Write the following series in sigma notation. 6 + 8 + 10 + 12 + 14 + 16 + 18​

Answer: y=-2x+8

Step-by-step explanation: Write a table of values where for every x y goes down 2 to find the y intercept (0,8) so it would be 8. The slope is -2 and that is all you need to write the equation.

The graph of each equation is attached below each showing the point of intersection to the y-axis.

To solve this question, we have to use a graphing calculator to plot the coordinates as well as show the point of intersection.

A line graph is a graphical representation of information that changes over a period of time. It is a chart made by joining points using line segments.

The graph of equation is attached below.

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According to the central limit theorem for sums, if you keep taking sums from bigger and bigger samples, the sums will eventually form their own normal distribution (the sampling distribution), which will become more similar to a normal distribution as the sample size grows.

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Answer: 60% chance or 3:5

Step-by-step explanation: well, 40/24 is 0.6, which is 60%, or you can see 4 is 10%, and 20 is 50%, and add them together to get 60%. 60% is also 6:10, which can be simplified to 3:5

Step-by-step explanation:

a linear function must follow the structure

y = ax + b

we use the given data point numbers for x and y to solve for the 2 variables a and b.

we use 2 data points to get a solution for the 2 variables. if the third data point then fits into the same equation, then all 3 points are on a line, and the function is therefore linear. if not, then not.

-8 2/5 = a×-7 1/2 + b

-6 = a×-1 1/2 + b

let's subtract the second from the first equation to eliminate b and solve for a :

-8 2/5 = a×-7 1/2 + b

- -6 = a×-1 1/2 + b

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

-2 2/5 = a×6 0

6a = -2 2/5 = (-2×5 - 2)/5 = -12/5

a = -12/5 / 6 = -2/5

and now we use one of the 2 original equations with the newly found information to solve for b :

e.g.

-6 = -2/5 × -1 1/2 + b = -2/5 × -3/2 + b = 6/10 + b = 3/5 + b

-6 - 3/5 = b

(-6×5 - 3)/5 = b

-33/5 = b

so, our proposed linear function is

y = -2x/5 - 33/5

let's see, if the third point is on the line (then the equality is true for its coordinates) or not :

-2 = -2/5 × 8 1/2 - 33/5 = -2/5 × (8×2 + 1)/2 - 33/5

-2 = -2/5 × 17/2 - 33/5 = -34/10 - 33/5 = -34/10 - 66/10

-2 = -100/10 = -10

that is not true (-2 is not equal to -10), so the third point is not on the line between the first 2 points.

that means the function is nonlinear.

The amount Annika should give to Susan is $3.12

What is Algebra?

One of the many branches of mathematics is algebra. Algebra is a common thread that runs through nearly all of mathematics. It involves the study of mathematical symbols and the rules for using them in formulas.

Given,

The amount of money Annika spend = $15.95

The amount of money Tamara spend = $18.46

The amount of money Susan spend = $22.80

The total amount of money:

$15.95 + $18.46 + $22.80 = $57.21.

The average money spent :

= $57.21/3

= $19.07 ,  for each girl.

Thus Annika should give Susan

= $19.07 - $15.95

= $3.12

Hence, Annika should give $3.12 to Susan

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After decreasing £16870 by 3% we get, £16363.90

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

First, find the percentage of £16870 by 3%

%value = 3% * 16870

            = (3 / 100) * 16870

            = 506.1

Now, just minus with actual value

New value = actual value - %value

We know, actual value = £16870 and %value = 506.1

so, New value = 16870 - 506.1

we get, New value = £16363.90

Therefore, After decreasing £16870 by 3% we get, £16363.90

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The graph of an inequality is a region in the Cartesian plane. To know which line is the limit of the graphical region, the inequalities are as if they were equations, that is, graph the following lines:

To do this, first clear y in each of the equations:

First equation

Second equation

Now, give x values ​​that are within the domain of each equation and replace them in each equation to find its corresponding value in y:

First equation

Second equation

Now, with the points found you can graph the lines that are the limit of the inequalities. So, you have

Finally, it only remains to paint the regions, taking into account the symbols of the inequalities

In the case of the first inequality, you can see that y "is less than" the rest of the terms, and in the second inequality, you can see that y "is greater than" the rest of the terms.

Therefore, the graph of the given system of inequalities is

[tex]\cfrac{13u^3 y^2 - 32u^2 y}{-4u^3 y^2}\implies \cfrac{13u^3 y^2}{-4u^3 y^2}-\cfrac{32u^2 y}{-4u^3 y^2}\implies -\cfrac{13}{4}+\cfrac{8}{uy}[/tex]

Firstly, we will need to try the following options one after the other in order to ascertain our answer

The first option

To find the distance between two points

Distance = Higher number - Lower number

-3 - 20

= - 23

This is very wrong because it has a negative sign

The second option

7 - (-16)

In mathematics, - x - = +

7 + 16

7 + 16 = 23

The answer is OPTION B

Answer:

-6

Step-by-step explanation:

by using -6 any value of x would make the equation true resulting in infinitly many solutions

The value of the car in very nice condition is $5177.

From the information, a car that originally cost $3,668 in 1955 is valued today at $62,125 if in excellent condition, which is 12 times as much as a car in very nice condition.

Let the value of the nice condition car be x

Therefore, the expression will be;

= (12 × x) = 62125

12x = 62125

Divide

x = 62125 / 12

x = 5177

The value is $5177.

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The vertices of the image are the points J'(x, y) = (3, - 1), K'(x, y) = (4, - 5) and L'(x, y) = (0, - 3), respectively.

Triangles are created by three non-colinear points called vertices and the location of the image of the triangle is found by using a reflection around a line parallel to the x-axis for every point of the figure. This operation is described by the following expression:

P'(x, y) = P(x, y) - 2 · [P(x, y) - (p, k)]

Where:

If we know that J(x, y) = (3, - 5), K(x, y) = (4, - 1), L(x, y) = (0, - 3) and k = - 3, then the coordinates of the vertices of the image of the triangle are:

J'(x, y) = (3, - 5) - 2 · [(3, - 5) - (3, - 3)]

J'(x, y) = (3, - 5) - 2 · (0, - 2)

J'(x, y) = (3, - 5) + (0, 4)

J'(x, y) = (3, - 1)

K'(x, y) = (4, - 1) - 2 · [(4, - 1) - (4, - 3)]

K'(x, y) = (4, - 1) - 2 · (0, 2)

K'(x, y) = (4, - 1) + (0, - 4)

K'(x, y) = (4, - 5)

L'(x, y) = (0, - 3) - 2 · [(0, - 3) - (0, - 3)]

L'(x, y) = (0, - 3) - 2 · (0, 0)

L'(x, y) = (0, - 3) + (0, 0)

L'(x, y) = (0, - 3)

The vertices of the image of the triangle are J'(x, y) = (3, - 1), K'(x, y) = (4, - 5) and L'(x, y) = (0, - 3).

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The surface age. The surface age is the amount of time that has passed between the start of a surface's or interface's creation and the observation or measurement. A continuous probability distribution called a normal distribution has values distributed symmetrically, primarily in an area around the mean.

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Answer:

|0.525| > |−0.067|

Step-by-step explanation:

Simplifying then comparing both terms |0.525| and |−0.067|, 0.525 is greater than 0.067, which means that the first term is greater than the second term.

Answer:

a. x=5

b. x=4

Step-by-step explanation:

Answer:

79.

Step-by-step explanation:

Replace the x by -5 and simplify:

f(-5) = 3(-5)^2 + (-5) + 9

       = 75 - 5 + 9

       =  79.

The value of f(-5) will be 79.

Step-by-step explanation:

An expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s) is called a polynomial.

The following table gives special names given to polynomials of low orders.

polynomial order polynomial name

2                         quadratic polynomial

3                         cubic polynomial

4                        quartic

5                         quintic

6                         sextic

Here, the given polynomial: f(x) = 3x² + x + 9

by putting value of x = -5

[tex]3*(-5)^{2} + (-5) + 9[/tex]

after putting we get,

[tex]75 - 5 + 9[/tex]

On solving the above numerical we get,

[tex]79[/tex].

So our final answer would be 79 on putting x = -5 in the given polynomial : f(x) = 3x² + x + 9

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In elementary algebra, the binomial expansion defines the algebraic expansion of powers of a binomial. The binomial equation be 27x² - 300 exists 3(3x + 10)(3x - 10).

In elementary algebra, the binomial theorem (or binomial expansion) defines the algebraic expansion of powers of a binomial. According to the theorem, it exists possible to extend the polynomial  [tex]$(x+y)^n$[/tex] into a sum involving terms of the form [tex]$a x^b y^c$[/tex], where the exponents b and c exists nonnegative integers with b + c = n, and the coefficient a of each term exists a specific positive integer depending on n and b.

Let the binomial equation be 27x² - 300

Factor out common term 3:

[tex]$\quad 3\left(9 x^2-100\right)$[/tex] [tex]$=3\left(9 x^2-100\right)$[/tex]

simplifying the above equation, we get

Factor [tex]$9 x^2-100: (3 x+10)(3 x-10)$[/tex]

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

If 3(3x - b)(3x + b) then we get

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

b = 10

The value of b = 10.

Therefore, the correct answer is option a. 10.

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Cost of the TV before sale £350

We come across phrases like cost price, tagged price, discount, and selling price when making a purchase. Shop owners give discounts to customers to encourage product sales. Discount is the term used to describe a rebate or an offer made to clients on the listed price of goods. Let's examine the connections between these concepts.

Given,

Sale% = 20%

The cost of TV after the sale = £280

Finding the original price:

                   100% - 20% = 80%

So 80% is the price £280

We have to find the 20% which has been less

Or, £280 = 0.80 x T

Let the original price be T,

                               280 = 0.80 x T

                               280/0.80 = T

                                      350 = T

Hence, the original price of the TV was £350.

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The equivalent expression of 8(x+3)−14(20x−56)​ is - 272x + 808.

Two algebraic expressions are equivalent, when the two expressions have the same value when we plug in the same value(s) for the variable(s).

In other words, two algebraic expressions are said to be equivalent if their values obtained by substituting the values of the variables are same.

Therefore, the equivalent expression of 8(x+3)−14(20x−56)​ can be found as follows;

8(x+3) − 14(20x−56)​

open the parenthesis

8x + 24 -  280x + 784

combine the like terms

8x + 24 -  280x + 784

8x -  280x + 24 + 784

Therefore, the equivalent expression is as follows:

- 272x + 808

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Answer:

  C) The circumcenter is on the outside of an obtuse triangle.

Step-by-step explanation:

You want to know where the circumcenter is in relation to the sides and vertices of different triangles.

The circumcenter of a triangle is the center of the circle through its vertices. As such, it will never lie on a vertex of the triangle.

As you can see in the attached figure, the circumcenter of an acute triangle is inside the triangle.

For a right triangle, the circumcenter is the midpoint of the hypotenuse.

The circumcenter of an obtuse triangle is outside the triangle.

__

Additional comment

The circumcenter is located at the point where the perpendicular bisectors of the sides meet.

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Answer:

0.315

Step-by-step explanation:

Answer:

u hv to do middle terms ig

Answer:

y-intercept= (0,0)

Step-by-step explanation:

4x+5y=0

4(0)+5y=0

5y/5=0/5

y=0

4x+5(0)=0

4x/4=0/4

x=0

same for x-intercept (0,0)

The area of a parallelogram is:

a = bh

The base, b, of the parallelogram is 14.

The issue with this particular figure? We need the perpendicular height. We are given the side width, but that cannot be used in the final equation. So, we employ the Pythagorean Theorem.

We know that in the right triangle, a = 4, and c = 8.

a^2 + b^2 = c^2
4^2 + b^2 = 8^2
16 + b^2 = 64
16 - 16 + b^2 = 64 - 16
b^2 = 48
√b^2 = √48
b ≈ 6.93

So, b in this right triangle is equal to h in the parallelogram. So:

a ≈ 14(6.93)
a ≈ 97.02

The complete table when Noah is running a marathon at a constant speed of 6 miles per hour is mentioned below:

Time                 Distance

 1                           6

 1/2                        3

 [tex]1\frac{1}{3}[/tex]                         8

 [tex]1\frac{1}{2}[/tex]                         9

  9                        54

 [tex]4\frac{1}{2}[/tex]                        27

The running speed of Noah is 6 mph.

The formula for distance is given as:

D = v × t

Where D is the distance, v is the speed and t is the time.

Now,

When t = 1 hour,

D = 6 × 1 = 6 miles

When t = 1/2hour,

D = 6 × 1/2 = 3 miles

When t = [tex]1\frac{1}{3}[/tex] hour,

D = 6 × [tex]1\frac{1}{3}[/tex] = 6 × 4/3 = 8 miles

When t = [tex]1\frac{1}{2}[/tex] hour,

D = 6 × [tex]1\frac{1}{2}[/tex] = 6 × 3/2 = 9 miles

When t = 9 hours,

D = 6 × 9 = 54 miles

When t = [tex]4\frac{1}{2}[/tex] hour,

D = 6 × [tex]4\frac{1}{2}[/tex] = 6 × 9/2 = 27 miles

Therefore, the table will be:

Time                 Distance

 1                           6

 1/2                        3

 [tex]1\frac{1}{3}[/tex]                         8

 [tex]1\frac{1}{2}[/tex]                         9

  9                        54

 [tex]4\frac{1}{2}[/tex]                        27

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The area of the iPhone 5s in the nearest hundredth is 7252.72 mm².

The iPhone 5s is rectangular in shape and has a base of 58.57 mm and a height of 123.83 mm.

The area of the iPhone 5s can be found as follows:

Therefore,

area of the iPhone 5s = lw

where

Therefore,

l = 58.57 mm

w = 123.83 mm

Hence,

area of the iPhone 5s = 58.57 × 123.83

area of the iPhone 5s = 7252.7231

Therefore,

area of the iPhone 5s = 7252.72 mm²

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Answer:

x = 6

Step-by-step explanation:

8x + 7x = 90

15x = 90

x = 6