What are possible solutions to a system of linear equations and what do they represent graphically?

geniusboy [140]

Answer:

$sin(2\alpha )=2(\frac{5}{12})(\frac{12}{13})=\frac{10}{13}\\cot(2\alpha ) = \frac{16511}{18720}$

Step-by-step explanation:

$\text{if } cos(\alpha)=\frac{12}{13}\\\text{That must mean we have a triangle with base 12, and hypotenuse 13.}\\\text{Using Pythagoras, we can determine the base of the triangle must be 5.}\\a^2+b^2=c^2 \text{, where c is the hypotenuse and a, b are the two other sides.}\\c^2-b^2=a^2\\\sqrt{c^2-b^2}=a\\\sqrt{13^2-12^2}=\sqrt{169-144}=\sqrt{25}=5\\\text{Therefore, }sin(\alpha) = \frac{5}{12}\\sin(2\alpha)=2sin(\alpha )cos(\alpha)\\\text{(From double angle formulae identities)}\\$

$sin(2\alpha )=2(\frac{5}{12})(\frac{12}{13})=\frac{10}{13}\\cos(2\alpha )=cos^2(\alpha)-sin^2(\alpha)\\cos(2\alpha )=(\frac{12}{13})^2-(\frac{5}{12})^2=\frac{16511}{24336}\\cot(2\alpha)=\frac{cos(2\alpha)}{sin(2\alpha)}=\frac{\frac{16511}{24336}}{\frac{10}{13}}=\frac{16511}{18720}$

8 0

2 years ago

How does it satisfy a linear function

Alina [70]

Multiple values of y for a single value of x is a sure giveaway that this is NOT a function. Please review definitions of "function." A function would be represented if no x value has more than one y value associated with it.

5 0

3 years ago

John ate 1/6 of a cake. Mike ate 1/12 of it. How much of the cake did the two boys eat?

Murrr4er [49]

Answer:

1/4

Step-by-step explanation:

1/6 + 1/12 = 1/4

3 0

2 years ago

Read 2 more answers

Please help me!

Alex73 [517]

<h3>Answer: angle T = 70</h3>

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Work Shown:

Quadrilateral RSTU is a kite. In geometry, any kite has two pairs of adjacent congruent sides. In this case, RU = RS is one pair of adjacent congruent sides (single tickmarks), while TU = TS is the other pair of adjacent congruent sides (double tickmarks).

Draw diagonal line segment TR. This forms triangles TUR and TSR.

Through the SSS (side side side) congruence theorem, we can prove that the two triangles TUR and TSR are congruent.

Then by CPCTC (corresponding parts of congruent triangles are congruent), we can say,

angle U = angle S = 90

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Re-focus back on quadrilateral RSTU (ignore or erase line segment TR). The four angles of any quadrilateral will always add to 360 degrees. Let x be the measure of angle T.

(angleU)+(angleR)+(angleS)+(angleT) = 360

90+110+90+x = 360

290+x = 360

290+x-290 = 360-290 ... subtract 290 from both sides

x = 70

<h3>angle T = 70</h3>

4 0

3 years ago

60:92=105:n what is n?

PIT_PIT [208]

Hey! I'll provide you the answers!

First you want to simplify the equation using cross-multiplication.

$15n = 2415$

Finally, you would want to divide both sides by 15.

n = 161

5 0

3 years ago

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