Write an Equation using the following arithmetic sequence: 5, _____, ______, 32

Answers

Answer 1

Answer:

The sequence is:

5, 14, 23, 32

Step-by-step explanation:

We know that an Arithmetic sequence with a₁ and the commo difference 'd' has the nth term such as:

aₙ = a₁ + (n-1)d

Given the arithmetic sequence

5, _____, ______, 32

here:

a₁ = 5

n = 4

aₙ

so substituting a₁ = 5, n = 4 and aₙ = 32 in the nth term

aₙ = a₁ + (n-1)d

32 = 5 + (4-1)d

32 = 5 + 3d

3d = 32-5

3d = 27

divide both sides by 3

3d/3 = 27/3

d = 9

Therefore, the common difference: d = 9

Determining the 2nd term:

Using the formula

aₙ = a₁ + (n-1)d

substitute n = 2, a₁ = 5, d = 9

a₂ = 5 + (2-1)9

a₂ = 5 + 1(9)

a₂ = 5 + 9

a₂ = 14

Determining the 3rd term:

Using the formula

aₙ = a₁ + (n-1)d

substitute n = 3, a₁ = 5, d = 9

a₃ = 5 + (3-1)9

a₃ = 5 + 2(9)

a₃ = 5 + 18

a₃ = 23

Thus, the sequence becomes:

5, 14, 23, 32


Related Questions

PLEASE HELP ASAP i am willing 30 points


You are a high school senior with a part-time job at a retail store. Your employer pays you $9.75 per hour. Last week, you worked a total of 30 hours.

The following payroll deductions were taken from your gross pay:

Federal income tax (withholding) at 10%
Social Security tax at 6.2%
Medicare tax at 1.45%
Use the check stub below to help you think through the problem.

You are encouraged to use scratch paper or Chrome Canvas as a scratch pad. You are allowed to check your calculations with a calculator.

check stub

The amount for FEDERAL INCOME TAX for this pay period was $

Answers

567

becoz it's merits in increment

IF ANY OF YOU SOLVE I WILL GIVE BRAINLIEST AND EVERYTHING ELSEEEE PLS HELP
4x - 4; x=7

6 - x + y; x=5, y=3

Answers

Answer:

1. 4x-4=24

2. 6-x+y=4

Step-by-step explanation:

Answer:

4x(7) - 4= 24

6 - 5 + 3 = 4

Step-by-step explanation:

please help the game hates me

Answers

Answer:

negative

Step-by-step explanation:

a positive divided by a negative is a negative

Identify the function by that reflects f(x)=5x^3-3 across the x axis and shifts up 2 units

Answers

f(x)= 5(-x^3)-3+2
f(x)=5(-x^3)-1

The new function after reflected across the x-axis and shifts up 2 units is g(x)= -5x³+5.

What is the function?

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given function is f(x)=5x³-3.

When a function f(x) is reflected over the x-axis, it becomes a new function g(x)= -f(x).

The given function reflected across the x-axis and shifts up 2 units.

Now, g(x)= -(5x³-3)+2

= -5x³+3+2

= -5x³+5

Therefore, the new function after reflected across the x-axis and shifts up 2 units is g(x)= -5x³+5.

To learn more about the function visit:

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Evaluate Expressions
Jan 15, 12:46:39 PM
What is the value of the expression below when x = 7?
5x - 7

Answers

5(7)-7
35-7
28
The answer is: 28

PLEASE HELP ME WITH THIS PROBLEM!!!!

Answers

Answer:

It is positive 3

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

Any numbers inside the absolute value are always positive, so in this case, 12 is 12, and -15 is 15.  Add these numbers to get 27 as your answer.

Can anyone Help me pleasee!

Answers

It’s reflected across the y axis

there is a ratio of 5 girls to 3 boys in the chorus.there are 24 boys in the chorus.how many girls are in chorus

Answers

Answer:

40

Step-by-step explanation:

3 x 8 = 24

5 x 8 = 40

24/3 = 8

5 x 8 = 40

There are 40 girls

please solve.
-7 = z over 2 + 1

Answers

-7=z/2+1

What you first need to do is to multiply both sides of the equation by 2

-14=z+2

Now you move the variable to the left side and change within it’s own sign

-z-14=2

Into

-z=2+14

Now you then add the numbers

-z=16

The last part you do is change the sign on both sides in this equation

z=-16

Therefore, z=-16 is your answer in number 16.
Z=-16 hopes this helps

HELP PLZZZ WILL GIVE BRAINLEAST

Answers

Answer:

b,c,d,f

Step-by-step explanation:

[tex]perimeter=2(3\sqrt{8} +4\sqrt{20} +2\sqrt{24} ) \\=2(3\sqrt{8} )+2(4\sqrt{20} +2\sqrt{24} ) \\=6\sqrt{8} +8\sqrt{20} +4\sqrt{24} \\=6.8^{\frac{1}{2} } +8.20^{\frac{1}{2} } +4.24^{\frac{1}{2} } \\or~ =12\sqrt{2} +16\sqrt{5} +8\sqrt{6} \\[/tex]

please give explanation cuz i dont know how to do this

Answers

Answer:

Step-by-step explanation:

y=a*b^x

a=$2,000

This is the amount that the homeowner borrowed from the lender

b=This would be represented as 1.04 in decimal form

The reason why it is 1.04 is that the 1 aka 100% counts as 2,000 which is the whole thing as well as 0.04 or 4% percent of the total amount($2000)

x= You would leave this as x because they did not give a value and the equation is written so that it could be used to solve the amount of money owed after 'x' years or a certain number of years

Therefore the equation would be y=2000*(1.04)^x

the table shows the relationship between the number of CDs and their cost at the flea market. Which equation shows the same relationship?

Answers

Answer:

probably 2.5/d

Step-by-step explanation:

my mathematical teacher

What is the y-intercept in the table of values

Answers

Answer:your mom

Step-by-step explanation:

cause i took it already

Which of the following is not a geometric tool?

A.Compass
B.Pen
C.Protractor
D.Set Squares

Answers

Answer:

C. Protractor

Answer:

A

Step-by-step explanation:

A compass is for directions.

How do you find the horizontal asymptote of a rational function?"
A. Set the denominator equal to zero
B. Set the numerator equal to zero
C.plug in zero for x
D. Use one of the 3 rules

Answers

Answer:

c

Step-by-step explanation:

I think is C sorry if I get it wrong

I WILL GIVE BRAINLIEST IF YOU GET IT RIGHT!!!!

The figure below shows a square ABCD and an equilateral triangle DPC:


ABCD is a square. P is a point inside the square. Straight lines join points A and P, B and P, D and P, and C and P. Triangle D


Jake makes the chart shown below to prove that triangle APD is congruent to triangle BPC:


Statements Justifications

In triangles APD and BPC; DP = PC Sides of equilateral triangle DPC are equal

Sides of square ABCD are equal

In triangles APD and BPC; angle ADP = angle BCP Angle ADC = angle BCD = 90° and angle ADP = angle BCP = 90° − 60° = 30°

Triangles APD and BPC are congruent SAS postulate

Which of the following completes Jake's proof? (1 point)


In triangles APD and BPC; AD = BC

In triangles APD and BPC; AP = PB

In triangles APB and DPC; AD = BC

In triangles APB and DPC; AP = PB.

Answers

9514 1404 393

Answer:

  (a)  In triangles APD and BPC; AD = BC

Step-by-step explanation:

We're not concerned with triangle APB, eliminating the last 2 choices.

We're not concerned with sides AP and BP, as they're not sides of the square, eliminating the second choice.

The choice that makes any sense in the proof is ...

  In triangles APD and BPC; AD = BC

Can I get some help here?

Answers

Answer:

AB, CB, AC

Step-by-step explanation:

All the angles in a triangle added up equal 180 degrees

Start by finding the measure of angle A

A + 86 + 27 = 180

A + 113= 180

A = 67 degrees

Now order them

86 is greater than 67 and 27 so B is the greatest

27 is less than 86 and 67 so C is the smallest

67 is less than 86 but greater than 27 so A is in the middle

Now for the sides..

AB is opposite angle C so it's the shortest

CB is opposite angle A so it's in the middle

AC is opposite angle B so it's the longest

I hope this helps!!!

can someone help with this

Answers

Answer: -1

Step-by-step explanation:

Find the Slope

(0, 2) , (1, 1)

Slope is equal to the change in y over the change in x, or rise over run.

     change in y

m =  _________

     change in x

The change in x is equal to the difference in x-coordinates (also called run), and the change in y

is equal to the difference in y-coordinates (also called r ise).

     y2 − y1

m = _____

     x2 − x1

Substitute in the values of x and y into the equation to find the s lope.

      1 − (2)

m = _____

      1 − (0)

Simplify.

Simplify the numerator.

       −1

m = ____

     1 − (0)  

Simplify the denominator.

      −1

m = ___

        1

Divide −1 by 1.

m = −1

Abey and Anoki are eating chocolate bars. The bars are the same size. Abey has ! 3 4 ! Left. Anoki has ! 7 8 ! Left. How much chocolate is left altogether?

Answers

Answer:

13/8 of the chocolate will be left altogether.

Step-by-step explanation:

Given that,

Abey and Anoki are eating chocolate bars. The bars are the same size.

Abey left 3/4 of chocolate and Anoki left 7/8 of chocolate.

Left amount = Abey left amount + Anoki left amount

[tex]=\dfrac{3}{4}+\dfrac{7}{8}\\\\=\dfrac{3(2)+7(1)}{8}\\\\=\dfrac{6+7}{8}\\\\=\dfrac{13}{8}[/tex]

Hence, 13/8 of the chocolate will be left altogether.

pls help with these two questions!

Answers

Answer:

1. D 2. A

Step-by-step explanation:

please tell me if you need an explanation.

Answer:

Question 1. CQuestion 2. A

Step-by-step explanation:

Question 1

Given equation

(-2/3)x - y = -9

Rewrite in slope-intercept form:

(-2/3)x - y = -9(-2/3)x + 9 = yy = -2/3x + 9

The slope is -2/3 and the y-intercept is 9

Correct answer option is C or third option

Question 1

Given equation

C = 10 + 0.25m

The bill of $25 is represented as:

25 = 10 + 0.25m

Correct option is A or the first option.

simplify 0.2×0.03055​

Answers

Answer:

[tex]0.2 = \frac{2}{10} = \frac{2}{10 ^{1} } = 2 \times {10}^{ - 1} \\ 0.03055 = \frac{3055}{100000} = \frac{3055}{ {10}^{5} } = 3055 \times {10}^{ - 5} \\ 0.2 \times 0.03055 = 2 \times {10}^{ - 1} \times 3055 \times {10}^{ - 5} \\ = 2 \times 3055 \times {10}^{ - 1 + ( - 5)} \\ = 2 \times 3055 \times 10^{ - 1 - 5} \\ = 2 \times 3055 \times {10}^{ - 6} \\ = 6110 \times {10}^{ - 6} \\ = \frac{6110}{ {10}^{6} } \\ = \frac{6110}{1000000} \\ = 0.006110[/tex]

Divide. Write your answer as a fraction in simplest form. −7/2÷7/5=

Answers

The answer i got for this question in simplest form as a fraction is - 5/2

Becca had of a yard of ribbon to use for her crafts projects. She used of a yard to make a bow. How much ribbon, r, does Becca have left?

Set up an equation and solve.

answers:46/105, 91/45, 3r/7, 3/7 - r , 136/105

only two space for two answers

Answers

Answer:

a y a r d = a 2 y r d a y a r d = a 2 y r d

Step-by-step explanation:

(5x + 5 - 2x)(4 + 7x - 1)

Answers

Answer: 21x^2 + 44x + 15

Step-by-step explanation:

first, i used the distributive property.

5x x (4 + 7x - 1) + 5 (4 + 7x - 1) - 2x x (4 + 7x - 1)

then, i removed the parentheses.

20x + 35x^2 - 5x + 20 + 35x - 5 - 8x - 14x^2 + 2x

then, i collected the like terms.

44x + 21x^2 + 15

finally, i reordered the terms.

21x^2 + 44x + 15

Someone please help me I only have until January 18th to turn this in. Question: Mr Lopez picks up 2 pallets of dog food to deliver to the animal shelter. Each pallet contains 40 bags of dog food, and the dog food weighs 37 1/2 pounds pet bag. What is the total weight, in tons, of the dog food Mr. Lopez delivers to the animal shelter?

Answers

Answer:

Mr. Lopez delivers 1.5 tons of dog food to the animal shelter.

Step-by-step explanation:

Mr Lopez picks up 2 pallets of dog food to deliver to the animal shelter. Each pallet contains 40 bags of dog food, and the dog food weighs 37 1/2 pounds pet bag.

The weight of 1 bag of dog food = [tex]37\frac{1}{2}\text{ pounds }[/tex]

The weight of 40 bags of dog food = [tex]40 \times 37\frac{1}{2} =1500 \text{ pounds }[/tex]

Each pallet weighs = 1500 pounds

2 pallets weighs = 1500×2=3000 pounds.

We know that 2000 pounds = 1 ton

[tex]\frac{3000}{2000} \text{ pounds}=1.5 \text{ tons}[/tex]

Hence, Mr. Lopez delivers 1.5 tons of dog food to the animal shelter.

Find the value of x. Round your answer to
the nearest tenth. Please help

Answers

Answer:

x=50.7°

Step-by-step explanation:

Use the given angle of x° to find which trigonometry ratio to use. We are given the side adjacent to the angle and the hypotenuse. Therefore, we use the cosine ratio:

[tex]cosineX=\frac{adjacent}{hypotenuse}[/tex]

Insert the given values:

[tex]cos.x=\frac{19}{30}[/tex]

In order to fin the angle, use the inverse:

[tex]x=cos^{-1}(\frac{19}{30} )[/tex]

Insert the equation into a calculator:

[tex]x=50.70351976[/tex]

Round to the nearest tenth:

[tex]x=50.7[/tex]

:Done

there are only r red counters and g green counters in a bag. a counter is taken at random from the bag. the probability that the counter is green is 4/9 the counter is put back in the bag. 4 more red counters and 2 more green counters are put in the bag. a counter is taken from the bag. the probability that the counter is green is 10/23 find the number of red counters and the number of green counters that were in the bag originally. your final line must say, ... red and ... green counters.

Answers

The number of red counters and the number of green counters that were in the bag originally is: 10 red and 8 green counters.

How to calculate the probability of an event?

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

Then, its probability is given as

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]

where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

For this case, let we had:

R numbers of red counters, and G number of green counters originally.

Then, total counters in the bag originally = R +G

One counter out of R+G counters can be chosen in R+G ways. But one green counter out of R+G counters can be chosen in G ways.

Thus, probability of taking green counter out in one random picking is:

[tex]\dfrac{G}{R + G}[/tex]

It is given that this probability is 4/9. Therefore, we get:

[tex]\dfrac{G}{R+G} = \dfrac{4}{9}\\\\\\9G = 4R + 4G\\\\5G = 4R[/tex](first equation)


When 4 more red counters and 2 more green counters were added, then:

Number of red counters in modified bag = R + 4Number of green counters in modified bag = G + 2Number of total counters in modified bag = R + 4 + G+ 2 = R + G + 6

One counter out of R+G+6 counters can be chosen in R+G+6 ways. But one green counter out of R+G+6 counters can be chosen in G+2 ways (since there are G+2 green counters in the considered bag) ways.

Thus, probability of taking green counter out in one random picking is:

[tex]\dfrac{G+2}{R + G+6}[/tex]

It is given that this probability is 10/23. Therefore, we get:

[tex]\dfrac{G+2}{R+G+6} = \dfrac{10}{23}\\\\\\23G + 46 = 10R + 10G + 60\\\\13G = 10R + 14[/tex](second equation)

Thus, we got a system of two linear equations as:

[tex]5G = 4R\\13G = 10R + 14[/tex]

From first equation, getting the value of G in terms of R,

[tex]G = \dfrac{4R}{5}\\[/tex]

Now, substituting this with G in the second equation, we get:

[tex]\\13\left(\dfrac{4R}{5} \right) =10R + 20\\\\52R = 50R + 20\\2R = 20\\R = 10[/tex]

From this value of R, and the value of G in terms of R, we get:

[tex]G = \dfrac{4R}{5}\\\\ = \dfrac{4 \times 10}{5} = 8[/tex]

Thus, R = 10 and G = 8.

Thus, the number of red counters and the number of green counters that were in the bag originally is: 10 red and 8 green counters.

Learn more about probability here:

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A repairman charges an inspection fee plus $22 per hour. A customer with a coupon for 40% off the inspection fee pays $118 for a 4-hour repair. How many hours are worked when a customer pays $94 without a coupon?

Answers

Answer:

Inspection fee = $50

h = 2 hours

Step-by-step explanation:

Let

x = the inspection fee

Charge per hour = $22

Number of hours = 4

A customer with a coupon for 40% off the inspection fee

This means the customer paid 60% of the inspection fee

118 = 60% of x + 22(4)

118 = 0.6x + 88

118 - 88 = .6x

30 = .6x

x = 30/0.6

x = $50

Inspection fee = x = $50

How many hours are worked when a customer pays $94 without a coupon?

94 = 50 + 22h

94 - 50 = 22h

44 = 22h

h = 44/22

h = 2 hours

A spinner with the numbers 1 through 8 is spun 25 times. What is the experimental probability of the spinner stopping on the number 4?

Answers

Answer: Because if you think about it it would be 4 because of the fact that it is in the middle of 1-8. So there is a higher chance to land on 4 than any other number.

Step-by-step explanation:

The experimental probability of the spinner stopping on the number 4 is 1/25.

What is experimental probability?

Experimental probability is a probability that is determined on the basis of a series of experiments.

A random experiment is done and is repeated many times to determine their likelihood and each repetition is known as a trial.

Given that, a spinner with the numbers 1 through 8 is spun 25 times.

we need to find the experimental probability of the spinner stopping on the number 4

So,

Experimental Probability =

P(E) = Number of times an event occurs / Total number of trials.

Number of times an event occurs = 1

Total number of trials = 25

Therefore,

P(E) = 1/25

Hence, the  experimental probability of the spinner stopping on the number 4 is 1/25.

Learn more about experimental probability click;

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pls help :( :) i’m a little lost

Answers

Answer:

B

Step-by-step explanation:

On a graph you go rise over run (or Y divided by X) which in this equation is 1 divided by 2 which equals 1/2. You also need to look at what number is being crossed on the y axis, which in this case is 1. Slope intercept form is y=mx+b with m being the slope (1/2) and b being the y intercept (1)

Answer:

B. y = 1/2x + 1

Step-by-step explanation:

I went ahead and graphed each of the answer options for you and when I graphed for B it gave me:

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