Solve for y=7x-3w for x

twenty students in A and 20 students in class B were asked how many hours they took to prepare for an exam.The data sets represe

SSSSS [86.1K]

Answer:

is there a graph i can read?

Step-by-step explanation:

6 0

2 years ago

A naval engineer uses the function, P, to analyze the effects of water pressure on submarines. The function P(d) measures the pr

saw5 [17]

The function that the naval engineer uses related P (pressure) and d (depth of ocean).

Is there any restriction on the domain ( d: depth of the ocean)? Yes!

The domain would be from 0 (at sea level or 0 depth) until the depth of the ocean (which is not infinite). Hence, we can write:

$0\leq d\leq DepthOfSeaFloor$

Choice D is the correct one.

ANSWER: D

5 0

3 years ago

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The length of a rectangle is four more than triple the width. if the perimeter is 120 inches, find the dimensions.

mezya [45]

120/2=60 (sum of both lengths)
4x+4=60
4x=56
x=14

length=46
width=14

5 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

3 years ago

For the following geometric sequence find the explict formula -1 ,3, -9.

Afina-wow [57]

Answer:

-1 x $-3^{n-1}$

Hope this helps

Step-by-step explanation:

5 0

3 years ago