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aleksandrvk [35]
3 years ago
13

There is a clown's face on the top of a spinner. The tip of his hat rotates to (−2, 5) during one spin. What is the cosine value

of this function?
Mathematics
1 answer:
uranmaximum [27]3 years ago
6 0
Remark
The point value is (-2,5) So we know the two sides. We need the hypotenuse. We should notice that the x value is minus (-2) and value is y value is plus (5). That means we are in quad 2. Be careful how you read that. (-2,5) is a point. It is not a tangent.

Step One 
Find the hypotenuse.

a = - 2
b = 5
c =  ??

c^2 = a^2 + b^2
c^2 = (-2)^2 + 5^2
c^2 = 4 + 25
c^2 = 29               Take the square root of both sides.
sqrt(c^2) = sqrt(29)
c = sqrt(29)

Step Two
Find the Cosine of the angle.
Cosine(theta) = adjacent / hypotenuse
Cosine(theta) = -2 / sqrt(29)  <<<<<<< Answer

Again, watch out for what you are given.
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Adding both equations cancels y:

<span>4x + 8y = 16 
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filling in x=2 in the first equation gives:

4*2 + 8y = 16 => 8y = 8 => y=1

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Answer:

Step-by-step explanation:

11388.8

Hope it helped you.

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4 0
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Read 2 more answers
Three officers -- president, treasurer, and secretary -- are to be chosen from among four people: Ann, Bob, Cyd, and Dan.
Kitty [74]

Answer:

18

Step-by-step explanation:

First choose the president. From the 4 people, everyone can be the president except Dan, so there are 3 choices.

Then, choose the treasurer. Neither Bob nor Dan can be the treasurer so there are only 2 choices.

Now choose the secretary. Cyd is the only person who can't take this position, so there are 3 choices.

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4 0
3 years ago
What are the zeros of the quadratic function?<br> y = x^2 - 2x - 15
Pie

Answer:

x=\frac{1+\sqrt{31}}{2},\:x=\frac{1-\sqrt{31}}{2}

Step-by-step explanation:

-> 0=2x^2-2x-15

-zeros means the solution aka x intercept, meaning y=0

x_{1,\:2}=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:2\left(-15\right)}}{2\cdot \:2}

=> according to quadratic formula

x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

where ax^2+bx+c=0

=> x_{1,\:2}=\frac{-\left(-2\right)\pm \:2\sqrt{31}}{2\cdot \:2}

simplify

x_1=\frac{-\left(-2\right)+2\sqrt{31}}{2\cdot \:2},\:x_2=\frac{-\left(-2\right)-2\sqrt{31}}{2\cdot \:2}

x=\frac{1+\sqrt{31}}{2},\:x=\frac{1-\sqrt{31}}{2}

Cannot simplify farther

3 0
2 years ago
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