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1 year ago

How do I find the value of x?

Mathematics

1 answer:

garik1379 [7]1 year ago

8 0

Answer: x = 15

Step-by-step explanation:

The formula for calculating the sum of the interior angles of a regular polygon is: (n - 2) × 180°. Where n is number of sides.

sum of angles = (n - 2) × 180

sum of angles = (7 - 2) × 180

sum of angles = 5 × 180

sum of angles = 900°

Now to find the value of x, we have to set each of the interior angles, added up, equal to 900°:

7x + 1 + 10x + 6x + 7 + 10x - 9 + 9x + 4 + 8x + 10 + 9x + 2 = 900

Combine like terms:

(7x + 10x + 6x + 10x + 9x + 8x + 9x) + (1 + 7 - 9 + 4 + 10 + 2) = 900

59x + 15 = 900

59x + 15 - 15 = 900 - 15 subtract 15 from both sides

59x = 885

59x/59 = 885/59 divide by 59 on both sides

x = 15

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2 years ago

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Solve each polynomial equation.

spayn [35]

Answers:

15) x = 8, $\frac{1}{3}, - \frac{2}{5}$

16) x = 9, $\frac{5+\sqrt{17}} {2}$ , $\frac{5 -\sqrt{17}} {2}$

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<u>Step-by-step explanation:</u>

15x³ - 119x² - 10x + 16 = 0

$\frac{p}{q}: \frac{16}{15}:+/- \frac{1*2*4*8*16}{1*3*5*15}$

So, the possible rational roots are: +/- $1, 2, 4, 8, 16,\frac{1}{3},\frac{2}{3},\frac{4}{3},\frac{8}{3},\frac{16}{3},\frac{1}{5},\frac{2}{5},\frac{4}{5},\frac{8}{5},\frac{16}{5},\frac{1}{15},\frac{2}{15},\frac{4}{15},\frac{8}{15},\frac{16}{15}$

Use synthetic division with each one until you find a remainder of zero. I am not going to go through each one because it is too time consuming, however, the first one that works is x = 8

(x - 8)(15x² + x - 2)

Next, factor 15x² + x - 2 using any method

(x - 8)(3x - 1)(5x + 2)

Now, solve for x.

x = 8, x = $\frac{1}{3}$ , x = $-\frac{2}{5}$

*******************************************************************

For #16 & 17, follow the same process as above.

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Answer:

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Step-by-step explanation:

a) The first die roll is bigger than the second or the first roll is a 3

Cases for 2 rolls are (1,1)(1,2)(1,3)....(1,6),(2,1)(2,2)..... (total 36)

We will get 6 cases when they are equal and 15 when 1st is bigger and 15 when 1st is smaller

So Let A is the event when first roll bigger

B is the event when First roll=3

P(A)=15/36

P(B) =1/6

P(A and B)=2/36

P(A or B)=P(A)+P(B)-P(A and B)

=15/36+1/6-2/36

=19/36

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How do I find the value of x?​

How do I find the value of x?