the sum of the measures of the interior angles is 1440 degrees. how many sides does the polygon have?
4
6
8
10​

Answer:

1,645 poles

Step-by-step explanation:

Here, we want to calculate the total number of poles

We can have an arithmetic progression here

Where the last term is the 58 piles , the first term is the top layer which is 12 and the common difference between the piles is 1

Firstly, we calculate the number of stacks which can be obtained using the nth term formula;

Tn = a + (n-1)d

58 = 12 + (n-1)1

58 = 12 + n - 1

58 = n + 11

n = 58-11

n = 47

So we have the stack high up to 47 units

So, using the sum of terms in an arithmetic sequence formula, we have;

Sn = n/2 ( a + L)

where a is the first term 12 and L is the last term 58

Thus, we have

Sn = 47/2( 12 + 58)

Sn = 47/2 * 70

Sn = 1,645

Answer:

3x

Step-by-step explanation:

You multiply the pervious number with 3 to get the next number

For example 2 times 3 = 6

6 times 3 = 18

18 times 3 =54

54 times 3= 162

So on and so forth

Answer:

Step-by-step explanation:

[tex]LHS = \\\\=(x+a)(x+b)(x+c) \\\\=(x+a)(x^2 + cx + bx + bc)\\\\=x(x^2 +(b+c)x + bc) + a(x^2 + (b+c)x + bc)\\\\=x^3 + (b+c)x^2 + bcx+ ax^2 + (b+c)ax+ abc\\\\=x^3 + ax^2 + (b+c)x^2 + bcx + abx + acx + abc\\\\=x^3 + (a+b+c)x^2 + (ab+ac+bc)x+ abc\\\\= RHS[/tex]

Answer:

Explanation:

Hey there!

Please look explanation in picture. As all the factor gives us "0" while putting them in equation, it is verified that they are the factors of f(x).

Hope it helps!

Answer:

1/2

Step-by-step explanation:

y2 - y1 / x2 - x1

-3 - 3 / -6 - 6

-6 / -12

= 1/2

We want to find the slope of a line given that we know that the line passes through the points (6, 3) and (-6, -3).

We will find that the slope is: 1/2

A general line can be written as:

[tex]y = a\cdot x + b[/tex]

Where a is the slope and b is the y-intercept.

If the line passes through the points (x₁, y₁) and (x₂, y₂) then we can write the slope as:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

We know that our line passes through (6, 3) and (-6, -3), then the slope of our line will be:

[tex]a = \frac{-3 - 3}{-6 - 6} = \frac{-6}{-12}[/tex]

Now to simplify this, we know that:

-12 = 2×(-6)

Replacing that in the above equation we get:

[tex]a = \frac{-3 - 3}{-6 - 6} = \frac{-6}{-12} = \frac{-6}{2\cdot -6} = \frac{1}{2}[/tex]

Then the slope written as a simplified fraction is:

a = 1/2

If you want to learn more, you can read:

https://brainly.com/question/3605446

Answer:

C

Step-by-step explanation:

my workings are in the image above

Answer:

8/27

Step-by-step explanation:

First, we figure out how many students chose each school activity, so that we can find the probability of a student at random choosing running by putting (total running students)/(all students).

39 students chose tennis, as stated in the problem.

37 students chose football, as stated in the problem.

The total number of students who chose running must therefore be the the students who chose tennis and football, subtracted from the total number of students. 108 - 39 - 37 = 32, so 32 students chose running.

Therefore, the probability that a student at random chose running would be 32/108 or 8/27.

Answer:

6

Step-by-step explanation:

The worst scenario is that of a slight possibility, the first 5 balls you took are completely different color. The chance of this happening is tiny, but if you want to be sure, then you should consider about it.

But, after taking out the sixth ball, you can be sure that the ball, now right on your hand, must share a same color with at least one of the balls you took out, since there are only five colors.

Answer:

Slope of line B: 1/3

Step-by-step explanation:

To find a slope perpendicular to another slope, you take its negative reciprocal.

Therefore, line B will have a slope of 1/3 because -3 -> -1/3 -> 1/3

Answer:

54

Step-by-step explanation:

Since triangle ABC ~ DEF

Angle A = Angle D

Angle A = 54

Answer:

30 girls

Step-by-step explanation:

         boys to girls

               4 to 6

since there are 50 players we have

    4*5= 20 to 6*5 =30

because 20+30 =50 players and we keep the ratio equivalent since we multiplied by the same number.

Answer:

Here you go!

Hope this helps!

Answer: 7 5/9

Step-by-step explanation:

8 1/9 - (5/9) = 68/9 = 7 5/9

Answer:

There is just one simple rules for find other side

Step-by-step explanation:

Think about a triangle and this triangle has 3 side it must have 90° on one edge. We assume the longest side is hipotenus x²+y²=hipotenus² . Look at your question hipotenus is 15 lets try to find other side. X²+12²=15² x=9

Answer:

no

Step-by-step explanation:

it is irrational.

Answer:

[tex]h=4m[/tex]

Step-by-step explanation:

Speed [tex]V=24m/s[/tex]

Time [tex]t=6.0s[/tex]

Generally the equation for Height is mathematically given by

 [tex]h=\frac{V}{t}[/tex]

 [tex]h=\frac{24}{6}[/tex]

 [tex]h=4m[/tex]

Answer:

4340.

Step-by-step explanation:

14-5 = 9 and 23-14 = 9 so this is an arithmetic series with common difference of 9.

Sum of n terms = (n/2)[2a1 + d(n - 1)]

Here n = 31, d = 9 and a1 = 5.

So, substituting, we have:

Sum of 31 terms = (31/2)[2*5 + 9(31-1)]

= 15.5 * 280

= 4340.

Answer:

About 1 1/2 :)

Step-by-step explanation:

The answer is 1.46 which is close to 1.5

Answer:

5x+8y

Step-by-step explanation:

We can first open the brackets by using the distrubitive propety.

2(x+4y)+3x

2x+8y+3x

Now we can combine like terms.

5x+8y.

I combined the 3x and the 2x. This works because imagined I have 3 of something then I got 2 more of that something I would now have 5 of that something.

Hoped this helped,

JoeLouis2

Answer:

ANSWER IS B

Step-by-step explanation:

5x - 3 = 3x + 1

5x - 3x = 1 + 3

2x = 4

x = 4/2

x = 2

Answer:

B. 2

Step-by-step explanation:

The sides 5x - 3 and 3x + 1 are the same length, so you can put an equal sign: 5x - 3 = 3x + 1, x = 2:

5(2) - 3 = 3(2) + 1

10 - 3 = 6 + 1

7 = 7

So x is 2

Answer:

A 99.96%

Step-by-step explanation:

The z score shows by how many standard deviations the raw score is above or below the mean. The z score is positive if the raw score is above the mean while the z score is negative if the raw score is below the mean. The z score is given by:

[tex]z=\frac{x-\mu}{\sigma} \\\\where\ z=z-score,\ x=raw\ score,\mu=mean, \ \sigma=standard\ deviation\\\\For\ a\ sample\ size(n):\\\\z=\frac{x-\mu}{\sigma/\sqrt{n} }[/tex]

The probability can be gotten from the normal distribution table. Therefore from the normal table:

P(z < 3.37) = 0.9996 = 99.96%

Answer:

x = 9 or x = -9

Step-by-step explanation:

The parameters of the given points are;

The location of the point T = (0, 7)

The location of the point U = (x, -5)

Then distance between points T and U = 15 units

The distance between points A and B, 'd', given their coordinates, A(x₁, y₁) and B(x₂, y₂) is found using the following formula;

[tex]d=\sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]

Therefore, for the given points, T(0, 7) and U(x, -5), we get;

[tex]15 = \sqrt{\left ((-5) - 7 \right )^{2}+\left (x - 0 \right )^{2}}[/tex]

Squaring both sides, gives;

[tex]15^2 = \left ((-5) - 7 \right )^{2}+\left (x - 0 \right )^{2}} = (-12)^2 + x^2[/tex]

∴ x² = 15² - (-12)² = 81 = 9²

x² = 9²

∴ x = ±√(9²) = ± 9

The possible values of x are x = 9 or x = -9

Answer:

diagonal, congruent triangles

Step-by-step explanation:

Given:

Length of rectangular table = [tex]\dfrac{4}{5}[/tex] meter

Width of rectangular table = [tex]\dfrac{2}{3}[/tex] meter

To find:

The area of the table.

Solution:

Area of a rectangle is:

[tex]A=l\times w[/tex]

Where, l is the length and w is the width.

Substitute [tex]l=\dfrac{4}{5}[/tex] and [tex]w=\dfrac{2}{3}[/tex] in the above formula to find the area of the rectangular table.

[tex]A=\dfrac{4}{5}\times \dfrac{2}{3}[/tex]

[tex]A=\dfrac{8}{15}[/tex]

Therefore, the area oft he table is [tex]\dfrac{8}{15}[/tex] square meters.

Answer:

540 jumps in 9 minutes.

Step-by-step explanation:

60 jumps a minute. Chen is fast, but we need to find how many jumps in 9 minutes.

Let's say one minute is m

m = 60

9m = 60x9

We do x9 because from m to 9m you need to multiply by 9, so lets do that on both sides.

9m = 540

9 minutes = 540 jumps

Hope this helps!

--Applepi101

Answer: -6y-12 and 5.5h+14

Step-by-step explanation:

-2(3y+6) = -6y-12

5.1h-2.6h+3(h+4)= 2.5h + 3h+14 = 5.5h+14

Answer:

4x + 5y = 20

Step-by-step explanation:

4x + 5y = 20

5y = -4x + 20      (Subtract 4x to isolate 5y. Put the 4x in front of the 20)

y = [tex]-\frac{4}{5}x[/tex] + 4         (Divide all by 5 to isolate y)

And then it's done and in slope-intercept form

[tex]-1< -\frac{4}{5} < 0[/tex]        or [tex]-\frac{4}{5}[/tex] is greater than -1 but less than 0

I hope this helped :)