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3 years ago

The diagram shows a regular polygon What is the value of x? How do I solve this

Mathematics

1 answer:

I am Lyosha [343]3 years ago

3 0

Answer: x=120°

Step-by-step explanation:

What you are looking for is the value of the exterior angle of the regular polygon.

For a n-sided regular polygon, the external angle is given by the formula 360°/n.

Because the shape in this example is a regular triangle, the value of n is 3.

360°/n

=360°/3

=120°

Therefore, x=120°

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Find the value of a1 for an infinite geometric series with S=12 and r=1/6

blondinia [14]

$S_n=a(1+r+\cdots+r^{n-1}+r^n)$
$rS_n=a(r+r^2+\cdots+r^n+r^{n+1})$
$(1-r)S_n=a(1-r^{n+1})$
$S_n=a\dfrac{1-r^{n+1}}{1-r}$

When $|r|$ , we have

$\displaystyle\lim_{n\to\infty}S_n=\dfrac a{1-r}$

as is the case here. Since $S=\lim\limits_{n\to\infty}S_n=12$ and $r=\dfrac16$ are given, we can find the first term $a$ immediately:

$12=\dfrac a{1-\frac16}\implies12=\dfrac65a\implies a=10$

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4 years ago

An object be a moving at the starting (0,0) on the graph. Average speed in miles per hour of the object for an entire trip five

Vikki [24]

Answer: 17 miles per hour.

Step-by-step explanation:

1. To solve this problem you must apply the following formula:

$S$ =Δx/Δt

Where Δx is the position variation and Δt is the time variation.

2. Then, based on the graph shown attached, you have:

$S=\frac{20mi+20mi+30mi+15mi}{1h+1h+1h+2h}$

3. Therefore, you have that the result is:

$S=17mi/h$

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3 years ago

element x is a radioactive isotope such that every 32 years, its mass decreases by half. given that the initial mass of the samp

VashaNatasha [74]

Answer:

the answer is 31.9 years

Step-by-step explanation:

initial mass, $M_{0}$ = 150 gram

half life, $t_{half\hspace{0.1cm}life}$ = 32 years

new mass = half of initial mass = M = 0.5 $M_{0}$

formula , M = $M_{0}$ $e^{\frac{\ln\frac{1}{2}}{t_{half} }\times x }$ where x is the number of years required.

therefore 0.5 $M_{0}$ = $M_{0}$ $e^{\frac{\ln\frac{1}{2}}{t_{half} }\times x } = M_{0} e^{-0.0217x}$

therefore -0.0217 x = $\ln{0.5} = -0.693$

therefore x = $\frac{-0.693}{-0.0217}$ = 31.942

8 0

3 years ago

Find m∠T of that triangle <br><br> ty!!!!

Harman [31]

Answer. 50 degrees

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180-90-40=50

Step-by-step explanation:

4 0

3 years ago

Find the slope, x-intercept, and y-intercept of the equation y = 10x - 20.

levacccp [35]

Answer:

slope=10, y-int=-20. x-int=2

Step-by-step explanation:

The equation y=10x-20 is in slope-intercept form, or y=mx+b with m being the slope and b being the y-int. In this scenarion, the m(the slope) is 10 and the b(the y-int) is -20. For the x-int, you have to find out what x is when y=0 and vice versa for the y-int. In this case, 0=10x-20 so x=2. Therefor the x-int is 2.

7 0

3 years ago