PLEASE HELP!!! Find the area of the shaded polygon:

How can the Pythagorean theorem be used to find the exact values of certain "special angles"?

Reptile [31]

In a 45-45-90 triangle, the two legs are congruent. Let's call them x. The hypotenuse is equal to 1 as we're using the unit circle. The hypotenuse of the triangle is the same as the radius of the unit circle.

a = x

b = x

c = 1

Use those values in the Pythagorean theorem to solve for x.

a^2 + b^2 = c^2

x^2 + x^2 = 1^2

2x^2 = 1

x^2 = 1/2

x = sqrt( 1/2 )

x = sqrt(1)/sqrt(2)

x = 1/sqrt(2)

x = sqrt(2)/2 ... rationalizing the denominator

So this right triangle has legs that are sqrt(2)/2 units long. Once we know the legs of the triangle, we can divide them over the hypotenuse to find the sine and cosine values.

sin(angle) = opposite/hypotenuse

sin(45) = (sqrt(2)/2) / 1

sin(45) = sqrt(2)/2

and

cos(angle) = adjacent/hypotenuse

cos(45) = (sqrt(2)/2) / 1

cos(45) = sqrt(2)/2

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For a 30-60-90 triangle, we would have

a = 1

b = x

c = 2

so,

a^2+b^2 = c^2

1^2+x^2 = 2^2

1+x^2 = 4

x^2 = 4-1

x^2 = 3

x = sqrt(3)

The missing leg is sqrt(3) units long.

Once we know the three sides of the 30-60-90 triangle, you should be able to see that

sin(30) = 1/2

sin(60) = sqrt(3)/2

cos(30) = sqrt(3)/2

cos(60) = 1/2

3 0

3 years ago

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Write the equation of the lines resented below in slope-intercept form

scoray [572]

Slope intercept form: y = mx + b

mx = slope

b = y-intercept

We know the y intercept is 0, so nothing will be written there.

To find the slope of this line, we can use the slope formula.

$\frac{y.2 - y.1}{x.2 - x.1} = m$

We'll use the points (1, 0) and (3, 1) to find the slope.

Now we can just plug these values into the equation to find the slope.

1 - 0 / 3 - 1

1 / 2

The slope of the line is 1/2, or 0.5.

The slope-intercept form of this line can be written as:

y = 0.5x

6 0

3 years ago

Perfect Pies charges $6 for an apple pie.

Aloiza [94]

Answer:

6 * p ≤ 30

p ≤ 5

The maximum number of pies she can buy is 5

Step-by-step explanation:

Let p equal the number of pies she will buy

Each pie costs 6 dollars. She will spend 6 * p

The cost must be less than or equal to 30 dollars

6 * p ≤ 30

To solve divide each side by 6

6 * p/6 ≤ 30/6

p ≤ 5

8 0

3 years ago

Read 2 more answers

I need help PLEASE!!!

Stella [2.4K]

9514 1404 393

Answer:

y = -4/3x +23/2

Step-by-step explanation:

The tangent of interest is perpendicular to the radius at the given point on the circle. To find the perpendicular, it helps to know the slope of the radius segment. To find that, we need the center of the circle.

The center of the circle can be found by completing the square for each variable.

(x^2 -2x) +(y^2 +4y) = 20

(x^2 -2x +1) +(y^2 +4y +4) = 20 +1 +4

(x -1)^2 +(y +2)^2 = 25

Comparing this equation to the standard form equation for a circle, we can find the center.

(x -h)^2 +(y -k)^2 = r^2 . . . . . . . circle of radius r centered at (h, k)

The center of circle P is (1, -2).

__

The slope m' of the line segment between (1, -2) and (5, 1) is given by ...

m' = (y2 -y1)/(x2 -x1)

m' = (1 -(-2))/(5 -1) = 3/4

The slope m of the perpendicular line is the opposite reciprocal of this, so is ...

m = -1/m' = -1/(3/4) = -4/3

The y-intercept of the desired line can be found from ...

b = y -mx . . . . . . . for m=-4/3 and (x, y) = (5, 1)

b = 1 -(-4/3)(5) = 23/3

Then the equation of tangent line AB is ...

y = mx +b

y = -4/3x +23/3

6 0

3 years ago

The answer to the problem

frez [133]

Could you take a better picture please?

6 0

3 years ago