Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false. Show all work.

A) 4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) = 4(4n+1)(8n+7)/6

B) 1^2 + 4^2 + 7^2 + ... + (3n - 2)^2 = n(6n^2 - 3n - 1)/2

For the given statement Pn, write the statements P1, Pk, and Pk+1.
C) 2 + 4 + 6 + . . . + 2n = n(n+1)

Answer:

x=11

Step-by-step explanation:

Answer:

x=11

Step-by-step explanation:

Triangles always add up to 180 degrees

Answer:

13.52 fluid ounces should be the right answer! :)

Step-by-step explanation:

Andre drank from the bottle 13.52 fluid ounces if he drank 80% of bottle.

Percentage is defined as the parts of a number in a whole of 100. This is denoted by the symbol '%'.

In other words, percentage can be defined as the ratio expressed as a fraction of 100.

Any number can be expressed as a percentage of another number by dividing the number with the whole of other number and then multiplying with 100.

Given that, fluid contained in a sports bottle = 16.9 fluid ounces.

Andre drank 80% of the fluid contained in the bottle.

80% of the bottle = 80% × 16.9

                             = (80 / 100) × 16.9

                             = 0.8 × 16.9

                             = 13.52

So this is the total fluid ounces Andre drink.

Hence Andre drank 13.52 fluid ounces from the bottle.

To learn more about Percentage, click on the link given below :

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Answer:

y = -x - 3

x = -y - 3

Step-by-step explanation:

If solving for y,

-7y = 7x + 21

-y = -x + 3 (dividing everything by 7)

y = -x - 3

If solving for x,

-7y = 7x + 21

-y = -x + 3

x = -y - 3

Answer:

x=20

Step-by-step explanation:

bc 25 divided by 10 is 2.5 so you just multiply 8 by 2.5

Answer: X= 20

If solving for x

Step-by-step explanation:  

x/25= 8/10    

1= reduce the fraction to x/25= 4/5

2= cross multiply 5x=100

3= divide both sides X=20

Hope this helps. pls mark me brainliest

Answer:

mid point = (5.5,3.5) distance = 5.830951895

Step-by-step explanation:

4+7=11, 11/2 = 5.5

6+1=7, 7/2 = 3.5

root (7-4)^2 + (1-6)^2 = 5.830951895

Answer:

c

Step-by-step explanation:

proportionality of 4 on all

Answer:

Hi, person.

Step-by-step explanation:

Step-by-step explanation:

first criss cross

then minus by 1 over 4

OR

find lcm of 3 6 4 and after you get it write the number out side let # be the lcm and let me show you #(2,5)&#(_1) and solve it

Answer:

168 in.²

Step-by-step explanation:

it is the correct answer

Answer:

the area is 50.27

Step-by-step explanation:

Use the formula and you can get the answer A=πr2

Answer: 50.27

Step-by-step explanation:

Answer:

Step-by-step explanation:

It's C.

Answer:

haha i feel bad i dont know lol

Answer:

1.08

Step-by-step explanation:

This is because it grows upon itself so it starts with a multiplier of 1, but it is growing with .08 (8 percent) on itself so you add these two numbers together to get 1.08

Answer:

It B

Step-by-step explanation:

This is because the y-intercept is 3 and it going down

Hope this Helped

Answer:

y = [tex]-\frac{10}{3}[/tex]x + 70

or

y = 70 [tex]-\frac{10}{3}x[/tex]

(They're both the same equation, whichever one you prefer you can use!)

Answer:

The first one

Step-by-step explanation:

Negative b plus and minus the square root of b squared minus 4ac divided by 2a

Answer:

x=-6

Step-by-step explanation:

3x+8=-10

Isolate x and its coefficient by subtracting 8 from both sides

3x=-18

Divide by 3

x=-6

Answer:

X = -6

Step-by-step explanation:

3 times -6 = -18, and -18 + 8 = -10

Answer:

Se requiere una fuerza de 854.473 newtons sobre el émbolo pequeño.

Step-by-step explanation:

Por el Principio de Pascal se conoce que el esfuerzo experimentado por el elefante es igual a la presión ejercida por el plato pequeño. Es decir:

[tex]\frac{F_{1}}{A_{1}} = \frac{F_{2}}{A_{2}}[/tex] (1)

Donde:

[tex]F_{1}[/tex] - Fuerza experimentada por el elefante, medida en newtons.

[tex]F_{2}[/tex] - Fuerza aplicada sobre el plato pequeño, medida en newtons.

[tex]A_{1}[/tex] - Área del plato grande, medida en metros cuadrados.

[tex]A_{2}[/tex] - Área del plato pequeño, medida en metros cuadrados.

La fuerza aplicada sobre el plato pequeño es:

[tex]F_{2} = \left(\frac{A_{2}}{A_{1}} \right)\cdot F_{1}[/tex]

La fuerza experimentada por el elefante es su propio peso. Por otra parte, el área del plato es directamente proporcional al cuadrado de su diámetro. Es decir:

[tex]F_{2} = \left(\frac{D_{2}}{D_{1}} \right)^{2}\cdot m\cdot g[/tex] (2)

Donde:

[tex]D_{1}[/tex] - Diámetro del plato grande, medido en centímetros.

[tex]D_{2}[/tex] - Diámetro del plato pequeño, medido en centímetros.

[tex]m[/tex] - Masa del elefante, medida en kilogramos.

[tex]g[/tex] - Aceleración gravitacional, medida en metros por segundo cuadrado.

Si sabemos que [tex]D_{1} = 0.75\,m[/tex], [tex]D_{2} = 0.13\,m[/tex], [tex]m = 2900\,kg[/tex] y [tex]g = 9.807\,\frac{m}{s^{2}}[/tex], entonces la fuerza a aplicar al émbolo pequeño es:

[tex]F_{2} = \left(\frac{0.13\,m}{0.75\,m} \right)^{2}\cdot (2900\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)[/tex]

[tex]F_{2} = 854.473\,N[/tex]

Se requiere una fuerza de 854.473 newtons sobre el émbolo pequeño.

Answer:

C. a^2 + b^2 = c^2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Ratio 4:5 means:

width: W = 4x

length: L = 5x

Area of rectangle:  A = W×L

Therefore:

              500 = 4x×5x

               500 = 20x²

               50 = 2x²

                x² = 25

                x = 5

W = 4×5 = 20 cm

L = 5×5 = 25 cm

Answer:

1: male + female [tex]\leq[/tex] 30

2: 140 + 25x [tex]\geq[/tex] 550

Step-by-step explanation:

Answer:

We can see the two triangles ABC and EDC are similar and their sides are proportional.

4 to 8, 6 to 12, 5 to 10

You could say,

1. ABC ~ EDC -- SSS criterion

2. ∠A = ∠E -- CPCTC

3. AB || ED -- Alternate Interior Angles Converse

Answer:$12 dollars and hour

Step-by-step explanation:

7 hours times 5 days a week equals 35 hours. 420/35 hours equals 12 dollars

Answer:

A w=V/ lh

b) 8cm

Step-by-step explanation:

w=V/ lh

w= 120/(3×5)

w= 120/15 = 8cm

Answer: Alright So, A bag is filled with green and blue marbles. There are 48 marbles in the bag. If there are 38 more green marbles than blue marbles, find the number of green marbles and the number of blue marbles in the bag.

------

Equations:

g + b = 48 marbles

g = b + 38

------

Substitute for "g" and solve for "b"::

b+38 + b = 48

2b = 10

b = 5 (# of blue marbles)

g = b+38 = 43 (# of green marbles)

Step-by-step explanation:

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

Explanation:

Start at the point (0,1). This is the y intercept, which is where the graph crosses the y axis.

Then move down 1 and over to the right 4 spaces. We arrive at (4,0) which is the x intercept.

The process of "down 1, over to the right 4" can be thought of like this

rise/run = -1/4

rise = -1

run = 4

A rise of -1 indicates we go down 1 unit

The run of 4 means we move to the right 4 units

So that's why slope = rise/run = -1/4

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Here's another approach using the slope formula:

m = (y2-y1)/(x2-x1)

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

m = -1/4

I used the two points (0,1) and (4,0) as (x1,y1) and (x2,y2) respectively. This formula basically says "subtract the y coordinates, subtract the x coordinates in the same order, then divide the differences y over x".

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Side note: The line moving downhill, as we read from left to right, indicates a negative slope.