How do I do this problem pls help!

When proving by induction, your first step is to show that a given claim is true for some minimal case (often called the base case). The given statement is a claim about the sum of numbers of the form 2n + 1 where n is a positive natural number. The least positive natural number is n = 1, so that seems like a reasonable place to start.

Now, we show the claim holds for n = 1:

3 + 5 + 7 + … + (2n + 1) = n (n + 2)

is a statement about an arbitrary positive integer n; the case of n = 1 reduces to

3 = 1 (1 + 2) = 1 • 3 = 3

which is obviously true.

Next, we assume that the statement is true for some arbitrary positive integer n = k, so that

3 + 5 + 7 + … + (2k + 1) = k (k + 2)

This is called the induction hypothesis.

We then use this assumption to show that the claim is also true for the next positive integer, n = k + 1. This is the claim that

3 + 5 + 7 + … + (2k + 1) + (2 (k + 1) + 1) = (k + 1) (k + 1 + 2)

or

3 + 5 + 7 + … + (2k + 1) + (2k + 3) = (k + 1) (k + 3)

By the induction hypothesis, we have

3 + 5 + 7 + … + (2k + 1) + (2k + 3)

= k (k + 2) + (2k + 3)

= k² + 2k + 2k + 3

= k² + 4k + 3

= (k + 1) (k + 3)

and this is exactly what we wanted to show, that if P(k) is true, then P(k + 1) is also true.

This means we have

P(1) = true   ⇒   P(2) = true   ⇒   P(3) = true   ⇒   …

and so on, and the claim is true for all positive integers n.

Answer:

Nick and Elaine can go on the boat safely

Elaine and Dario can go on the boat safely

Nick and Dario can NOT go on the boat safely

Step-by-step explanation:

Nick's weight + Elaine's weight = 268, 288<310

Elaine's weight + Dario's weight = 287, 287<310

Nick's weight + Dario's weight = 315, 315>310

Answer:

Nick And Elaine Can Go On The Boat Safely

Elaine And Dario Can Go On The Boat Safely

Nick And Dario can Not Go On The Boat Safely

Nick's weight + Elaine's Weight = 268

Elaine's Weight + Dario's Weight = 287

Nick's Weight + Dario's Weight = 315

◊ YusuCr ◊

Answer:

[tex]x=1[/tex]

Step-by-step explanation:

[tex]1+(3x-3)=1[/tex]

First, you have to take the one that is outside of the Parenthesis and take it to the other side. That would mean it would be this:

[tex]3x-3=1-1[/tex]

1 - 1 is 0

[tex]3x-3=0\\[/tex]

Move the -3 to the other side, which makes it positive;

[tex]3x=3[/tex]

Divide both sides by 3

[tex]x=1[/tex]

If you want to check it, you can replace 1 in the original equation:

[tex]1+(3X1-3)=1[/tex]

[tex]1+(0)=1[/tex]

[tex]1=1[/tex]

So x=1

Answer:

A.

Step-by-step explanation:

Rule:

When 2 or more exponents divide, they subtract.

Divide using the rule:

[tex] {4}^{36} \div {4}^{9} = {4}^{36 - 9} = {4}^{27} [/tex]

B, C, and D are incorrect.

A is the correct option.

[tex]( {4}^{9} )^{3} = {4}^{9 \times 3} = {4}^{27} [/tex]

Answer:

2) [tex](4 - 9x) {}^{ \frac{7}{2} } (4 - 9x) {}^{ \frac{7}{2} } [/tex]

3) in image 2

Answer:

78

Step-by-step explanation:

A fraction equivalent to 1 would be 2/2. 78 X 2/2 is 78

Answer:

no

Step-by-step explanation:

Answer:

y = 3

Step-by-step explanation:

Subtract 3 from both sides of the equation

y + 3-3 = -y + 9-3

Simplify

y = -y + 6

Add y to both sides of the equation

y+y=-y+6+y

Simplify

2y = 6

Divide both sides of the equation by the same term

2y/2 = 6/2

Simplify

y = 3

[RevyBreeze]

The solution of the Equation is y= 3.

We have, the equation is

y + 3 = -y + 9

y + y = 9 - 3

2y = 6

Now, divide both side we get

2y = 6

2y/ 2 = 6/ 2

y = 3

Thus, the solution of y is 3.

Learn more about equation here:

https://brainly.com/question/29657983

#SPJ7

Answer:

The answer is A only.

Step-by-step explanation:

Hope that helps!

Answer:

A only.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Time is inversely proportional to speed for the same distance covered. The ratio of commercial to private speeds is ...

  2.4 : 1.6 = 3 : 2

If p is the speed of the private plane, then 3/2p is the speed of the commercial plane and the difference of speeds is ...

  3/2p -p = 180

  1/2p = 180 . . . collect terms

  p = 360 . . . . . . speed of the private plane

  3/2p = 540 . . . . speed of the commercial plane

The commercial jet flies 540 mph; the private plane flies 360 mph.

Answer:

this what i got

Step-by-step explanation:

=1.73205081i

All roots:

1.73205081i

−1.73205081i

3 is not a perfect square

Answer:

1/27

Step-by-step explanation:

Answer:

1/27 is correct give brainliest to fist respond

Answer:

je

Step-by-step explanation:

suis suis pasforet en anglais

We're dealing with percentage. hence, our universal set: U=100%.

Let:A = set of those that read magazine A

B = set of those that read magazine B

C = set of those that read magazine C

(i) we are looking for n{(A n B) u (B n C)}

so, n{(A n B) u (B n C)} = n(A n B) + n(B n C) -n(A n B n C)

n{(A n B) u (B n C)} = 20% + 30% - 10%

: n{(A n B) u (B n C)} = 40%

(ii) We're looking for {A' n B' n C'}

{A' n B' n C'} = n(U) - n(A u B u C)

{A' n B' n C'} = 100% - n(A u B u C)

n(A u B u C) = n(A) + n(B) + n(C) - n{(A n B) - n(A n C) -n(B n C) + n(A n B n C)

n(A u B u C) = 60% + 50% + 50% -30% - 30% - 20% + 10%

n(A u B u C) = 90%

however, {A' n B' n C'} = 100% - n(A u B u C)

: {A' n B' n C'} = 100% - 90%

{A' n B' n C'} = 10%

let me know if you think there's a reason to doubt my answer.

Answer:

  2/3 gallon

Step-by-step explanation:

If y is the amount Tommy should use, and he want to keep the same proportion, then the proportion is ...

  y/(2 gal) = (1/2 gal)/(3/2 gal) = yellow/blue

  y = (2 gal)(1/3) = 2/3 gal

Tommy should use 2/3 gallon of yellow paint.

Answer:

C. the next fraction is 243/324

Step-by-step explanation:

In A, we can see that 12/16 does not fall under the sequence.

In B, all the values in the sequence is 0.75.

In C, the next fraction is determined by multiplying numerator and  denominator by 3. therefor the correct solution is found.

In D, its wrong and does not match.

Check option C

Hence option C is correct as all are equal in this sequence

Answer:

the answer is 19.0384615385

Answer:

33

Step-by-step explanation:

divide 858 by 26

P.S. sorry I am really tired that is why it not as good of an explanation

[tex]A\left[\begin{array}{ccc}1&0&5\\0&-5&7\\0&3&-4\end{array}\right][/tex]

[tex]B\left[\begin{array}{ccc}3&-5&3\\2&3&1\\4&1&-3\end{array}\right][/tex]

[tex]Now,\\\\2B-A\\\\2\left[\begin{array}{ccc}3&-5&3\\2&3&1\\4&1&-3\end{array}\right]-\left[\begin{array}{ccc}1&0&5\\0&-5&7\\0&3&-4\end{array}\right]\\\\=\left[\begin{array}{ccc}6&-10&6\\4&6&2\\8&2&-6\end{array}\right] -\left[\begin{array}{ccc}1&0&5\\0&-5&7\\0&3&-4\end{array}\right]\\\\=\left[\begin{array}{ccc}5&-10&1\\4&11&-5\\8&-1&-2\end{array}\right][/tex]

Row 1 column 2(a12)=-10

Hence,-10 is your answer.

Answer:

https://brainly.com/question/24093265

Step-by-step explanation will be provided in the link above!

Answer:

Two ways to get the solution:

slope = rise

            run

slope =   1  

               3

or

slope = y2- y1

            x2 - x1

slope = -4 - (-5)

              3 - 0

slope =   1  

               3

Answer:

n^3/m^2

Step-by-step explanation:

I simplified the expression and I got ( n^3/m^2)

m^(-2) * n^(3) = n^3/m^2

Answer:

24

Step-by-step explanation:

2×2(3×2)

2×2(6)

2×12

24

Answer:

18

Step-by-step explanation:

33 - 3 = 30

30 ÷ 2 = 15

15 + 3 = 18

answer:

= 3n^2 + 3

...........

[tex]\huge\mathbb\pink{ANSWER:}[/tex]

[tex]\huge\tt\blue{3n² + 3}[/tex]

[tex] \large\tt\pink{••••••••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

[tex](6n^{2} + 5) + ( - 3^{2} - 2)[/tex]

[tex]6 {n}^{2} + 5 - 3 {n}^{2} - 2[/tex]

[tex](6 {n}^{2} - 3 {n}^{2} ) + (5 - 2)[/tex]

[tex](6 - 3) {n}^{2} + (5 - 2)[/tex]

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

[tex]\large\tt\blue{3n² + 3}[/tex]

[tex] \large\tt\pink{••••••••••••••••••••••••••••••••••••••••••••••••••••••••}

[/tex]

Answer:

Q 6.

[tex]2x - x + 4(x - (x + 7) - 2) \\ x + 4(x - x - 7 - 2) \\ x + 4( - 9) \\ = x - 36[/tex]

____o___o___

Q 7.

o 1)

[tex] \frac{ {x}^{2} - 4 }{5 - x} \times \frac{ {x}^{2} - 8x + 15}{ {x}^{2} - 5x + 6 } \\ \\ \\ \frac{(x + 2)(x - 2)}{5 - x} \times \frac{(x - 5)(x - 3)}{(x - 3)(x - 2)} \\ \\ \\ \frac{(x + 2)}{5 - x} \times \frac{(x - 5)}{1} \\ \\ \\ \frac{(x + 2)}{ - ( - 5 + x)} \times (x - 5) \\ \\ \\ \frac{(x + 2)}{ - (x - 5)} \times (x - 5) \\ \\ \\ \frac{(x + 2)}{ - 1} \\ \\ = - (x + 2) \\ \\ = - x - 2[/tex]

___o___o___

o 2)

[tex] \frac{ {x}^{2} - 2x - 8 }{ {x}^{3} + 3 {x}^{2} } \div \frac{x - 4}{ {x}^{2} - 9} \\ \\ \\ \frac{ {x}^{2} - 2x - 8}{ {x}^{3} + 3 {x}^{2} } \times \frac{ {x}^{2} - 9 }{x - 4} \\ \\ \\ \frac{(x - 4)(x + 2)}{ {x}^{2}(x + 3) } \times \frac{(x + 3)(x - 3)}{x - 4} \\ \\ \\ \frac{x + 2}{ {x}^{2} } \times \frac{x - 3}{1} \\ \\ \\ = \frac{(x + 2)(x - 3)}{ {x}^{2} } \\ \\ \\ = \frac{ {x}^{2} - x - 6 }{ {x}^{2} } [/tex]

__o___o__

Q 8.

a.

[tex]10 {x}^{2} + 7x - 12 \\ = (5x - 4)(2x + 3)[/tex]

Answer:

C. The amount at a given time can be calculated by multiplying the previous amount by a value less than 1.

Step-by-step explanation:

Exponential decay is when an exponential function decreases per x-value. These functions go by a multiplier and are therefore, not linear, so you cannot add or subtract. Because the function is decaying, it is multiplying by an amount less than 1, since the multiplier is 1 - r, where r is the percent.

Answer:

[tex]z = 24.5[/tex]

solving similarities:

steps:

[tex]\frac{2}{14} =\frac{7/2}{z}[/tex]

[tex]2z = \frac{14*7}{2}[/tex]

[tex]2z = 49[/tex]

[tex]z = 24.5[/tex]

Answer:

[tex]z = \dfrac{49}{2}[/tex]

Step-by-step explanation:

If the trapezoids are similar, then the ratio of side lengths will be equal.

[tex]\implies 14 : 2 = z : \dfrac72[/tex]

[tex]\implies \dfrac{14}{2}=\dfrac{z}{\frac72}[/tex]

[tex]\implies z=\dfrac{14}{2} \times \dfrac72[/tex]

[tex]\implies z = \dfrac{49}{2}[/tex]