Given:
First term of an arithmetic sequence = 5
Second term = 3
To find:
The explicit formula for the given arithmetic sequence.
Solution:
We have,
First term: [tex]a_1=5[/tex]
Second term: [tex]a_2=3[/tex]
Common difference is
[tex]d=a_2-a_1[/tex]
[tex]d=3-5[/tex]
[tex]d=-2[/tex]
Now, the explicit formula for an arithmetic sequence is
[tex]a_n=a+(n-1)d[/tex]
where, a is first term and d is common difference.
Putting a=5 and d=-2, we get
[tex]a_n=5+(n-1)(-2)[/tex]
It can also be written as
[tex]a_n=5-2n+2[/tex]
[tex]a_n=7-2n[/tex]
Here, n is an integer greater than or equal to 1.
Domain is the set of input values.
Therefore, the explicit equation is [tex]a_n=5+(n-1)(-2)[/tex] or [tex]a_n=7-2n[/tex] and domain is all interest greater than or equal to 1.
If the population changes by 2.5% per year, what percentage does it change in 5 years
The population changes to 12.5% in 5 years.
Dan charges $15 per hour for walking dogs. How much will he earn for 5
hours? *
$70
$65
O $75
All you have to do is do 15 times 5 = 75
Answer:
I'm pretty sure its 75 cause 15 x 5 is 75
Step-by-step explanation:
6x + 3 > -33 on a number line
Answer:
Step-by-step explanation:
Select the correct answer. Based on the table, which city has the highest temperature in January? City January Temperature (°C) New Orleans 7 Philadelphia -4 Phoenix co Rochester -8 San Antonio 5 OA New Orleans B. Philadelphia O C. Phoenix D. Rochester O E. San Antonio
Answer:
knew Orleans
Step-by-step explanation: i think i'm not really sure
Based on the table, Phoenix has the highest temperature in January. Therefore, the correct option is option C among all the given options.
What is temperature?The physical concept of temperature indicates in numerical form how hot or cold something is. A thermometer is used to determine temperature. Thermometers are calibrated using a variety of temperature scales, which historically defined distinct reference points including thermometric substances.
The most popular scales are the Kelvin scale (K), which is mostly used for scientific purposes, the Celsius scale (°F), as well as the Celsius scale, which has the unit symbol °C. Based on the table, Phoenix has the highest temperature in January.
Therefore, the correct option is option C.
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help please i need to get this done
Answer:
x = 4
y = -7 or (-7, 4)
Step-by-step explanation:
y = -2x + 1
4x + y = 9 replace y in the second equation with (-2x + 1) since y is equal to it
4x + (-2x + 1) = 9 add like terms
2x + 1 = 9 subtract 1 from both sides
2x = 8 divide both sides by 2
x = 4 since y = -2x + 1 replace x with the value we found
y = (-2) × 4 + 1 = -7
You decide to invest $997.90 at an interest rate of 17% l, how long will it take to triple your money? Round to the nearest whole number.
Answer:
Approximately 18 years
Step-by-step explanation:
Triple: 997.90*3. which is 2993.7
997.90*0.17*x=2993.7
(x is time)
169.643x=2993.7
x=2993.7/169.643
x= approximately 17.64....... years/
18 years.
Hope this helps plz hit the crown :D
Tyra competed on a trivia game show. 10 points were awarded for correct answers, and 5 points were deducted for incorrect answers. She answered 2 questions correctly, but answered one incorrectly. How many points does she have?
Answer:
15
Step-by-step explanation:
10+10-5=15
Answer:
It is 15
Step-by-step explanation:
Hope this helped have an amazing day!
An electrician charges $75 per hour on top of a set fee of $50 for every house call. Write an equation for C, in terms of t, representing the total cost of the electrician's services if the electrician spends t hours at the house working.
C=?
Please help
Answer:
C= 75t + 50
This is the equation to use.
The equation that represents the total cost for a house will be C = 75t + 50.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
An electrical expert charges $75 each hour on top of a set expense of $50 for each house call.
Let 't' be the number of hours and 'C' be the total cost of the service. Then the equation is given as,
C = 75t + 50
The condition that addresses the all-out cost for a house will be C = 75t + 50.
More about the linear equation link is given below.
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Solve for x: -3x - 3 = - 12
Answer:
-3x-3=-12 +3
-3x=-9 ÷(-3)
x=3
Step-by-step explanation:
prove me wrong
Answer:
x = 3
Step-by-step explanation:
-3x - 3 = -12
+3 +3
-----------------------
-3x = -9
-3x/3 = -9/3
-----------------------
-x = -3; x = 3
Check Work:
-3(3) - 3 = -12
-9 - 3 = -12
-12 = -12 (true)
write an equation in slope- intercept form (0,4) slope 5
I need help so pls
Answer:
5,4
Step-by-step explanation:
What is an additional expression that has the value of -8?
Answer:
-12 + 4
Step-by-step explanation:
Please help I’m in finals and I have to complete all my missing assignments
Answer:
Between 3 and 3.5
Step-by-step explanation:
more than 9 and less than 16. 9 is closer to 10 making it c.
Which of the following best describes the graph above?
OA. both a relation and a function
OB. function only
OC. neither a relation nor a function
OD. relation only
Answer:
The answer you are looking for is B) Function only.
Step-by-step explanation:
A function graph would mean that each x value corresponds to one y value, in a function multiple x values can have the same output but one x value cannot have more than one output.
A relative graph means each x value has their own unique output value and each x value (f(x)) has one output but cannot share that output with any other x value.
In this case x=5 which means it can only be a function.
Hope this helps!
BRO I NEED HELP THIS DUE IN 4 MINS!
Answer:
440 computers in warehouse B
Step-by-step explanation:
1030=A+B
A=b+150
replace the formula.
a=b+150
so replace the "a"+b=1030
so then it'd be b+150+b=1030
now that's easy.
2b+150=1030
-150 -150
2b=880
/2 /2
b=440
i neeeedd helpp asap
Answer:
oh it c .
Step-by-step explanation:
a golfer hits a golf ball up in the air from a platform which is 10 feet above the ground. The table models the height h of the golf ball in feet as it travels a horizontal distance d. Consider the graph of the coordinates below which model the balls path. Which of the following is the domain for the graph?
Answer:
The domain (x) is the height of the ball
the answer is 0 is less then or equal to d is less then or equal to 412
The Mathletes Club is printing t-shirts for its 15 members. The printing company charges a certain amount for each shirt plus a setup fee of $20.
If the t-shirt order costs a total of $162.50, how much does the company charge for each shirt?
Answer:
it is $10.83
Step-by-step explanation:
The graph of y = f(x) is shown below. What are all of the real solutions of f(x) = 0?
Answer:
0, -6, 4
Step-by-step explanation:
did it
plzzz help i will give brainliest if i can
Answers: choice C and choice E
Plugging x = 3 and y = -1 into both equations of choice C lead to a true result (the same number on both sides). This is why the system of equations listed in choice C is one possible answer. Choice E is a similar story.
If your teacher didn't mean to make this a "select all that apply" type of problem, then it's likely your teacher may have made a typo.
Miranda mixed 34.5 fluid ounces of blue paint, 40.5 fluid ounces of red paint, and 2 fluid ounces of black paint to make purple paint. She poured the same amount of the purple paint into 14 jars. How much paint did she pour in each jar
Answer:
5.5
Step-by-step explanation:
Miranda mixes 34.5 fluid ounces of blue paint
40.5 fluid ounces of red paint.
2 fluid ounces of black paint to produce a purple paint
She pours this purple paint into 14 jars
Therefore the amount of paint in each jar can be calculated as follows
= 34.5 + 40.5 + 2
= 77/14
= 5.5 fluid ounces
Hence there are 5.5 fluid ounces of purple paint in each jar
Answer:
5.5
Step-by-step explanation:
how many solutions can be found for the equation 4x-8-4x=9
Answer:
no solutions
Step-by-step explanation:
Can a regular polygon have an interior angle of 132 degrees?
Given:
The interior angle of a regular polygon is 132 degrees.
To find:
The given statement is possible or not.
Solution:
Let as assume the interior angle of a regular polygon with n vertices is 132 degrees.
Then, the exterior angles are
[tex]180^\circ-132^\circ=48^\circ[/tex]
We have, n vertices. So, the number of exterior angles is n.
Sum of all exterior angles = 48n degrees
We know that, sum of all exterior angles of a regular polygon is always 360 degrees.
[tex]48n=360[/tex]
[tex]n=\dfrac{360}{48}[/tex]
[tex]n=7.5[/tex]
Number of vertices is always a whole number. So, it cannot be a fraction value.
So, our assumption is wrong.
Therefore, a regular polygon cannot have an interior angle of 132 degrees.
What is 8×9÷6+2-8.53²+⅖
8×9÷6+2-8.53²+⅖
= -58.3609
what does ( 7.8 x 10 to the 3rd) x (1.0 x 10 to the 4th) equal?
Answer:
7.8 * 10^7
Step-by-step explanation:
Group coefficients together and exponents together to multiply numbers in scientific notation.
( 7.8 * 1 ) ( 10 ^3 * 10^4)
Multiply 7.8 times 1.
7.8 * (10^3 * 10^4)
Use the power rule a^m * a^n = a^(m+n) to combine exponents. So, add 3 and 4
7.8 * 10^7
1. This two-way table shows the results of asking students if they prefer to have gym class in the morning or the afternoon. morning afternoon total grade 6 15 8 23 grade 8 18 21 38 grade 10 12 26 38 total 45 55 100 a. How many students participated in the survey? b. How many students in grade 8 prefer to have gym in the morning? c. How many grade 10 students participated in the survey? d. How many students prefer to have gym in the afternoon? **When you give your answers, label them as a, b, c, and d.
a)There are 200 students who attended the survey.
b)There are 18 students who prefer the gym in the morning.
c)There are 38 grade 10 students who participated in the survey.
d)There are 110 student students who prefer to have a gym in the afternoon.
What is a data table?A data table is a piece of writing made up of rows, columns, and cells that each contain a particular value. They keep data that people can access later and update as required.
The given data is shown in table,
The data table's title, column headers, and row headers can all aid a user in better comprehending the data in the table. Data tables present information in a format resembling a grid with rows and columns.
To enable users to find patterns and draw conclusions from data, they arrange information in ways that are simple to scan.
Thus, there were 200 students who participated in the poll, 18 of whom preferred the gym in the morning, 38 grade 10 students, and 110 of them preferred to have a gym in the afternoon.
Learn more about the table here,
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Need help please...........
Answer:
49 is the missing angle.
Step-by-step explanation:
just add the other angles then subtract by 180 to get your answer! have a nice day!
the equation of a line going through the point (9,2) and (-15,2)
Answer:
y = 2
Step-by-step explanation:
Total consumption of fruit juice in a particular country in 2006 was about 2.05 billion gallons. The population of that country in 2006 was 500 million. What was the average number of gallons of fruit juice consumed per person in the country in 2006?
Answer:
4.1 gallons per person
Step-by-step explanation:
The total consumption of fruit juice is 2.05 billion
The total population is 500 million
Therefore the average number of gallons fruit juice consumed per person can be calculated as follows
=total consumption/total population
= 2,050,000,000/500,000,000
= 4.1 gallons per person
amys mom.made.60 cookies her mom made her.brother Jeff has eaten 10 cookies what is the percentage of the cookies that are remaining?
Answer:
the answer is c
Step-by-step explanation:
At 5.45p.M .,lixin,khairul and Devil are at the starting point of a 1-km circular path. Lixin Takes 18 minutes to walk one round ,khairul needs 360 seconds to run 1 round ansd Devi cycles 2 rounds in 4 minutes .Find the time when all three of them will next meet
Answer:
[tex]Meeting\ Time = 6:03\ pm[/tex]
Step-by-step explanation:
Given
[tex]Start\ Time= 5:45pm[/tex]
[tex]Lixin = 18\ min/round[/tex]
[tex]Khairul = 360\ seconds/round[/tex]
[tex]Devi = 4minutes/2\ rounds[/tex]
Required
Determine their next meeting time
First, we need to get their unit rate in minutes per round
[tex]Lixin = 18\ min/round[/tex]
[tex]Khairul = 360\ seconds/round[/tex]
Convert 360 seconds to minutes
[tex]Khairul = \frac{360}{60} min/round[/tex]
[tex]Khairul = 6 min/round[/tex]
[tex]Devi = 4minutes/2\ rounds[/tex]
Divide by 2/2
[tex]Devi = 2mins/round[/tex]
So, we have:
[tex]Lixin = 18\ min/round[/tex]
[tex]Khairul = 6 min/round[/tex]
[tex]Devi = 2mins/round[/tex]
Next, is to determine the LCM of 18, 6 and 2
[tex]18=2 * 3 * 3[/tex]
[tex]6 = 2 * 3[/tex]
[tex]3 = 3[/tex]
Their LCM is:
[tex]LCM = 2 * 3 * 3[/tex]
[tex]LCM = 18[/tex]
This means that they will meet 18 minutes after their initial time of departure.
So:
[tex]Meeting\ Time = 5:45\ pm + 18\ minutes[/tex]
[tex]Meeting\ Time = 6:03\ pm[/tex]