the sum of an arithmetic series is given be Sn= 6n-3n2. find the common difference and the first 4 terms of the sequence

The equation of line which passes through (-2, 8) and perpendicular to the line conatining (0, 1) and (4, 5) is y = -x + 6 .

Let the equation of line passes through the point (-2, 8) be y = mx + b.

Where m is the slope of the line and b is the y intercept of the line.

According to the given question.

A line passes through the points (-2, 8).

And it is also perpendicular to the line containing (0, 1) and (4, 5).

Since, the line is perpendicualr to the line conatining (0, 1) and (4, 5).

So, the slope of the line whose equation is to be find is given by

m = -1/(5 - 1/4-0)

⇒ m = -1/4/4 = -1

Thereofre, the equation of line with slope -1 is

y = -1x + b

Also, it passes through (-2, 8)

So,

8 = -1(-2) + b

⇒ 8 - 2 = b

⇒ b = 6

Thereofore, the equation of line which passes through (-2, 8) and perpendicular to the line conatining (0, 1) and (4, 5) is y = -x + 6 .

Find out more information about equation of line here:

https://brainly.com/question/21511618

#SPJ1

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

An equation represents a represents only when there is a unique value of x for every value of y. when it represents u as a function of x.

i.e if we draw lines parallel to y axis and it cuts the curve two or more than two times at a particular value of x then it doesn't represent a function at all.

And as we can see in the given tables,

1.) 12.23 is the value of x for both 5.4 and 6.4

2.) 0.31 is the value of x for both 55 and 59

4.) 20 is the value of x for both 245 and 255

So, the only table representing y as a function of x is table 3.

Answer:

table 3 is correct i took the test

Step-by-step explanation:

Answer:

2^2×3×5

Step-by-step explanation:

hope this works :)

Answer:

The answer is 7 for C.

Step-by-step explanation:

7+7=14 and 7x7=49

The diamond just asks for numbers that make up a pattern for the two given numbers.

The value of x is -160.

An equation in which the power of any variable is not more than one is called a linear equation.

Here, we are given a linear equation as follows-

5 × x + 860 = 2 × x + 380

⇒ 5x + 860 = 2x + 380

Let us solve the given equation-

Subtracting 2x from both sides, we get

5x - 2x + 860 = 2x - 2x + 380

3x + 860 = 380

Subtracting 860 from both sides-

3x + 860 - 860 = 380 - 860

3x = -480

dividing both sides by 3,

3x/3 = -480/3

x = -160

Thus, the value of x comes out to be -160.

Learn more about linear equations here-

https://brainly.com/question/13738061

#SPJ9

The shape of the distribution of the given data set is : Bell shaped

What is Frequency distribution ?

Frequency distribution, in statistics, a graph or data set organized to show the frequency of occurrence of each possible outcome of a repeatable event observed many times. Simple examples are election returns and test scores listed by percentile. A frequency distribution can be graphed as a histogram or pie chart.

Data: 12 6 4 9 11 1 7 8 9 8 9 13 5 15 7 6 8 8 2 1

Classes = 5

Class  Frequency

1-3      →3

4-6     →4

7-9     →9

10-12  →2

13-15   →2

The shape of the distribution is peak at the center and down at both the ends,

Therefore, we can say that the shape of the distribution is bell shaped.

Read more about Frequency distribution at :

https://brainly.com/question/14926605

#SPJ1

Answer:

$4,218.75

Step-by-step explanation:

The formula for computing simple interest I on a principal amount P for t years at an interest rate of R% is given by

I = Prt

The ending balance amount is found by adding the principal to the interest computed

Ending balance = P + I

Here r is the interest rate in % converted to a decimal. This is done by dividing by 100

r = R/100 = 2.75%/100 = 0.0275 per year

I = 2500 x 0.0275 x 25 = 1718.75

So interest I = $1718.75

Ending balance = $2,500 + $1718.75 = $4,218.75

Answer:

$7.4

each bag of milk cost $7.4

Answer: $7.4

Step-by-step explanation: i did this and i remember it!

Answer:

x = 23

Step-by-step explanation:

The two angles are supplementary angles.

Supplementary angles sum 180°

(6x+4) + 38 = 180

6x + 42 = 180

6x = 180 - 42

6x = 138

x = 138/6

x = 23

Check:

6*23  + 4 + 38 = 180

138 + 42 = 180

Answer:

Step-by-step explanation:

We know that the sum of angles of a linear pair is always equal to 180°. These angles are also known as supplementary angles.

[tex]\bf 6x+4+38^o=180^o[/tex] (Add numbers)

[tex]\bf 6x+42=180[/tex] (Simplify)

[tex]\bf 6x+42-42=180-42[/tex](Subtract both sides by 42)

[tex]\bf 6x=138[/tex] (Simplify)

[tex]\bf \cfrac{6x}{6}=\cfrac{138}{6}[/tex] (Divide both sides by 6)

[tex]\bf x=23[/tex]

Therefore, x = 23.

_____________________

Hope this helps!

Have a great day!

The equivalent expression of (10⁻² . 4⁵)⁻² is 10⁴ / 4¹⁰

We have to find the expression that is equivalent to the expression below:

(10⁻² . 4⁵)⁻².

Therefore, using the law of indices,

[tex](x^{a} )^{b} = x^{ab}[/tex]

Hence, let's find the equivalent expression by applying the laws of indices.

(10⁻² . 4⁵)⁻² = 10⁴ . 4⁻¹⁰

Also, applying the law of indices,

[tex]x^{-b} = \frac{1}{x^{b} }[/tex]

Therefore,

10⁴ . 4⁻¹⁰ = 10⁴ / 4¹⁰

learn more on exponential expression here:https://brainly.com/question/10628562

#SPJ1

Answer:

[tex]\mathrm{b = 2\frac{A}{h} - a}[/tex]

Translation:

Option C.

Answer:

5/3 + 15/4 are the fractions

Answer: x=-3-[tex]\sqrt{7}[/tex] or x=-3+[tex]\sqrt{7}[/tex]

Step-by-step explanation:

f(x)=x+1. g(x)=x+5

(f * g)(x)=

f(x)*g(x)=

(x+1)(x+5)=

x^2+5x+x+5=x^2+6x+5

x^2+6x+5=3

x^2+6x+9=7 ==> Add 4 on both sides of the equation

(x+3)^2=7

x+3=[tex]\sqrt{7}[/tex]

x=-3+[tex]\sqrt{7}[/tex]

x+3=-[tex]\sqrt{7}[/tex]

x=-3-[tex]\sqrt{7}[/tex]

The fraction that is greater is 36/104 since 34.62% is greater than 32.11%

Fractions are written as the ratio of two integers. For instance a/b is a fraction.

In order to determine which of the fractions is greater, we will express them as percentage as shown:

35/109 * 100

3500/109

32.11%

Similarly;

36/104 * 100

3600/104

34.62%

Hence the fraction that is greater is 36/104 since 34.62% is greater than 32.11%

Learn more on percentages here: https://brainly.com/question/24877689

#SPJ1

Answer:

[tex]1cm = 20 \times 100 \\ = 2000cm \\ 1cm = 2000cm[/tex]

Answer:

True

Step-by-step explanation:

Because you never expect when something may show up once your doing something and forget about what you lost a while back. Sometimes it just pops up and we're like, "Oh that's where it was".

Can't say true or false because both can be answers in different cases, mathematically speaking you can select one thing from a set of similar things having similar chance to be selected. and again you can also select one thing at random from a set of things having different chance of being selected. in my perspective:)

and maybe the question has more chance to be false because if a statement is false at least in one case it is false.

Since the values on both sides of the expression are different, hence the equation has no solution.

Linear equation are equations that has a linear degree of 1. The standard linear equation is y = mx + b

Given the expression 4x+3x-x=-5+6x

Collect the like terms

4x+3x-x = -5+6x

4x+3x-x-6x = -5

7x - 7x = -5

Simplify

-0x = -5

0x = 5

x = 5/0

Since the values on both sides of the expression are different, hence the equation has no solution.

Learn more on linear function here; https://brainly.com/question/15602982

#SPJ1

The value of x is -5

Algebraic expressions are expressions that comprised of;

They are also made of mathematical operations such as addition, subtraction, multiplication, division, bracket, etc

Given the equation;

4x + 3x = -5 + 6x

Let's solve for x

We have;

collect like terms

4x + 3x - 6x = -5

Add or subtract like terms

7x - 6x = - 5

x = -5

Thus, the value of x is -5

Learn more about algebraic expressions here:

#SPJ1

Answer:

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

y is greater by 100 times

Answer:

[tex](x-1)(x+4)[/tex]

Step-by-step explanation:

Given:

[tex]x^2+3x-4[/tex]

The best way to write a polynomial with three terms as a product of binomials is to FACTOR!

The middle number is 3 and the last number is -4.

Factoring means we want something like

[tex](x+?)(x+?)[/tex]

We need two numbers that...

ADD together to get 3 and

MULTIPLY together to get -4

Test the numbers -1 and 4:

[tex]-1+4=3\\(-1)4=-4[/tex]

These are the right numbers! Now, I can write them as factored binomials!

[tex](x-1)(x+4)[/tex]

Answer:

172 kilowatts.

Step-by-step explanation:

Energy : 237.188 billion = 237,188,000,000 = 2.37188 × 10¹¹

People : 1.379 billion = 1,379,000,000 = 1.379 × 10⁹

Divide both values : 2.37188 ÷ 1.379 = 1.72; 10¹¹ ÷ 10⁹ = 10² ⇒ 1.72 × 10² or 172 kilowatts.

Answer:

4 and 5

Step-by-step explanation:

We need 2 positive numbers that are right beside each other, like 1 and 2. When the problem is translates into number format we get:

y^2+4x=41

x = 1st # and y = 2nd #

so if we do 4 (x) and 5 (y)

5^2+4(4)=41

the statement is true.

Answer:

1/81

Step-by-step explanation:

[tex](3^2)^{-2}=3^{-4}=\frac{1}{3^4}=\frac{1}{81}[/tex]

Main Answer:1) (x + 2)

                     2) The numbers are 19 and 21.

Concept and definitions should be there:

An odd integer n is an integer which is not a multiple of 2 (or equivalently one more than a multiple of 2). The odd integers are ..., -5, -3, -1, 1, 3, 5, ... Every odd integer can be written in the form 2k + 1 for some unique integer k.

The product of any two odd integers is odd and the result of a division where both the dividend and the divisor are odd is odd. But the sum and difference of any two odd integers are even.

The sum and difference of an even integer and odd integer are odd. Besides 2, all prime numbers are odd. Also, odd integers are really cool

This article is a stub. Help us out by expanding it.

Given data:

1) We have two consecutive odd integers.

Solving part:

Remember that the distance between any two consecutive odd numbers is 2.

5 - 3 = 2

7 - 5 = 2

13 - 11 = 2

etc.

So if the smaller of the two odd numbers is x, then the larger one will be (x + 2).

Given that:

2) We have two consecutive odd numbers, let's write them as:

Solving part:

(2*n + 1) and (2*n + 3)

Where n is an integer number.

We know that the smaller one is 12 more than one third of the larger one, so we have:

(2*n + 1) = 12 + (2*n + 3)/3

Now we can solve this for n

2*n + 1 = 12 + (2/3)*n + 1

2*n - (2/3)*n = 12 + 1 - 1

(4/3)*n = 12

n = (3/4)*12 = 9

n = 9

Then the two consecutive odd integers are:

(2*n + 1) = (2*9 + 1) = 19

(2*n + 3) = (2*9 + 3) = 21

Final Answer:1) (x + 2)

                      2) The numbers are 19 and 21.

To learn about more about the visit: https://brainly.com/question/24551236 #SPJ9.

Answer:

$ 850.25

Step-by-step explanation:

I will assume anything over 40 hours is 'overtime'

total pay will be

   regular pay    +   overtime pay

 17.90 * 40 hr    +   (17.90 * 1.5)(5hr) = $ 850.25