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3 years ago

Find the 22nd term of the following sequence: 5, 8, 11, ... 63 71 14 68

Mathematics

1 answer:

Wittaler [7]3 years ago

5 0

68 is the 22nd term of the following sequence.

Step-by-step explanation:

The given sequence is with the same common difference between the two consecutive number in the series thus it is said to be the Arithmetic progression ( AP).
For finding the nth term in the AP we have a formula tn = a + (n-1) × d
Here a is the first term , n is the number of the term to be founded and d is the common difference between the two consecutive number in the series.
Thus here tn = 5 + ( 22 - 1 ) × 3.
On subtracting we get tn = 5 + (21 ) × 3
On multiplying we get tn = 5 + 63
After adding we get tn = 68. It is the 22nd term in the given series.

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2 years ago

The water level in a lake was monitored and was noted to have changed -2 1/3 inches in one year. The next year it was noted to h

Diano4ka-milaya [45]

Answer:

The total change in water level over the past 2 years is $\displaystyle -4 \frac{1}{6}$ .

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Fractions

Proper and Improper

Numbers

Least Common Multiple (LCM)

Step-by-step explanation:

Step 1: Define

Identify

Year 1 water change: $\displaystyle -2 \frac{1}{3}$

Year 2 water change: $\displaystyle -1 \frac{5}{6}$

Step 2: Find Total Water Change

[Set up] Add yearly water changes: $\displaystyle -2 \frac{1}{3} + -1 \frac{5}{6}$
[Fractions] Convert to improper: $\displaystyle \frac{-7}{3} - \frac{11}{6}$
[Fraction] Rewrite [LCM]: $\displaystyle \frac{-14}{6} - \frac{11}{6}$
[Order of Operations] Subtract: $\displaystyle \frac{-25}{6}$
[Fraction] Convert to proper: $\displaystyle -4 \frac{1}{6}$

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2 years ago

If a projectile is launched vertically upward from 800 ft above the ground with an initial velocity of 80 ft per second, its hei

tiny-mole [99]

Hello!

10 seconds to return to the ground.

7 seconds to reach 576 feet above the ground.

Find the amount of time taken to reach the ground by setting the equation equal to 0:

0 = -16t² + 80t + 800

Factor out -16 from the equation:

0 = -16(t² - 5t - 50)

Factor the terms inside of the parenthesis:

0 = -16(t - 10)(t + 5)

Find the zeros:

t - 10 = 0

t = 10

t + 5 = 0

t = -5

Time can only be positive in this instance, so the correct answer is 10 sec.

Find the time by substituting in 576 for the height:

576 = -16t² + 80t + 800

Subtract 800 from both sides:

-224 = -16t² + 80t

Rearrange:

0 = -16t² + 80t + 224

Simplify:

0 = -16(t² - 5t - 14)

0 = -16(t - 7)(t + 2)

t = 7 seconds.

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3 years ago

Complete the table. f(x)=2x+4 0 _ 1 _ 2 _ 3 _

Westkost [7]

Answer:

0,4

1,6

2,8

3,10

Step-by-step explanation:

if x=0, 2*0+4=0+4=4

if x=1, 2*1+4=2+4=6

if x=2, 2*2+4=4+4=8

if x=3, 2*3+4=6+4=10

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3 years ago

Jaxon is deciding between two landscaping companies for his place of business. Company A charges $45 per hour and a $150 equipme

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Answer:

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2 years ago