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kow [346]
2 years ago
12

Does anyone have the answers for this?!

Mathematics
1 answer:
geniusboy [140]2 years ago
7 0

We don't need the answers.  Let's do the problems.

In triangle ABC with sides a,b,c labeled in the usual way, the Law of Sines is

\dfrac{\sin A}{a} = \dfrac{\sin B}{b} = \dfrac{\sin C}{c}

Side a is opposite vertex A, etc.

1. A=46, B=29, a=x, b=5

a/sin A = b/sin B

a = b(sin A)/sin B

x = (5) sin 46 / sin 29 = 7.41878636786

Answer: x=7.4

2.  We don't have to spell it all out with a, b and c.

x/sin 65 = 22/sin 53

x = 22 (sin 65)/sin 53 = 24.96604654309146

Answer: x=25.0

3. x/sin 15 = 12/sin 128

x = 12 sin 15/sin 128 = 3.941352991713482

Answer: 3.9

4. x = 18 sin 73 / sin 59 =  20.081827192002002 = 20.1

5. Trickier, we need the missing angle 180-19-26=135

x = 32 sin 19 / sin 135 = 14.73353278 = 14.7

6. 180-78-75=27

x = 28 sin 27 / sin 75 = 13.16015541 = 13.2

7. 180-51-70=59

x = 9 sin 59 / sin 70 = 8.20960549830328 = 8.2

8. 180-52-33=95

x/ sin 33 = 16/sin 95

x = 16 sin 33 / sin 95 = 8.747511482 = 8.7

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Solve the following quadratic by<br> completing the square.<br> y = x^2 - 6x+7
kozerog [31]

Answer:

x= 3+\sqrt{2}, \quad x= 3 -\sqrt{2}

Step-by-step explanation:

<u>Given quadratic equation</u>:

y = x^2 - 6x+7

To complete the square, begin by adding and subtracting the square of half the coefficient of the term in x:

\implies y = x^2 - 6x+\left(\dfrac{-6}{2}\right)^2-\left(\dfrac{-6}{2}\right)^2+7

\implies y = x^2 - 6x+\left(-3\right)^2-\left(-3\right)^2+7

\implies y = x^2 - 6x+9-9+7

Factor the perfect square trinomial:

\implies y=(x-3)^2-9+7

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\implies (x-3)^2-2=0

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\implies x= 3\pm\sqrt{2}

Therefore, the solution to the given quadratic equation is:

x= 3+\sqrt{2}, \quad x= 3 -\sqrt{2}

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