The 8th term of a linear sequence is 18 and the 12th term is 26. Find the first term, the common difference and the 20th term

Answers

Answer 1

Answer:

see explanation

Step-by-step explanation:

the sequence is linear, that is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

given a₈ = 18 and a₁₂ = 26 , then

a₁ + 7d = 18 → (1)

a₁ + 11d = 26 → (2)

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

4d = 8 ( divide both sides by 4 )

d = 2

substitute d = 2 into (1) and solve for a₁

a₁ + 7(2) = 18

a₁ + 14 = 18 ( subtract 14 from both sides )

a₁ = 4

then

a₂₀ = 4 + (19 × 2) = 4 + 38 = 42


Related Questions

Please help .!!!!!!!!!

Answers

Answer:

-60 = x

Step-by-step explanation:

(-1/4)x - 12 = x + 3

(-1/4)x = x + 15

-0.25x = x + 15

-60 = x

Answer:
12

Explanation:
Check out the work I’ve attach

Hope it helps, Let me know if you have any other questions!
Have a nice rest do your day :)

If
5sin 2x +4 = 10 sin ²x, show
that tanx = 2 or tan x =-1/3

Answers

[tex]~~~~~5\sin 2x +4 =10 \sin^2 x\\\\\implies 5\cdot 2\sin x \cos x+4 =10 \sin^2 x\\\\\implies 10 \sin x \cos x +4 = 10\sin^2 x\\\\\implies 10\tan x + 4\sec^2 x = 10\tan^2 x~~~~~;[\text{Divide both sides by}~ \cos^2 x]\\\\\implies 10\tan^2 x -10 \tan x -4(1+ \tan^2 x)=0\\\\\implies 10\tan^2 x -10 \tan x -4 -4\tan^2 x =0\\\\\implies 6 \tan^2 x -10 \tan x -4 =0\\\\\implies 3 \tan^2 x -5 \tan x -2 =0~~~~~;[\text{Divide both sides by 2}]\\\\\implies 3\tan^2 x - 6\tan x +\tan x -2 =0\\\\[/tex]

[tex]\implies 3 \tan x( \tan x -2) + (\tan x -2) = 0\\\\\implies (\tan x -2) ( 3 \tan x +1) = 0\\\\\implies \tan x = 2 ~~ \text{or}~~ \tan x = - \dfrac 13\\\\\text{Showed.}[/tex]

PLEASE HELP!!!! CUMULATIVE EXAM!!!! 50 POINTS


Gina wants to take dance classes. She compares two dance studios to determine which has the best deal for her. Dance World charges a rate for each class. Toe Tappers charges a rate for each class plus a one-time registration fee. The system of equations shown models the total costs for taking x classes at each.

Dance World: y = 15x
Toe Tappers: y = 25 + 12.5x

How many classes would Gina need to take for the total cost to be the same at both dance studios?

10
15
100
150

Answers

Answer:

10

Step-by-step explanation:

My guy just plug in the number for x it's not that hard

At Shannon's Pancake House there are 228 dirty coffee mugs and 247 clean coffee mugs. What percentage of the coffee mugs at the pancake house are dirty? Write your answer using a percent sign

Answers

Answer:

48%

Step-by-step explanation:

First, we need to add the amounts together to be able to see what percent of all the cups are dirty. (228 + 247 = 475). Now we can find one percent of 475 we can do this by moving the decimal point two to the left. (4.75). so If 4.75 is 1% we can multiply 4.75 until we get 228.

4.75 x 20 = 95.

4.75 x 40 = 190

4.75 x 45 = 213.75

4.75 x 50 = 237.5

4.75 x 48 = 228

Since every time we multiplied by 1 more we went up 1%. We multiplied by 48 so 48%.

this is what i need help with

Answers

Answer:

It's B

Step-by-step explanation:

All you're doing is adding 1.5 each time

Hope this helps :)

Solve the following equation. Then place the correct number in the box provided.

6(x - 1) = 4(x - 2)

Answers

Answer:

x = -1

Step-by-step explanation:

First we expand both sides :

Let's start with the right side:

6(x-1) = 6x-6

Now we do the left side:

4(x-2) = 4x-8

Now we add 6 to both sides:

(6x-6)+6 = (4x-8)+6

Simplify:

6x = 4x -2

Subtract 4x from both sides:

6x - 4x = (4x-2) - 4x

Simplify:

2x = -2

Divide both sides by 2:

2x÷2 = -2÷2

Simplify:

x = -1

I dont see a box so can't do the second part.

Hope this helps and brainliest please

An elevation of-89ft.is 89 feet_______
See level.

Answers

Answer:

- sign indicates the fact that it's Below sea level

help please. this doesn't make sense ​

Answers

Answer:

a = 39.2650873379cm

b = 11.5529459767cm

Step-by-step explanation:

a - Use the area of a triangle equation -  1/2 * a * b * Sin(C)

1/2 * 8 * 10 * Sin(79) = 39.2650873379cm

b - Use the cosine rule - c^2 = a^2 + b^2 - (2 * a * b * Sin(C)

64 + 100 - (2 * 8 * 10 * Cos(79)) = 133.4705607398

c = square root of 6.9396506484 = 11.5529459767cm

Put to however many significant figures / decimal places required.

:)

need help with this asap​

Answers

Answer:

they are three I will explain

Step-by-step explanation:

x+4/3÷6/x

this 3 expressions are equivalent to the equation above

1. x+4/3{x/6}

2. {x/6}x+4/3

3. x^2 + 4x /18

How many meters are in 360in?

Answers

Answer:

9.411

Step-by-step explanation:

Answer:9.144

Step-by-step explanation:

Pls help i need this so I can pass

Answers

Answer:

i cant see the photo, but i would love to help

Step-by-step explanation:

Make it quick please!

What are the coordinates of the hole in the graph of the function f(x)?

f(x)=x2−9/x−3

Answers

Factor out the numerator first

y=x²-9/x-3y=x²-3²/x-3y=(x+3)(x-3)/(x-3)y=x+3

The hole is at x-3=0 i.e x=3

And

y=3+3=6

The hole is at (3,6)

Our basketball team won 60 percent of their games. If they lost 8 games, how many games did they play altogether?

Answers

Answer:

they played 20 games together

Step-by-step explanation:

use percentages

Let x be the number of total games.

If 60% is won games then 40% is lost games.

(8/x)*100 = 40

8/x = 4/10

80 = 4x

X = 80/4

Therefore the number of games is 20

If they won 60% of games. That means they lost (or drew) 40%.

They lost 8 games. So those 8 games accounts for 40% of all the matches they played.

8 games = 40%
(divide by 8)

1 game = 5%

To get 100% ie the total number of games played you do 5% x 20

So you also do 1 x 20 to get 20 games played in total.

A right triangle has one angle that measures 48°. What is the measure of the other acute angle?

Answers

Answer:

minus 48 to 90 then divide the answer by 2

Answer:

42°

Step-by-step explanation:

The 2 acute angles in a right triangle add up to 90°

90° - 48° = 42°

Hope this helps

The image shows a circle with center (4,6) and radius 10 units.

Answers

A circle is a curve sketched out by a point moving in a plane. The point that lies on the circle is (-4, 12), (-6, 6), and (4, 16).

What is a circle?

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

The simple way to do such questions is to make the given circle and plot the points on the graph. As shown below.

The other way to do the question is to find the distance between the centre point of the circle and the point if it is equal to the radius of the circle, the point will lie on the circle, otherwise not.

The formula to find the distance between the two points on a graph is,

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Hence, the point that lies on the circle is (-4, 12), (-6, 6), and (4, 16).

Learn more about Circle:

https://brainly.com/question/11833983

#SPJ1

What is the slope of the line that passes through the points (-1, 6) and (14, 3)? Write your answer in simplest form.

Answers

Slope: m= -1/5
If it doesn’t work then just do -1/5

the slope is m= -1/5.

What is slope?

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

y_2 - y₁ = m(x₂ - x₁).

here, we have,

the slope of the line that passes through the points (-1, 6) and (14, 3)

Slope: m=  y_2 - y₁/(x₂ - x₁).

              = 3-6/14+1

              = -1/5.

hence, the slope is m= -1/5.

To learn more on slope click:

https://brainly.com/question/3605446

#SPJ2

the probability of a certain hockey player making a goal after hitting a slap shot is 1/5. How many successful slapshots would you expect her to make after 120 attempts?

Answers

600 attempts

Please mark Brainly-est if I’m right

Ally surveyed 5 classrooms. She wanted to know the number of students in each class who love painting. The data she collected from the 5 classrooms is below.
10, 7, 9, 11, 8

The value that could be the best measure of the center of this data is__.

Answers

Answer:

45 im not to shur

Step-by-step explanation:

10 + 7 + 9 + 11 + 8 = ?

? = 45

Write the missing number to make these equivalent fractions correct
?/20=2/5

Answers

Answer:

8

Step-by-step explanation:

From 5 to get to 20 it would be (X4), so we would do the same for the 2, and 2 times 4 would be 8. The answer is 8.

From 5 to get to 20 it would be (X4), so we
would do the same for the 2, and 2 times 4
would be 8. The answer is 8/20=2/5

Alex is 6 years older than Frank. The sum of their ages is 50. Find Alex's age and
Frank's age.
HELP

Answers

Answer: Alex 28

Frank 22

Step-by-step explanation: Age difference is 6. Addition is 50

Which of the following is a geometric series? 6 13 20 27 7 21 35 45 14 21 28 35 2 14 98 686

Answers

The geometric series will be D. 2 + 14 + 98 + 686 because it is having a common ratio 7.

What is geometric series?

In mathematics, a geometric series is the sum of an infinite number of terms that have a constant or common ratio between successive terms

A. 6 + 13 + 20 + 27 .

the difference between two terms are 13-6 = 7 , 20-13= 7

The terms are increasing by 7. So it is not geometric

B. 7 + 21 + 35 + 45

the difference between two terms are 21-6 = 14 , 35-21= 14

The terms are increasing by 14. So it is not geometric

C. 14 + 21 + 28 + 35

the difference between two terms are 21-14 = 7 , 28-21= 7

The terms are increasing by 7. So it is not geometric

D. 2 + 14 + 98 + 686

Here the difference is not same, so we find the ratio

14/2= 7

98/14= 7

686/98= 7

So common ratio is 7

When the common ratio is same then it is Geometric series

Hence the geometric series will be D. 2 + 14 + 98 + 686 because it is having a common ratio 7.

To know more about geometric progression follow

https://brainly.com/question/24643676

Answer:

D

Step-by-step explanation:

multiplied by 7 each time

What is the value of 4(x−2)(x−3)+7(x−2)(x−5)−6(x−3)(x−5) when x=5? Type the answer in the box below.

Answers

Answer:

24

Step-by-step explanation:

when x = 5,

4(5-2)(5-3) + 7(5-2)(5-5) - 6(5-3)(5-5)

= 4(3)(2) + 7(3)(0) - 6(2)(0)
= 24

The store pays 120 for a bike the store is going out of business and is selling all of the bikes at a 30% discount what is the sil price of the bicycle

Answers

84

Because 30% of 120 is 36 and 120-36 is 84
The sale price is $84 because
120-30% = 84
100%-30%=70%=0.7
120 x 0.7 = 84

I need some help please

Answers

Answer:

24

Step-by-step explanation:

The way you calculate the volume of a shape is length x width x height. 4 x 3 x 2 = 24.

1. What is( - 1/2 + 2)
2. 4( 1/2+5/4) + (-5)
(please answer, I will mark brainliest)
:)​

Answers

1)

[tex]\longrightarrow (-\dfrac{1}{2} +2)[/tex]

[tex]\longrightarrow (-\dfrac{1}{2} +\dfrac{4}{2} )[/tex]

[tex]\longrightarrow \dfrac{-1+4}{2}[/tex]

[tex]\longrightarrow \dfrac{3}{2}[/tex]

[tex]\sf \bold{\longrightarrow 1\dfrac{1}{2}}[/tex]         (final answer)

2)

[tex]\longrightarrow \sf 4(\dfrac{1}{2} +\dfrac{5}{4} ) + (-5)[/tex]

[tex]\longrightarrow \sf 4(\dfrac{2}{4} +\dfrac{5}{4} ) + (-5)[/tex]

[tex]\longrightarrow \sf 4(\dfrac{7}{4} ) + (-5)[/tex]

[tex]\longrightarrow \sf 7-5[/tex]

[tex]\longrightarrow \bold{\sf 2}[/tex]        (final answer)

pls help me with this

Answers

Answer:

7 with a remainder of 2

Step-by-step explanation:

i just did the math rn

7 R2

12 goes into 86 7 times and has 2 left over

What is the Volume of the square pyramid? (Round to the nearest tenth as needed)

Answers

given:

base= 25 mm

height= 28 mm

to find:

the volume of the square pyramid.

solution:

[tex]volume = {a}^{2} \frac{h}{3} [/tex]

[tex]v = {25}^{2} \frac{28}{3} [/tex]

[tex]v = 5833.33333 {mm}^{3} [/tex]

[tex]v = 5833.3 {mm}^{3} [/tex]

help plese will markbrainliest

Answers

Your answer is 53

Yw :D

A tank is being filled with water at a rate of 5.5 gallons per
minute. Write the first five terms of the arithmetic sequence
being represented after each minute if the tank started with
10 gallons of water.

Answers

Arithmetic sqaure: a + (n-1) * d

              where "a" is the first term, "d" is the common difference

Here given:

a = 10 gallons

d = 5.5 gallons

nth term: 10 + (n-1) * 5.5

Solve for first 5 terms:

10 + (1-1) * 5.5 = 10

10 + (2-1) * 5.5 = 15.5

10 + (3-1) * 5.5 = 21

10 + (4-1) * 5.5 = 26.5

10 + (5-1) * 5.5 = 32

first five terms: 10, 15.5, 21, 26.5, 32

First term=a=10common difference a=5.5

General formula

a_n=a+(n-1)da_n=10+(n-1)5.5

So

a_1=10a_2=10+5.5=15.5a_3=10+11=21a_4=10+16.5=26.5a_5=10+22=32a_6=10+27.5=37.5

A triangle has sides with lengths of 13ft, 82ft, and 83ft. Is it a right triangle

Answers

Answer:

NOT a right triangle

Step-by-step explanation:

IF it is a right triangle, then the Pythagorean theorem would apply

13^2 + 82^2  = 83^2   ?????

169  + 6724  = 6889

6893  = 6889 ?     No...it is NOT a right triangle

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