The first three terms of an arithmetic progression are 2x, x+4, 2x - 7 respectively.
a. Find the value of x
b. Find the three terms
(6 m
c. What is the common difference?

Answers

Answer 1

Answer:

a)  x = 7.5

b)  15,  11.5,  8

c)  -3.5

Step-by-step explanation:

As there is a common difference between consecutive terms of an arithmetic progression, then:

[tex]a_3-a_2=a_2-a_1[/tex]

Given:

[tex]a_1=2x[/tex][tex]a_2=x+4[/tex][tex]a_3=2x-7[/tex]

Therefore:

[tex]\implies a_3-a_2=a_2-a_1[/tex]

[tex]\implies (2x-7)-(x+4)=(x+4)-2x[/tex]

[tex]\implies 2x-7-x-4=x+4-2x[/tex]

[tex]\implies x-11=-x+4[/tex]

[tex]\implies 2x=15[/tex]

[tex]\implies x=7.5[/tex]

Inputting the found value of x into the term expressions to find the three terms of the arithmetic progression:

[tex]a_1=2(7.5)=15[/tex][tex]a_2=(7.5)+4=11.5[/tex][tex]a_3=2(7.5)-7=8[/tex]

The common difference (d) is the difference between each consecutive term.  To find the common difference, subtract one term from the next term:

[tex]\implies d=a_3-a_2= 8 - 11.5 = -3.5[/tex]

[tex]\implies d=a_2-a_1= 11.5-15 = -3.5[/tex]

Therefore, the common difference is -3.5


Related Questions

7th grade math probability
Super easy
(Look at picture)

Answers

Answer:

3/6

I say that the probability is 3/6 because there are 3 spaces, and we are counting one spin. There are 6 spots total.

Answer:

maybe the answer is 3/5.

Do message me if the answer is wrong

how to simplify (4i)^2 ?​

Answers

Answer:

-16

Step-by-step explanation:

Simplify:

        [tex](a*b)^m=a^m * b^m\\[/tex]

        i² = -1

(4i)² = 4² * i²  

        = 16 * (-1)

       = -16

Let's examine what we know:

 [tex](ab)^x=a^x * b^x[/tex]

So, In the equation: [tex](4i)^2[/tex]

  ⇒ is equivalent to ⇒ [tex]4^2*i^2= 16 * (-1) = -16[/tex]

Answer: - 16

Hope that helps!

I don’t understand and I need the answer

Answers

Answer:

y2 + 2y + 80

Step-by-step explanation:

Hope this helpd :) Mark brainliest?

Answer:-21

Step-by-step explanation:

-21 i think but im pretty sure

There are 3 people fishing at a lake. Each person caught 5 fish. What was the total number caught by 9 people? ​

Answers

Each person caught 5 fish.

Multiply 5 fish by total people.

5 x 9 = 45

Answer: 45 fish

Answer:

45 fish

Step-by-step explanation:

Given :

Each of the 3 people caught 5 fish

Solving :

For 9 people, multiply the number caught by each into 95 × 945 fish

What is the discriminant of the quadratic equation 2x + 5x = 1?
0-18
0-16
022
24

Answers

The discriminant of the quadratic equation 2x + 5x2 = 1 is 24.

--

Use this formula

b²-4ac

Plug in

You get 24

Answer:

24

Step-by-step explanation:

Discriminant

b² - 4ac   (when ax² + bx + c = 0)

Assuming the given equation is:   2x + 5x² = 1

Rewrite the equation so that it equals zero:

⇒ 5x² + 2x - 1 = 0

Therefore,  a = 5    b = 2    c = -1

Input these into the discriminant formula and solve:

⇒ 2² - 4(5)(-1) = 4 + 20

                      = 24

Therefore, the discriminant of the quadratice equation is 24.

Can you guys help me please :(

Answers

Answer:

720 m²

Step-by-step explanation:

Area = base × height

= 12 × 6

= 72 mm²

≈ 720 m² (1 mm = 10 m)

Solve x^2 - 3x + 5 = 0.

Answers

Answer: A

Step-by-step explanation:

x^2 - 3x + 5 = 0 - quadratic equation

Standard quadratic equation form: a^2 + bx + c = 0

Here a = 1, b = -3, c = 5

Discriminant formula: D = b^2 - 4ac

D = (-3)^2 - 4*1*5 = 9 - 20 = -11 (-11 < 0 => no real roots)

x1 = (-b - sqrt(D)) / (2*a)x2 = (-b + sqrt(D)) / (2*a)

x1 = (3 - sqrt(-11)) / 2

x2 = (3 + sqrt(-11)) / 2

Which of the following is the absolute value parent function?​

Answers

Answer:

A. F(x) = |x|

Step-by-step explanation:

Any number that substitutes for x inside of the absolute value parent function will be converted to a positive. Example: |-43| = 43

Need help with this question and also need to know how to put this on a calculator. It's in the picture.​

Answers

Answer:

f(-3) = 36g(5) = -21

Step-by-step explanation:

f(x) = 3x² - 3x

g(x) = -5x + 4

Find the value of the function when x = -3:

f(x) = 3x² - 3x

f(-3) = 3(-3)² - 3(-3)

f(-3) = 3(9) + 9

f(-3) = 27 + 9

f(-3) = 36

Find the value of the function when x = 5:

g(x) = -5x + 4

g(5) = -5(5) + 4

g(5) = -25 + 4

g(5) = -21

Hope this helps!

In order to predict future housing needs the population of two towns, Appletown and Callwood, have been monitored and plotted on a graph for the past four years. The results are shown on the graph above. If both towns continue to grow at their current rates, which town will have the largest population at year 10 of the study? A

Answers

If both towns, Appletown and Callwood, continue to grow at their current rates, Callwood will have the larger population at year 10 because it is increasing exponentially.

What is exponential growth?

Exponential growth occurs when the pattern of increase is higher with the passage of time.

The formula for the exponential increase is as follows:

f(x)=a(1+r)^{x}

Where:

f(x) = exponential growth function

a = initial number or amount

r = growth rate

{x} = number of time intervals

Thus, if both towns, Appletown and Callwood, continue to grow at their current rates, Callwood will have the larger population at year 10 because it is increasing exponentially.

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14. Which is a true statement if Line XY is tangent to Circle P?

a. ab=bc
b. a^2 = bc
c. a = bc
d. a^2 = 5(b + c)​

Answers

Answer:

d. [tex]a^2 =b(b+c)[/tex]

Step-by-step explanation:

Option d is the correct answer.

Noel works as a driver for a transportation company. On average, he drives 152 hours to make 19 successful deliveries. Assume this rate is his constant rate for delivering goods. If you graph this relationship with time along the x-axis and number of deliveries along the y-axis, the slope of the line you get gives Noel's unit rate for a successful delivery. Which unit rate can be interpreted as the slope?

Answers

The  unit rate can be interpreted as the slope will give  [tex]\dfrac{1}{8}[/tex] of a delivery per hour

What is graph?

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

Given: The total time for which Noel drives = 152 hours

The total number of successful deliveries = 19

Now, Noel's unit rate for successful delivery is given by:-

[tex]\rm =\dfrac{Total\ succesful\ deliveries}{Total\ hours}=\dfrac{19}{152}=\dfrac{1}{8}[/tex]

Hence, Noel's unit rate for the successful delivery 1/8  of a delivery per hour

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Paul's mom gave him $25.00 on Monday morning to use on lunches. At his school, the school lunch costs $1.50, which he bought
Monday through Thursday. On Friday, he decided to buy 4 slices of pizza instead of buying the school lunch. If the pizza costs $1.60 per slice, then how much of the money is left at the end of the school week?
A. $18.80
B. $14.10
C. $12.60
D. $14.20

Answers

Answer:

C. $12.60

Step-by-step explanation:

he has $25.00 for the whole week

monday through thursday, or four days, he buys school lunch for $1.50

1.5 x 4 = 6

on friday, he buys 4 slices of pizza for $1.60 per slice

4 x 1.6 = 6.4

Expenses together:

6.4 + 6 = 12.4

Find what he has left:

25-12.4 = 12.6

C. $12.60

On a map. 1 inch equals 10 miles. Two cities are 2 inches apart on the map. What is the actual distance between the cities? The actual distance between the cities is miles.​

Answers

Answer:

20 mile

Step-by-step explanation:

One inch is equivalent to 10 miles. Given this comparison in regards to scale, 2 inches would simply be 2 times that. In basic terms, 2 times or inches multiplied by each 10 mile increment would be stated as 2 inches x 10 miles, resulting in a 20 mile distance between the two cities.

PLEASE HELP !!!!!!
If a prism is placed into a basin of water (density: 32.5 lb/ft3) and displaces 3.7 pounds of water, what is the volume of the water that was displaced (in cubic inches)?

Answers

The volume of the water that was displaced will be equal to 0.06 cubic feet.

How are the density, volume, and mass of a substance-related?

Suppose that a finite amount of substance is there having its properties as:

mass of substance = m kg

density of substance = d kg/m³

volume of that substance = v m³

Then, they are related as:

[tex]d = \dfrac{m}{v}[/tex]

If a prism is placed into a basin of water (density: 32.5 lb/ft3) and displaces 3.7 pounds of water, then the volume of the water that was displaced will be

We know that the density of the water is 62.4 pounds per cubic foot.

Then we get

3.7 = 62.4 × volume

Volume = 0.059

Volume ≅ 0.06 cubic-foot

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Step-by-step explanation:

' MLB

ML Ĺ

bryon yuuù 6553w2 wasmay what is this portion insulator used for

What is the name of this polygon? rhombus rectangle square trapezoid A quadrilateral. What is the name of this polygon?

rhombus

rectangle

square
trapezoid
A quadrilateral. Each angle has a small square.ach angle has a small square.

Answers

Step-by-step explanation:

Rectangle: A quadrilateral with four right angles; a rectangle is a type of parallelogram. Square: A quadrilateral with four congruent sides and four right angles; a square is both a rhombus and a rectangle. Trapezoid: A quadrilateral with exactly one pair of parallel sides (the parallel sides are called bases)

Can someone answer theese questions I WILL GIVE BRAINLIST and thanks and a 5 star if they are correct

Answers

The first question I think it’s A because 1.13 is larger than 1.2
I hope this helps

Two lines intersect at a point, forming angle 1, angle 2, angle 3, and angle 4.
Angle 1 and angle 3 are vertical angles.
Angle 2 and angle 4 are vertical angles.
m angle1 = 70
What is the measure of angle 2?
O 20°
O 70°
O 90°
O 110°

Answers

the measurement of angle 110°

valuate if x = 2 and y = 6 4x + 5y

Answers

Answer:

38

Step-by-step explanation:

4(2)+5(6)

=8+30

The answer=38

Chihuahua ccfyi case sweet

The residents of a city voted on whether to raise property taxes. The ratio of yes votes 5 to 8 no votes was
to
. If there were 7761
total votes, how many yes votes were there?

Answers

Answer:

2985 yes votes.

Explanation:

Yes : No

5x : 8x

Total Ratio: 5x + 8x = 13x

Solve for x

13(x) = 7761

divide both sides by 13

x = 597

Yes-Votes: 5(x) = 5(597) = 2985

No-Votes: 8(x) = 8(597) = 4776

A boat takes 2 hours to travel 15 miles upriver against the current. if the rate of the boat in still water is 12 miles per hour, what is the rate of the current ?

Answers

Answer:

4.5 mph or 9/2 mph

Step-by-step explanation:

Let x be the rate of the current

Formula: Distance = rate x time

where rate upstream =(12-x) and time =2 hours

15=(12-x)(2)

15=24–2x

2x=24–15

2x= 9

x=9/2=4.5 miles per hour (rate of current)

The swimming pool at Spring Valley High School is a rectangle with a width of 60 meters and a length of 30 meters. Around the perimeter of the pool is a tiled floor that extends w meters from the pool on all sides. Which expression represents the area of the tiled floor?

A. (2w2 + 90w) m2
B. (6w2 + 120w + 875) m2
C. (4w2 + 180w + 1800) m2
D. (4w2 + 180w) m2

Answers

Answer:

d.  (4w2 + 180w) m2

Step-by-step explanation:

Area of tiled floor = (area of tiled floor+ pool ) - area of pool

area of pool =l x b = 30 x 60 =1800  ...............a

length of pool + tiled floor = 30+2w

breadth of pool + tiled floor = 60+2w

Hence, (area of tiled floor+ pool ) =

(30+2w) x(60+2w) = 1800+60w+120w+4w2 = 1800 + 180w+4w2.....b

b-a =(1800+ 180w+4w2)- 1800 = 4w2 + 180w

I need help on question b

Answers

Answer:

B=25

Step-by-step explanation:

Simply plug in 10 where x is

2(10)2(10-5)/10(10) = 25

Britney is buying a shirt and a hat at the mall. The shirt costs $30.50, and the hat costs $19.75. If Britney gives the sales clerk$100.00, how much change should she receive? (Ignore sales tax.)
A. $49.75
B. $50.25
C. $59.50
D. $46.65

Answers

Answer: A. 49.75
Explanation:
Add 30.50 and 19.75 to get 50.25
Subtract 100-50.25 to get 49.74
Hope it helped!

One angle in a pair of supplementary angles has a value of 2x. The other angle is 30 degrees less than two times the first angle. Which of these equations can be used to find the measurement of each angle?
6x-30=90
6x+60=90
6x-30=180
6x+60=180

Answers

The equations which can be used to find the measurement of each angle will be 6x-30=180.

What is the supplementary angle?

The supplementary angles are defined as the angles whose sum is equal to 180°.

It is given that:-

One angle in a pair of supplementary angles has a value of 2x

The other angle is 30 degrees less than two times the first angle.

Now from the first condition, One angle in a pair of supplementary angles has a value of 2x we can write that:-

2x   +    A   =     180 .........................1

Now from the second condition,The other angle is 30 degrees less than two times the first angle

A     =    4x  -   30 ..............................2

Hence from the above two equations put the value of A in equation 1

the equation will be:-

2x    +   4x    -   30    =    180

6x      -      30        =   180

Hence the equations which can be used to find the measurement of each angle will be 6x-30=180.

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Question 1:
Your goal this year is to earn a B or better in Algebra class.
If you do, your parents said they would give you $200.
Write an inequality to represent the grades you can earn
and receive money from your parents for it. Then explain
the graph for the inequality. Hint: Remember you cannot
earn higher than a 100 in any class.

Answers

[tex]b \geqslant x \leqslant a[/tex]

the table shows the enrollment in a university class so far, broken down by student type.
adult education 7
graduate 2
undergraduate 9
Considering this data, how many of the next 12 students to enroll should you expect to be undergraduate students?

Answers

Answer:

6

Step-by-step explanation:

The number of students in the next 12 to enroll should you expect to be undergraduate students is 6.

What is Probability?

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

From the table,

Total number of students = 7 + 2 + 9 = 18

Number of undergraduates = 9

Probability of having a undergraduate student to enroll = 9/18 = 1/2

When the next 12 students are enrolled,

Number of undergraduates = 1/2 × 12 = 6

Hence 6 students are expected to be undergraduates in the next 12 students.

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On June 1, Bonnie's car had 23,825 miles. On
September 1, her car had 24,385 miles. What is
the average rate of change?

Answers

560 miles is correct

Step-by-step explanation:

well, it changed by 560 miles overall. in a matter of 3 months.

but for the rate of change I have to ask what is the unit of time for that consideration ?

the rate of change is the change of the functional value over an interval divided by the length of the interval.

if 3 months is the unit of time, then the change rate is 560/1 = 560 miles per quarter.

if the unit of time is 1 month, then the change rate is 560/3 miles per month.

if the unit of time is days, then we have 30+31+31 = 92 days in that interval, and the change rate is 560/92 = 140/23 miles per day.

and so on.

Find the measure of each angle in the diagram.

Answers

The measure of each angle in the diagram are 4y° = -82°, (6y - 41)° = 164°, (3x + 2)° = 98°, 2(x + 17)°= 98

What are vertical angles?

Each of the pairs of opposite angles made by two intersecting lines is called a vertical angle.

Two lines are intersecting each other at a point making two pairs of vertical angles.

The pair of vertical angles are equal in measure.

4y° = (6y + 41)° [Vertical angles]

4y - 6y = 41

2y = -41-----(1)

(3x + 2)° = 2(x + 17)° [Vertical angles]

(3x + 2)° = 2x + 34°

x = 32 ------(2)

Therefore, 4y° = -82°

(6y - 41)° = 164°

(3x + 2)° = 98°

2(x + 17)°= 98

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to win at lotto in one state one must correctly select 7 numbers from a collection of 57 numbers. how many different selections are possible

Answers

57C7, the answer is 264,385,836 different selections
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