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Dmitry_Shevchenko [17]
2 years ago
5

Find the number of sides of a regular polygon in which the measure of an interior angle is three times the measure of an exterio

r angle.
Mathematics
1 answer:
Serhud [2]2 years ago
6 0
The sum of the interior angles of any polygon is given by (n-2)180°, where n is the number of sides.

Also sum of all the exterior angles of any polygon is 360°

Given (n-2)180° = 3(360°)

=> n-2 = 6

=> n = 8.

Hence the number of sides of a polygon is 8
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Given P(x) = 2x3 - 11x2 + 18x - 15 is divided by x – 3. Use synthetic division to find the quotient and the remainder.
katrin [286]
You can find the remainder right away by simply plugging in x=3. The polynomial remainder theorem guarantees that the value of p(3) is the remainder upon dividing p(x) by x-3, but I digress...

Synthetic division yields

3   |   2   -11   18   -15
.    |           6   -15     9
- - - - - - - - - - - - - - - - -
.    |   2     -5     3     -6

which translates to

\dfrac{2x^3-11x^2+18x-15}{x-3}=2x^2-5x+3-\dfrac6{x-3}

(and note that p(3)=2(3)^3-11(3)^2+18(3)-15=-6, as expected)
5 0
3 years ago
I WILL GIVE U BRAINLIEST, NO LINKS. ITS JUST 1 QUESTION
4vir4ik [10]
It’s the first one :)
6 0
3 years ago
A line passes through the points (0, 9) and (9, 19). What is its equation in slope-intercept form?
STatiana [176]

Answer:

y = 10/9x + 9

Step-by-step explanation:

To write the equation in its slope-intercept form, y = mx + b, we need to find the slope (m) of the line and its y-intercept (b).

Given the points (0, 9) and (9, 19), we can solve for the slope of the line using the following formula:

m = \frac{y2 - y1}{x2 - x1}

Let (x1, y1) = (0, 9)

and (x2, y2) = (9, 19)

Substitute these values on the formula:

m = \frac{y2 - y1}{x2 - x1} = \frac{19 - 9}{9 - 0} = \frac{10}{9}

Therefore, the slope (<em>m </em>) = 10/9.

Next, the <u>y-intercept</u> is the point on the graph where it crosses the y-axis, and has the coordinates, (0, <em>b </em>). It is also the value of the y when x = 0.

One of the given points is the y-intercept of the line, given by (0, 9). The y-coordinate, 9, is the value of b.

Therefore, the linear equation in slope-intercept form is: y = 10/9x + 9

3 0
2 years ago
Any help is wanted pls and thxs
podryga [215]

Answer:

1:3
3:9
5:15

25:75
30:90

35:105

Step-by-step explanation:

Multiply the number of students by 3

8 0
2 years ago
Read 2 more answers
Josh went to applebee and enjoyed a delicious steak. He enjoyed his server and wanted to give an extra special tip. Usually josh
Sonbull [250]

Answer:

Josh's total bill is $ 27.825

Step-by-step explanation:

Given:

The subtotal of the Josh Bill =   $21.00

<u>Finding the usual amount Josh gave as Tip To his sever:</u>

Usually josh tips 20% to all servers

So Tip = 20% of his subtotal

=> 20\% \times 21

=>\frac{20}{100} \times 21

=>0.2 \times 21

=>4.2

So Josh usually tips $4.2 to his server

<u>Finding the amount Josh gave 25%</u><u> </u><u>as Tip To his sever:</u>

But now he tips 25% which is

=> 25% of 21

=> \frac{25}{100} \times 21

=> 0.25 \times 21

=> 5.25

Thus the tip amount will be $5.25

So he will be giving (5.25 - 4.2) = $1.05 more than the usual tip

<u>Finding the total bill</u>

The total bill  = subtotal+ 7.5% sales tax +  25% tip

=> 21 + 7.5 % of 21 + 25% of 21

=> 21 + \frac{75}{100} \times 21 +  \frac{25}{100} \times 21

=>21 +0.075 \times 21 +  0.25 \times 21

=> 21 +1.575 +5.25

=>27.825

3 0
2 years ago
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