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3 years ago

Do these equations have infinite solutions 2x + 5y= 31 and 6x -y = 13

Mathematics

1 answer:

katovenus [111]3 years ago

8 0

$2x = 31 - 5y \\ x = \frac{31}{2} - \frac{5}{2}y$

$6x = 13 + y \\ x = \frac{13}{6} + \frac{1}{6} y$

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let sin(θ) =3/5 and tan(y) =12/5 both angels comes from 2 different right trianglesa)find the third side of the two tringles b)

statuscvo [17]

In a right triangle, we haev some trigonometric relationships between the sides and angles. Given an angle, the ratio between the opposite side to the angle by the hypotenuse is the sine of this angle, therefore, the following statement

$\sin (\theta)=\frac{3}{5}$

Describes the following triangle

To find the missing length x, we could use the Pythagorean Theorem. The sum of the squares of the legs is equal to the square of the hypotenuse. From this, we have the following equation

$x^2+3^2=5^2$

Solving for x, we have

$\begin{gathered} x^2+3^2=5^2 \\ x^2+9=25 \\ x^2=25-9 \\ x^2=16 \\ x=\sqrt[]{16} \\ x=4 \end{gathered}$

The missing length of the first triangle is equal to 4.

For the other triangle, instead of a sine we have a tangent relation. Given an angle in a right triangle, its tanget is equal to the ratio between the opposite side and adjacent side.The following expression

$\tan (y)=\frac{12}{5}$

Describes the following triangle

Using the Pythagorean Theorem again, we have

$5^2+12^2=h^2$

Solving for h, we have

$\begin{gathered} 5^2+12^2=h^2 \\ 25+144=h^2 \\ 169=h^2 \\ h=\sqrt[]{169} \\ h=13 \end{gathered}$

The missing side measure is equal to 13.

Now that we have all sides of both triangles, we can construct any trigonometric relation for those angles.

The sine is the ratio between the opposite side and the hypotenuse, and the cosine is the ratio between the adjacent side and the hypotenuse, therefore, we have the following relations for our angles

$\begin{gathered} \sin (\theta)=\frac{3}{5} \\ \cos (\theta)=\frac{4}{5} \\ \sin (y)=\frac{12}{13} \\ \cos (y)=\frac{5}{13} \end{gathered}$

To calculate the sine and cosine of the sum

$\begin{gathered} \sin (\theta+y) \\ \cos (\theta+y) \end{gathered}$

We can use the following identities

$\begin{gathered} \sin (A+B)=\sin A\cos B+\cos A\sin B \\ \cos (A+B)=\cos A\cos B-\sin A\sin B \end{gathered}$

Using those identities in our problem, we're going to have

$\begin{gathered} \sin (\theta+y)=\sin \theta\cos y+\cos \theta\sin y=\frac{3}{5}\cdot\frac{5}{13}+\frac{4}{5}\cdot\frac{12}{13}=\frac{63}{65} \\ \cos (\theta+y)=\cos \theta\cos y-\sin \theta\sin y=\frac{4}{5}\cdot\frac{5}{13}-\frac{3}{5}\cdot\frac{12}{13}=-\frac{16}{65} \end{gathered}$

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1 year ago

O número 2021 tem resto 5 quando dividido pelo nmr 6, 7, 8, e pelo nmr 9. Quantos múmeros inteiros positivos menores do que 2021

Leokris [45]

336

Step-by-step explanation:

2021-5=2016÷6=336

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3 years ago

If two orders are selected, find the probability that they are both from Restaurant D. a. Assume that the selections are made w

Katena32 [7]

Answer:

The probability is

nothing.

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3 years ago

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Alex787 [66]

Answer:

The answer is 1/8 pints left

Step-by-step explanation:

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3 years ago

Practicing Function Inverses, find values a,b,c,d,e <br> 50 Points = 25 points <br> Thank you.

o-na [289]

Answer:

a = -3.8

b = -2.6

c = 1.7

d = 4.4

e = 1.0

Step-by-step explanation:

Inverse just means that the x- and y-values are reversed. Notice how I didn't need to do any math to fill in the blanks; all the points are already given!

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3 years ago