Find an Equation of the line L Points : (1,1) and (4,-2)

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference. The value of the nth term of the sequence will be 2748.

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

The explicit formula for any arithmetic series is given by the formula,

\(a_n = a_1 + (n-1)d\)

where d is the difference and a₁ is the first term of the sequence.

For the given arithmetic series, the first term of the series is 57.

The value of difference, d can be written as,

d = 66 - 57 = 9

The 300th term of the sequence can be written as,

a₃₀₀ = 57 + (300-1)•9

a₃₀₀ = 2748

Hence, the value of the nth term of the sequence will be 2748.

Learn more about Arithmetic sequence:

https://brainly.com/question/3702506

#SPJ1

The donuts are cheaper in bakery B which implies that Kevin is right.

In order to solve a problem for two different values of a quantity, its unit value is first derived. This method is known as unitary method. The ratio of two numbers are taken in this method. There can be two relations between the ratio a direct or n indirect. For the direct relation the quantities simultaneously increase or decrease while in the indirect it happens reverse.

The price of donuts for both bakeries are given as,

For Bakery A,

The price of 10 donuts is $15.

Unit rate is given as 15/10 = $1.50 per donut.

For Bakery B,

The price of 12 donuts is $17.

Unit rate is given as 17/12 = $1.41 per donut.

Thus, price of donuts from Bakery B is less than Bakery A.

It implies that Kevin is right.

Hence, the price of donuts is cheaper in case of bakery B which implies that Kevin is right.

To know more about unitary method click on,

https://brainly.com/question/28276953

#SPJ1

Kevin is correct. And he used the correct unit rate formula to find the inequality.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

Bakery A.

She used the equation 10 donuts $15 to show that their donuts cost about $0.67 per donut.

This is less than Bakery B's price, 12 donuts $17= about $0.71 per donut.

Kevin thinks they should order donuts from Bakery B.

He used the equation

$17 ÷ 12 donuts to show that their donuts cost about $1.42 per donut.

This is less than Bakery A's price,

$15÷ 10 donuts = about $1.50 per donut.

The inequality:

1.42 < 1.50

To find the unit rate:

Unit rate = the total price of donut / the number of total donuts

Kevin used the above formula to find the unit rate.

So, Kevin is right.

Therefore, Kevin is right.

To learn more about the inequality;

brainly.com/question/28823603

#SPJ1

The cross-sectional area will be π*(y^2-x^2) as area of a circle with radius r is π*r^2.

Hence, The cross-sectional area will be π*(y^2-x^2) as area of a circle with radius r is π*r^2.

learn more about equations click here:

brainly.com/question/25976025

#SPJ4

Answer:

Closed boundary point

Step-by-step explanation:

It says greater than OR equal too and having a closed boundary will indicate that 21 is apart of the inequality also.

I hope this helps

Answer:

E number

Step-by-step explanation:

First add the value of x component and solve the equation (eg. (1,2) here 1 is x component

Answer:

N+1

Step-by-step explanation:

It begins with = 2

then n+1=3

then n+2=4 and so on it is n+1

Answer:

9 pi

Step-by-step explanation:

If the radius is 12, then the diameter would be 24 and the entire circle would be 24 pi.

24 times 3/8= 9

I used 3/8 because the unit circle has a circumference of 2pi so I divided it by 2.

Answer:

Step-by-step explanation:

If the variables x and y vary inversely, this is expressed as;

x ∝ 1/y

x = k/y

k is the constant of proportionality

Given;

x = 7/2 and y = 3/5

Substitute;

7/2 =k/(3/5)

Cross multiply

k = 7/2 * 3/5

k = 21/10

Substitute the value of k into the formula;

x = k/y

x = (21/10)/y

x = 21/10 * 1/y

x = 21/10y

Hence the equation relating x and y is x = 21/10y

The ratio of the length of AB to the length of BC is 10 : 3. The length of AC is 26 cm.

In the given rectangle, we know that the ratio of the length of AB to the length of BC is 10:3. Let's assume the length of AB is 10x, and the length of BC is 3x.

Using the tangent function, we have tan(x) = 1/4, where x is the angle at point B. By taking the inverse tangent (arctan) of both sides, we find that x = arctan(1/4).

Now, we can set up a right triangle using the values we have. The opposite side of angle x is 10x, and the adjacent side is 3x. Using the Pythagorean theorem, we can calculate the hypotenuse:

(10x)^2 + (3x)^2 = AC^2

100x^2 + 9x^2 = AC^2

109x^2 = AC^2

AC = sqrt(109)x

To find the length of AC in centimeters, we need to determine the value of x. Using the given ratio, we know that 10x/3x = 10/3 = 20/6. Therefore, x = 6.

Substituting x = 6 into the equation for AC, we get:

AC = sqrt(109) * 6 ≈ 26 cm.

Hence, the length of AC is approximately 26 cm.

To learn more about Pythagorean theorem click here

brainly.com/question/14930619

#SPJ11

Answer:

128.06

Step-by-step explanation:

think about the diagonal of the field, breaking up a rectangle into 2 right angled triangles. we are already given the legs of the triangle (80, and 100) and now we have to solve for the hypotenuse (or the diagonal). so use pythagorean theorem :

80^2 + 100^2 = c^2

16400 = c^2

c = 128.06

Answer:

Step-by-step explanation:

1.   9

2. 32

3. 813

4. 264

5. 169

Answer:  3. Distributive

Step-by-step explanation:

Distributive property of multiplication over addition is the only property that is require to multiply an expression to the other expression with two or more than two terms.

For example: a (b+c)= a b+ac  , where a,b,c can be any expression.

Given expression:  -5(x-3) = -5x +15 , which illustrates the distributive property of multiplication over addition.

Hence, the correct option is 3. Distributive.

The rest of properties cannot work for multiplication over addition as they are used for one operation.

The random variable in an experiment which consists of determining the speed of automobiles on a highway by the use of radar equipment is a continuous random variable. Option c is correct.

A random variable is a variable whose value is subject to variations as a result of a random event. Random variables can be classified as continuous or discrete.

A continuous random variable is a variable that can take on any value within a specified range of values, whereas a discrete random variable is a variable that can take on only specific values, with gaps between them.

The random variable in the experiment given is the speed of automobiles on a highway, and it can take on any value within a specified range of values, making it a continuous random variable.

Thus, option (c) - continuous - is the correct answer.

Learn more about random variable https://brainly.com/question/30789758

#SPJ11

The integral of du/sqrt(a^2 - u^2) is arcsin(u/a) + C, where a is a constant and C is the constant of integration.

To evaluate the integral of du/sqrt(a^2 - u^2), we can use a trigonometric substitution. Let's substitute u = asin(theta), where theta is a new variable. Differentiating u with respect to theta gives du = acos(theta)*d(theta).

Now, let's substitute these expressions back into the integral:

∫(du/sqrt(a^2 - u^2)) = ∫((acos(theta)d(theta))/sqrt(a^2 - a^2sin^2(theta)))

Simplifying the expression under the square root:

= ∫((acos(theta)d(theta))/sqrt(a^2(1 - sin^2(theta))))

= ∫((a*cos(theta)d(theta))/(acos(theta)))

= ∫d(theta)

= theta + C

Since we made the substitution u = asin(theta), we need to express the result in terms of u. Using the relationship u = asin(theta), we can find theta = arcsin(u/a). Therefore, the integral becomes:

∫(du/sqrt(a^2 - u^2)) = theta + C = arcsin(u/a) + C

Hence, the integral of du/sqrt(a^2 - u^2) is arcsin(u/a) + C, where a is a constant and C is the constant of integration.

To learn more about integral click here: brainly.com/question/31433890

#SPJ11

The exponential equation is y = 2,642(2.5)^x. x represents the number of days.

What is a function?

A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two varying quantities.

Given that a video was released to the public, it already had 2,642 views.

One day later, the number of views increased to 3,963.

The number of viewers after one day is ( 3,963 + 2,642 ) = 6,605

Assume that the exponential function y = a(b)^x represents the number of viewers. x represents the number of days.

Putting x = 0 and  y = 2,642 in y = a(b)^x:

2,642 = a(b)⁰

a = 2,642

Putting x = 1 and  y = 6,605 in y = a(b)^x:

6,605 = a(b)¹

Putting a = 2,642:

6,605 = 2,642(b)¹

b = 6,605/2,642

b = 2.5

To learn more about  exponential function, click on the below link:

https://brainly.com/question/27733251

#SPJ1

Answer:

3

Reasoning:

\(3(5+3)=15+9\)

Distribute three to the numbers to get 15+9.

*dot plot is shown in the attachment below

Answer:

Mean = 6.3

Median = 6

Step-by-step explanation:

Measures of centre, mean and median, can be calculated as follows:

First, bear in mind that each dot represents a value in the data set.

==>Mean:

Mean is the sum of all values in the data set divided by the number of data set we have.

The sum can be calculated as follows:

0 (1) = 0

4 (3) = 12

5(8) = 40

6(3) = 18

7(1) = 7

8(5) = 40

9(2) = 18

10 (3) = 30

Sum = 0+12+40+18+7+40+18+30 = 165

No of data set = 26

Mean = 165/26 = 6.346 ≈ 6.3 (nearest tenth place)

==>Median: this is the middle value in the data set. Since the number of data set is even number (26) , the middle value lies between the 13th and 14th data points. The average of the 13th and 14th data points will give us the median value.

Thus, the 13th and 14th values are both 6.

Therefore, median = (6+6) ÷ 2 = 6

Answer:

The mode is 5, because 5 occurs 8 times, which is more than any other numbers occurring more than once. The median is 6, and this is because when you line up the numbers in order and cross them off to find the middle number, it is 6. I rounded to the mean to about 6.4. I got this by adding all of the numbers up, or by doing 12 + 40 +18 +7, etc, and got the total of 165. Because there is a total of 26 data points, I divided those numbers and got 6.3461, which ends up rounding to 6.4.

Step-by-step explanation:

change wording

The Total cost for a tour group consisting of n number of people is 20n

An equation is an expression that shows the relationship between two or more numbers and variables.

Let T represent the total cost if a tour group consisting of n people

Since A walking tour of Washington, D.C., costs $20 per person. Hence, for n number of people:

Total cost = $20 per person * n persons = 20n

The Total cost for a tour group consisting of n number of people is 20n

Find out more on equation at: https://brainly.com/question/13763238

#SPJ1

Answer:

The answer is 135 I'm pretty sure.

Step-by-step explanation:

It seems very reasonable for it to be 135

Given:

Face value = $101,000

Carrying value = $97,900

Bonds call price = $95,500

Find:

Gain or loss on retirement = ?

So, the formula to find the gain or loss on retirement is:

Carrying value – bonds call price

Substituting their values, we get:

$97,900 - $95,500

= $2,400

The journal entries are:

Dr Bonds payable $101,000

Dr Gain on retirement of bonds $1,200

Cr Cash $95,500

Therefore, you gained $2,400 on retirement.

To add, when a bond is retired at any time before its maturity date, it is said to be retired early.

Based on this model, we can say that accounting for bonds retired at maturity is pretty straight forward: the company pays out cash and removes the bond payable from its balance sheet.

Answer:

Answer in explanation

Step-by-step explanation:

if the price per cup is $0.75, then the amount of money made from selling c cups will be;

m = $0.75c

the reason why 2 will not be part of this functions range is because, 2 is not exactly divisible by 0.75

What this means is that 2/0.75 will not give a whole number

And since the number of cups sold is a while number, no fractional sales, then y will not have a value of $2

Answer:

Neither, Perpendicular, Parallel, Neither

Step-by-step explanation:

Parallel lines have the same slope.

Perpendicular lines have slopes that are negative reciprocals.

The pair of functions that are not inverse functions is (f(x) = -124, g(x) = 197 + 41x).

Explanation:

To determine if a pair of functions are inverse functions, we need to check if the composition of the two functions in either order results in the identity function, which is denoted as f(g(x)) = x or g(f(x)) = x.

For option (a), f(x) = 6 and g(x) = 1/3x, we have f(g(x)) = f(1/3x) = 6, and g(f(x)) = g(6) = 2x. Neither of these compositions result in the identity function, so this pair of functions is not inverse functions.

For option (b), f(x) = -124 and g(x) = 197 + 41x, we have f(g(x)) = f(197 + 41x) = -124, and g(f(x)) = g(-124) = (124 + 197)/41. Since these compositions do not result in the identity function, this pair of functions is not inverse functions.

For option (c), f(x) = 35 and g(x) = 57 - x, we have f(g(x)) = f(57 - x) = 35 + x and g(f(x)) = g(35) = 22. Since neither of these compositions result in the identity function, this pair of functions is not inverse functions.

For option (d), f(x) = 17/20 and g(x) = 1 - 19x/20, we have f(g(x)) = f(1 - 19x/20) = 17/20 and g(f(x)) = g(17/20) = 1 - 19(17/20)/20 = 1/20. Since neither of these compositions result in the identity function, this pair of functions is not inverse functions.

Therefore, the pair of functions that is not inverse functions is (f(x) = -124, g(x) = 197 + 41x).

To learn more about compositions click here, brainly.com/question/13808296

#SPJ11

The product of 1. 61 and 63​ gives 101.43

Answer:

add 8 and 7= 4d + 3y + 15

Step-by-step explanation:

trust me :)

Answer:

5% of 117.50 is 5.875

117.50- 5.875= 111.625 => round it to two decimal places.

£111.63

Hope this helps :)

Answer:

  a) interior angle: 156°

  b) exterior angle: 24°

Step-by-step explanation:

The sum of the exterior angles of a convex polygon is 360°. Then the exterior angle of a regular 15-gon will be ...

  360°/15 = 24°

__

The interior angle of a convex polygon is the supplement of the exterior angle at that vertex. For an exterior angle of 24°, a regular 15-gon will have an interior angle of ...

  180° -24° = 156°

_____

Additional comment

We find it easier to work this problem by finding the exterior angle first. Note that the results only apply to a 15-gon in which all interior angles are congruent.

Answer:

they trained arrived at 9:25pm

Answer:

9:25

Step-by-step explanation:

7:15 + 2 hours and 10 minutes

\(\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}\)

Let the number be 4x and 7x respectively !

Then ,

\(\bold{7x - 4x = 9} \\ \\ \bold{\longrightarrow \: 3x = 9} \\ \\ \bold{\longrightarrow \: x = \cancel\frac{9}{3}} \\ \\ \bold{\longrightarrow \: x = 3}\)

therefore ,

first number = 4x = 4 × 3 = 12

second number = 7x = 7 × 3 = 21

hope helpful ~

The difference of two numbers is 9 and they are in the ratio 4 : 7. Find the numbers.

In this question we are provided with the ratio of two numbers that is 4 : 7 and it is also given that the difference between two numbers is 9. We are asked to calculate the two numbers.

\( \small \purple{ \underline{ \underline{\rm{ First \: we \: will \: form \: an \: equation }}}}\)

Let us assume the number as 4x and 7x.

It is given that the difference is 9

According To Question

\( \small \blue{\sf{7x - 4x = 9}}\)

\( \small \green{ \underline{ \underline{\rm{ Now \: we \: will \: solve \: this \: equation \: and \: find \: the \: value \: of \: x}}}}\)

Let us solve this equation

\( \small\sf{7x - 4x = 9} \)

\(⟹ \small\rm{3x = 9} \)

\(⟹ \small\rm{x = \dfrac{ \cancel{9} \: \: 3}{ \cancel{3}} } \)

\( \small\sf{x = 3} \)

Substitute the value of x = 3

7x = 7 × 3 = 21

4x = 4 × 3 = 12

Hence the two numbers are 21 and 12.