The first term of an arithmetic progression is 3 and the fifth term is 9. Find the number of terms in the progression if the last term is 81.

Answers

Answer 1

Answer:

n = 53

Step-by-step explanation:

the sum to n terms of an arithmetic progression is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 3 and a₅ = 9 , then

3 + 4d = 9 ( subtract 3 from both sides )

4d = 6 ( divide both sides by 4 )

d = 1.5

then solving for n

3 + 1.5(n - 1) = 81 ( subtract 3 from both sides )

1.5(n - 1) = 78 ( divide both sides by 1.5 )

n - 1 = 52 ( add 1 to both sides )

n = 53

there are 53 terms in the progression

Answer 2

Answer:

53 terms

Step-by-step explanation:

Finding common difference :

a = 3a + 4d = 94d = 6d = 1.5

Solving :

a_{n} = a + (n - 1)d81 = 3 + 1.5n - 1.579.5 = 1.5nn = 53

Related Questions

Please give answer
It’s for a school work

Answers

Answer:

x=60

Step-by-step explanation:

x+2x=3x

180/3=60(interior angles add up to 180)

Consider the equation. Which graph shows a line that is perpendicular to the line defined by the given equation? A. In a linear graph line diagram, A line passes through (minus 4, minus 2) and (2, minus 0.5) which intersects the x-axis at 4 units and the y-axis at minus 1 unit. B. In a linear graph line diagram, A line passes through (2, 0.5) and (minus 4, 2) which intersects the x-axis at 4 units and the y-axis at minus 1 unit. C. In a linear graph line diagram, A line passes through (2, 4) and (0.5, minus 2) which intersects the x-axis at 1 unit and the y-axis at minus 4 units. D. In a linear graph line diagram, A line passes through (2, minus 4) and (0.5, 2) which intersects the x-axis at 1 unit and the y-axis at minus 4 units.

Answers

The graph second represents the line that is perpendicular to the line y = 4x - 2 option  (B) is correct.

What is a straight line?

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The question is incomplete:

The complete question is:

Consider the equation y = 4x - 2 Which graph shows a line that is perpendicular to the line defined by the given equation?

Please refer to the attached picture.

The given line:

y = 4x - 2

The slope of the line m = 4

The slope of the line which is perpendicular to the above line:

M = -1/4 = -0.25

The graph second has a slope of -0.25

[tex]\rm y\ -2\ =\ \dfrac{\left(2-0.5\right)}{-4-2}\left(x+4\right)[/tex]

y - 2 = -0.25x - 1

y = -0.25x + 1

Thus, the graph second represents the line that is perpendicular to the line y = 4x - 2 option  (B) is correct.

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This question is based on the box plot below: How is the data distributed?

Answers

The distribution is right skewed.

What is the data distribution?

A box plot is graph that is used to display data. The box plot is made up of two whiskers that are on either sides of a box. The first line on the box is the first quartile, the second line is the median and the third line is the third quartile.

When the median is closer to the bottom of the box, and if the whisker is shorter on the lower end of the box, the data is right skewed.

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Which expressions are equivalent to the one below? Check all that apply.log(10^7)

Answers

The value of expression is 7.

What is expression?

An expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)

Given:

[tex]log 10^{7}[/tex]

Now, using property of log

[tex]log b^{a} =[/tex] a log b

So,

[tex]log 10^{7}[/tex]= 7 log 10

As log 10 = 1

[tex]log 10^{7}[/tex]= 7 (1)

[tex]log 10^{7}[/tex]= 7

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Using the quadratic formula to solve x2 + 20 = 2x, what are the values of x?

Answers

Answer:

[tex]x=1[/tex] ± [tex]i\sqrt{19}[/tex]

Step-by-step explanation:

First off let's state the quadratic formula

Quadratic formula

[tex]\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex]

[tex]\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]

For this question our quadratic equation is

[tex]x^2+20=2x[/tex]

Now before we can apply the quadratic formula we first have to set the equation equal to zero. We do this my moving everything to one side and setting it equal to zero.

In this case, we simply move the 2x to the other side making it negative and setting the equation equal to zero.

[tex]x^2-2x+20=0[/tex]

From here we plug in the values to the quadratic equation.

Now incase you don't know

[tex]a =[/tex] Coefficient of [tex]x^2[/tex] value

[tex]b=[/tex] Coefficient of [tex]x[/tex] value

[tex]c=[/tex] The Constant

Now plug in values

[tex]a=1[/tex]

[tex]b=-2[/tex]

[tex]c=20[/tex]

To get the values of x using the quadratic formula we have the plug in the values, we also have to both subtract and add the [tex]\sqrt{b^2-4ac}[/tex] to [tex]-b[/tex]

Plug in values into formula

[tex]\frac{2+\sqrt{(-2)^2-4(1)(20)} }{2(1)}[/tex]

[tex]\frac{2+\sqrt{-76} }{2}[/tex]

[tex]\frac{2+\sqrt{-1} *\sqrt{76} }{2}[/tex]

[tex]\frac{2+i *\sqrt{76} }{2}[/tex]

[tex]\frac{2+i *\sqrt{4(19)} }{2}[/tex]

[tex]\frac{2+i *\sqrt{2^2(19)} }{2}[/tex]

[tex]\frac{2+2i \sqrt{19} }{2}[/tex]

[tex]x=1+i\sqrt{19}[/tex]

Now repeat the steps except subtract from -b rather than add to it.

Final Answer

[tex]x=1[/tex] ± [tex]i\sqrt{19}[/tex]

BTW

± = plus and minus

Evaluate the expression (8×6) +(8-3)

Answers

Answer:

(8×6)+8-3

48+8-3

53

Step-by-step explanation:

please mark me as brainlest

12a-10b+6
Term:
Coefficient:

Answers

Terms : “a” and “b”
Coefficients: 12, -10, and 6
Hope this helps :)

Item 18
What is the volume of the prism?



Enter your answer, as a mixed number in simplest form, in the box.


cm³


The figure contains a right rectangular prism. The length of the prism is labeled 6 and one half centimeters, the width is labeled 2 and one half centimeters, and the height is labeled 2 and one half centimeters.

Answers

A mixed number in simplest form, in the box is 40  5/8 cm^3.

We have given that,

The figure contains a right rectangular prism. The length of the prism is labeled 6 and one-half centimeters, the width is labeled 2 and one-half centimeters, and the height is labeled 2 and one-half centimeters.

What is the volume of the prism?

The figure is a rectangular prism, so the formula would be Volume = length x width x height.

length = 6 .5cm

width  =  2.5cm

height  =  2.5cm

If you plug everything you have in the problem into the volume equation, you would get

volume = 6.5cm x 2.5cm x 2.5 cm.

Without a calculator first, turn the mixed numbers into improper fractions.

6 .5=13/2

2.5 = 5/2

Volume = 13/2  x 5/2   x 5/2

When you multiply everything together you should get.

As a mixed number, that would be 40 5/8.

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Does the table of values below represent a proportional relationship?

x
2
3
4
5
y
10
15
24
25

Answers

Answer:

No

Step-by-step explanation:

The constant of proportionality is k = y/x. In this case, k is 5. When you multiply k which is 5 with the x value you should get the y value. You will see that 2 X 5  = 10, 3 X 5 = 15, and 5 X 5  = 25 but 4X 5 is not equal to 24. This means the ordered pair (4, 24) does not lie on the straight line that is formed where all the other ordered pairs (2,10), (3,15), and (5,25) lie.

For a proportional relationship in a table, the k is constant for all the ordered pair x and y values. All the ordered pairs in the table should also lie on the same straight line.

So the answer is no.

Please help me i would really appreciate it, I really dont want to fail the assignment!!!

Answers

The ordered pair of the solution for the system of equation area are (2, -3) and (3, -3)

How to solve system of equation?

f(x) = x² - 5x + 3

f(x) = -3

Therefore,

-3  = x² - 5x + 3

x² - 5x + 3 + 3 = 0

x² - 5x + 6 = 0

x² - 2x - 3x + 6 = 0

x(x - 2) - 3(x - 2) = 0

(x - 3)(x - 2) = 0

x = 3 or 2

when x = 2

f(x) = 4 - 10 + 3 = -3

when x = 3

f(x) = 9 - 15 + 3 = -3

Therefore, the ordered pair of the solution for the system of equation are (2, -3) and (3, -3)

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The question is in the photo! Please help

Answers

the answer is the second one because in order to create a perpendicular line, the slope of the new equation has to be the opposite reciprocal of the previous slope. An opposite is simply switching signs (Ex: 5 become -5), and a reciprocal is simply switching the numerator and denominator. (Ex: 2 becomes 1/2). so the opposite reciprocal would be switching the sign then flipping the numerator and denominator.
the y intercept does not matter with linear equations
the answer is the second one.

help me now !!!!!!!!!!!!!!!!

Answers

In the first diagram the value of k is 10 and in the second diagram the value of k is 15/2.

What is the triangle?

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

In the first diagram:

The sum of the 5k + 20 and 7k + 40 is 180

5k + 20 + 7k + 40 = 180

12k + 60 = 180

12k = 180 -60

12k = 120

k = 10

In the second diagram:

The sum of the two interior angles is equal to the exterior angle.

40 + 12k + 10 = 8k + 80

4k = 30

k = 30/4 = 15/2

Thus, in the first diagram the value of k is 10 and in the second diagram the value of k is 15/2.

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What is the equation for the graph shown below?

Answers

Answer: D

Explanation:

Since we don't know the y-value of the vertex, let's do this an easy way: plugging in.

Let's use the y intercept since that would be the easiest. Since x=0, the terms with x cancel, and you will get a leading result of -5

A) results in 2, so eliminate it

B) results in -2, so eliminate it

C) results in 5, so eliminate it

D) results in -5, so keep it

Since D was the only one that worked, that is our correct answer.

ABD and DBC are complementary angles 43 what is the measure of x

Answers

The value of x is 60

How to determine the value of x?

The complete question is added as an image

From the image, we have:

ABD = 30

DBC = x

The sum of complementary angles is 90.

So, we have:

30 + x = 90

Subtract 30 from both sides

x = 60

Hence, the value of x is 60

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The value of x must be greater than
0
1
3
7

Answers

Answer:

The value of x should be greater than 3.

Step-by-step explanation:

Given that,

The AB is 12 units.

The AC is 15 units.

We need to find the value of BC.

Based on the above information, the calculation is as follows:

As we know that

The sum of two sides length is always more than the 3rd one.

Based on this,

12 + 15 > x

x < 27

15 + x >12

x >-3

12 + x > 15

x >3

Elaine saw statistics showing that union employees make an average of 30 percent more than nonunion workers, so when she was looking for a new job, she looked for one at a company that was unionized. Elaine was motivated by

Answers

Elaine saw statistics showing that union employees make an average of 30 percent more than nonunion workers, so when she was looking for a new job, she looked for one at a company that was unionized. Elaine was motivated by Economic needs.

What do we mean by economic needs?

By economic need Elaine is trying to get a company that would pay her more. Hence the need to go for the Unionized company.

This is given that the Unionized company is said to earn more than the other company. Hence her motivation is due to her economic needs.

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Which of the following is the missing justification?
picture is provided

Answers

Answer: Choice C

Subtraction property of equality

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

Explanation:

Let's say we started with the equation a = b

Subtract c from both sides to get a-c = b-c

This is the subtraction property of equality

-----------------

Example:

x+5 = 12

x+5-5 = 12-5 ... using the subtraction property of equality

x+0 = 7

x = 7

------------------

For this current problem, we're subtracting 3 from both sides in the second step.

A very closely related property is the addition property of equality where we add the same thing to both sides.

Technically we could add -3 to both sides to get the same task done in the second step. But the subtraction property is more direct and straight-forward in my opinion.

share 518 in ratio 2:5
please answer fast with the steps

Answers

Answer:

148:370

Step-by-step explanation:

2+5=7 parts

518÷7=74

1 part =74

2×74=148

5×74=370

find [-4/5]×3/7×15/16×[-14/9]​

Answers

The given expression is [tex]\frac{-4}{5} \times \frac{3}{7} \times \frac{15}{16} \times (\frac{-14}{9})[/tex].

We need to simplify the given expression.

What is a rational number?

In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.

Now group the rational numbers [tex](\frac{-4}{5}\times \frac{15}{16} ) \times (\frac{3}{7}\times (\frac{-14}{9}))[/tex]

[tex]=(\frac{-4}{16}\times \frac{15}{5} ) \times (\frac{3}{9}\times (\frac{-14}{7}))[/tex]

[tex]=(\frac{-1}{4}\times \frac{3}{1} ) \times (\frac{1}{3}\times (\frac{-2}{1}))[/tex]

[tex]=(\frac{-3}{4} ) \times (\frac{-2}{3})=\frac{1}{2}[/tex]

Therefore, the simplified value of the given expression is [tex]\frac{1}{2}[/tex].

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Why [tex]\lim _{x\to -3}\left(x^2-2x+4\right)[/tex] is 19 and not 1??? I don't understand how lim x to -3 (x^2) become 9 and not -9???

PLEASEEEEEEEEEEEEE

Answers

The quadratic is continuous over its entire domain, which is to say we can evaluate the limit by direct substitution:

[tex]\displaystyle \lim_{x\to-3} (x^2 - 2x + 4) = (-3)^2 - 2(-3) + 4 = 9 + 6 + 4 = \boxed{19}[/tex]

You are mistaking (-3)² for -3². They are not the same number.

(-3)² = (-1 × 3)² = (-1)² × 3² = 1 × 9 = 9

-3² = -1 × 3² = -1 × 9 = -9

I need some help with this an explanation would be nice as well thanks

Answers

Answer:

Step-by-step explanation:

add the following rational number7/-27 and 11/18

Answers

Answer:

19/54

Step-by-step explanation:

- 7/27 + 11/18

LCM of the 27, 18 is 54

- 7/27 * (2/2) + 11/18 * (3/3)

- 14/54 + 33/54

33 - 14/54

19/54

please mark me brainlist

1) Which situations are BEST modeled by an exponential function?
es
A) The yearly depreciation of a car.
B) An investment compounded annually.
C) The cost of screws sold by the pound.
D) The amount of sugar to make a pound of fudge.
E) The annual growth rate of a city's population.

Answers

A function assigns the values. The correct options are A, B, and E.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

The situations that can be best modelled by exponential functions are:

A) The yearly depreciation of a car.

B) An investment compounded annually.

E) The annual growth rate of a city's population.

Hence, the correct options are A, B, and E.

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write a function rule for the table

hours worked 2,4,6,8 and pay 15,30,45,60

Answers

Answer:

f(x) = 7.5x

Step-by-step explanation:

you can find the slope by using the slope formula (y2-y1)/(x2-x1). you can use any of the values but for this example I'll be using (2, 15) and (4, 30).

(30-15)/(4-2) = 15/2 = 7.5.

now we can use one of the coordinates to find the y-intercept by plugging the known values in the equation y=mx+b where m is the slope and b is the y-intercept.

for this example I'll be using (2, 15) but you could use any of the values you gave.

15 = 7.5(2) + b

15 = 15 + b

0 = b

so now we have the function rule

f(x) = 7.5x + 0 or just f(x) = 7.5x

{
5x−y=19
13x−3y=51

Can anybody help me to understand this equation ASAP

Answers

Answer:

×=-3

y=-4

Step-by-step explanation:

13×-3y=51

(-) 5×-y=19

-5×+y=-19

13×-3y=51

8×-2y=32

2/8x-2y=32

4x-y=16

4×-y=16

-5×+y=-19

-×=-3

×=3

Answer:

x = 3
y = -4
(3,-4)

Step-by-step explanation:

Hello!

We can use the Elimination Method to solve the system.

To eliminate, we want atleast one variable to have the same coefficients on both equations. To do that, we can multiply the first equation by 3 to get -3y.

[tex]5x - y = 19[/tex][tex]3(5x - y = 19)[/tex][tex]15x - 3y = 57[/tex]

Now, we can vertically subtract them to eliminate -3y.

[tex]-\left \{ {{15x - 3y = 57} \atop {13x - 3y = 51}} \right.[/tex][tex]2x + 0 = 6[/tex]

Solve for x

[tex]2x + 0 = 6[/tex][tex]2x = 6[/tex][tex]x = 3[/tex]

The value of x is 3.

To solve for y, we can plug in 3 into the original first equation and solve for y.

Solve for y

[tex]5x - y = 19[/tex][tex]5(3) - y = 19[/tex][tex]15 - y = 19[/tex][tex]-y = 4[/tex][tex]y = -4[/tex]

The value of y is -4.

The solution to the system is (3,-4).

HELP ME PLEASE AND JUST GIVE ME THE ANSWER NO EXPLANATION

Answers

The missing end of the line segment [tex]\overline {GH}[/tex] whose midpoint is M(x, y) = (5, 3) and known endpoint is G(x, y) = (1, -5) is the point H(x, y) = (9, 11).

How to locate the missing end of a line segment

In this question we know an end and a midpoint of a line segment. The missing end can be found from the following formula:

M(x, y) = G(x, y) + 0.5 · [H(x, y) - G(x, y)]

M(x, y) = 0.5 · G(x, y) + 0.5 · H(x, y)

0.5 · H(x, y) = M(x, y) - 0.5 · G(x, y)

H(x, y) = 2 · M(x, y) - G(x, y)     (1)

If we know that M(x, y) = (5, 3) and G(x, y) = (1, -5), then the coordinates of the point H are:

H(x, y) = 2 · (5, 3) - (1, -5)

H(x, y) = (10, 6) - (1, -5)

H(x, y) = (9, 11)

The missing end of the line segment [tex]\overline {GH}[/tex] whose midpoint is M(x, y) = (5, 3) and known endpoint is G(x, y) = (1, -5) is the point H(x, y) = (9, 11).

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Answer:

its A

Step-by-step explanation:

the answer to this question

Answers

Answer:

positive 1!

Step-by-step explanation:

i got it right on the test trust me!

A club consists of 5 girls (Kirsten, Sarah, Suzie, Monica, and Katie) and 3 boys (Kevin, Steve and Samuel).

Find P(S-name U Boy)

Answers

The probability of selecting a person with a name that starts with S or a boy is [tex]\frac{5}{8}[/tex]

What is probability?

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.

Given that, a club consists of 5 girls (Kirsten, Sarah, Suzie, Monica, and Katie) and 3 boys (Kevin, Steve and Samuel)

To find P(S-name U Boy), that is the probability of selecting a person whose name starts with S or boy.

n(S-name U Boy) = 5   {2 girls (Sarah, Suzie), 3 boys( Kevin, Steve and Samuel )}

Number of favourable outcomes=5

Total number of outcomes=5+3=8

P(S-name U Boy) [tex]=\frac{Number of favourable outcomes}{Total number of outcomes}[/tex]

[tex]=\frac{5}{8}[/tex]

Therefore, the probability of selecting a person with a name that starts with S or a boy is [tex]\frac{5}{8}[/tex].

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smone answer ASAP please.

Answers

The measure of the angle x is 117 degrees

Line geometry.

To determine the value of x in the given diagram, we will use the alternate angles theorem

The value of x is expressed as shown;

p + q= x

If the value of p = 51, then;

51 + q. = x

Determine the value of. q

q = 108 - 42

q = 66

Determine the value of x

x = 66 + 51

x = 117 degrees

Hence the measure of the angle x is 117 degrees

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a and b are positive integers and 7a+5b=49. Find the values of a and b.

a and b are positive integers and 23a+17b=320. Find the values of a and b.

please hel you can get 30 points

Answers

Solving a system of equations, it is found that the value of a is of -191.75 and the value of b is of 278.25.

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the equations are:

7a + 5b = 49.23a + 17b = 320.

Multiplying the first equations by 17 and the second by -5, we have that the system is:

119a + 85b = 833.-115a - 85b = -1600.

Then, adding them:

4a = -767

a = -767/4

a = -191.75

Then:

[tex]b = \frac{49 - 7a}{5} = \frac{49 - 7(-191.75)}{5} = 278.25[/tex]

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