Mathematics High School

Determine whether each sequence below is arithmetic, geometric, or neither. Provide support for you conclusions. sequence1: 1/2, 7/6, 11/6, 5/2

Answers

Answer 1

The sequence 1/2, 7/6, 11/6, 5/2 is an arithmetic sequence

The given sequence is:

[tex]\frac{1}{2}, \frac{7}{6},\frac{11}{6},\frac{5}{2}........[/tex]

A sequence is an arithmetic sequence if it has a common difference d

In the given sequence:

[tex]T_1=\frac{1}{2} , T_2 = \frac{7}{6}, T_3=\frac{11}{6}, T_4=\frac{5}{2}[/tex]

[tex]T_2-T_1=\frac{7}{6}-\frac{1}{2} \\\\T_2-T_1=\frac{2}{3} \\\\T_3-T_2=\frac{11}{6}-\frac{7}{6} \\\\T_3-T_2=\frac{2}{3}[/tex]

Since the sequence has a common difference of 2/3, it is an arithmetic sequence

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Related Questions

three teachers have purchased candy for a school carnival. each bag of candy weigh is 1 1/4 pounds

Answers

Answer:

3 * 1.25 = 3.75

Step-by-step explanation:

3.75 also equals 3 3/4

hi please help, I can't understand.
If the sides of a rectangle with area 12cm² are (3x-2) and (x+1)
a)X-? b)P-?

Answers

The sides of a rectangle with area 12cm² are (3x-2) and (x+1).We know, area of a rectangle = length × breadthTherefore, by the problem

[tex](3x - 2)(x + 1) = 12 \\ = > {3x}^{2} - 2x + 3x - 2 = 12 \\ = > {3x}^{2} + x - 2 = 12 \\ = > {3x}^{2} + x - 12 - 2 = 0 \\ = > {3x}^{2} + x - 14 = 0 \\ = > {3x}^{2} + 7x - 6x - 14 = 0 \\ = > x(3x + 7) - 2(3x + 7) = 0 \\ = > (x - 2)(3x + 7) = 0 \\ = > x = 2 \: \: \: or \: \: \: \frac{ - 7}{3} \\ [/tex]

But a negative number cannot be the side of a rectangle.So, x = 2 cmNow, length = (3x - 2) = (3 × 2 - 2) cm = (6 - 2) cm = 4 cmBreadth = (x + 1) = (2 + 1) cm = 3 cm.We know, perimeter of a rectangle = 2( length + breadth)Therefore, the perimeter of the rectangle

[tex] = 2(4 + 3)cm \\ = 2 \times 7cm \\ = 14cm[/tex]

Answer:

The value of x is 2 cm and the perimeter of the rectangle is 14 cm.

Hope you could get an idea from here.

Doubt clarification - use comment section.

So first of all u have to make an equation. u know that length times width is the area 12. (3x-2) multiplied by (x+1) which is 3x^2+3x-2x-2 then simplified its 3x^2+x-2. THEN MAKE IT EQUAL TO 12 BC 12 IS THE AREA. so 3x^2+x-2=12 then use the quadratic formula to find x u can either use quadratic formula or factorising. I used factorising to get (x-2)(3x+7)=0 x=2 or x=-7/3. Sub in 2 into the equation 3x^2+x-2=12 to get 3(2)^2+2-2=12 so it will be 36+2=38 and then 38-2=36. That doesn’t sum up 12 so that isnt x. Then sub in -7/3 as x. So 3(-7/3)^2+(-7/3)-2. When u multiple that out it will give you 12. SO X IS 12. Then to work out the perimeter double the sides given (3x-2) and (x+1). That will be 6x-4+2x+2. Simplify to get to 8x-2. Then sub in your x (-7/3) to get 392/9. If u want u can leave it as a fraction or decimal 43.55555… where 5 is recurring. That is your perimeter. It looks confusing but trust me you will get :). Thank you

A small bag of trail mix contains 3 cups of dried fruit and 4 cups of almonds. A large bag contains $4 1/2 cups of dried fruit and 6 cups of almonds. Write and solve a system of linear equations to find the price of 1 cup of dried fruit and 1 cup of almonds. Let f represent the price of one cup of dried fruit and let a represent the price of one cup of almonds.What is the equation for the small bag and the large bag.

Answers

Answer:

Let's call:

f = price of 1 cup of dried fruit

a = price of 1 cup of almonds

In order to build the linear system, you need to consider that the total price of a bag is given by the sum of the price of cups times the number of cups in each bag, therefore:

Solve for a in first equation:

a = (6 - 3f) / 4

Then substitute in the second equation:

41/2 f + 6 · (6 - 3f) / 4 = 9

41/2 f + 9 - 9/2 f = 9

16 f = 0

f = 0

Now, substitute this value in the formula found for a:

a = (6 - 3·0) / 4

= 3/2 = 1.5

Hence, the cups of dried fruit are free and 1 cup of almond costs 1.5$

Step-by-step explanation:

Sam currently 100 followers on TikTok, and gains 8 subscribers a week. Alex currently has 220 followers, and gains 3 followers each week.
Part A: Set up a system of equations to shows each person's subscribers. (2 points)
Part B: After how many weeks will Sam and Alex have the same number of subscribers? (1 point)
Part C: How many subscribers will Sam and Alex have when their subscriber count is equal? (1 point)

Answers

Part A: The system of equations to shows each person's subscribers is:

S = 100 + 8x

A = 220 + 3x

Part B: Sam and Alex will have the same number of subscribers after 24 weeks

Part C: Sam and Alex will have 292 subscribers when their subscriber count is equal

Let the number of weeks be x

The initial number of followers that Sam has = 100

Sam gains 8 subscribers every week

Let the total number of subscribers that Sam has be S

The equation that represents Sam's total subscribers is:

S = 100 + 8x..................(1)

The initial number of followers that Alex has = 220

Alex gains 8 subscribers every week

Let the total number of Alex's subscribers be A

A = 220 + 3x....................(2)

If Sam and Alex have the same number of subscribers:

S = A

100 + 8x = 220 + 3x

8x - 3x = 220 - 100

5x = 120

x = 120/5

x = 24

Sam and Alex will have the same number of subscribers after 24 weeks

To find the number of subscribers that Sam and Alex will have when their subscriber count is equal, substitute x = 24 into equation (1)

S = 100 + 8x

S = 100 + 8(24)

S = 292

Sam and Alex will have 292 subscribers when their subscriber count is equal

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If ARST = ANPQ, which of the following is true?

Answers

Answer:

T=Q

Step-by-step explanation:

They are in te same position on the comparison

If the average ticket price for movie A in its first week was 1.4 times the average ticket price in its third week, what was the average ticket price for movie A in its first week?

Answers

8.35x1.4= $11.69 So the ticket price for movie A in its first week would be $11.69

Hope this helped :)

Sketch the graph of each line

Answers

The standard equation of a line is y = mx+ b

where:

m is the slope of the lineb is the y-intercept of the line

The y-intercept is the point where the line cuts the y-axis

For the equation y = -2x -4

For the equation, the line will cut the y-intercept at y = -4 with a negative slope of -2.

For the equation y = -5/2x

For the equation, the line will cut the y-intercept at y = 0 with a negative slope of -5/2.

Find the graphs attached.

Learn more on graphs here: https://brainly.com/question/25020119

how do i solve this

Answers

Answer:

m <E = 134

Step-by-step explanation:

Triangle DEF looks like an isosceles triangle to the base angles are the same measure.

6x+11 = 10x+3

Subtract 11 from both sides

6x = 10x-8

Subtract 10x from both sides

-4x = -8

Divide -4 from both sides

x = 2

Substitute 2 into both equations to make sure it works

6 (2) + 11

12+11

10 (2) +3

20+3

Both angles equal 23 degrees.

Now subtract both angles from the total angle measure of 180.

180-23-23=134

Point O is the center of this circle. What is m CAB?
A.55
B.48
C.45
D.35

Answers

Answer is B. 48

By circle theorem, the angle at the centre of the circle is twice the angle at the circumference.

Find the slope of the line containing the points (3,2) and (6,9).

Answers

Answer:

7/3

Step-by-step explanation:

Which congruence criteria is met in the following scenario?
HL
ASA
SSS
AAS
SAS

Answers

SSS. the side they share is the same and it tells you the other two sides of both triangles are congruent.

3. Mama has her opinions about things concerning Walter. Determine which statements are TRUE/FALSE about what Mama thinks.

Answers

Answer:

False

Step-by-step explanation:

Hope this helped

The sum of a number and six is 22. What is the number?

Answers

Answer:

Step-by-step explanation:

22-6=16 16+6=22

hope this helps! :)

16 because if you add 16 you should get your answer

order the numbers from least to greatest .

Answers

least to greatest

-4.5

-4

-3 1/2

-3

2.5

Answer:

-4.5, -4, -3 1/2, 2.5, 3

Step-by-step explanation:

evaluate p-q if p=14 and q=13

Answers

Answer:

Value of [tex]p-q=1[/tex]

Step-by-step explanation:

We need to find [tex]p-q[/tex]

[tex]p-q=14-13\\\\=1[/tex]

[tex]\huge\boxed{\sf{Hello\:there!}}[/tex]

We are asked to evaluate p-q.

Now, if we aren't given the value of every variable, evaluating this expression is impossible. However, we do have the value of p (14) and the value of q (13)

We plug these numbers instead of the variables:

p-q

p=14

q=13

14-13

Hence, the value of the expression is 1.

[tex]\huge\boxed{\sf{Hope\:it\:helps.\:Please\:mark\:Brainliest.}}[/tex]

[tex]\huge\bold{Good\:luck!}}[/tex]

[tex]\huge\mathfrak{LoveLastsAllEternity}[/tex]

71 points what is 12x 8=...........................96

Answers

Answer: 12 x 8 = 96

Step-by-step explanation:

Thanks c:

Dont know how to calculate it

Answers

Answer:

AB = 105

Step-by-step explanation:

Since ∠ A and ∠ B are equal then Δ ABC is isosceles with 2 congruent legs.

AC = BC , substitute values

6x - 7 = 5x + 7 ( subtract 5x from both sides )

x - 7 = 7 ( add 7 to both sides )

x = 14

Then

AB = 7x + 7 = 7(14) + 7 = 98 + 7 = 105

Given that two terms of an arithmetic sequence are u5 = -3.7 and u15 = -52.3, find the value of the 19th term.

Answers

Answer:

a19 = -71.74

Step-by-step explanation:

The general term of an arithmetic sequence with first term a1 and common difference d is ...

an = a1 +d(n -1)

The given 5th and 15th terms tell us ...

-3.7 = a1 +d(5 -1)

-52.3 = a1 +d(15 -1)

Subtracting the first of these equations from the second, we find ...

10d = -48.6

d = -4.86 . . . . . . divide by 10

The 19th term will be ...

a19 = a1 +d(19 -1)

Subtracting the 15th term from this, we find ...

a19 -a15 = 4d

a19 = 4d +a15 = 4(-4.86) +(-52.3)

a19 = -71.74

can someone help me figure this out

Answers

Answer:

b ≥ 8

Step-by-step explanation:

b + 4 + 2(-2b + 4) ≤ -12

b + 4 - 4b + 8 ≤ -12

-3b + 12 ≤ -12

-3b ≤ -24

b ≥ 8

Complete the pairs of corresponding parts if RST=TXY

Answers

Answer:

R ⇔ TS ⇔ XT ⇔ YRS ⇔ TXRT ⇔ TYST ⇔ XY

Step-by-step explanation:

Corresponding parts are listed in the same order in the congruence statement:

RST ≅ TXY

R ⇔ T

S ⇔ X

T ⇔ Y

RS ⇔ TX

RT ⇔ TY

10 divided by 3 step-by-step guideStep 1

The first step is to set up our division problem with the divisor on the left side and the dividend on the right side, like we have it below:

3| 10

Step 2

We can work out that the divisor (3) goes into the first digit of the dividend (1), 0 time(s). Now we know that, we can put 0 at the top:

_0_

3 | 10

Step 3

If we multiply the divisor by the result in the previous step (3 x 0 = 0), we can now add that answer below the dividend:

_0_

3 | 10

Step 4

Next, we will subtract the result from the previous step from the second digit of the dividend (1 - 0 = 1) and write that answer below:

___

3 | 10

- 0

Step 5

Move the second digit of the dividend (0) down like so:

__0_

3 | 10

- 0

-----------

Step 6

The divisor (3) goes into the bottom number (10), 3 time(s), so we can put 3 on top:

__03_

3 | 10

- 0

___

Step 7

If we multiply the divisor by the result in the previous step (3 x 3 = 9), we can now add that answer below the dividend:

_03_

3 | 10

- 0

Step 8

Next, we will subtract the result from the previous step from the third digit of the dividend (10 - 9 = 1) and write that answer below:

__03_

3 | 10

- 0

-9

So, what is the answer to 10 divided by 3?

Your answer is the top number, and any remainder will be the bottom number. So, for 10 divided by 3, the final solution is:

3 - Remainder 1Extra calculations for you:Using a calculator, if you typed in 10 divided by 3, you'd get 3.3333.You could also express 10/3 as a mixed fraction: 3 1/3If you look at the mixed fraction 3 1/3, you'll see that the numerator is the same as the remainder (1), the denominator is our original divisor (3), and the whole number is our final answer (3).

Help asap pls!!! Put steps if possible 3

Answers

Answer:

i. 15.4

ii.45.2

Step-by-step explanation:

correct me if im wrong

tnx

a cook starts baking pies at the clock shown below. The first pie is done 25 min later. The 2nd pie is done 30 min later after the first pie which clock shows when the second pie was done

Answers

Answer:

1:45 pm

Step-by-step explanation:

its the hand thats a littke more on the left after 6

Find the slope-intercept form of the line whose slope 5 is and that passes through the point (-5,8).

The equation of the line is

Answers

Answer:

y=5x+33

Step-by-step explanation:

y-y1=m(x-x1)

y-8=5(x-(-5))

y-8=5(x+5)

y=5x+25+8

y=5x+33

The temperature dropped 4 1/2 degrees each hour for 5 hours. By how many degrees did the temperature fall during those five hours?

Answers

Answer:

22.5

Step-by-step explanation:

You take the unit rate and multiple that by how many hours are going by. 4.5x5

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