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3 years ago

What is the measure of abc in the figure below?

Mathematics

2 answers:

Anit [1.1K]3 years ago

7 0

Answer:

APEX

Step-by-step explanation:

rusak2 [61]3 years ago

3 0

We need to see the figure to answer the question

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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

Explain how to find the distance between two integers using the difference

maksim [4K]

Answer:

Step-by-step explanation:

When we want to find the distance between two integers using the difference, the best way is to plot them on number line. And then count distance between them.

For example -3 and -1.

When we want to find difference we have:

-3-(-1)=-2

But distance can not be negative.

Now, we need to count distance between numbers -3 and -1 on the number line.

So we have from -3 to -2, one place and from -2 to -1 one place it is 2 places.

So distance is 2.

6 0

3 years ago

Read 2 more answers

URGENT I NEED HELP PLEASE

mario62 [17]

Answer:191/94 i hope this helps!!(✿◠‿◠)

6 0

3 years ago

Please help !!

Rama09 [41]

Just add the two given angles together.

6 0

3 years ago

Read 2 more answers

Divide 7/24 by 35/48 and reduce the quotient to the lowest fraction

Ahat [919]

Well, an easier way than to divide fractions is to multiply the fractions, but to do that, flip the numerator and denominator for the second fraction.
For example, it becomes: 7 48 2
-------- × -------- = --------- (top×top & bottom×bottom)
24 35 5

Answer is: 2/5

5 0

3 years ago