The 2th term of The A.P is 7 and 4th term is 28 Find The Common difference and The first term.
help me please

Answers

Answer 1

Answer:

d = 10.5, a₁ = - 3.5

Step-by-step explanation:

The n th term of an AP is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₂ = 7 and a₄ = 28 , then

a₁ + d = 7 → (1)

a₁ + 3d = 28 → (2)

Subtract (1) from (2) term by term to eliminate a₁

2d = 21 ( divide both sides by 2 )

d = 10.5 ← common difference

Substitute d = 10.5 into (1)

a₁ + 10.5 = 7 ( subtract 10.5 from both sides )

a₁ = - 3.5 ← first term


Related Questions

Find -0.5D D=[18. 16] [-14 -6]
Options are: A. [9 8] [-14 -6] B. [9 8] [7 3] C. [9. 8] [-7 -3] D. [-9 -8] [7 3]

Answers

Answer:

The correct answer is Option D: [-9 -8] [7 3]

Step-by-step explanation:

Given that

D = [18 16][-14 -6]

We have to find -0.5D

In order to find the required values of D we only have to multiply the individual elements with -0.5, this might change the signs of elements and reduce the magnitude.

So,

[tex]-0.5D = [-0.5*18\ \ -0.5*16][-0.5*-14\ \ \ -0.5*-6]\\-0.5D =[-9\ \ \ -8][7\ \ \ 3][/tex]

Hence,

The correct answer is Option D: [-9 -8] [7 3]

what is x ? pleasee help !!!

Answers

Answer:

It is an unknown number but add 16 + 32 degrees and you get 48x degrees then multiply 48 X 72 degrees and you get 336 degrees.

Step-by-step explanation:

WILL MARK BRAINLIEST !!!! Which equation is an equation of a circle with a radius of 3 and its center is at (5, -2)?

(x - 5)² + (y + 2)² = 3

(x - 5)² + (y + 2)² = 9

(x + 5)² + (y – 2)² = 3

(x + 5)² + (y - 2)² = 9

Answers

Answer:

the first one

Step-by-step explanation:

Answer:

(x + 5)² + (y – 2)² = 3

Step-by-step explanation:

A Cinema has 240 seats. 144 seats were sold for the current movie. What percent of seats are empty?

Answers

240 - 144 = 96

96/240 = 0.4 = 40%

Emma made a scale model of the Sam Houston's monument. The monument's actual height is 67 ft tall. Emma is using a scale where 1 inch is 10 ft. What is the height of Emma's model?

Answers

Answer: 6.7inch

Step-by-step explanation:

From the question, we are informed that Emma made a scale model of the Sam Houston's monument and that the monument's actual height is 67 ft tall but Emma is using a scale where 1 inch is 10 ft.

The height of Emma's model will therefore be 67ft divided by 10 since he's using a scale of 1:10. This will be:

= 67/10

= 6.7inch

Please help me with this

Answers

Answer:

emily 37.44$ Andy 22.15$

Step-by-step explanation:

Andy needs 23 feet multiply 23 feet by 12 you get the amount of inches so 276 inches if the cost for 130 inches is 10.40 we need to increase this number proportionally to 276 So 130+113%=276.9 so 276. Now 10.40x113%=22.15.

Emily needs 13 yards, 13 yards is 39 feet, 39 feet is 468 inches, Now do same thing we did for Andy. 130+360%=468 exactly 10.40+360%=37.44

does this graph represent a function? if yes why?

Answers

Yes, it is a function because each member in the domain is assigned to exactly one member in the range

Simplify each and state the excluded values.
8x^3/12x^2+16

Answers

Answer:

Cancel the common factor of 8 and 12x²+6.

Tap for more steps...

4x³/6x²+3

Factor 3

out of 6x²+3.

4x³/3(2x²+1)

Step-by-step explanation:

What is the equation of the line that has a slope of 1/3 and goes through the point (6,−2)?

A. y = 1/3x − 4
B. y = 1/3x + 4
C. y = 1/3x − 8
D. y = 1/3x

Answers

Answer: A) y = 1/3x − 4

Step-by-step explanation:

Find the Equation Using Point-Slope Formula

slope: 1/3

point: (6, −2)

Use the slope 1 and a given point (6, −2) to substitute for [tex]x_1[/tex]  and [tex]y_1[/tex]  in the point-slope form  

y - [tex]y_1[/tex] = m(x - [tex]x_1[/tex]), which is derived from the slope equation m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

  y − (−2) = 1/3 ⋅ (x − (6))

Simplify the equation and keep it in point-slope form.

  y + 2 = 1/3 ⋅ (x − 6)

Solve for y.  

  1/3 ⋅ (x − 6).

Apply the distributive property.

  y + 2 =  1 /3 x +  1 /3 ⋅ − 6

Combine 1/3 and x.

  y + 2 =  x/3 +1/3 ⋅ −6

Cancel the common factor of 3.

  y + 2 =  x /3 − 2

Move all terms not containing y to the right side of the equation.

Subtract 2 from both sides of the equation.

  y = x/3 − 2 − 2

Subtract 2 from −2. x

  y = x/3 − 4

Reorder terms.

  y = 1/3x − 4

List the equation in different forms.

Slope-intercept form:  

y = 1/3x − 4

Point-slope form:

y + 2 = 1/3 ⋅ (x − 6)

A bear cub walks
5/6 miles in 5/12
age
hours. What is its
speed in terms of miles per hour?

Answers

Answer:use math(way

Step-by-step explanation

It help

Answer: 2 miles per hour

Step-by-step explanation: Reduce the common factor which would be 5 and then you divide and you get 2

29% expressed as a fraction in simplest form is?

Answers

The Answer: 7.25/25

Hope this helps!

In Mr. Layden's class, three students
brought in their baseball card
collections. For their three
collections, the mode was 126 and
the range was 26. What are two
possibilities for the number of cards
in each student's collection?

Answers

Answer: 126, 126, 152

or

100, 126, 126

Step-by-step explanation:

ben jogged 4 1/2 miles in 1 1/4 hours at a constant rate. how far did ben jog in one hour

(the answer on top)

Answers

Answer:

b is the answer

Step-by-step explanation:

4 1/2 divided by 1 1/4 = 3 3/5

The distance Ben jogged in one hour is 3 3/5 miles. The correct option is B. 3 3/5 miles

Distance, Rate, and Time

From the question, we are to determine how far Ben jogged in one hour. That is, how far he jogged per hour.

This means we should determine the rate

Using the formula,

Rate = Distance / Time

From the given information,

Distance = 4 1/2 miles

Time = 1 1/4 hours

∴ Rate = 4 1/2 ÷ 1 1/4

Rate = 3 3/5  miles/hour

Hence, the distance Ben jogged in one hour is 3 3/5 miles. The correct option is B. 3 3/5 miles

Learn more on Calculating Rate here: https://brainly.com/question/20654411

#SPJ2

PLEASE HELP ME PLEASEEEEEEEEEEE
A triangle is inscribed in a square, as shown. Write a simplified function r​ in terms of x​ that represents the area of the shaded region.

Answers

Answer:  0.5x^2

This is the same as (1/2)x^2 because 1/2 = 0.5

We could rewrite that into [tex]\frac{x^2}{2}[/tex]

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

Explanation:

The base of the white triangle (aka unshaded region) is x, while the height is also x

The area of the white triangle is

A = 0.5*base*height

A = 0.5*x*x

A = 0.5*x^2

The area of the entire square is x*x = x^2. Subtract off the area of the white triangle to get the area of the two blue shaded regions combined

shaded region = (square area) - (white triangle area)

shaded region = (x^2) - (0.5x^2)

shaded region = x^2 - 0.5x^2

shaded region = 1x^2 - 0.5x^2

shaded region = (1-0.5)x^2

shaded region = 0.5x^2

So the white triangle occupies half of the square, while the blue shaded region occupies the remaining 50% of the square.

Because 0.5 = 1/2, we can write this as (1/2)x^2, but I think using decimals in this case is easier.

Happy Paws charges $22.00 plus $4.50 per hour to keep a dog during the day. Woof Watchers charges $11.00 plus $5.75 per hour. Write an equation and solve it to find for how many hours the total cost of the services is equal. Use the variable h to represent the number of hours.

Answers

Answer:

Total amount charged by Happy Paws = 22 + 4.50h

Total amount charged by Woof Watchers =  11 + 5.75h

3.2 hours

Step-by-step explanation:

Total amount charged by Happy Paws = 22 + 4.50h

Total amount charged by Woof Watchers =  11 + 5.75h

22 + 4.50h =  11 + 5.75h

Collect like terms

22 + 11 = 4.5h + 5.75h

33 = 10.25h

Solve for h

33/10.25 = h

h = 3.22

Jenn wants to measure the height of a tree. She walks exactly 125 feet from the base of the
tree and looks up. The angle of elevation from the ground to the top of the tree is 33º. How
tall is the tree? Which equation would be used to solve this problem?

Answers

Answer:

[tex]81.2\:\mathrm{ft}[/tex]

Step-by-step explanation:

We can form a right triangle and use basic trig for a right triangle to solve this problem:

[tex]\tan33^{\circ}=\frac{h}{125}[/tex], where [tex]h[/tex] is the height of the tree.

Solving, we get:

[tex]h=125\cdot \tan 33^{\circ},\\h\approx \fbox{$81.2\:\mathrm{ft}$}[/tex].

The sum of the angle measures of any triangle is 180°. If one angle of a triangle measures 35º and another angle measures 72º, what is the measure of the third angle?​

Answers

Answer:

73°

Step-by-step explanation:

Start with 35° + 72° = 107°

Then 180° - 107° = 73°

Answer:

[tex]we \: knw \: that \: total \: angle = 180 \\ 35 + 72 + x = 180 \\ 107 + x = 180 \\ x = 180 - 107 \\ x = 73 \\ thank \: you[/tex]

At the science fair, Adriana uses 8 fluid ounces of vinegar to make her volcano erupt. How many times can she make her volcano erupt with 1 quart of vinegar?

Answers

Answer:

4 times

Step-by-step explanation:

We known that 1 quart is equivalent to 32 fluid ounces

Suppose each eruption consumes 8 fluid of ounces, if we also assume that the amount of vinegar required per eruption is constant, then the number of times Adriana can make her volcano erupt is

n = 32 / 8

n = 4 times

Adriana can make her volcano erupt 4 times with 1 quart of vinegar

The sum of 5 times one number, x, and 4 times a second number, y, is 87. If the sum of the two numbers is 20, find the two numbers. Pls hurry need it before schools is over
(hint will mark brainiest)

Answers

Step-by-step explanation:

We have 5x + 4y = 87 and x + y = 20.

=> 5x + 4y = 87 and 4x + 4y = 80.

5x + 4y = 87

- (4x + 4y = 80)

=> x = 7

Therefore (7) + y = 20, y = 13.

The answers are x = 7 and y = 13.

What is the surface area of a right cylinder which has a base with radius 9 units and has a height of 12 units
оооо
508.7 units squared
678.2 units squared
1,186.9 units squared
1,256.0 units squared

Answers

1,186.9 units squared

2 equivalent rations for 6/5 ? please help !!!

Answers

Answer: 12/10 and 24/20
Explanation if you simplify these fractions it’s becomes 6/5

PLEASE HELP! WILL MARK BRAINLIEST

Answers

The third option. Lmk if u need work
The third I believe :)

A real estate agency an agent salty house for 313,000. The commission rate is 4.5 for the real estate agency in the commission rate for the agent is 20% of the amount the real estate agent gets. How much did the agency make on the house? How much did the agent earn in comission

Answers

Answer:

313000/100 X 4.5 = 14085

14085/100 X 20 = 2817

14085 - 2817 = 11268

agency = 11268

agent = 2817

HELP NEEDED HELP NEEDED!

Answers

I think it is j but I do not now

Answer:

G. 8.625 [tex]ft^{2}[/tex]

Step-by-step explanation:

Area of first rectangle:

1.5 × 2.5 = 3.75 ft

Area of second rectangle:

1.5 × 2.5 = 3.75 ft

Area of triangle:

1.5 × 1.5 = 2.252.25 ÷ 2 = 1.125

Put them together:

3.75 + 3.75 + 1.125 = 8.625 [tex]ft^{2}[/tex]  

I hope this helps!

solve h+9.7=-9.7 and show me the steps​

Answers

Answer:

h = -19.4

Step-by-step explanation:

1. Take the constant on the left side of the equation by changing the positive to a negative ---> h = -9.7 -9.7

2. Solve the right side, and you have yuor answer. ---> h = -19.4

Please help me lol!!!!!!

Answers

Answer:

A

Step-by-step explanation:

Im pretty sure it’s “ A “

help me plez There are 100 bolts in 5 bookcases.

What is the unit rate in bolts per bookcase?


2 bolts per bookcase

20 bolts per bookcase

50 bolts per bookcase

200 bolts per bookcase

Answers

20 bolts per bookcase

Answer:

20 bolts per bookcase

Step-by-step explanation:

Paul volunteered at the senior center for 3 9/10 hours on Saturday and 5 1/6 hours on Sunday. How many hours did Paul volunteer at the senior center on both days?

Answers

Answer:

Saturday 3 9/10 hours = 60/10 = 6, 6 X 9 =54

3 hours 54 mins

Sunday 5 1/6 hours = 60/6 = 10, 10 X 1 = 10

5 hours 10 mins

3 hrs 54 mins + 5 hrs 10mins = 9 hrs 4 mins

Answer:9 4/10

Step-by-step explanation:

1 I am thinking of a 6-digit number. • The sum of the digits is 38. • The number is under 600 000. What could my number be? Find twelve different possibilities.

Answers

Answer:

A 6 digit number can be written as:

abcdef

Where each letter represents a single digit.

We know that this number is smaller than 600,000, and we also know that:

a + b + c + d + e + f = 38

Now, we have a lot of variables, so we can play a little.

I will suppose that:

f = 6

e = 7

d = 3

c  = 9

then we have:

a + b + 9 + 3 + 7 + 6 = 38

a´+ b + 25 = 38

a + b = 38 - 25 = 13

now let's suppose that b = 8

a + 8 = 13

a = 13 - 8 = 5

Then our number is:

589,376

This number is smaller than 600,000, and if we add the sum of the digits is 38.

Now we want to find 11 other numbers like this.

We can simply change the places of some of the digits, like:

598,376  (also meets the condition)

Where i just changed the positions of the 9 and the 8.

589,367  (also meets te condition)

Where i just changed the position of the 6 and 7.

Now just keep doing that, only take care that the number can not be larger than 600,000, so i will leave the first 5 fixed in that position.

589,673 (also meets the condition)

598,736 (also meets the conditions)

536,798  (also meets the conditions)

536,897  (also meets the conditions)

536,978  (also meets the conditions)

563,798  (also meets the conditions)

563,987  (also meets the conditions)

563,879  (also meets the conditions)

573,689  (also meets the conditions)

573,869  (also meets the conditions)

Calculate the pay for the following day of a
weekly time card given a wage of $13/hr.
Name
Week of:
Morning
In Out
Monday 08:00 12:00
Afternoon
In Out
12:45
17.30
pay = $[?]
Round your answer to the nearest hundredth.
Please help if you can.

Answers

Answer:

dfsfsffsfsdfsfsfsfsfsfsefsfsdfsff

Step-by-step explanation:sfsfsfsf

fsfsfdfdsfsdfsfsf

Other Questions
determine the intercept of the line. why did Jerry keep repeating the number 115 in through the tunnel? Someone pls help! X*2(4x+3^2%)/23/21^2 Grade it Now scoring options Averaging: The score that is reported to your instructor is the average score of your attempts as of the deadline, including any work you have saved but not submitted for grading. For example, in the following table, the final score is 6.3 because it is the average of the (4106.3). 4,10 three scores Keep the Highest: Your score is calculated by taking the highest score of the attempts you make. Using the example in the following table, the final score is 10 because it is your highest scote. The other attempts are not counted. Do No Harm: The goal of this method is to encourage you to practice without fear of decreasing your score. Your first attempt is your base score; the second attempt counts and is averaged with the first only if it is higher than the first; the third attempt counts (as an equal part) if it is higher than the average of the previously counted attempts. In other words, additional attempts that will negatively affect your overall average will not be taken into account. The example in the following table shows the final score is 7.5 (the average of score and is, therefore, not included. because the second attempt would lower your overall 5 and 10, 0r Grade it Now Scoring Examples Final Score Third Attempt Second Attempt First Attempt 6.3 10/10 4/10 5/10 Averaging 10/10 10.0 4/10 5/10 Keep the Highest 7.5 10/10 4/10 5/10 Do No Harm Which Grade it Now scoring option ensures that each attempt always attects your tinal score? O Do No Harm O Averaging Keep the Highest Imagine that your instructor chose to use the Averaging scoring method in Grade it Now mode. Here are your scores: First attempt: 4/10 Second attempt: 6/10 Third attempt: 2/10 What would be your final score? a. 4 b. 5 c. 6 what type of reaction is AsCl+H2S --> As2S3+HCl Fill in the blanks with present continuous tense.Please help! what are the three places where digestion takes place in the digestive system? The American Management Association created a statement of ethics to guide members in the marketing professionTrueFalse Michelle lives 4.5 miles from work. Kelly lives 5.6 kilometers from work. Staci lives 4,200 meters from work. Kyle lives 670,000 centimeters from work. During the late Precambrian era, enoughaescaped from volcanoes to beginperiod ofglobal warming. Why was Napoleon eager to sell the Louisiana Territory to the United States at a reasonable price? A.The United States was friends with Napoleon. B.France did not want the territory anymore. C.France was about the enter into war with Spain. D.France was about to enter into war with Great Britain. Given that f(x)=x^2-1 A) find f(5)B) find f^-1(x)C)f^-1(8) True or false Side effects from steroid use include mood swings and lung damage. a small refrigerator is a cube with a side length of 12 inches use the formula S= 6s2 to find the surface area of the cube can someone please help me with this it's the last problem on my exam Identify part A, B and C. What is the function of part B? You have a globe that has a radius of 11 inches. Find the volume of your globe 100 POINTS THREE QUESTIONS IM ON AN EXAM HELPHinduism grew out of the beliefs of what earlier religion?IslamJudaismChristianityBrahmanismWhich statement is part of the dharma of Buddhism?To end suffering, you must stop wanting things.The true path to enlightenment is giving to others.Suffering is caused by treating other people poorly.Enlightenment is rewarded by the gods approval.How did early hunter-gatherers affect the physical environment?They spread seeds when they farmed new areas.They contributed to a decline in animal populations.They mined metals to make arrowheads and spearheads.They used fire to destroy forests across large regions. solve the inequality 1/3x+811 Hello please help me !!!!! Complete the static method stringSearch, which returns a String that tells where the first occurrence of the characters (chr) were found ("The characters were found at ____ index.") or it says, "Those characters could not be found." The String to be searched (phrase) and the characters that are being looked for (chr) are passed in as arguments. (9 points) public static String stringSearch (String phrase, String chr) { ** Complete the code ** }