Multiple choice please answer please

Mathematics

2 answers:

pogonyaev3 years ago

7 0

Answer:

15/8

Step-by-step explanation:

Use SOH-CAH-TOA

Tangent -> TOA -> opposite/adjacent

<A is adjacent to 8 and opposite to 15.

So, 15/8 is opposite/adjacent.

faust18 [17]3 years ago

3 0

Answer:

15/17

Step-by-step explanation:

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Suppose a and b are the solutions to the quadratic equation 2x^2-3x-6=0. Find the value of (a+2)(b+2).

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Answer:

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Step-by-step explanation:

We are given the following quadratic equation:

$2x^2-3x-6=0$

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Solving the equation:

$2x^2-3x-6=0\\\text{Using the quadratic formula}\\\\x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\\\\\text{Comparing the equation to }ax^2 + bx + c = 0\\\text{We have}\\a = 2\\b = -3\\c = -6\\x = \dfrac{3\pm \sqrt{9-4(2)(-6)}}{4} = \dfrac{3\pm \sqrt{57}}{4}\\\\a = \dfrac{3+\sqrt{57}}{4}, b = \dfrac{3-\sqrt{57}}{4}$

We have to find the value of (a+2)(b+2).

Putting the values:

$(a+2)(b+2)\\\\=\bigg(\dfrac{3+\sqrt{57}}{4}+2\bigg)\bigg(\dfrac{3-\sqrt{57}}{4}+2\bigg)\\\\=\bigg(\dfrac{11+\sqrt{57}}{4}\bigg)\bigg(\dfrac{11-\sqrt{57}}{4}\bigg)\\\\=\dfrac{121-57}{156} = \dfrac{64}{16} = 4$