What is the area of the parallelogram below?

Mathematics

1 answer:

andreyandreev [35.5K]3 years ago

5 0

Answer:

Step-by-step explanation:

length = 4

width= 2

4 x 2 = 8

Just count the squares like you would normally do to a rectangle and do the area like you would normally do with a rectangle

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If θ is an angle in standard position that passes through (-3, 4), find sin2θ.

julia-pushkina [17]

Answer:

Correct answer: sin 2Θ = - 24/25

Step-by-step explanation:

If under the standard position you think that the first arm (side) belongs to the positive direction of the x axis and the second one passes through a given point then it is:

if we form a right triangle with sides 3 and 4 then the hypotenuse is 5.

sin Θ = 4/5 and cos Θ = - 3/5

we know that the formula for double the value of the angle is:

sin 2Θ = 2 sinΘ cosΘ = 2 · 4/5 · ( - 3/5) = - 24/25

sin 2Θ = - 24/25

God is with you!!!

8 0

3 years ago

(HURRY! I'M BEING TIMED)Write the partial fraction decomposition of the rational expression.

Aleonysh [2.5K]

Answer:

The partial fraction decomposition is $\frac{- 4 x^{2} + 13 x - 12}{\left(x + 1\right)^{2} \left(x + 2\right)}=\frac{50}{x + 1}+\frac{-29}{\left(x + 1\right)^{2}}+\frac{-54}{x + 2}$ .

Step-by-step explanation:

Partial-fraction decomposition is the process of starting with the simplified answer and taking it back apart, of "decomposing" the final expression into its initial polynomial fractions.

To find the partial fraction decomposition of $\frac{- 4 x^{2} + 13 x - 12}{\left(x + 1\right)^{2} \left(x + 2\right)}$ :

First, the form of the partial fraction decomposition is

$\frac{- 4 x^{2} + 13 x - 12}{\left(x + 1\right)^{2} \left(x + 2\right)}=\frac{A}{x + 1}+\frac{B}{\left(x + 1\right)^{2}}+\frac{C}{x + 2}$

Write the right-hand side as a single fraction:

$\frac{- 4 x^{2} + 13 x - 12}{\left(x + 1\right)^{2} \left(x + 2\right)}=\frac{\left(x + 1\right)^{2} C + \left(x + 1\right) \left(x + 2\right) A + \left(x + 2\right) B}{\left(x + 1\right)^{2} \left(x + 2\right)}$