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2 years ago

What is the value of x in the equaton

itle=" {25}x^{2} = 16" alt=" {25}x^{2} = 16" align="absmiddle" class="latex-formula">

Mathematics

1 answer:

lisov135 [29]2 years ago

5 0

$25x^2=16\ \ \ |:25\\\\x^2=\dfrac{16}{25}\to x=\pm\sqrt{\dfrac{16}{25}}\\\\x=-\dfrac{\sqrt{16}}{\sqrt{25}}\ \vee\ x=\dfrac{\sqrt{16}}{\sqrt{25}}\\\\\boxed{x=-\dfrac{4}{5}\ \vee\ x=\dfrac{4}{5}}$

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Find the degree of the polynomial<br> 2x^4y^2+9x^2y^5-3x^4y^4

coldgirl [10]

Answer:

the polynomial has degree 8

Step-by-step explanation:

Recall that the degree of a polynomial is given by the degree of its leading term (the term with largest degree). Recall as well that the degree of a term is the maximum number of variables that appear in it.

So, let's examine each of the terms in the given polynomial, and count the number of variables they contain to find their individual degrees. then pick the one with maximum degree, and that its degree would give the actual degree of the entire polynomial.

1) term $2\,x^4\,y^2$ contains four variables "x" and two variables "y", so a total of six. Then its degree is: 6

2) term $9\,x^2\,y^5$ contains two variables "x" and five variables "y", so a total of seven. Then its degree is: 7

3) term $-3\,x^4\,y^4$ contains four variables "x" and four variables "y", so a total of eight. Then its degree is: 8

This last term is therefore the leading term of the polynomial (the term with largest degree) and the one that gives the degree to the entire polynomial.

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3 years ago

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What is the sum of all positive integers less than 300 which are divisible by 3

drek231 [11]

Answer:

14,850

Step-by-step explanation:

You need the sum of

3 + 6 + 9 + 12 + ... + 294 + 297

Factor out a 3 from the sum

3 + 6 + 9 + 12 + ... + 294 + 297 = 3(1 + 2 + 3 + 4 + ... + 98 + 99)

You need to add all integers from 1 to 99 and multiply by 3.

The sum of all consecutive integers from 1 to n is:

[n(n + 1)]/2

The sum of all consecutive integers from 1 to 99 is

[99(99 + 1)]/2

The sum you need is 3 * [99(99 + 1)]/2

3 + 6 + 9 + 12 + ... + 294 + 297 =

= 3 * [99(99 + 1)]/2

= 3 * [99(100)]/2

= 3 * 9900/2

= 14,850

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2 years ago

Please answer ASAP! Photo below!

Maru [420]

B

-2 1/4 = -9/4
(-9/4)/(-2/3)

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2 years ago

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The expression 0.09x+(x-30) models the final price of a bicycle is its an instant rebate in a state that charges a sales tax. Th

svlad2 [7]

Answer:

Step-by-step explanation:

The original price of the bicycle is x.

The discounted price of the bicycle is x - 30. It is a $30 discount.

The tax goes on the original price. 0.09x is the 9% tax applied to the original price x.

Answer: 0.09x

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DIscrete Math

Daniel [21]

Answer:

Step-by-step explanation:

As the statement is ‘‘if and only if’’ we need to prove two implications

$f : X \rightarrow Y$ is surjective implies there exists a function $h : Y \rightarrow X$ such that $f\circ h = 1_Y$ .
If there exists a function $h : Y \rightarrow X$ such that $f\circ h = 1_Y$ , then $f : X \rightarrow Y$ is surjective

Let us start by the first implication.

Our hypothesis is that the function $f : X \rightarrow Y$ is surjective. From this we know that for every $y\in Y$ there exist, at least, one $x\in X$ such that $y=f(x)$ .

Now, define the sets $X_y = \{x\in X: y=f(x)\}$ . Notice that the set $X_y$ is the pre-image of the element $y$ . Also, from the fact that $f$ is a function we deduce that $X_{y_1}\cap X_{y_2}=\emptyset$ , and because $f$ the sets $X_y$ are no empty.

From each set $X_y$ choose only one element $x_y$ , and notice that $f(x_y)=y$ .

So, we can define the function $h:Y\rightarrow X$ as $h(y)=x_y$ . It is no difficult to conclude that $f\circ h(y) = f(x_y)=y$ . With this we have that $f\circ h=1_Y$ , and the prove is complete.

Now, let us prove the second implication.

We have that there exists a function $h:Y\rightarrow X$ such that $f\circ h=1_Y$ .

Take an element $y\in Y$ , then $f\circ h(y)=y$ . Now, write $x=h(y)$ and notice that $x\in X$ . Also, with this we have that $f(x)=y$ .

So, for every element $y\in Y$ we have found that an element $x\in X$ (recall that $x=h(y)$ ) such that $y=f(x)$ , which is equivalent to the fact that $f$ is surjective. Therefore, the prove is complete.

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