Someone help me please! will give brainliest.

Use the distributive property to simplify the expression. 4 (1/4a + b - 6)

nadya68 [22]

Answer:

a+4b-24

Step-by-step explanation:

4 0

1 year 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

2 years ago

an art teacher has 1 1/2 pounds of red clay and 3/4 pound of yellow clay.The teacher mixes the red clay and yellow clay together

Nataly [62]

Well, seeing as how she mixed the clay, she has a total of 2 2/8 pounds clay (unsimplified). Although we don't know how many students she has in one class, with simple division of this number we can figure out how many student can finish the project. Removing the 2/8, we can already tell 2 students can do it, so that's a start. Now to divide the 2 pounds into 8ths. Each pound is enough for 8 students, so the 2 pounds totals to 16. Now add the extra 2 students, it's 18 total students. Hope I explained it well enough!

7 0

2 years ago

PLZ HELP!!!! WILL GIVE BRAINLIEST IF CORRECT! The social studies teacher wants to know whether the students in the entire school

natta225 [31]

3 is the answer

you're welcome

8 0

2 years ago

Read 2 more answers

A prism with a volume of 148 cubic cm is dilated by a factor of 5.5.

OLEGan [10]

volume = 148 × 5.5 cube