arithmetic series
A4 = 24 = A1 + (4-1)d
A4 = 24 = A1 + 3d
A12 = 56 = A1 + (12-1)d
A12 = 56 = A1 + 11d
Subtract A4 from A12 to get d (distance)
(56 = A1 + 11d) - (24 = A1 +3d)
32 = 8d
d = 4
Substitute d = 4 into A4
A4 = 24 = A1 + 3(d)
24 = A1 + 3(4)
24 = A1 + 12
24 - 12 = A1
12 = A1
You might be interested in
7. Which expression is the exponential form of 3√m
borishaifa [10]
Rewrite the rational (fraction) exponents using the formula ^n<span>√a^x= a x/n

3m 1/2 </span>
7 0
3 years ago
Read 2 more answers
In ΔBCD, the measure of ∠D=90°, DC = 16, CB = 65, and BD = 63. What ratio represents the cosine of ∠B?
Alisiya [41]

Answer:

15:17

Step-by-step explanation:

Since the triangle has a right angle, we may find the length of the unknown side using the trigonometric notations SOH CAH TOA where

SOA stands for

Sin Ф = opposite side/hypotenuses side

Cosine Ф = adjacent side/hypotenuses side

Tangent Ф = opposite side/adjacent side

With respect to ∠B given that ∠D=90°,

BD is the adjacent side

CB is the hypotenuse side

and DC is the opposite side

Hence Sin B = 15/17

8 0
3 years ago
Read 2 more answers
Factor completely. 10xy + 3y + 20ax +6a
julsineya [31]

Answer:

(y+2a)(10x+3) that it

6 0
3 years ago
Which statements about quadrilaterals are true?
USPshnik [31]
D)A rectangle is always also a parallelogram.
5 0
2 years ago
Read 2 more answers
In May you used 900 ​kilowatt-hours of energy for electricity.
Sloan [31]

Answer:

a) "The total electrical energy use was 3,240,000,000 joules."

b) "The average power use is 1210 watts."

c)

<u>Part 1:</u> "To generate the electricity you​ used, 810 L is needed."

<u>Part 2:</u> "To generate the electricity you​ used, 214.00 gal is needed."

Step-by-step explanation:

a)

1 kilowatt-hours = 3.6x10^6 joules

Converting 900 kilowatt-hours to joules, we have:

900*(3.6*10^6)=3.24*10^9 joules, or

Total Electrical Energy use = 3,240,000,000 joules

"The total electrical energy use was 3,240,000,000 joules."

b)

The month of May has 31 days and 1 day  is 24 hours. So May has:

31*24=744 hours

Now, we divide 900 kW-hr by the number of hours in the month (744 hrs) to get average power use:

\frac{900}{744}=1.21 kW. Since 1000 Watts = 1 kW, we multiply this by 1000 to get the answer in Watts:

1.21 * 1000 = 1210 Watts

"The average power use is 1210 watts."

c)

<u>Part 1:</u>

The conversion efficiency of most generating stations is 33%. So we need to multiply the total electrical energy use (in joules) by a factor of 3 to get the amount of joules required. So:

(3.24 * 10^9)*3 = 9.72 * 10^9 joules

We divide this by 12 million joules to get the number of liters:

\frac{9.72*10^9}{12*10^6}=810

So, 810 liters is needed

"To generate the electricity you​ used, 810 L is needed."

<u>Part 2:</u>

We know that 0.2642 gallons is equal to 1 liters. To get the number of gallons needed, we multiply 810 by 0.2642. So:

810 * 0.2642 = 214.00 gallons

"To generate the electricity you​ used, 214.00 gal is needed."

7 0
3 years ago
Other questions:
  • This is a polygon. I can’t find the missing angle ?
    5·1 answer
  • Use one or more transformations to transform the pre-image (purple) onto the image (white).
    6·1 answer
  • Horizontal lines are __________ perpendicular to vertical lines. question 10 options:
    13·1 answer
  • Round to the nearest hundredth<br> 1.359.377
    12·1 answer
  • A boat is anchored 2.2 km due south of a lighthouse. Along the shore, the town of Beachton is 16.8 km due east of the lighthouse
    6·1 answer
  • Pls help!!!
    5·1 answer
  • Which statement about|-8 is true?
    14·1 answer
  • Please help answer either both or one question please! Best answer will get brainliest :)
    10·2 answers
  • jackson has a rectangular piece of paper with a width of six units and a length of four units as shown below. He cuts the paper
    15·1 answer
  • If a+ b = 6 and ab = 2 find a^3 + b^3
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!