in an arithmetic sequence, the 5th term is equal to 75 and the 7th term is equal to 111 write an expression for the nth term of the sequence

Answers

Answer 1

Answer:

               [tex]\bold{\underline{a_n=18n-15}}[/tex]

Step-by-step explanation:

[tex]a_n=a_1+d(n-1)\\\\a_5=a_1+d\cdot4\\\\a_7=a_1+d\cdot6\\\\a_7-a_5=a_1+6d-(a_1+4d)=2d\\\\111-75=2d\\\\2d=36\\\\d=18\\\\\\a_1+18\cdot4=75\\\\a_1=75-72=3\\\\\\a_n=3+18(n-1)=3+18n-18\\\\\underline{a_n=18n-15}[/tex]


Related Questions

solve for x: |3x+12|= 18

Answers

Two Answers:  x = 2 or x = -10

=====================================================

Work Shown:

|3x+12| = 18

3x+12 = 18 or 3x+12 = -18

3x = 18-12 or 3x = -18-12

3x = 6 or 3x = -30

x = 6/3 or x = -30/3

x = 2 or x = -10

The rule used in step 2 is the idea that if |x| = k, for some positive number k, then x = k or x = -k. One equation breaks into two separate ones. From there we solve each equation for x as normal. Follow PEMDAS in reverse, undoing each operation, to isolate x.

If you're curious why the absolute value breaks into two parts, consider something like |x| = 7. This means x is 7 units away from zero on a number line. There are two possible locations where x could be: 7 and -7. This is one example showing why we get two different results. The same applies to our equation as well, just it's a bit more complicated.

The LCM of 4 and 7 is __.
Numerical Answers Expected!
Answer for Blank 1:

Answers

Answer:

28

Step-by-step explanation:

its ans may be 28 hope you will know

Answer:

28

Step-by-step explanation:

According to the table, what is omar’s bank balance? $761.25 $810.30 $814.75 $1,186.25

Answers

The total remaining bank balance in the account of Omar after reducing all the debit and adding paycheck is $761.25

What do you mean by debit and credit amount?

The money which is paid from an account is called the debit amount and the money which is paid into an account is called the credit amount.

To know the remaining balance of account, all the debit amount is subtracted from it and all the credit amount is added into it.

The table for the Omar's transaction is attached below. The data given in the table is,

Pharmacy       - $15.20-DebitedRent                - $425.00-DebitedDinner             - $22.30-DebitedMovie Ticket  - $26.70-DebitedPay Check     - $1015.50-CreditedInitial Balance- $219.80

The initial balance is $219.80, and a pay check of $1015.50 is credited in his account. Thus, the total balance in his account without any debit is,

[tex]A_i=1015.50+219.80\\A_i=1253.30[/tex]

The total amount debited from the account of Omar is,

[tex]A_d=15.20+425.00+22.30+26.70\\A_d=474.05[/tex]

Thus, the total remaining amount in his account is,

[tex]A=1253.3-474.05\\A=761.25[/tex]

Hence, the total remaining bank balance in the account of Omar after reducing all the debit and adding paycheck is $761.25

Learn more about the debit and credit amount here

https://brainly.com/question/24164976

Answer:

$761.25

Step-by-step explanation:

took the quiz on edge

I have an equation
H (T) = -16 x T^2 + 64 x T
Please make a graph that represents this equation. If you want the whole problem, make a comment asking for it! 100 POINTS

Answers

Answer:

  see attached

Step-by-step explanation:

A graphing calculator can graph your function nicely. See the attachment.

__

Additional comment

A spreadsheet can do this, too. However, that generally requires you compute a number of points on the graph.

Is 5 x 3^{x} equal to 15x?

Answers

Here's your answer, folks:

Without substitution, yes, here? No.

The value of the substituted numbers is essential to finding the correct answer in algebra.

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

5 x 3 = 15

15 squared or cubed = 15 x 15 || 15 x 15 x 15

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

In that case, 15 times a number could not possibly be equal to 5 x 3 unless x was actually 1, which we do not know.

Answer:

NO

Step-by-step explanation:

5*3^x[tex]\neq[/tex]15x

because 3 is raised to the x power not multiplied by it, so it is not equal

Triangle ABC underwent a sequence of transformations to give triangle A′B′C′. Which transformations could not have taken place? A. a reflection across the line y = x followed by a reflection across the line y = -x B. a reflection across the x-axis followed by a reflection across the y-axis C. a rotation 180° clockwise about the origin followed by a reflection across the line y = x D. a reflection across the y-axis followed by a reflection across the x-axis

Answers

Answer:

C. a rotation 180° clockwise about the origin followed by a reflection across the line y = x

Step-by-step explanation:

Let us assume that the coordinate of A in triangle ABC is A(x, y)

A) If there is a reflection across line y = x, the new coordinate is at A'(y, x).

If a reflection across the line y = -x is then followed, the new coordinate is at A"(-x, -y)

B) If there is a reflection across line x axis, the new coordinate is at A'(x, -y).

If a reflection across the line y axis is then done, the new coordinate is at

A"(-x, -y)

C) If there is a rotation 180° clockwise about the origin, the new coordinate is at A'(-x, -y).

If a reflection across the line y = x is then followed, the new coordinate is at A"(-y, -x)

D) B) If there is a reflection across line y axis, the new coordinate is at A'(-x, y).

If a reflection across the line x axis is then done, the new coordinate is at

A"(-x, -y)

Since only option C has a different result from the remaining options, hence option C would not five triangle A'B'C'

Answer:

C. a rotation 180° clockwise about the origin followed by a reflection across the line y = x

Step-by-step explanation:

Let us assume that the coordinate of A in triangle ABC is A(x, y)

A) If there is a reflection across line y = x, the new coordinate is at A'(y, x).

If a reflection across the line y = -x is then followed, the new coordinate is at A"(-x, -y)

B) If there is a reflection across line x axis, the new coordinate is at A'(x, -y).

If a reflection across the line y axis is then done, the new coordinate is at

A"(-x, -y)

C) If there is a rotation 180° clockwise about the origin, the new coordinate is at A'(-x, -y).

If a reflection across the line y = x is then followed, the new coordinate is at A"(-y, -x)

D) B) If there is a reflection across line y axis, the new coordinate is at A'(-x, y).

If a reflection across the line x axis is then done, the new coordinate is at

A"(-x, -y)

Since only option C has a different result from the remaining options, hence option C would not five triangle A'B'C'

a On January 1, Rose's bank balance was $200. During the month, she wrote checks for $115.25 and $350.00 and made one deposit of $150.50. Which best represents her checking account balance at the end of the month?​

Answers

Answer:

LOL she has a negative balance of "-114.75"

Step-by-step explanation:

to solve, all you need to do is "200-115.25-350+150.5"

we subtract the 2 values since she wrote the checks for someone to cash, which would empty from her bank, and then she made a deposit of 150.50, so we add that value.

please rate and mark as brainlest.

What is he answer for b)

Answers

Answer:

70

Step-by-step explanation:

triangle xbc is an isosceles triangle.

there are 180 degrees in a triangle.

angle xbc=55.

so that means angle xcb is also 55.

55+55=110

180-110=70

hope this helps

OUICK PLEASE HELP!!

The rectangles shown below can be folded to make a rectangular prism. To the nearest square centimeter, what is the total surface area of the prism formed by this net?

Answers

Answer:

b

Step-by-step explanation:

The answer is A. 1,512 cm^2

Each month, Kim donates the same amount of money to a charity. If
she donates $1,800 in one year, how much does she donate each
month?
There are 12 months in a year.

Answers

1,800/12=150. So Kim donates $150 a month

Solve the equation.
6.4= 4x
Ox=2.4
Ox=1.6
Ox=4
Ox= 10.4

Answers

Divide 4 on both sides, x=6.4/4 which is 1.6

Answer:

x= 1.6

Step-by-step explanation:

A karate school offers a package of 12 group lessons and 2 private lessons for $110. It also offers a package of 10 group lessons and 3 private lessons for $125. Write and solve a system of equations to find the cost of a single group lesson and a single private lesson.

Answers

Answer: The cost of a single group lesson is $5 and a single private lesson is $25

Step-by-step explanation:

Let the cost of a single group lesson be y.

Let the cost of a single private lesson be z.

A karate school offers a package of 12 group lessons and 2 private lessons for $110. This can be written as:

12y + 2z = 110 ..... equation i

It also offers a package of 10 group lessons and 3 private lessons for $125. This can be written as:

10y + 3z = 125 ...... equation ii

Combining equation i and ii

12y + 2z = 110 ..... equation i

10y + 3z = 125 ...... equation ii

12y + 2z = 110 × (3)

10y + 3z = 125 × (2)

36y + 6z = 330 ....... equation iii

20y + 6z = 250 ...... equation iv

Subtract equation iv from iii

16y = 80

y = 80/16

y = 5

From equation ii

10y + 3z = 125

10(5) + 3z = 125

50 + 3z = 125

3z = 125 - 50

3z = 75

z = 75/3

z = 25

The cost of a single group lesson is $5 and a single private lesson is $25

A group lesson costs = $5.

A private lesson costs = $25.

Let a group lesson costs = $x

A private lesson costs = $y.

According to the question:

12x + 2y = 110

10x + 3y = 125

Solving them we get x = 5, y = 25

Learn more: https://brainly.com/question/8806877

Sylvia buys a case of water that contains 24 bottles and sells x number of bottles to her co-workers. Sam buys a case of water than contains 36 bottles and sells three times as many bottles as Sylvia sold to his co-workers. How many bottles of water did Sylvia sell if they ended up with the same number of bottles of water left over?

Answers

It is given that Sylvia sells x number of bottles and Sam sells three times as many bottles as Sylvia sold to his co-workers.

So, number of bottles Sam sold is 3x.

It is also given that, number of remaining bottle Sylvia and Sam have same.

So,

24 - x = 36 - 3x

3x - x = 36 - 24

2x = 12

x = 6

Therefore, Sylvia sells 6 bottles.

Hence, this is the required solution.

The relationship between a bacteria population p, in thousands, and time d, in days, since it was measured to be 1,000 can be represented by the equation. Select all statements that are true about the situation. © 2019 Illustrative Mathematics. All Rights Reserved. Select all that apply:A: Each day, the bacteria population grows by a factor of 2B: The equation p=2^d also defines the relationship between the population in thousands and time in daysC: The population reaches 7,000 after log2(7,000) daysD: The expression log2(10) tells us when the population reaches 10,000. E: The equation d=log2(p) represents a logarithmic functionF: The equation 7=log2(128) tells us that the population reaches 128,000 in 7 days

Answers

d = log₂p represents a logarithmic function, The expression log₂(10) tells us when the population reaches 10,000 and the equation 7 = log₂(128) tells us that the population reaches 128,000 in 7 days.

What is an exponential function?

An exponential function is in the form:

y = abˣ

Where a is the initial value of y and b is the multiplication factor.

Let p represent the bacteria population in thousand after d days.

Since each day, the bacteria population grows by a factor of 2, hence:

[tex]p=2^d[/tex]

Hence, d = log₂p represents a logarithmic function

The expression log₂(10) tells us when the population reaches 10,000 and the equation 7 = log₂(128) tells us that the population reaches 128,000 in 7 days.

Find out more on exponential function at: https://brainly.com/question/12940982

Please help with the bonus. I beg

Answers

Answer:

8-8/8+8

Step-by-step explanation:

answer = 8-8/8+8

            = 8-1+8

            = 7+8

            = 15

A heptagon has angles that measure 120°, 110°, 140°, 135°, 160°, 100°, and b. What is b?

Answers

Answer:

Here,

We know that,

Sum of interior angles of a heptagon=900°

So,

b+120+110+140+135+160+100=900

or, b+765= 900

or, b=900-765

Therefore, b= 135°

Answer:

135

Step-by-step explanation:

Anastasia put a bowl under a leaking pipe in her kitchen. After 2 1/4 hours Anastasia had collected 1/2 cup of watwe. What is the rate, in cups per hour, at which the water was leaking from the pipe?

Answers

B because if u do 2 1/4 and 1/2 together u get the answer b

Which set represents a Pythagorean triple?
A: 27, 38, 42
B: 33, 44, 55
C: 35, 38. 42
D: 68. 72.81​

Answers

Answer:

Step-by-step explanation:

B

The set that represents a Pythagorean triple  is B: 33, 44, 55

What is a Pythagorean triple ?

A Pythagorean triple consists of three positive integers such that the square of the larger one of them is equal to the sum of the squares of the other two .

Let (a, b, c) represents a Pythagorean triple where a, b, c  are positive integer and a is the larger one  then a² = b² + c²

For A: 27 ,38, 42

Let a = 42 , b= 38 ,c= 27

= 42² = 1764

and b² + c² =  38² + 27² = 1444 + 729 = 2173

∴a² ≠ b² + c²

Thus , A: 27 ,38, 42 is not a Pythagorean triple

For B: 33 ,44, 55

Let a = 55 , b= 33 ,c= 44

⇒a² = 55² = 3025

and b² + c² =  33² + 44² = 1089 + 1936 = 3025

a² = b² + c²

Thus , B: 33 ,44, 55  is a Pythagorean triple

For C: 35 ,38, 42

Let a = 42 , b= 35 , c= 38

⇒a² = 42² = 1764

and b² + c² =  35² + 38² = 1225 + 1444 = 2669

a² ≠ b² + c²

Thus ,   C: 35 ,38, 42 is not a Pythagorean triple

For D: 68 ,72, 81

Let a = 81 , b= 68 , c= 72

⇒a² = 81² = 6561

and b² + c² =  68² + 72² = 4624 + 5184 = 9808

a² ≠ b² + c²

Thus ,  D: 68 ,72, 81  is not a Pythagorean triple

Therefore, Only set B: 33, 44, 55 represents a Pythagorean triple.

Also, Learn more about Pythagorean triple from the link below:

https://brainly.com/question/15190643

#SPJ2

marco needs to buy some cat food.At the nearest​ store, 3 bags of food cost ​17.25$. How much would marco spend on 6 of cat ​food?

Answers

Answer: $34.50

Step-by-step explanation:

If 3 bags of cat food cost $17.50 this means that 6 will be double that or $34.50.

Consider a dust mite that measures 10^-3 millimeters in length and a gecko that measures 10 centimeters long. How many orders of magnitude as long as the mite is the gecko?

Answers

The order of magnitude as long as the mite is to the gecko is 9.9999

What is Measurement?

A measurement unit is a standard quantity used to express a physical quantity.

The dust mite measures 10⁻³ millimetres in length.

The wall gecko measures 10 centimetres in length.

The orders of magnitude as long as the mite is the gecko is as follows;

1 mm = 0.1 cm

10⁻³ mm (0.001 mm)= ?

length(cm) = 0.0001 / 1 = 0.0001 cm

length of mite = 0.0001 cm

The order of magnitude as long as the mite is to the gecko is 10  - 0.0001  = 9.9999

learn more on measures here: https://brainly.com/question/24743600

can someone help please

Answers

Answer:

hope it help

Step-by-step explanation:

step by step naYn

(6x+20)+(4x+10)=180 degrees

Then simplify

10x+30=180

10x=150

x=15

Kat's dog runs around the perimeter Of a rectangular field. The diagonal Of the field is 25 yards in length and the field has a length Of 20 yards. HOW many total yards did Kat's dog run?

Answers

You figure it out lol

(400 POINTS + BRAINLIEST) Does graph b represent a proportional relationship? Give at least 2 reasons.

Answers

Answer:

Yes, because the ratios will always be the same between them, and it is a straight line

Hope this helps! :)

Answer:

yes, see explanation below...

Step-by-step explanation:

1). A graph that represents a proportional relationship means that as [tex]x[/tex] increases, [tex]y[/tex] increases.

2). The graph is a straight line through the origin.

If the height of an object at time t can be represented by
h(t) = -16t2 + 38t + 9, find h(7).

Answers

Answer:

-509

Step-by-step explanation:

h(t) = -16t² + 38t + 9

h(7) = - 16(49) + 38(7) + 9

h(7) = -784 + 266 + 9

h(7) = -509

Solution:

It should be noted:

Given equation: h(t) = -16t² + 38t + 9

To find h(7), let's find "t" by comparing h(7) and h(t).

Compare h(7) and h(t):

h(7) = h(t)=> h(7)/h = h(t)/h=> 7 = t

Now, find h(7) by substituting the value of t into the equation.

Substitute the value of t into the equation:

h(t) = -16t² + 38t + 9=> h(t) = (-16)(t²) + (38)(t) + 9=> h(7) = (-16)(7²) + (38)(7) + 9=> h(7) = -784 + 266 + 9=> h(7) = -509

Thus, h(7) is -509.

Which graph represents the equation y = (x + 2)(x-4)?

Answers

Answer:

where are the graphs?

Step-by-step explanation:

6. Moe and Curly went to Best Buy. Moe bought four CDs and five DVDs and
paid $123. Curly bought two CDs and four DVDs and paid $84. What is the
cost of one CD? What is the cost of one DVD?
(Can y’all help me out real quick please)
How do I write my two equations for this??

Answers

Answer: one CD cost $12 and  one DVD cost $15 .  

Step-by-step explanation:

In this situation we will represent the cost o one CD by x and the number of  one DVD by y.  Four CDs  plus five DVDs cost 123  so we will represent it by the equation  4x + 5y = 123  

The same or the second part of the statement. 2 CDs plus 4 DVDs cost $84  so we will also represent that by the equation , 2x + 4y = 84

Since we have two equations we will use it to solve or x and y using the elimination method.

4x + 5y = 123

2x + 4y = 84         Multiply the down equation by -2 to eliminate the x variable.

-2(2x + 4y ) = -2(84)

-4x -8y = -168    

We will now have the new equations ,

4x + 5y = 123

-4x - 8y = -168    Add both equations to      

      -3y = -45  

        y= 15  

This means each DVD cost $15 .

Now we will now have to solve for x by plotting in the value of y into the equation .

4x + 5(15) = 123

4x + 75 = 123

      -75     -75

4x = 48  

x = 12        

This also means that  one CD cost $12.

Joseph and his family were going to the beach. Joseph's sister was running late so Joseph left their house with his mom. Joseph's dad waited for his sister to get ready and left one hour later driving 75 km/hour in an effort to catch up to Joseph and mom. After
driving for four hours Joseph's dad finally caught up. How fast was Joseph's mom driving?

Select the correct response:
100 km/hour
30 km/hour
60 km/hour
50 km/hour

Answers

Answer:

60 km/hr.

Step-by-step explanation:

When Dad caught up the the time he had been  driving was 4 hours and the time Mom had been driving was 1 + 4 = 5 hours.

They both drove the same distance, d km.

For Dad:

speed = d / time

75 = d / 4

d = 75 * 4 = 300 km.

Mom took 5 hours to travel this distance, so

Mom's speed was 300 / 5 = 60 km/hr.

Step-by-step explanation:

Answer:

a solid 50 km/hour

Step-by-step explanation:

what is 5x + 7 and 2x + 3 as a verbal expression

Answers

Answer:

Five multiplied by a number increased by seven.

Two multiplied by a number increased my three.

Step-by-step explanation:

A line segment has endpoints (−3,−14) and (7,6) Which point could partition the line segment into the ratio 1:4?

Answers

m:n=1:4

[tex]\\ \sf\longmapsto P(x,y)=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]

[tex]\\ \sf\longmapsto P(x,y)=\left(\dfrac{(1)(-14)+(4)(-3)}{1+4},\dfrac{(1)(7)+(4)(6)}{1+4}\right)[/tex]

[tex]\\ \sf\longmapsto P(x,y)=\left(\dfrac{-26}{5},\dfrac{31}{5}\right)[/tex]

(12,-18),(7,-9) find the slope of this equation

Answers

Answer: 1.8

Step-by-step explanation:

(-18-(-9))/(12-7)=-9/5

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