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Your sequence has 6 terms:

1, 5, 127, 383, 1,151, 3,455,

NONE of them is divisible by 6

Find AC such that AB= 5sqrt2 and angle b= 45 and angle a=15.

\(\begin{array}{|rcll|} \hline \dfrac{ \sin(45^\circ) } {AC} &=& \dfrac{ \sin\Big(180^\circ-(15^\circ+45^\circ)\Big) } {5\sqrt{2}} \\\\ \dfrac{ \sin45^\circ) } {AC} &=& \dfrac{ \sin(15^\circ+45^\circ) } {5\sqrt{2}} \\\\ \dfrac{ \sin(45^\circ) } {AC} &=& \dfrac{ \sin(60^\circ) } {5\sqrt{2}} \quad | \quad \sin(60^\circ) =\dfrac{\sqrt{3}}{2} \\\\ \dfrac{ \sin(45^\circ) } {AC} &=& \dfrac{ \sqrt{3} } {10\sqrt{2}} \quad | \quad \sin(45^\circ) =\dfrac{\sqrt{2}}{2} \\\\ \dfrac{ \sqrt{2} } {2*AC} &=& \dfrac{ \sqrt{3} } {10\sqrt{2}} \\\\ \dfrac{ \sqrt{2}\sqrt{2} } {2*AC} &=& \dfrac{ \sqrt{3} } {10} \\\\ \dfrac{ 1 } {AC} &=& \dfrac{ \sqrt{3} } {10} \\\\ AC &=& \dfrac {10}{ \sqrt{3} } * \dfrac{\sqrt{3}} {\sqrt{3}} \\\\ AC &=& \dfrac {10}{3} \sqrt{3} \\\\ \mathbf{AC} &=& \mathbf{5.7735026919} \\ \hline \end{array}\)

In triangle ABC, AB = AC. Point P lies on line AB such that CP = BC. If angle APC = 125 degrees, what is angle ACP(in degrees)? 

This question is not right!!! Angle APC cannot be 125º!!!

If angle APC = 115º, then angle ACP = 15º 

Try proof-reading your question.

By inverse proprtion, x = 2*4/1 = 8.

A triangle has side lengths of 10, 24, and 26.  Let a be the area of the circumcircle, and let b be the area of the triangle.  Compute a - b in terms of pi.    

Hint:   Recognize that a 10, 24, 26 triangle is a right triangle, so the right angle subtends half of the circle, or in other words the hypotenuse is a diameter of that circle.  Will that get you going?  

Hint:

The top of the rectangle and the bottom of the rectangle are the same length.

floor x and floor y each have an equal chance of being even or odd.

even + even = even

odd+odd = ?

even+ odd = ?

odd + even = ?

So what is the prob of the sum being even?

the 2 rightmost columns remain unshaded so the answer is 100-2*10=80

Thank You!

https://web2.0calc.com/questions/confusing-algebra: Link To Actuall Response

Some people seem to have some difficulty in understanding how r=7 and k=30 were obtained above!!!.

Solve for k in  equation (1) above and you should get this:

k = 6 r^2 - 35 r - 19

Solve for k in equation (2) above and you should get this:

k = 6 r^2 - 57 r + 135

Equate the above 2 equations and solve for r:

  6 r^2 - 57 r + 135 = 6 r^2 - 35 r - 19, solve for r 

 -57r +35r =-19 - 135                                                                                                  

-22r = - 154

r = 7 sub this into one of the equations above and you should get:

k = 30

Let Mr. Simple's budget = S

He spent a total of =9/4S

9/4S = 405, solve for S

S = 180 Euros - Mr. Simple's original budget.

405 - 180 =225 Euros  - extra money that Mr. simple spent.

Let Mrs simple original budget = B

(8/5)B = 405 - 5, solve for B

B = 250 Euros - Mrs.Simple's original budget.

400 - 250 =150 Euros - extra money that Mrs. simple spent.

180 + 250 =430 Euros - original budget of Mr. and Mrs. Simple

225 + 150 =375 Euros - money over budget that Mr. and Mrs. Simple spent.

h = -4.9t^2 + 10t + 1.2

==> dh/dt = -4.9t + 10

Setting dh/dt to 0 and solving for t gives t = 10/4.9 = 2.04 seconds

(b) There are 108/3 = 36 unique sets.

(c) For the first card, there are 3 ways to choose the number.  For the second, there 2 choices, and then there is only 1 choice.  So there are 3*2*1 = 6 ways that the numbers can be chosen.  Doing this for the other attributes, we get 6*6*24*6 ways.  But the order of cards doesn't matter in a set, so we divide by 3!: 6*6*24*6/3! = 864.  So there are 864 sets for part (c).

(d) The cards can have the same number, color, shape, or shading.  If all the colors are the same, then there are 6*24*6/3! = 144 sets.  If all the numbers are the same, then there are 144 sets.  We get the same number for shape and shading, so there are 4*144 = 576 sets for part (d).

(e) We need to choose two of the attributes.  There are C(4,2) = 6 ways of choosing two attributes.  For each of these two attributes, there are 3 options.  For the other two attributes, there are 3 ways of assigning the choices, so there are 6*3*3*3*3 = 486 sets for part (e)

(f) First we choose which attributes are the same.  There are C(4,3) = 4 ways of choosing which attributes are the same.  There are then 3*3*4 = 36 ways to assign which is which for each of these three attributes, and there are 4 ways to assign the choices for the fourth attribute, so there are 4*36*4 = 576 sets for part (f).

The roots of x^5 + 7x^4 - 2 = 0 are

r[1] = -6.99917

r[2] = -0.752186

r[3] = 0.0188858 - 0.729393i

r[4] = 0.0188858 + 0.729393i

r[5] = 0.713581

Plugging these value into the expression, we get an answer of 17.

Well let us name the side lengths $x$

$4x=148$

$x=37$
we know a side of diagonal, divide it by 2 and it is 12, by the Pythagorean theorem

12^2+(y^2)=37^2

y^2=1225

$y=35$

thereofre the other length of the diagonal is 35*2=$70$

The distance from the earth to the sun is 93,000,000 miles, and light travels at 186,000 miles per second. How many seconds does light from the sun take to reach the earth?   c  

      93,000,000 miles 

———————————   =   500 seconds  

  186,000 miles/second 

_.

Thank you!

Thank you!

I think, that the number of shaded squares will be as much as half of 100 squares. 100/2 = 50 so the number of shaded squares will be 50

ok, im sorry

u welcome

Thanks 

We can use long division.  We get a quotient of x^997 - x^996 + x^994 - x^993 + ... and a remainder of x^2 + x + 1.

2+3 / 4x = 2/5

      5/4x = 2/5

we return them to the common denominator 20x.

25/20 x = 8x/20x

20x is simplified by 20 x and fractions are removed

25=8x

x=25/8

x=3.125