All Answers 356019 Answers

Probably a troll guest. Or didn't know the steps

Let's make a system of equations to express the system to make it easier to not make a mistake (as the guest answerer unfortunately did).
 

m = max's baseball cards
p = pauls baseball cards

5p = m
p + 28 = m
 

... using substitution of the term m...
 

5p = p + 28

4p = 28
p = 7

... solve for m...

5p = m
5*7 = m
m = 35

Therefore, Max has 35 baseball cards.

What are the coordinates of the point on the directed line segment from P1 (-4,3) to P2 (-2,-5) that partitions the segment into a ratio of 1 to 3?

Hello Guest!

The function equation is

\(f(x)=\frac{y_2-y_1}{x_2-x_1}\cdot (x-x_1)+y_1\\ f(x)=\frac{-5-3}{-2-(-4)}\cdot (x-(-4))+3\\ \color{blue}f(x)=-4x-13\)

 The coordinates of the point on the directed line segment from P1 (-4,3) to P2 (-2,-5) that partitions the segment into a ratio of 1 to 3 are (-3.5, 1) or (-2.5, -3).

  !

Lines y=(3a+2)x-2 and 2y=(a+4)x+2 are parallel. What is the value of a?

Hello Guest!

\(3a+2=\frac{a+4}{2}\\ 6a+4=a+4\)

\(a=0\)

  !

Find the radius of the circle passing through the points (0,0), (2,0), and (-1,3).

Hello Guest!

The functional equation of the circle passing through the points (0,0), (2,0), and (-1,3) is

\(f(x)=\pm \sqrt{(\sqrt{5})^2-(x-1)^2}-2\)

The radius of the circle is \(\sqrt{5}\approx 2.236\).

  !

The only conditions that work are A and B.

a - b = 23/3.

Statements B, C, D are true.

XY = 12*sqrt(3) - 18.

Hint:       C+D+E = 180

angle C = 44 degrees 

The possible values of a and b are 37 and 111.

The probability is 4/13.

The sum of the fraction is 25/2.

The sum telescopes to 1 + 1/2 - 1/99 - 1/100 = $\boxed{1.5}$.

Kidding aside:   x = arcos(sqrt(3)/2) = 30^o

It is a square, so each side is (sqrt(52))       I think you can find the correct answer with this info....

Only conditions (B) and (C) must be true.

Triangle ABC can be placed in 12 different locations.

There are 285 such integers.

The value of n is 10.

The sum of the squares of the coefficients is 4^2 + (4*3)^2 = 160.

I count 6 pairs of congruent triangles.