Divide. Reduce the answer to lowest terms.

3/4 ÷ 1/3

Answer:

Where α is an acute angle (first figure)

The area of the shaded triangle = ((√3)·a²/4)·sin(α)·csc(120 - α))

Where α is an obtuse angle (second figure)

The required area of the shaded region = (√3)·a²/4 + (√3)·a²/4)·sin(α)·sec(α + π/6)

Step-by-step explanation:

Where α is an acute angle (first figure)

The given parameters are;

The given triangle = Equilateral Triangle

Let the sides of the equilateral triangle = 2·a

Therefore;

The measure of each interior angles of the given triangle = 60°

Let c represent the side of the shaded triangle opposite ∠α and b represent the side of the shaded triangle opposite ∠60° and c, represent the third side of the shaded triangle, we have;

The sides of the equilateral triangle = 2·a

By sine rule, we have;

c/sin(α) = b/sin(60°) = a/sin(180 - (60 + α)) = a/sin(120 - α))

b = sin(60°) × a/sin(120 - α)) = (√3)/2 × a/sin(120 - α))

The area of the shaded triangle = 1/2 × a × b × sin(α) = 1/2 × a × (√3)/2 × a/sin(120 - α)) × sin(α) = ((√3)·a²/4)·sin(α)·csc(120 - α))

The area of the shaded triangle = ((√3)·a²/4)·sin(α)·csc(120 - α))

Where α is an obtuse angle (second figure)

The required area of the shaded region = The area of the equilateral triangle - The area of the small unshaded triangle, with base side a and interior angles, (180° - α), 60° and ((180 - (180° - α) - 60°) = ) α - 60°

The area of the unshaded triangle is found as follows;

By sine rule, we have;

c/sin(180° - α) = b/sin(60°) = a/sin(α - 60°)

b = sin(60°) × a/sin(α - 60°) = (√3)/2 × a/sin(α - 60°)

The area of the unshaded triangle = 1/2 × a × b × sin(α) = 1/2 × a × (√3)/2 × a/sin(α - 60°) × sin(α) = -((√3)·a²/4)·sin(α)·sec(α + π/6)

The area of the shaded triangle =  -((√3)·a²/4)·sin(α)·sec(α + π/6)

The required area of the shaded region = 1/2×a²·sin(60°)  - (-((√3)·a²/4)·sin(α)·sec(α + π/6))

The required area of the shaded region = (√3)·a²/4 + (√3)·a²/4)·sin(α)·sec(α + π/6)

Answer:

-3x=12

-3x/-3=12/-3

X=-4

Answer:

Opposite angles formed by two intersecting lines are equal, so angle 1 is the same as angle 4. That means angle 1 = angle 5 as well.

When a line intersects two parallel lines, the corresponding angles are equal. That is, if r and s are parallel, then the angles formed when l intersects r are the same s the angles formed when l intersects s. Angle 1 = Angle 5, Angle 2 = Angle 6, and so forth. Since we know angle 1 = angle 5, we can conclude that r and s are parallel.

Answer:

The other person is correct!

Step-by-step explanation:

( I wanted to give them credit because if I put close to what they put I would be reported for Plagiarism so I Just wanted to say they are correct!) :)

Answer:

No solutions

Step-by-step explanation:

Let's solve your equation step-by-step.

3(6d−24)=6(12+3d)

Step 1: Simplify both sides of the equation.

3(6d−24)=6(12+3d)

(3)(6d)+(3)(−24)=(6)(12)+(6)(3d)(Distribute)

18d+−72=72+18d

18d−72=18d+72

Step 2: Subtract 18d from both sides.

18d−72−18d=18d+72−18d

−72=72

Step 3: Add 72 to both sides.

−72+72=72+72

0=144

Answer:

There are no solutions.

Answer:

Obviously condensation

Step-by-step explanation: because it is

Answer:

Step-by-step explanation:

(1+4i)-(-16+9i)

1+4i+16-9i

17-5i

Answer:

-6

Step-by-step explanation:

on a number labled for example -10 through 10, -6 would be lower then 5

Answer:

(-2,-3)

Step-by-step explanation:

this is because when any point is flipped over y=-x, it makes both y and x negative.

hope this helps :)

Answer:

football

Step-by-step explanation:

also known as soccer

Answer: 8. 3^4+n^4, 9. 7^3+m^4, and 10. s+2t^3.

Step-by-step explanation:

Answer:

8. 4n + 12

9. 6m + 28

10. 3s + 6t

Step-by-step explanation:

8. As can be seen in the image, there are four sides that are n long and four sides that are 3 long. This can represented like this:

4n + 3(4)

Simplify the expression:

4n + 12

9. In this figure, there are 3sides with the length 7 and 4 sides with the length m. However, the length of the top of the figure seems to be unknown. Its length is the same as the length of the bottom half of the figure, which is 2m and one 7. So, add two more m and one more 7 to our expression. Now our expression looks like this:

6m + 7(4)

Simplify:

6m + 28

10.There are 3 sides with length s + 2t. This can be represented like this:

3(s + 2t)

Multiply the 3 by both terms in the parentheses:

3 * s = 3s

3 * 2t = 6t

The simplified expression is:

3s + 6t

Hope this helps :)

Answer:

x= 5/3

Step-by-step explanation:

Answer:

ŷ = -0.18363X + 19.71681

-0.9685

Step-by-step explanation:

Given the data:

Mileage, x: 22 14 18 30 8 24

Price, y: 16 17 17 14 18 15

Using the online regression calculator :

The regression equation obtained is :

ŷ = -0.18363X + 19.71681

Where ;

y = predicted variable

- 0.18363 = slope or gradient

X = predictor variable

19.71681 = intercept

The correlation Coefficient R = -0.9685

This signifies a strong negative relationship between the x and y variable.

The line of best fit has an equation of:

y = -0.1875x + 19.625

A linear equation is given by:

y = mx + b;

where y, x are variables, m is the slope of the line and b is the y intercept.

Let x represent the mileages (in thousands of miles) and y the selling prices(in thousands of dollars) of used automobiles.

Plotting the points using geogebra graphing calculator, the line of best fit has an equation of:

y = -0.1875x + 19.625

Therefore the slope is -0.1875 and the y intercept is 19.625

Find out more at: https://brainly.com/question/11324911

Answer:

I love and want to see you in your underwear

Step-by-step explanation:

Answer:

7.07107cm

Step-by-step explanation:

d= [tex]\sqrt{2} a =\sqrt{2} (5) = 7.07107[/tex]

Explanation:

We have three numbers that aren't even, and they are {1,3,5}

There are three numbers that are even, and they are {2,4,6}

The odds in favor of not getting an even number is 3:3 = 1:1

To list the odds in favor, you write the number of ways to get what you want, followed by a colon, then the number of ways to get what you don't want. In this case, both counts are 3. The ratio 3:3 reduces to 1:1 after dividing both parts by 3.

Answer:

1:1

Step-by-step explanation:

how many odd sections are even: 3

how many sections are not even: 3

the odds are 3 : 3= 1:1

odds are what you expect to come out versus what you don't expect(favorable to un favorable).

confusion comes in when talking about probability

probability is what you want to come out versus the total chances whether odd or even(favorable to total outcomes). eg

in this example

the probability of it not landing on the even number is:

number of odd sections=         3     =   1:2

number of total outcomes=     6

Answer:

340 more fans

Step-by-step explanation:

550 - 210 = 340

p.s. There shouldn’t be anyone at a basketball game anyway.

Answer:

1 over negative 6

Step-by-step explanation:

okay so first you said you had negative 1 over 6, this can be written as -1/6.

You then had -6/1 twice and finally you had 1 over negative 6, which can also be written as -1/6.

Ask questions if you are confused

Answer:

1 over negative 6

Step-by-step explanation:

okay so first you said you had negative 1 over 6, this can be written as -1/6.

You then had -6/1 twice and finally you had 1 over negative 6, which can also be written as -1/6.

Answer:

n<22

Step-by-step explanation: That is the best i can do it

Answer: 24

Step-by-step explanation:

Answer:

30 X .8=24 30-24=6 bill got 6 questions wrong

Answer:

The value of x in this equation is -23

Step-by-step explanation:

The given equation is:

[tex]-x-8 = 15[/tex]

The given equation is a linear equation in one variable. The solution of the equation requires isolating x on one side of the equation.

Properties of equality will be used to find the solution.

Using Addition property of equality

Adding 8 on both sides

[tex]-x-8+8 = 15+8\\-x = 23[/tex]

Multiplication property of equality

Multiplying both sides by -1

[tex]x = -23[/tex]

Verification:

[tex]-x-8 = 15\\-(-23)-8 = 15\\23-8 = 15\\15 = 15[/tex]

Hence,

The value of x in this equation is -23

Answer:

$216.50

Step-by-step explanation:

Set up a proportion

5/21.65= 50/x

Answer:

0.46428571428

Step-by-step explanation:

Answer:

Step-by-step explanation:

3/8 + 1/8 = 4/8 = 1/2 = 0.5

1/2 - 2/7 = 3/14 = 0.214285714286

3/14 + 1/4 = 13/28 = 0.464285714286

Hope this helps! <3

Answer:

Yes, I do for my Spanish class!

Do you have any questions about it?