Find a formula for the sum of the first n even integers : 2 + 4 + 6 + ... + 2n.

Answer:

18

Step-by-step explanation:

[tex]3(5 + 1) \\ 3(5) + 3(1) \\ 15 + 3 \\ 18[/tex]

The distributive property means you distribute the multiple to all terms in the parenthesis, in this case the terms are 5 and 1.

Answer:

5

Step-by-step explanation:

The distance between two points [tex]P[/tex] and [tex]Q[/tex] is  [tex]d = \sqrt{\sum_{i=1}^{n} \left(q_{i} - p_{i}\right)^{2}}[/tex] ([tex]n[/tex] s the number of coordinates of each of the two points, [tex]p_i[/tex] , [tex]i=1..n[/tex] and [tex]q_i,i=1..n[/tex]

are the coordinates of the first and the second points respectively).

Thus, [tex]d = \sqrt{\left(2 - 5\right)^{2} + \left(-3 - 1\right)^{2}}=5.[/tex]

Answer:

The diameter is 12.

Explain: i used this formula C= Dπ  or C= 2rπ  

(37.68) = Dπ Divide by 3.14, as the instructions in this question specify to do so.

37.68/3.14 = D π/ 3.14

D = 12  The diameter equals twelve.

Hope This Helped

Answer:

x = 5 and y = 22

Step-by-step explanation:

See attached image.

Answer:

[tex]f(x)= \sin(6x)+3[/tex]

Step-by-step explanation:

The parent function of this graph is:  y = sin(x)

The sine function is periodic, meaning it repeats forever.

Standard form of a sine function:

[tex]f(x) = \sf A \sin (B(x + C)) + D[/tex]

The parent function y = sin(x) has the following:

From inspection of the given graph:

[tex]\sf If\:Period=\dfrac{\pi}{3} \implies \dfrac{2 \pi}{B}=\dfrac{\pi}{3}\implies B=6[/tex]

Substituting the values into the standard form:

[tex]\implies f(x) =1 \sin (6(x + 0)) + 3[/tex]

[tex]\implies f(x) = \sin (6x) + 3[/tex]

Therefore, the equation of the given trigonometric graph is:

[tex]f(x)= \sin(6x)+3[/tex]

Answer(s):

[tex]\displaystyle y = cos\:(6x - \frac{\pi}{2}) + 3 \\ y = -sin\:(6x \pm \pi) + 3 \\ y = sin\:6x + 3[/tex]

Step-by-step explanation:

[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 3 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{\pi}{12}} \hookrightarrow \frac{\frac{\pi}{2}}{6} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{3}} \hookrightarrow \frac{2}{6}\pi \\ Amplitude \hookrightarrow 1[/tex]

OR

[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{3}} \hookrightarrow \frac{2}{6}\pi \\ Amplitude \hookrightarrow 1[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the sine graph, if you plan on writing your equation as a function of cosine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = cos\:6x + 3,[/tex]in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cosine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{12}\:unit[/tex]to the left, which means that in order to match the sine graph [photograph on the left], we need to shift the graph FORWARD [tex]\displaystyle \frac{\pi}{12}\:unit,[/tex]which means the C-term will be positive, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\frac{\pi}{12}} = \frac{\frac{\pi}{2}}{6}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle y = cos\:(6x - \frac{\pi}{2}) + 3.[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit [tex]\displaystyle [-\frac{5}{12}\pi, 2],[/tex]from there to [tex]\displaystyle [-\frac{\pi}{12}, 2],[/tex]they are obviously [tex]\displaystyle \frac{\pi}{3}\:unit[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \frac{\pi}{3}.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 3,[/tex]in which each crest is extended one unit beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

Answer:

10/3 or 3.333333

Step-by-step explanation:

-   4 x 5/6 is 3 1/3

-   3 1/3 is a mixed number

- 3 1/3 reduced is 10/3

Answer:

(-1,4)

Step-by-step explanation:

For x     the midpoint between   -2 and 0    is -1

for y the midpoint between -1 and 9 is  4

Answer:

(-1,4)

Step-by-step explanation:

Midpoint can be found by:

(x1+x2)/2 ; (y1+y2)/2

So, if we substitute, we can find:

(-2+0)/2 ; (-1+9)/2

This gives us -2/2 and 8/2, which is:

(-1, 4)

Hope this helps!

Explanation:

Provided 2 length sides and one angle also need to find one missing side.

So, use cosine rule:

a² = b² + c² - 2bc cos(A)

c² = 9² + 11² - 2(11)(9) cos(57)

c² = 94.16147

c = √94.16147 = 9.70 cm

d² = 5² + 7² - 2(5)(7) cos(48)

d² = 27.16

d = √27.16 = 5.21

5² = 7² + 9² - 2(7)(9) cos(H)

-126cos(H) = 25 - 49 - 81

cos(H) = -105/-126

cos(H) = 5/6

H = cos⁻¹(5/6) = 33.56°

8² = 4² + 7² - 2(4)(7) cos(J)

-56cos(J) = 64 - 16 - 49

cos(J) = -1/-56

J = cos⁻¹(1/56) = 88.98°

Passcode: 3142

Answer:

No

Step-by-step explanation:

NO...... any two sides added together must be GREATER THAN the third side .... 2 + 8 is NOT greater than 19

Answer:

x³ - ((x+1)(x+1))

Step-by-step explanation:

x³ + 2x -3 - x² - 2x + 4

x³ - x² + 1

x³ - ((x+1)(x+1))

Answer:

x^3−x^2+4x−7

Step-by-step explanation:

Hope this helps! Have a great day!!

Answer:

130 m²

Step-by-step explanation:

Area of a parallelogram is given by the formula :

A = bh (b is the base length and h is the perpendicular height)

Now we simply substitute values given in diagram to find our answer:

A = bh

A = (13)(10)

A = 130

Units will be m² as this is area

Hope this helped and have a good day

answer:

483.5

step by step explanation:

2x-45y=22

2x-45(21)=22

2x-945=22

2x =22+945

2x=967

x=483.5

Answer:

206.17

Key(s):

[tex]A = 2\pi \frac{d}{2} h + 2\pi \left(\frac{d}{2}\right)^2[/tex]

Substitute d for the actual diameter, 7.5, and h for the height, which is 5.

Step-by-step explanation:

[tex]A = 2\cdot\pi \cdot\frac{7.5}{2} \cdot5 + 2\cdot\pi \cdot\left(\frac{7.5}{2}\right)^2[/tex] ≈ 206.17(2 DP)

The error Kevin made was in step 2 when he added before he multiplied.

This question would be solved using the BODMAS rule. The BODMAS rule provides the order in which mathematical problems should be solved. The order is:

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Answer:

Step-by-step explanation:

Volume = (1/3) * base_area * height

1/3 * 4 * 4 * 9 =

48 cm³

a) TI = 7√3 in

b) IR = 7 in

Using cosine rule:

[tex]\sf cos(x) = \dfrac{adjacent}{hypotenuse}[/tex]

[tex]\hookrightarrow \sf cos(30) = \dfrac{TI}{14}[/tex]

[tex]\hookrightarrow \sf TI = 14cos(30)[/tex]

[tex]\hookrightarrow \sf TI = 7\sqrt{3}[/tex]

Using sine rule:

[tex]\sf sin(x) = \dfrac{opposite}{hypotenuse}[/tex]

[tex]\hookrightarrow \sf sin(30) = \dfrac{IR}{14}[/tex]

[tex]\hookrightarrow \sf IR = 14sin(30)[/tex]

[tex]\hookrightarrow \sf IR = 7[/tex]

Tables are created by substitute a set of input values into the function to create outputs. The required table is as shown below

x | y

0   -3

1   -2.5

2   -2

Tables are created by substitute a set of input values into the function to create outputs

Using x = 0, 1 and 2 as the input values

Given the function

y = 1/2x - 3

If x = 0

y = 1/2(0) - 3

y = -3

If x = 1

y = 1/2(1) - 3

y = -2.5

If x = 2

y = 1/2(2) - 3

y = -2

Hence the required table is as shown below

x | y

0   -3

1   -2.5

2   -2

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4,7,3,2

Step-by-step explanation:

THESE ARE THE THE ARRANGEMENT OF NUMBERS IN ORDER TO GET THE CLOSEST TO 5000

Answer:

Hi,

Step-by-step explanation:

Let's say y=a*b^x the equation of the exponential function.

0.9=a*b^1 (1)

1.62=a*b² (2)

(2)/(1) ==> b=1.62/0.9=1.8

and

0.9=a*1.8 ==> a=0.5

y=0.5*1.8^x

The solution to the equation x² – 4x + 4 = 2x + 1 + x² is x = 2.5 and the graph is shown in the picture.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have an equation:

x² – 4x + 4 = 2x + 1 + x²

After solving:

-4x + 4 = 2x + 1

6x = 3

x = 1/2 = 0.5

Thus, the solution to the equation x² – 4x + 4 = 2x + 1 + x² is x = 2.5 and the graph is shown in the picture.

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Answer:

what ya need man I can help but give me a question

Answer:

The graph will open to the right and will be mostly in quadrant 1

Step-by-step explanation:

Answer:

it would end up being about $40.73

Step-by-step explanation:

multiply 0.078 by 3 then multiply that by 33

Answer:

hope you can understand

Answer: Analytic geometry

Answer: B.

Explanation and reasoning:

The true statement is (c) Neither. Both events are equally likely.

The probability of Sandy flipping a coin twice and getting heads both times is 0.25. The probability of John's spinner stopping on the color red is 1/4.

Which of these events is more likely?

-Sandy flips a coin twice and gets heads both times.

-John's spinner stops on the color red.

-Neither. Both events are equally likely.

The given parameters are:

P(Head twice) = 0.25

P(Red) = 1/4

Rewrite P(Red) as:

P(Red) = 0.25

By comparison, we have:

P(Red) = P(Head twice) = 0.25

This means that both events are equally likely

Hence, the true statement is (c)

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Answer:

  84 cm²

Step-by-step explanation:

The figure has a uniform horizontal cross section, so its area is the product of that cross section length and its vertical dimension.

__

  A = bh

  A = (6 cm)(14 cm) = 84 cm²

The area of the shape is 84 square centimeters.

_____

Additional comment

You could decompose the figure into a rectangle with base 6 and height 8, and a parallelogram with base 6 and height 14-8=6. The area formula is the same for each: A = bh, so the area of the composite figure is ...

  A = 6×8 +6×(14 -8)

  = 6×(8 +(14 -8))

  = 6×14 . . . . same as above.