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I don't believe  the  series is correct  as written

The  common difference  between  the   first two terms =  -2y

But...the common difference  between second and third terms  = 4y

Add the three equations together to get

5(a + b + c) = 25  so   a + b + c = 5

Write the first equation as  2a + (a + b + c) = -3   so 2a + 5 = -3   or a = -4

Write the other two equations in a similar manner to find b and c, then multiply the three values together.

I am trying to find an + b, how would I do that?

Presumably you mean find a and b (or, possibly, a + b).

I'm sure you can finish from here. 

Terms in the  series =     (271  - 1)   /  6     +    1 = 270 / 6  +  1  =   45 + 1  =     46 terms 

Each  term can be expressed  as    ( 1 + 6n )      where n = 0,1,2,3.....43, 44,45

And each term  divided by 6 leaves a remainder of 1

So   summing all the remainders  we  get   46

And  46 /  6  =   7 * 6  +  4   =    remainder  of  4

lmao do you have cheung

you can notice that you are adding 6 more to the previous number, starting with 1. if we divide each of these numbers by 6, we will always get a remainder of 1. we can subtract 1 from the last number and divide it by 6, to see how many numbers in total are in the sequence. we get (271-1)/6=270/6=45.

now that we know there are 45 digits and each of the remainders when divided by 6 is 1, we know that the remainder of the sum divided by 6 is 45/6=7 3/2=$\boxed3$

Indianguy arrives  at  the answer  through using the  intersecting  Chord Theorem

The product  of the  segments of one chord  = the product of the segments of the other chord...so....

6 * 4   = 3 * x

24  /  3  =  x  =   8

8 i think

28  +  3T     =  37       where T =  the  number  of trips

3T =  37  - 28

3T  =  9

T  =  9 / 3    =   3  trips

Wie hoch ist die Höhe eines Zylinders mit einem Radius von 10 cm und einem Volumen von 942 cm3?

Hallo Gast!

\(V=\pi r^2h\\ h=\dfrac{V}{\pi r^2}\\ h=\dfrac{942cm^3}{\pi \cdot 10^2cm^2}\\ \color{blue}h=3cm\)

Die Höhe des Zylinders ist 3cm.

  !

Total angles in a triangle is 180

To find angle ACB, you take 135 away from 180 (180 - 135) = 45

25 + 45 + x = 180

70 + x = 180

x = 110

Angle ABC = 110

\(\frac{75}{45} = \frac{100}{60}\). This means you can paint 100 square feet every 60 minutes. 8ft x 5ft = 40 square feet

\(\frac{40}{x} = \frac{100}{60}\)

\(2400 = 100x \)

\(x = 24\)

This means it will take you 24 minutes to paint an 8ft by 5ft wall :)

let a = adult ticket and c = child ticket.

2a + c = 25.50

3a + 2c = 41

Use system of equations..

4a + 2c = 51

3a + 2c = 41

-----------------

a = 10

2a + c = 25.50

2(10) + c = 25.50

c = 5.50

An adult ticket is $10.00

In a 12-hour period of time, a drawbridge opens 8 times, holding traffic for 15 minutes each time. If a car approaches the bridge during this 12-hour time, find the probability that the bridge is open.    

open 8 times for 15 minutes each time

makes a total of open for 120 minutes, which is 2 hours  

                                                                    2  

in the 12 hour period, the bridge is open  —–—  of the time 

                                                                   12   

                                                                                                    2  

i think this means the probability of finding the bridge open is  —–—  

                                                                                                   12   

            1  

this is  —–   or in decimal form, 16.67   

            6  

0,5 (20x - 50y + 36) - 0.25 (-100x + 40y - 12) vereinfacht

Hallo Gast!

\(0,5 (20x - 50y + 36) - 0.25 (-100x + 40y - 12)\\ =10x-25y+18+25x-10y+3\\ \color{blue}=35x-35y+21=7(5x-5y+3)\)

  !

Senkrecht zu 5x - 3y = 11 und durchläuft (-5, 2)

Hallo Gast!

\( 5x - 3y = 11\\ y=\dfrac{5}{3}x-\dfrac{11}{3}\\ m_1=\dfrac{5}{3}\\ \color{blue}m=-\dfrac{3}{5}\)

\(y=m(x-x_P)+y_P\\ y=-\dfrac{3}{5}(x+5)+2\\ \color{blue}y=-\dfrac{3}{5}x-1\)

  !

The volume of a sphere = 4/3 * pi * (radius)³

So, the volume of the sphere = 4/3 * pi * 2³

i believe you are the same Guest as the one who asked a very similar question, except about parallelograms. 

so, again, i'm not sure how to explain this, but i believe the answer is option 3.

here is a site that has more information on rhombuses: 

https://byjus.com/maths/rhombus/

hope this helped! if you are interested in why 1, 2, or 4 are all properties of rhombuses, feel free to ask here, check the site i linked above, or do a quick internet search! 

the volume of the larger prism is 8*9*5 = 360.

the volume of the small cube is 2^3 = 8.

the area that is in the large prism but not in the cube is just the volume of the larger prism minus the volume of the cube.

so, the answer would be 360 - 8 = 352. 

i see that your initial answer was 64? if you like, feel free to explain how you got that as your answer, and i can help you see what you did wrong 

hope this helped!

a) yes, the two rectangles are similar. this is because PQRS is made by applying a scale factor to ABCD, meaning that each side of PQRS has a constant ratio to ABCD. 

(yikes, sorry if this explanation wasn't too good)

b) the area is simply length * width, which is 9*4 = 36.

c) the side lengths of PQRS are 9*5 = 45, and 4*5 = 20. the area of PQRS is 45*20 = 900.

d) the ratio of the area of ABCD to the area of PQRS is 36/900 = 1/25. this means that the area of PQRS is 25 times that of ABCD, which is also the square of the scale factor.

hope this helped! again, sorry if my explanations weren't that good. feel free to ask any further questions :)

we can set up equations for this one. let's define a variable x, to be the first piece of pipe cut.

so, we know the sum of all the pieces is 84.

x {this is for the first pipe} + x - 3 {this is for the second pipe} + x + 4 {this is for the third pipe} = 84.

now, we can combine the like terms, and then isolate the variables.

3x + 1 = 84

3x = 84 - 1

3x = 83

x = 83/3

well, the numbers did not end up quite as nice, but we can still solve for each piece.

the first piece is just 83/3.

the second piece is 83/3 - 9/3 = 74/3.

the third piece is 83/3 + 12/3 = 95/3.

if you would like to double check, you can add up all of those and see if they add up to 84!

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

since PQ and JL are parallel, we can determine that triangles KJL and KPQ are similar. 

now, we can use the similar triangle ratios to help us find x:

\(\frac{x-6}{x-6+3} = \frac{x-6}{x-3}\)

and we also have

\(\frac{x}{x+5}\)

we know that these two equal each other. so we get an equation:

\(\frac{x-6}{x-3}= \frac{x}{x+5}\)

let's cross multiply, and then continue simplifying -

\((x-6)(x+5) = (x-3)x\)

\(x^2-x-30 = x^2-3x\)

\(2x = 30\)

\(x=15\), which is option D

as you can see, the equation ended up simplifying quite nicely!

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

(a)  7y(-4xy + 5) = (7y* -4xy) + (7y*5) = -28xy² + 35y

(b) 7x(-4x + 5y) = (7x* -4x) + (7x*5y) = -28x² + 35xy

(c) 7x(-4y + 5y) = (7x* -4y) + (7xx*5y) = -28xy + 35xy

(d) 7y(-4x + 5) = (7y* -4x) + (7y*5) = -28xy + 35y

So, the bottom-most option is the right answer.

the shaded area is essentially the area of the trapezoid minus the area of that semi-circle.

the area of the trapezoid is 

\(\frac{50+80}{2} \cdot (20 \cdot 2)\)

= \(\frac{130}{2} \cdot 40\)

= \(65 \cdot 40\)

= \(2600\)

the area of the semi-circle is 

\(\frac{20^2 \cdot \pi}{2}\)

= \(\frac{400 \cdot \pi}{2}\)

= \(200 \pi\)

so, the area of the shaded region is \(2600 - 200\pi\).

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