For each line there is one and only one line segment?<br> True?<br> or<br> False?

15(−22.38−10.12) HELP PLEASE!!!

kompoz [17]

The answer to this question is -345.82
In a fraction it would be -17291/50

5 0

4 years ago

Read 2 more answers

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

kondaur [170]

$\text{Proof by induction:}$
$\text{Test that the statement holds or n = 1}$

$LHS = (3 - 2)^{2} = 1$
$RHS = \frac{6 - 4}{2} = \frac{2}{2} = 1 = LHS$
$\text{Thus, the statement holds for the base case.}$

$\text{Assume the statement holds for some arbitrary term, n= k}$
$1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2} = \frac{k(6k^{2} - 3k - 1)}{2}$

$\text{Prove it is true for n = k + 1}$
$RTP: 1^{2} + 4^{2} + 7^{2} + ... + [3(k + 1) - 2]^{2} = \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2} = \frac{(k + 1)[6k^{2} + 9k + 2]}{2}$

$LHS = \underbrace{1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2}}_{\frac{k(6k^{2} - 3k - 1)}{2}} + [3(k + 1) - 2]^{2}$
$= \frac{k(6k^{2} - 3k - 1)}{2} + [3(k + 1) - 2]^{2}$
$= \frac{k(6k^{2} - 3k - 1) + 2[3(k + 1) - 2]^{2}}{2}$
$= \frac{k(6k^{2} - 3k - 1) + 2(3k + 1)^{2}}{2}$
$= \frac{k(6k^{2} - 3k - 1) + 18k^{2} + 12k + 2}{2}$
$= \frac{k(6k^{2} - 3k - 1 + 18k + 12) + 2}{2}$
$= \frac{k(6k^{2} + 15k + 11) + 2}{}$
$= \frac{(k + 1)[6k^{2} + 9k + 2]}{2}$
$= \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2}$
$= RHS$

Since it is true for n = 1, n = k, and n = k + 1, by the principles of mathematical induction, it is true for all positive values of n.

3 0

3 years ago

Help

Alex Ar [27]

Answer:

I have given the answer

3 0

3 years ago

A surface area of a cube is related to its volume V by A = 6. V(2/3). If the volume of a

Luda [366]

The surface area of the cube is 64 cm².

<h3 /><h3>What is volume?</h3>

Volume is the amount of space that is enclosed within a container.

To calculate the surface area of the cube, we use the relation below.

Formula:

A = 6V ${2/3}$ ............ Equation 1

Where:

A = Surface area of the cube
V = Volume of the cube.

From the question,

Given:

V = 35 cm³

Substitute this value into equation 1

A = 6(35) ${2/3}$
A = 6(10.6999)
A = 64.2
A = 64 cm²

Hence, The surface area of the cube is 64 cm².

Learn more about volume here: brainly.com/question/1972490

8 0

2 years ago

A round pizza was cut into 8 equal pieces. 7 pieces were eaten. What is the angle measure of the piece not eaten?

Reika [66]

Answer:

sorry didnt mean to answer

edit: it should be around 45

3 0

3 years ago

For each line there is one and only one line segment? True? or False?