All categories

3 years ago

Indicate which property is illustrated in Step 3.

Mathematics

1 answer:

olga55 [171]3 years ago

8 0

Step 3 is the associative property of addition.
The 12 and -12 are grouped together.

You might be interested in

Give two rational numbers whose product equals (-1)

motikmotik

Product is times so try that as it’s the product of a number

6 0

3 years ago

Solve the following 2 equation. I will Make Brainliest

Levart [38]

Answer:

d. $x = 10$

e. $x=\sqrt[3]{\dfrac{15}{4}}$

Step-by-step explanation:

I've typed up my workings in MS Word and attached them (as it's very difficult to type this in the Brainly equation editor).

I've used the product, quotient and power log laws.

Product: $log_a(x)+log_a(y)=log_a(xy)$

Quotient: $log_a(x)-log_a(y)=log_a(\dfrac{x}{y})$

Power: $p\log_a(x)=log_a(x^p)$

8 0

3 years ago

Use a proof by contradiction to show that the square root of 3 is national You may use the following fact: For any integer kirke

Ierofanga [76]

Answer:

1. Let us proof that √3 is an irrational number, using reductio ad absurdum. Assume that $\sqrt{3}=\frac{m}{n}$ where $m$ and $n$ are non negative integers, and the fraction $\frac{m}{n}$ is irreducible, i.e., the numbers $m$ and $n$ have no common factors.

Now, squaring the equality at the beginning we get that

$3=\frac{m^2}{n^2}$ (1)

which is equivalent to $3n^2=m^2$ . From this we can deduce that 3 divides the number $m^2$ , and necessarily 3 must divide $m$ . Thus, $m=3p$ , where $p$ is a non negative integer.

Substituting $m=3p$ into (1), we get

$3= \frac{9p^2}{n^2}$

which is equivalent to

$n^2=3p^2$ .

Thus, 3 divides $n^2$ and necessarily 3 must divide $n$ . Hence, $n=3q$ where $q$ is a non negative integer.

Notice that

$\frac{m}{n} = \frac{3p}{3q} = \frac{p}{q}$ .

The above equality means that the fraction $\frac{m}{n}$ is reducible, what contradicts our initial assumption. So, $\sqrt{3}$ is irrational.

2. Let us prove now that the multiplication of an integer and a rational number is a rational number. So, $r\in\mathbb{Q}$ , which is equivalent to say that $r=\frac{m}{n}$ where $m$ and $n$ are non negative integers. Also, assume that $k\in\mathbb{Z}$ . So, we want to prove that $k\cdot r\in\mathbb{Z}$ . Recall that an integer $k$ can be written as

$k=\frac{k}{1}$ .

Then,

$k\cdot r = \frac{k}{1}\frac{m}{n} = \frac{mk}{n}$ .

Notice that the product $mk$ is an integer. Thus, the fraction $\frac{mk}{n}$ is a rational number. Therefore, $k\cdot r\in\mathbb{Q}$ .

3. Let us prove by reductio ad absurdum that the sum of a rational number and an irrational number is an irrational number. So, we have $x$ is irrational and $p\in\mathbb{Q}$ .

Write $q=x+p$ and let us suppose that $q$ is a rational number. So, we get that

$x=q-p$ .

But the subtraction or addition of two rational numbers is rational too. Then, the number $x$ must be rational too, which is a clear contradiction with our hypothesis. Therefore, $x+p$ is irrational.

7 0

4 years ago

Thomas has a scale drawing for his club house. The measurements are 4 in. by 8 in. What will the actual club house measurements

slava [35]

Answer:4=8feet 8=16 feetso in that case it would be 8 by 16

Step-by-step explanation:

7 0

3 years ago

8. What is the result of (11x + 18i)(117 - 18i)?

Nonamiya [84]

1287x + 342 +(-198x + 2106) i

5 0

3 years ago