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2)  Call the center of the circle "Q". 

     Since CD || AB, angle(DCB) + angle(ABC)  =  180^o.

     QC bisects angle(DCB) and QB bisects angle(ABC).

     Therefore angle(QBC) + angle(QCB) = 90^o, making angle(CQB) a right angle.

     The line segment from Q to the point of tangency on line BC is perpendicular to BC and has length r.

     Being an altitude of a right triangle, it is the mean proportional between the segments of BC.

     Therefore, r is the mean proportional between x and y, making r = sqrt(x·y).

Welcome! Don't worry about typing out all the e's. Lol!

Sorry I just realized that 57 isn't prime...it factors into 3 * 19 which makes 19 the largest prime factor.

Each worker m works d days, so the total amount of days worked is m * d. 1/3 of the work would be \(\frac{md}{3}\). This means that it would take n workers \(\frac{md}{\frac{3}{n}}\) which simplifies to \(\frac{md}{3n}\).

wow!, thank you so much HELPMEEEE! 

thank you but it is wrong

Using difference of squares, \(309^2-147^2=(309-147)(309+147)=(162)(456)\). 162 prime factorizes into \(2*3^4\) and 456 prime factorizes into \(2^3*57\). The prime factorization of their product would be \(2^4*3^4*57\). Therefore 57 is the largest prime factor.

1/4

30*1/6=5

5/20=1/4

Thank you H!!!

Half circumference= (112 * pi) / 2 = 56 pi

Diameter= 112

Perimeter= 112 + 56 pi.

The amount of diagonal tiles can be written as 2x-1 where x is the side length of the square. That means that 2x-1 = 89; x= 45. The area of the square is 45 * 45= 2025. 2025-89 yellow tiles= 1936 gray tiles.

1. \(a=\frac{k}{b} \)

2. \(-3=\frac{k}{-6} \)

3. \(k=18\)

4. \(a=\frac{18}{8}\)

Yes!! It was correct, and the solution was on point!

:)

\(\frac{8pi}{4}\) radians = 360 degrees

The area of the sector is equal to the area of the whole circle, 16 pi.

You might be missing parts of you're question because it was written in LaTex. Can you please check if there are any missing parts to your question, i.e. exponents.

Thanks!

\(f=ma\)

f is force, m is mass, a is acceleration

f=200\({a}_{1}\)for the softball and f=150\(a_2\) for the baseball

Since they both have the same amount of force, then 200\(a_1\)=150\(a_2\). This means that the ratio of the acceleration of the softball to the baseball is 150:200 or \(\frac{3}{4}\).

1)  If all we know about the triangle is that two of its sides measure 14 and 8 and, from this information, we can calculate the answer, then that answer must be true for however we draw the figure. (I find this hard to believe; is there something else about the triangle that we know?)

Assuming that we do not need to know anything else, I'll choose to draw a right triangle.

I'm going to place point X at the origin of the coordinate plane; point W at point (0,8); and point Y t point (14,0).

Then, the center of the circumcircle (call it "C") will be the midpoint of the hypotenuse (7, 4).

The slope of the line from X to C is 4/7; this line is a radius of the circle.

The tangent drawn through point X will be perpendicular to line CX, so its slope is -7/4.

Line WZ is parallel to this tangent and, therefore, also has slope = -7/4.

The equation of the line through C with this slope is:  y - 7  =  (-7/4)(x - 4)

     --->     4y - 28  =  -7x + 28     --->     7x + 4y  =  56

To find where this line intersects XY (the x-axis), substitute 0 for y:  7x + 4(0) = 56     --->  x = 8.

So, the distance ZY = 6.

\(x+4+\frac{5}{x-3}\)

Maybe it's just my personal preference, but I would have listed the temps either in alphabetical order of the cities, or in numerical value of the midday temperatures. 

Example (alphabetical):     London    Munich    Oslo    Paris    Rome    

_.

thank you!

302 l     /   ( 9.5 l / 90 sec)  = .........  sec

x = second week

x+24 = first week      summed = $ 86

x        +    x+24 = 86    solve for 'x' the amount in week 2

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