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3 years ago

Expand log7 (x^3/y)^3

Mathematics

2 answers:

EleoNora [17]3 years ago

5 0

Answer:

b.) 9 log7 x - 3 log7 Y

Step-by-step explanation:

$log_{7}\bigg( \frac{ {x}^{3} }{y} \bigg)^{3} \\ \\ = 3log_{7}\bigg( \frac{ {x}^{3} }{y} \bigg) \\ \\ = 3log_{7} {x}^{3} - 3log_{7}y \\ \\ = 3 \times 3log_{7} {x} - 3log_{7}y \\ \\ = 9log_{7} {x} - 3log_{7}y \\ \\$

weqwewe [10]3 years ago

4 0

Answer:

A resposta é a C

Eu com certeza apostaria na c

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Problems 2.21, 2.22, 2.23

RoseWind [281]

Statements can be proved by contrapositive, contradiction or by induction.

2.21 and 2.23 are proved by contrapositive
2.22 is proved by induction

2.21: If $n^3$ is even, then n is even (By contrapositive)

The contrapositive of the above statement is that:

If n is odd, then $n^3$ is odd

Represent the value of n as:

$n = 2k + 1$ , where $k \ge 0$

Take the cube of both sides

$n^3 = (2k + 1)^3$

Expand

$n^3 = 8k^3 + 6k^2 + 6k + 1$

Group

$n^3 =[ 8k^3 + 6k^2 + 6k] + 1$

Factor out 2

$n^3 =2[4k^3 + 3k^2 + 3k] + 1$

Assume w is an integer; where:

$w =4k^3 + 3k^2 + 3k$

So, we have:

$n^3 =2w + 1$

The constant term (i.e. 1) means that $n^3$ is odd.

Hence, the statement has been proved by contrapositive.

i.e. If n is odd, then $n^3$ is odd

2.22 $3n + 4$ is even, if and only if n is even

We have: $3n + 4$

Assume that: $n = 2k + 2$ for $k \ge 0$

So, we have:

$3n + 4 = 3(2k + 2) + 4$

Open bracket

$3n + 4 = 6k + 6 + 4$

$3n + 4 = 6k + 10$

Factorize

$3n + 4 = 2(3k + 5)$

The factor of 2 means that $3n + 4$ is even.

Hence, $3n + 4$ is even, if and only if n is even

2.22: $s \ne -1$ and $t \ne -1$ , then $s + t + st \ne -1$

To do this, we prove by contrapositive.

The contrapositive of the above statement is:

If $s = -1$ and $t=-1$ , then $s + t + st = -1$

We have:

$s + t + st = -1$

Substitute the values of s and t in: $s + t + st = -1$

$-1 -1 -1 \times -1 = -1$

$-1 -1 + 1 = -1$

$-1 = -1$

Hence, by contrapositive:

If $s = -1$ and $t=-1$ , then $s + t + st = -1$

Read more about proofs at:

brainly.com/question/19643658

7 0

3 years ago

What is the point-slope form of a line with slope 3 that contains the point (2,1)

Ilya [14]

<h3>Answer: y - 1 = 3(x - 2)</h3>

Explanation:

The point-slope form is this general template

y - y1 = m(x - x1)

We replace m with the given slope 3, so we get to this

y - y1 = 3(x - x1)

Then replace the given point (x1, y1) with (2, 1) to end up with

y - 1 = 3(x - 2)

4 0

3 years ago

Helppp plezzzzzzes will give braniniilist

BabaBlast [244]

Answer:

1. Equivalent
2. Not equivalent

Step-by-step explanation:

1. Equivalent because there's 4 x's that you add all together and that makes 4x
2. Not equivalent because 5x means there's 5 x's or x + x + x + x + x not only 1 x plus a number 5

6 0

2 years ago

Read 2 more answers

Find the area of the right triangle. If necessary, round to the nearest tenth

Ad libitum [116K]

Answer:

B. 150 yards

Step-by-step explanation:

Area of a Triangle = .5 * Base * height

So we need the height of the triangle, or the missing side.

We have to use Pythagorean Theorem to solve this:

A^2 + B^2 = C^2

15 ^ 2 + B ^ 2 = 25 ^2

b^2 = 25^2 - 15 ^ 2

b^2 = 625 - 225

b^2 = 400

sqrt (400) = 20

The missing height is 20. Now we plug it into 1/2 * b * H

.5 * 15 * 20

7.5 * 20 = 150

150 Yds

6 0

4 years ago

Which of the following is a correct equation for the line passing through the point (-1,4) and having slope m=-3

timurjin [86]

Answer:

y = -3x + 1

Step-by-step explanation:

Starting with the point (-1, 4) and the slope m = -3, write out the point-slope equation of a straight line: y - k = m(x - h) becomes y - 4 = -3(x + 1), or:

y = -3x - 3 + 4

y = -3x + 1 This is the same as answer choice (b).

5 0

3 years ago