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3 years ago

12

What is the purpose and structure of a proof in Geometry?

1 answer:

KatRina [158]3 years ago

6 0

Answer: A geometric proof involves writing reasoned, logical explanations that use definitions, axioms, postulates, and previously proved theorems to arrive at a conclusion about a geometric statement.

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I NEED HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Lubov Fominskaja [6]

>
the answer is “>” because 12.312 is greater than 12.132

5 0

3 years ago

Please solve 5 f <br> (Trigonometric Equations)<br> #salute u if u solved it

Zanzabum

Answer:

$\beta=45\degree\:\:or\:\:\beta=135\degree$

Step-by-step explanation:

We want to solve $\tan \beta \sec \beta=\sqrt{2}$ , where $0\le \beta \le360\degree$ .

We rewrite in terms of sine and cosine.

$\frac{\sin \beta}{\cos \beta} \cdot \frac{1}{\cos \beta} =\sqrt{2}$

$\frac{\sin \beta}{\cos^2\beta}=\sqrt{2}$

Use the Pythagorean identity: $\cos^2\beta=1-\sin^2\beta$ .

$\frac{\sin \beta}{1-\sin^2\beta}=\sqrt{2}$

$\implies \sin \beta=\sqrt{2}(1-\sin^2\beta)$

$\implies \sin \beta=\sqrt{2}-\sqrt{2}\sin^2\beta$

$\implies \sqrt{2}\sin^2\beta+\sin \beta- \sqrt{2}=0$

This is a quadratic equation in $\sin \beta$ .

By the quadratic formula, we have:

$\sin \beta=\frac{-1\pm \sqrt{1^2-4(\sqrt{2})(-\sqrt{2} ) } }{2\cdot \sqrt{2} }$

$\sin \beta=\frac{-1\pm \sqrt{1^2+4(2) } }{2\cdot \sqrt{2} }$

$\sin \beta=\frac{-1\pm \sqrt{9} }{2\cdot \sqrt{2} }$

$\sin \beta=\frac{-1\pm3}{2\cdot \sqrt{2} }$

$\sin \beta=\frac{2}{2\cdot \sqrt{2} }$ or $\sin \beta=\frac{-4}{2\cdot \sqrt{2} }$

$\sin \beta=\frac{1}{\sqrt{2} }$ or $\sin \beta=-\frac{2}{\sqrt{2} }$

$\sin \beta=\frac{\sqrt{2}}{2}$ or $\sin \beta=-\sqrt{2}$

When $\sin \beta=\frac{\sqrt{2}}{2}$ , $\beta=\sin ^{-1}(\frac{\sqrt{2} }{2} )$

$\implies \beta=45\degree\:\:or\:\:\beta=135\degree$ on the interval $0\le \beta \le360\degree$ .

When $\sin \beta=-\sqrt{2}$ , $\beta$ is not defined because $-1\le \sin \beta \le1$

4 0

3 years ago

70*6000 associative and commutative properties

stealth61 [152]

The commutative property of multiplication is 6000*70

8 0

3 years ago

egoroff_w [7]

Answer:

Step-by-step explanation:

Set up an equation, where x is the number of gallons of 60% antifreeze solution.

Represent the percentages of antifreeze with decimal values.

0.6x + 0.3(80) = 0.5(x + 80)

Simplify and solve for x:

0.6x + 24 = 0.5x + 40

0.1x = 16

x = 160

So, you have to mix 160 gallons of a 60% antifreeze solution

6 0

3 years ago

A hat contains 5 red balls, 14 green balls, and 11 yellow balls. Alexa chooses one ball at random from the hat. What is the prob

dem82 [27]

Answer:

The answer is A) 5/6

Step-by-step explanation:

first you add all the balls together

30

then you add just the yellow and green balls together

25

the fraction would be 25/30

simplify it and you get 5/6

4 0

4 years ago