The Information about Geometric sequence is:
[tex]a_{1}=23 , a_{n}=9\times a_{n-1}[/tex]
→nth term of sequence = 9× (n-1) th term
Also , Common Ratio of a Geometric Sequence =[tex]\frac{\text{Second term }}{\text{First term}}[/tex]
[tex]\frac{a_{n}}{a_{n-1}}= \text{Common ratio}}=9\\a_{n}= a_{1}\times r ^{n-1}\\\\a_{n}=23\times 9^{n-1}[/tex]
Option 4 : [tex]a_{n}= 23 \times 9^{n-1}[/tex] is true.
Combining like terms
simplify each expression
4n - n
The Watertown science contest allowed teams of 5 students compete. If 45 students entered the contest, how many teams competed? What type of problem is it?
Miss Connor asks her class to guess her mystery number she tells him this number has two digits is a prime less than 20 and a factor of 34 what is the number and the mystery number missed Connor has in mind
Answer:
17
Step-by-step explanation:
You are to follow the clues. Since it is 2 digits and is prime, go through the prime numbers between 10 and 20. They are 11, 13, 17, and 19. Then you find the factors of 34 which are 1×34 2x17. That leaves only 1 possible answer: 17
In the afternoon, a television station reported the temperature as 3.7°F . That evening, they reported the temperature as −1.5°F .
Which expression represents the total temperature change from afternoon to evening?
A:
|−1.5+3.7|
B:3.7+(−1.5)
C:|3.7−(−1.5)|
D:−1.5+3.7
An expression is a way of writing a statement with a mathematical operation such as addition, subtraction, multiplication, and division.
If the temperature in the afternoon is 3.7°F and in the evening is -1.5°F
The expression that represents the temperature change from afternoon to evening is:
-1.5 - 3.7
Option D is the correct answer.
What is an expression?An expression is a way of writing a statement with a mathematical operation such as addition, subtraction, multiplication, and division.
Example: 2x + 3 - 8 is an expression.
We have,
The temperature in the afternoon = 3.7°F
The temperature in the evening = -1.5°F
The temperature change from afternoon to evening:
= -1.5 - 3.7
= -5.2°F
Thus,
If the temperature in the afternoon is 3.7°F and in the evening is -1.5°F
The expression that represents the temperature change from afternoon to evening is:
-1.5 - 3.7
Option D is the correct answer.
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Please help me with math please, they are number lines.
Is 1.47 irrational or rational
A line passes through (2, −1) and (4, 5).
Which answer is the equation of the line?
A)−3x+y=−7
B)−3x+5y=−13
C)−3x+5y=13
D)−3x+y=17
Answer:
1. A line passes through (2, −1) and (4, 5).
Which answer is the equation of the line?
−3x+y=−7
2. A line has slope −3/4 and y–intercept 5.
Which answer is the equation of the line?
y=−3/4x+5
3. There are 6 quarters in a jar. Jill adds 2 quarters to the jar every day.
Which linear equation represents the total amount of quarters in the jar after x days?
y = 2x + 6
4. Which answer is an equation in point-slope form for the given point and slope?
Point: (1, 9); Slope: 5
y−9=5(x−1)
Step-by-step explanation:
If 12 gallons of gas costs $25.20, how much is the gas per gallon?
$1.98
$2.05
$2.10
$2.25
,if the swimmer is in a 100m race she swims the first half of the race and 32.34 seconds and the last half of the race and 34.83 seconds how long did it take her to swim the whole race?
What’s 2(2x+10)=3(x+6)
Help. Write the ratio as a unit rate.
A+B=44
A:B is equivalent to 4:7
what are A and B?
A is 16 and B is 28.
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Given
A:B = 4:7
A + B = 44
Let the common factor between A and B is x
then
4x + 7x = 44
11x = 44
x = 4
Therefore,
A = 16
B = 28
Hence, 16 and 28 are A and B respectively.
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What is the conclusion of the following conditional?
A number is divisible by 2 if even.
A. The sum of the digits of the number is divisible by 2.
B. If a number is even, then the number is divisible by 2.
C. The number is even.
D. The number is divisible by 2.
Answer: Option 'B' is correct.
Step-by-step explanation:
Since we have given that
"A number is divisible by 2 if even."
It means that if the number is even , then that number is always be divisible by 2.
So, the conclusion of the conditional is that
"If a number is even, then the number is divisible by 2."
Hence, Option 'B' is correct.
In skate boarding an ollie is a move in which the athlete pops the skateboard in the air, making it appear that the board and skateboarder are attached.At the 2009 X Games, one skateboarder completed 34 allies in 30 seconds. if he could keep up that rate, what would be his rate of allies per minute? What would be his rate per hour
The skateboarder's rate of ollies per minute would be 68 ollies per minute. The skateboarder's rate of ollies per hour would be 4080 ollies per hour.
Explanation:To find the rate of ollies per minute, we need to divide the number of ollies completed in 30 seconds by the number of seconds in a minute. In this case, the skateboarder completed 34 ollies in 30 seconds, so the rate of ollies per minute would be:
Rate per minute = (34 ollies / 30 seconds) × (60 seconds / 1 minute) = 68 ollies per minute
To find the rate of ollies per hour, we need to divide the number of ollies completed in 30 seconds by the number of seconds in an hour. In this case, the skateboarder completed 34 ollies in 30 seconds, so the rate of ollies per hour would be:
Rate per hour = (34 ollies / 30 seconds) × (3600 seconds / 1 hour) = 4080 ollies per hour
A lawyer charges his clients a consultation fee of $500 and $100 per hour to work on a case. This is represented by the linear function C = 100x + 500. If the lawyer increases his hourly rate to $150, how much more will he make on a 10-hour case? A) $250 B) $500 C) $750 D) $1000
What's the function rule, I don't understand how to write a function rule using the ordered pairs in this table
If a bookshelf is 28 1/8 inches long,how many 1 7/8 inch thick books will it hold?
Answer: Bookshelf can hold 15 books.
Step-by-step explanation:
Given : The length of the book shelf = [tex]28\dfrac{1}{8}[/tex] inches
In improper fraction , [tex]28\dfrac{1}{8}=\dfrac{8(28)+1}{8}=\dfrac{225}{8}[/tex]
i.e. Length of the book shelf = [tex]\dfrac{225}{8}[/tex] inches
Similarly, Thickness of a book = [tex]1\dfrac{7}{8}=\dfrac{8(1)+7}{8}=\dfrac{15}{8}[/tex] inches
Now, the number of books the shelf can hold = Length of the bookshelf ÷Thickness of a book
[tex]=\dfrac{225}{8}\div\dfrac{15}{8}\\\\=\dfrac{225}{8}\times\dfrac{8}{15} \\\\=\dfrac{225}{15}=15[/tex]
Hence, the bookshelf can hold 15 books.
What is the value of 6x^3 +8x when x = 5
how do mental math strategies help you solve problems such as the ones above?
With mental math, you can perform equations quickly and efficiently. They also help you to develop your own strategies and solve more complex math equations. Hope this helps;)
how do you solve 7+1/4r=-17
Answer:
It helped thankyou very much
Step-by-step explanation:
I didn't even need it
Frank needs to memorize words on a vocabulary list for Latin class. He has memorized
6
of the words, which is two-thirds of the list. How many words are on the list?
Frank has memorized 6 words which is two-thirds of his vocabulary list, so by dividing 6 by 2/3, we find out that the total number of words on the list is 9.
Frank has memorized 6 words on his Latin vocabulary list, which is two-thirds of the total number of words. To find out the total number of words on the list, we can set up a proportion where 6 words corresponds to 2/3. Therefore, we need to find a number that, when multiplied by 3/2 or 1.5, gives us 6.
We can set up the equation like this: 2/3 * total words = 6 words. To find the total words, we divide 6 by 2/3:
total words = 6 ÷ (2/3)
total words = 6 * 3/2
total words = 9
So, the vocabulary list has a total of 9 words.
Set up an equation to represent the distance the cheetah covered in terms of t minutes running at maximum speed. Remember, units of distance and time must agree. Use the conversion information from the warm-up to write a rate in miles per minute.
math question down below
what is the square root of negative 2 times the square root of negative 18. Please show work.
Which set is the subset of every set
The set which is the subset of every set is:
Empty set or null set.
Step-by-step explanation:Set--
A set is a well defined collection of the distinct objects.
The number of objects in the set is the cardinality of the set.
The set whose cardinality is zero is known as the empty set or the null set.
i.e. it is the set which is having zero element i.e. no element.
Such a set is unique.
Also, the null set or the empty set is the subset of every set.
Omar has 8 marbles.joy has 7marbles.how many marbles do they have together?
find the slope of the line through P(5,7) and Q( -1 + 7)
Final answer:
The slope of the line through points P(5,7) and Q(-1,7) is calculated to be 0, indicating a horizontal line.
Explanation:
To find the slope of the line through points P(5,7) and Q(-1,7), we can use the formula for the slope of a line through two points: slope (m) = (y2 - y1) / (x2 - x1). In this case, the coordinates for P are (x1, y1) = (5, 7) and the coordinates for Q are (x2, y2) = (-1, 7).
Plugging these values into the slope formula, we get:
m = (7 - 7) / (-1 - 5)
m = 0 / (-6)
m = 0
So the slope of the line is 0, which means that the line is horizontal.
A department store's customer parking lot has 4 rows with an equal number of parking spots in each row. The lot also has 15 parking spots for store employees. If c cars can be parked in each of the 4 main rows of the parking lot, what is the expression for the maximum number of cars that can be parked in the parking lot?
15c − 4
c(15 − 4)
4c + 15
4(c + 15)
The expression for the maximum number of cars that can be parked in the parking lot is:
4c+15
Step-by-step explanation:As there are a total of 4 rows.
and If c cars can be parked in each of the 4 main rows of the parking lot then the total number of cars that are parked in all the rows are:
4c
Also, 15 parking spots are for store employees.
Hence, the maximum number of cars that can be parked is represented by the expression as:
4c+15
find the next 3 terms of the following sequence 22 21 18 13 6
The next 3 terms of the sequence 22, 21, 18, 13, 6 are 2, -3, and -8.
Explanation:The next 3 terms of the sequence 22, 21, 18, 13, and 6 can be found by analyzing the pattern in the sequence. The difference between each term is decreasing by 1 each time. So, the next difference would be 5 - 1 = 4. Subtracting 4 from 6 gives us 2. Therefore, the next term in the sequence is 2. Repeating this process, we can find the following terms: 2, -3, and -8.
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Show one way to count from 82 to 512