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Radda [10]
3 years ago
14

98 POINTS MATH!

Mathematics
1 answer:
patriot [66]3 years ago
6 0

Let a be the length of the leg with one tick mark and b the length of the leg with two tick marks.

In the upper triangle, the law of cosines says

6^2=a^2+b^2-2ab\cos43^\circ

In the lower triangle, it says

4^2=a^2+b^2-2ab\cos(4y-5)^\circ

Subtract the second equation from the first to eliminate a^2+b^2:

6^2-4^2=-2ab(\cos43^\circ-\cos(4y-5)^\circ)

10=ab(\cos(4y-5)^\circ-\cos43^\circ)

a and b are lengths so they must both be positive. 10 is also positive, so in order to preserve the sign on both sides of this equation, we must have

\cos(4y-5)^\circ-\cos43^\circ>0

\cos(4y-5)^\circ>\cos43^\circ

Now we have to be a bit careful. If x is an acute angle, then as x gets larger, the value of \cos x gets smaller. So if we have two angles \theta and \varphi, with 0^\circ, then we would have \cos\theta>\cos\varphi.

This means in our inequality, taking the inverse cosine of both sides would reverse the inequality:

(4y-5)^\circ

We know that (4y-5)^\circ is an angle in a triangle, so it must be some positive measure:

(4y-5)^\circ>0^\circ\implies y>\dfrac54^\circ

So we must have

\dfrac54^\circ

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Now we simplify


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Part B: To find the length of the 4th side, we need to subtract the combined length of the 3 sides we know from the total length (perimeter).


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Simplify, subtract like terms.


4y³ + (18y² - 12y²) + (16y - 9y) + (-26 + 21)


4y³ + 6y² + 7y - 5 is the length of the 4th side.


Part C (sorry for the bad explanation): A set of numbers is closed, or has closure, under a given operation if the result of the operation on any two numbers in the set is also in the set. For example, the set of real numbers is closed under addition, because adding any two real numbers results in another real number. Likewise, the real numbers are closed under subtraction, multiplication and division (by a nonzero real number), because performing these operations on two real numbers always yields another real number.

<em>Polynomials are closed under the same operations as integers. </em>

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3 years ago
In a multiple regression analysis ssr = 1,000 and sse = 200. the f statistic for this model is
IgorLugansk [536]
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4 0
3 years ago
please help me explain what his mistake was. If possible does anyone think they can explain it in a simplified way? Thank You fo
slava [35]

Answer:

Dont think eh multiplied both sides by 4. That would be the first step.

Step-by-step explanation:

1/4(x+12)=2

multiply both sides by 4

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move the 8 to the right side of the equation and change its sign

x=8-12

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Given : x + y = 99 ------------ [1]

Given : x² - y² = 99

We know that : (x² - y²) = (x + y)(x - y)

⇒ (x + y)(x - y) = 99

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So, The Ordered pair (x , y) = (50 , 49)

5 0
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