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Find the value of y if the measures of the interior angles of a convex decagon are 5yº, 5yº, 8yº, 8yº, 9yº, 9yº, 9yº, 9yº, 9yº, and 9yº.​    

I added them up and got 80y. 

The sum of the interior angles of a polygon of n sides is given by (n – 2)(180^o).  

A decagon has 10 sides, so the sum of its interior angles is (8)(180^o).  

Thus,                        80y  =  1440^o   

                                     y  =  18^o  

_.

25-1=24

sqrt24+25=29.8989795

sqrt29.8989795=5.46799593

Yay!

100-49=51

Answer:sqrt51

Yay!

Igor würde gebeten, die Gleichung cos q = 0,809 zu lösen. Stellen Sie die richtige Lösung für q2 bereit.

Hallo Gast!

\(cos\ q = 0.809\\ q=arccos\ 0.809\\ q \in \{0.628347, 2\pi-0.628347\}\)

\(\color{blue}q^2\in \{0.39482, 31.977196\}\)

  !

Thanks Hectictar   

Sorry guest, I did not realize that you were asking a question.

tysm!!

we can use Pythagorean's theorem for this one. let's just call x the missing side length.

21^2 + 28^2 = x^2

441 + 784 = x^2

1225 = x^2

x = 35

so the missing side length is 35. 

by the way, the Pythagorean's theorem is \(a^2+b^2=c^2\). 

hope this helped! please let me know if you are still confused :)

since a square has 4 equal sides, the perimeter would be 4 * (side length of the square). 

so, each side length of the square would be \(\frac{80-64y}{4}\). 

80 / 4 = 20 and 64y / 4 = 16y

each side length of the square is 20 - 16y, or the third option.

it seems that you are asking many questions about factoring simple expressions. here is a site that may help:

https://www.factoring-polynomials.com/factoring-2.htm

i have mentioned this before, but Symbolab's simplifying calculators are helpful as well, in providing step-by-step solutions and tips. feel free to explore!

hope this helped! sorry if my explanations weren't that great. a quick search online will also always provide you with many resources and tips! 

Ok so if you flip the triangle, it's a regular right triangle.

36+49=85

The answer is \(\sqrt85\)

\(\sqrt85\)=9.21954446

Yay!

i will first separate 12b into two different factors: 12 and b - we will factor these out one at a time (hopefully this step makes sense). this way it will be easier to understand, and solve. 

first, let us factor out the 12 from the expression. 60 / 12 = 5, and 72 / 12 = 6. 

this would be the current expression: 12(5ab - 6b). now, let's disregard the 12 factor for a moment, so we can factor out the b in the other factor. (sorry if the wording here is a bit strange)

5ab / b = 5a, and -6b / b = -6. 

here is the resulting expression (make sure to remember the 12 we factored out at the beginning!):

12b(5a - 6), which is the second option.

hope this helped! please let me know if you have any questions :)

Ramsay Theory tells us that the answer is n = 8.

let's start by converting all of these into grams. this way, it will be easier to put in order. 

1 kilogram = 1000 grams.

so, 7 kg would be 7000 grams, and 3 kg would be 3000 grams.

now, we have:

7000 grams

600 grams

100 grams

3000 grams

we can now order these from least to greatest, because they are all in the same unit.

the final order would be:

100 grams

600 grams

3000 grams

7000 grams

now we have to convert it back, to suit the original problem.

100 grams

600 grams

3 kg

7 kg

and we're done! hope this helped 

A rectangular tank with a base area of 24 cm² is filled with water and oil to a depth of 9 cm. The oil and water separate into two layers when the oil rises to the top. If the thickness of the oil layer is 4 cm, what is the volume of the water?

angle 1 would just be 24, because all the triangles inside the rhombus are congruent.

angle 2 would be 90, because the diagonals of a rhombus are perpendicular (if you would like proof, i believe Khan Academy has a video on that). 

angle 3 would be 180 - (90 + 24) = 180 - 114 = 66.

hope this helped! please let me know if you are still confused or have any questions :)

to expand this polynomial, we should multiply the factors in order from left to right. hopefully you can follow this process - 

5w + 5*4 + w^2 + 4w.

to simplify, we combine the like terms, to get:

w^2 + 9w + 20

hope this helped! sorry if this wasn't too clear. 

here are a few websites that may help you understand this better:

https://www.brainfuse.com/jsp/alc/resource.jsp?s=gre&c=35257&cc=108827#:~:text=A%20polynomial%20is%20expanded%20if%20no%20variable%20appears,3x(4%20-%20x)%20%2B%20(2x%20-%205)%202 

also try out Symbolab's expansion calculator. it provides a step-by-step expansion of polynomial expressions as well.

if you have some time, give these a try! Google searches are also useful to help you learn more too! 

Thanks!

the area of the circle is simply \(1^2 \cdot \pi = \pi\), and the area of the square would be \((1 \cdot 2)^2 = 2^2 = 4\).

the area of the circle / the area of the square would be \(\frac{\pi}{4}\). because we are calculating the percentage, we should multiply the numerator and the denominator by 25, so that the denominator would be 100.

for this question, i will round \(\pi\) to 3.14. 

\(3.14 \cdot 25 = 78.5\), and rounding that to the nearest integer, the answer would be ~ 79%.

hope this helped! please let me know if you have any questions 

the large cube has a surface area of \(6 * 10^2 = 600\), and the smaller cubes have a total area of \(6 * 1000 = 6000\).

so, the ratio is \(\frac{600}{6000}\) = \(\frac{1}{10}\)

hope this helped! please let me know if you are still confused 

Thank you so much!

if the diameter of the semicircle is 4 units, then the radius would be 4 / 2 = 2 units.

the shaded area is a right triangle with its two legs being the radius of the semicircle, so the area of that would be:

\(\frac{2*2}2\) = \(\frac42\) = \(2\)

hope this helped! please let me know if you are still confused :)

2x-y=2 parallel  y=2x-2  

(1,10)

so y=1/2x+b  put (1,10) get b=19/2

 the euation : y=1/2x-19/2

since the punch recipe calls for 7 parts water and 2 parts powder, that means it consists of 7 + 2 = 9 parts total.

because you make 108 fluid ounces of punch, we do 108 / 9 = 12. 

now we multiply 12 by the 7 parts of water and the 2 parts of powder, to get that you need 84 fluid ounces of water and 14 fluid ounces of punch.

hope this helped! sorry if my explanations didn't make much sense. feel free to ask any further questions