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What is the value of b?

Hello Guest!

\((4-x)^2:x^2=9:16\\ (4-x):x=3:4\\16-4x=3x\\ 7x=16\\ \color{blue}x=\dfrac{16}{7}\)

\(m=-\frac{4}{4-x}=-\frac{4}{\frac{28-16}{7}}=-2.\overline 3\)

\( b=-m\cdot x=-\frac{16}{7}\cdot -2.\overline 3\)

\(b=5.\overline 3\)

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They are the only ones I can think of too.

I got down to

\(a^2+b^2 -ab=1\)

Not sure how to determine if those are the only 4 answers.

$2 : $5 = 5 : 8 

15-27-51

Square side => x

x / 28 = 68 / x

x² = 1904 square units

Area = 10² - (3√2)²

cos(2x) = 2cos^2(x) - 1

cos(2x) = 2cos(x)

2cos^2(x) - 1 = 2cos(x)

Any idea on what to do from here?

=^._.^=

In triangle ABC, cos B = 3/5 and angle A is 90 degrees. What is cos A?     

The cosine of 90^o is 0 (zero).  

Let the number of muffins that Jane baked ==J

Let the number of muffins that Linda baked==L

J / L ==3 / 5

J + 42 ==5/6L, solve for J, L

J==108 muffins that Jane baked

L==180 muffins that Linda baked.

108  +  180 ==288 total muffins baked by both girls.

Let the amount of $2 notes ==T

Let the amount of $5 notes ==F

T  -  3/5T ==2/5T - still left

F  -  1/4F ==3/4F - still left

2/5T  +  3/4F ==238

 3/4F  -  2/5T ==182, solve for T, F

F ==280 - original amount of $5 notes.

T==70 - original amount of $2 notes.

The ratio is: 70 / 280 == 1/4

Angle B = 4[(180 - 18) / 9] + 9         (If I understood the question correctly)

Find the inradius of triangle JKL if JK=JL=17 and KL=18.

Hello Guest!

\(18^2=17^2+17^2-2\cdot17^2\cdot cos\ J\\ cos \ J=\dfrac{2\cdot 17^2-18^2}{2\cdot17^2}=0.439446\\ \color{blue}J=63.931°\\ \color{blue}K=L=58.034°\)

\(y=tan\dfrac{J}{2}\cdot x=-tan\dfrac{K}{2}\cdot (x-17)\\ tan\dfrac{J}{2}\cdot x+tan\dfrac{K}{2}\cdot x=tan\dfrac{K}{2}\cdot 17\\ x= \dfrac{tan\dfrac{K}{2}\cdot 17}{tan\dfrac{J}{2}+tan\dfrac{K}{2}}=\dfrac{tan\dfrac{58.034°}{2}\cdot 17}{tan\dfrac{63.931°}{2}+tan\dfrac{58.034°}{2}}\)

\(x=8\)                   \(y=tan\dfrac{J}{2}\cdot x=tan\dfrac{63.931°}{2}\cdot x\)

\(y=4.992\)

The inradius of triangle JKL is 4.992.

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230.4 units perimeter

Factors of 5400

All Factors of 5400: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 27, 30, 36, 40, 45, 50, 54, 60, 72, 75, 90, 100, 108, 120, 135, 150, 180, 200, 216, 225, 270, 300, 360, 450, 540, 600, 675, 900, 1080, 1350, 1800, 2700 and 5400.

Count the black ones

https://web2.0calc.com/questions/find-the-radii-of-the-circles-a-b-and-c

There are 6 divisors of 5400 that work.

A    r = 7.5

B    r = 6.5

C    r = 11.5

Thank you so much!!

13 out of 22

180 - 120 = 60 degrees = angle B

pi/6

For how many integers where 2 <= n <= 100 is n(n + 1) odd?     

Let's see if we can detect a trend  

    n        n + 1        Product  

    2           3                6  

    3           4              12  

    4           5              20  

    5           6              30  

    6           7              42    

I don't think we have to go any further to see what's always going to happen.  

This illustrates that no matter what n equals, then either n or n+1 will always be even.  

The product of an even number and any other number is always even.   

The answer to the problem is NONE of them will be odd.   

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