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3 years ago

ABCDE is aregular pentangon X=?

Mathematics

1 answer:

Viefleur [7K]3 years ago

6 0

Answer:

x = 5.2

Step-by-step explanation:

Measure of interior angle of a regular polygon = $\frac{(n-2)\times180}{n}$

Here n = number of sides of the polygon

Interior angle of a regular pentagon = $\frac{(5-2)\times180}{5}$

= 108°

By applying cosine rule in ΔABK,

(BK)² = (AK)² + (AB)² - 2(AK)(AB)cos(108)°

(x + 3)² = 4² + 6² - 2(4)(6)cos(108)°

x² + 6x + 9 = 16 + 36 - (-14.83)

x² + 6x = 57.83

x² + 6x - 57.83 = 0

x = $\frac{-6\pm \sqrt{6^2-4(1)(-57.83)}}{2(1)}$

x = $\frac{-6\pm16.35}{2}$

x ≈ -11.2, 5.2

Since, x can't be negative,

x = 5.2 will be the answer.

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Line segment AB is shown on a coordinate grid:

Roman55 [17]

Answer:

The statements which describe A'B' is:

A'B' and AB are equal in length ⇒ (B)

Step-by-step explanation:

Let us take about reflication:

⇒ Reflections are mirror images, means the shape or the size of

the figure does not affect by reflection, think of "folding" the

graph over the y-axis or the x-axis

⇒ On a grid, you used the formula (x, y) → (-x, y) for a reflection in

the y-axis and used the formula (x, y) → (x, -y) for a reflection in

the x-axis.

In our question segment AB, where A = (1, 3) and B = (5, 3) is

reflected about the y-axis

By using the rule above

∴ A' =(-1, 3)

∴ B' = (-5,3)

∵ Reflection does not change the shape or the size of the original figure

∴ Line segment A'B' has the same length of line segment AB

The correct answer is:

A'B' and AB are equal in length

You can check your answer by finding the lengths of AB and A'B'

∵ The length of AB = 5 - 1 = 4 units

∵ The length of A'B' = -1 - (-5) = -1 + 5 = 4 units

∴ AB = A'B'

Note:

If the y-coordinates of two points are equal, then the line joining them is horizontal and its length is the difference between the x-coordinates of the two points.

4 0

3 years ago

PLSSSS HELLPPPP I NEEED A ANSWER

noname [10]

Answer:

x = 50°

Step-by-step explanation:

By vertical angles, we have

50° + 2x = 150°

2x = 100°

x = 50°

7 0

3 years ago

Please Help Me with this permutations and combinations math problem

Paraphin [41]

Step-by-step explanation:

you do know what a combination stands for ?

n over r = n! / (r! × (n-r)!)

and you know what "!" (factorial) means ?

it means it is the product of

n × (n-1) × (n-2) × (n-3) × ... × 3 × 2 × 1

so, now we only need to calculate the whole thing.

10 over 4 = 10! / (4! × (10-4)!) = 10! / (4! × 6!) =

= 10×9×8×7 / 4×3×2 = 5×3×2×7 = 210

10 over 6 = 10! (6! × (10-6)!) = 10! / (6! × 4!) =

= the same as 10 over 4 = 210

8 over 7 = 8! / (7! × (8-7)!) = 8! / (7! × 1!) = 8

6 over 2 = 6! / (2! × (6-2)!) = 6! /(2! × 4!) =

= 6×5 / 2 = 15

6 over 4 = the same as 6 over 2 = 15

9 over 6 = 9! / (6! × (9-6)!) = 9! / (6! × 3!) =

= 9×8×7 / 3×2 = 3×4×7 = 84

so, we have then

210×210 - 8×15 + 15×84 = 44100 - 120 + 1260 =

= 45240

6 0

3 years ago

Rewrite with only sin x and cos x. cos 3x

Feliz [49]

Answer:

cos(3x) --> cos³(x) - 3sin²(x)cos(x)

Step-by-step explanation:

The text in pink are the trig identities I used to convert cos(2x) and sin(2x) into their other equivalent forms.

This question is pretty much asking if you know how to use your trig identities if i understand it correctly.

4 0

4 years ago

8/7 divided by 5/8.

maksim [4K]

Answer:

64/35

Step-by-step explanation:

To divide fractions, multiply the first fraction by the second fraction's reciprocal.

The reciprocal of a fraction is just the top and bottom number switched.

So the reciprocal of 5/8 would be 8/5.

Now, you can multiply 8/7 by 8/5.

This gives you 64/35.

And that's it!

Please mark as Brainliest! :)

3 0

3 years ago