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What is the equation of the line that passes through the point (5,1) and has a slope of 5/6?

Hello Guest!

\(y=m(x-x_1)+y_1 \)

\(y=\frac{5}{6}(x-5)+1\\ y= \frac{5}{6}x-\frac{25}{6}+\frac{6}{6}\)

\(y=\frac{5}{6}x-\frac{19}{6}\)

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How many ways to chose the units digit?

how many ways to choose the tens digit?

 how ways to choose the hundreds digit?

multiply the answers together.

If f(x) = (x + 4)/(x^2 + ax + b) and f(x) has two vertical asymptotes at x=1 and x=2, then find the sum of a and b.

Hello Guest!

x^2 + ax + b = 0

1^2 + a*1+ b = 0      a + b = -1

2^2 + a*2 + b = 0    2a + b = 4

a = -3      b = 2     a + b = -1

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1/   Similar math problem::: https://web2.0calc.com/questions/help_54234

Scale factor = - 4/3

A / [XYZ] = 851 / 999

If x, y, and z are real numbers for which

x + y - z = -8

x - y + z = 18

-x + y + z = 30

 Then what is xyz?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

2x = -8 + 18         x = 5

2y = -8 + 30         y = 11

2z = 18 + 30        z = 24

xyz = 1320

The size of angle BDC is arctan (tan^–1) of BC/DC.   

Once you get the value of angle BDC, use sine(BDC) = CE/DC and solve for CE.      

_.

BY / YA = 6√2 / 6√8

The answer is 17/27.

abc = 21.

By the Cosine Law, BD = 4.

First graph the points to see your square.... a line of any slope must go through the point   1/2 , 1/2   to separate the square into equal areas

y = 5x + b    sub in the 1/2 1/2 point

1/2 = 5(1/2) + b

      b = -2

Here is a graph:

https://www.desmos.com/calculator/fiksxrruja

y = 0.5(x-3.5)(x+k) 

        when x = 0       1.75k  = y intercept

        when y = 0         x = 3.5  or -k  = x intercept  

Formula for area of a triangle 1/2 b h      or     1/2  x intercept * y intercept    for this problem

1/2  (1.75k  *  3.5) = 1.5

     k = .4897959

1/2 ( 1.75k * (-k)) = 1.5

    k = imaginary

I often verify answers like these with Desmos.....here is a picture:

Mmm they must end in 1,3,5,7, or 9

1a1        10     sum = 10(101)+450 

3a3         10    sum = 10(303)+450

5a5         10    sum=  10(505)+450

7a7         10

9a9          10

for each a can be any integer from 0 to 9

So I get 50 numbers

The sum of 0+10+20+ ..... 90 = 5(0+90) = 450

10(101)+450

Total sum = 10(101+303+505+707+909) +5*450 = 10*2525 + 1250 = 26500

That is what I get but I haven't checked it for careless errors

y = (x - 4)^2 - 10 is a parabola in 'vertex form'      the vertex is 4, -10 and the axis of symmetry is x = 4    (vertical axis of symmetry)

y=3/4*x^2−16x+15     re - arrange to 'vertex form' for a parabola

y = 3/4 (x^2 - 21 1/3 ) + 15               complete the square for 'x'

y = 3/4 ( x- 32/3)^2 - 70 1/3             now you can see the vertex (h,k) = ( 10 2/3, - 70 1/3)

Try to in the future do two seperate posts. :)))

=^._.^=

You can always post 2 seperate posts. 

I'm going to try the second problem. 

There are equations to use to find the volume/surface area of the frustum. 

https://www.cuemath.com/measurement/volume-of-frustum/

https://www.varsitytutors.com/hotmath/hotmath_help/topics/surface-area-of-a-cone

Try to imagine the frustum as a complete cone, with the base being 12 radius and a line cutting it at 9 radius. The height would be from 12 radius to the tip (0 radius). For the height to increase by 4 the radius subtracted by 3.  (12/3)*4 = 16, the height of the whole cone is 16. 

To find the volume, we're looking for the big cone (radius of 12) subtracted by the little cone (radius of 9). The volume of the big cone is 12^2*pi*16/3 = 768pi. 

The volume of the small cone is 9^2*pi*(16-4)/3 = 324pi. 

768pi - 324pi = 444pi.

To find the surface area, we're going to start by focusing on the lateral surface.

The lateral surface of the big cone (radius of 12) is sqrt(16^2+12^2)*12*pi = 240pi. 

The lateral surface of the little cone (raduis of 12) is sqrt(9^2+12^2)*9*pi = 135pi. 

The lateral surface of the frustum is 240pi - 135pi = 105pi. 

Next the bases. pi*9^2 + pi*12^2 = 225pi.

225pi + 105pi = 330pi. 

330pi + 444pi = 774pi.

Sorry if the explanation is the bit confusing, please ask questions if you don't understand anything. 

=^._.^=  

Since you know you are not supposed to put more than one question per post why did you do it?

When you do the wrong thing it cuts down on the number of good answers you may get.

You can always add a link to your second post. That would be an option.

Attn:  CCeed

Please limit yourself to one question per post.

3 seconds

In the diagram below, circles represent students and bars represent the "walls" of different rooms. 

We can see that there are 4 configurations of "bars". Zero bars, one bar, two bars, and three bars, which represent different ways to separate the students respectively. 

There are 3 slots that the bars can be in, so counting the different numbers of combinations for each of the scenarios gives $1 + 3 + 3 + 1 = \boxed{8}$

Alternativly, 1 + 3 choose 1 + 3 choose 2 + 3 choose 3 = 8 also works (if anyone knows how to type Combination in LaTeX, please tell me. 

Going TO Austin    812 / 7 = 116 m/hr

  going BACK         812/14 = 58

(116+58)/2 = plane speed = 87 m/hr     then wind is    116 - 87 = 29 m/hr

The domain of the function will be all values of t such that the denominator is non-zero.

Find the values of t that make the denominator zero and the domain will be all other values of t:

(1-t)² - (1+t)² = 0

(1-t)² = (1+t)²

Taking the square root of both sides, there are two possibilities:

Either:

1-t = 1+t

2t = 0

t = 0

Or:

1-t = -(1+t)

1-t = -1-t

2 = 0

No solution for this case.

Therefore the domain of the function is all values of t except t=0.

In interval notation, the domain can be expressed as:

(-∞,0) U (0,∞)

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