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Excuse me but what does the Pythagorean theorem?

What are S I X fractions equivalent to 3/4?

Plot the complex number. Then write the complex number in polar form. Express the argument in degrees.

13 + 13i

Plot the complex number. Write the complex number z= 13 + 13i in polar form. 

If u =<2, -5> and v =<4, 2>, find the dot product of u and v; and determine if u and v are orthogonal.

Why ${\displaystyle \cos \left(4{\cos }^{-1}\left(\frac{x}{2}\right)\right)=\frac{x^4}{2}-2x^2+1}$

Sketch the graph of the inequality.(x + 2)2 + y2 > 1

Why must ${\displaystyle x^2+x+1}$ be a factor of ${\displaystyle x^5+x^4+x^3+x^2+x+1}$ ?

Bottles of a popular cola are supposed to contain 400 milliliters (ml) of cola. There is some variation from bottle to bottle because the filling machinery is not perfectly precise. The distribution of the contents is Normal with standard deviation 3 ml. An inspector suspects that the bottle is under filling. He measures the contents of six bottles. The results are 399.4, 397.5, 401.5, 398.9, 400.5, 401.0. Is this convincing evidence that the mean content of cola bottles is less than the advertised 400 ml? I. State the hypothesis that you will test. II. Calculate the test statistic. III. Find the P-value. IV. Do we reject the null hypothesis at the significance level 5%? State your conclusion.

16. Give an example of a function from N to N that isa) one-to-one but not onto.b) onto but not one-to-one.c) both onto and one-to-one (but different from the identity function).d) neither one-to-one nor onto

Without induction How to prove that
${\displaystyle \sin \left(2nx\right)=2n\sin x\cos x\prod _{k=1}^{n-1}(1-\frac{{\sin }^2\left(x\right)}{{\sin }^2\frac{k\pi }{2n}})}$
for Natural n
I Tried by several way and the last try is to use euler formula which lead me to
${\displaystyle \sin \left(2nx\right)=\sin x{\cos }^{2m+1}x\sum _{k=0}^{n-1}\left({(-1)}^k\left(\begin{array}{c}2n\\ 2k+1\end{array}\right){\left(\cos x\sin x\right)}^{2k}\right)}$
and no idea how to continue or if this method lead to the answer

( 2x+3y =103x+4y=20

Write v as a linear combination of ${\displaystyle u_1,U_2}$, and ${\displaystyle u_3}$, if possible. (Enteryour answer in terms of ${\displaystyle u_1,U_2}$, and ${\displaystyle u_3}$. If not possible enter IMPOSSIBLE.)
${\displaystyle v=(-1,7,2),u_1(3,2,8),u_2(2,-3,1),u_3(-2,3,-1)}$
v=_____

A poll is given, showing 35% are in favor of a new building project.If 3 people are chosen at random, what is the probability that exactly 1 of them favor the new building project?

simplify by combining like terms 4x-6x

What if matrix AB = BA = -I. Assume that matrices A,B and I are nxn size matrices.

find the polynom

Degree 3. Zeros at 

x = −5,

 

x = −2,

 and 

x = 1.

 y-intercept at 

(x, y) = (0, 7).

4-th derivative of ${\displaystyle \frac{(1+x+x^2)}{(1-x+x^2)}}$ usibg Taylor polynomial for ${\displaystyle \frac{1}{1-x}}$

A closed curve in the ${\displaystyle (x,y)}$ -plane is represented by the functions
${\displaystyle x\left(\theta \right)=\frac{1}{2}(\cos \theta +\sqrt{2}\left(\sin \theta \right))}$
${\displaystyle y\left(\theta \right)=\frac{1}{2}(-\cos \theta +\sqrt{2}\left(\sin \theta \right))}$

Find an equation for the line with the given properties. Parallel to the line 2x-3y=-4containing the point (-5,3)

A particle executes SHM of amplitude 25cm and time period 3s. What is minimum time required for the particle to move between two points 12.5cm on either side of mean position?