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3 years ago

PLEASE HELP ASAP WILL MARK BRAINLIEST!!

Mathematics

1 answer:

Papessa [141]3 years ago

7 0

Answer:

Prime.

Step-by-step explanation:

$x^2-7x+8\\$

First let's multiply our outer coefficients in this case 1 and 8, so we have 1x8=8. Now the point of this is to get the factors of 8 and see if we can get that middle term -7. Factors of 8 are 1x8, 2x4 and that's it. From there I notice that -8+1 = -7 and so:

$x^2-7x+8 = x^2-8x+x+8 = x(x-8)+(x+8)$

Notice that the (x-8) and (x+8) are not the same factors, therefore the factors are not any of those answer choices and so it's prime. You can calculate the factors by using the quadratic formula, however I think that is beyond the scope of this question.

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Answer:

16. Angle C is approximately 13.0 degrees.

17. The length of segment BC is approximately 45.0.

18. Angle B is approximately 26.0 degrees.

15. The length of segment DF "e" is approximately 12.9.

Step-by-step explanation:

By the law of sine, the sine of interior angles of a triangle are proportional to the length of the side opposite to that angle.

For triangle ABC:

$\sin{A} = \sin{103\textdegree{}}$ ,
The opposite side of angle A $a = BC = 26$ ,
The angle C is to be found, and
The length of the side opposite to angle C $c = AB = 6$ .

$\displaystyle \frac{\sin{C}}{\sin{A}} = \frac{c}{a}$ .

$\displaystyle \sin{C} = \frac{c}{a}\cdot \sin{A} = \frac{6}{26}\times \sin{103\textdegree}$ .

$\displaystyle C = \sin^{-1}{(\sin{C}}) = \sin^{-1}{\left(\frac{c}{a}\cdot \sin{A}\right)} = \sin^{-1}{\left(\frac{6}{26}\times \sin{103\textdegree}}\right)} = 13.0\textdegree{}$ .

Note that the inverse sine function here $\sin^{-1}()$ is also known as arcsin.

By the law of cosine,

$c^{2} = a^{2} + b^{2} - 2\;a\cdot b\cdot \cos{C}$ ,

where

$a$ , $b$ , and $c$ are the lengths of sides of triangle ABC, and
$\cos{C}$ is the cosine of angle C.

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$b = 21$ ,
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The length of $a$ (segment BC) is to be found, and
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$a^{2} = b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}$ .

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$a = 14$ ,
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Start by finding the cosine of angle B. Apply the law of cosine.

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$\displaystyle \cos{B} = \frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}$ .

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The length of segment DF is to be found,
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