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I just learned this but I'll give it a shot:) I hope I can help!

You can solve for the other length of the triangle by using the pythagorean theorem, a^2 + b^2 = c^2. Substitute your values.

So, 2.6^2 + 5.6^2 = c^2

6.76 + 31.36 = c^2

38.12 = c^2

Sqrt 38.12 = c

c = 6.174139616

Now you must find the semi-perimeter by using (a+b+c)/2. Substitute your values.

(2.6+5.6+6.2)/2 = s

14.4 / 2 = s

s = 7.2

Now use your semi-perimeter to solve for the area using the formula, a = [sqrt (s (s - a) (s - b) (s - c) ) ]. Substitute your values where s is your semi-perimeter. 

a = sqrt [ 7.2 (7.2 - 2.6) (7.2 - 5.6) (7.2 - 6.2) ]

a = sqrt [ 7.2 (4.6) (1.6) (1) ]

a = sqrt [ 52.992 ]

a = 7.3 

If you have any questions, then let me know! I'm glad to help!

Use law of cosines to find the 3rd side length

   then use Heron's Rule to calcualte the area of a triangle given three side lengths.

Or drop a vertical from the apex......use law of sines to find height  (2.44)      then area = 1/2  b x h   = 1/2   * 5.6  * 2.44    yd²

Draw a picture!

It's in Quadrant IV, so the x-value (cos) will be positive and the y-value (sin) will be negative.

sec(theta)  =  5/2   --->   1/cos(theta)  =  5/2   --->   cos(theta)  =  2/5

In your reference triangle, the x-value  =  2  and the hypotenuse  =  5

Using the Pytagorean Theorem, the y-value  =  - sqrt(21)

sin  =  y / r   --->   sin(theta)  =  - sqrt(21) / 5

I think that the best way to approach these problems is to draw the picture ...

Area of WHOLE circle   =  pi r^2  =  49 pi   in²

Central angle of  4pi/15   radians is a FRACTION of  the total  of  2 pi radians

      4pi/15  /  2pi     =  2/15   fraction of the TOTAL area

2/15  x  49 pi = .........  in²   

Therefore the equation should be (x+7)(y-1)=-10.

I see what you did wrong when you expanded  y(x + 7)  =  x - 3 and got xy - 7y  =  x - 3, the -7 should have been a +7.

Factor both the numerator and the denominator:

                  f(x)  =  [ 2(x + 5)(x - 5) ] / [ (x + 5)(x - 3) ]

Since the factor (x + 5 ) is found in both the numerator and the denominator, it produces a hole in the function at x = -5.

Cancelling out that term, we have:  f(x)  =  [ 2(x - 5) ] / [ (x - 3) ]

There will be a vertical asymptote at x = 3 (because it makes the denominator zero).

I tried the answer -7, -1, 4. But it was incorrect.

y  =  (x - 3) / (x + 7)

Multiply by (x + 7):     y(x + 7)  =  x - 3

Simplify:                      xy - 7y  =  x - 3

                               xy - 7y - x  =  -3

                               y(x - 7) - x  =  -3

                         y(x - 7) - x + 7  =  4

                        y(x - 7) - (x - 7)  =  4

                             (y - 1)(x - 7)  =  4

Since the area of an equilateral triangle = ( sqrt(3) / 4 ) · side²

and a regular hexagon is composed of six equilateral triangles,

the area of a reular hexagon = ( 3 · sqrt(3) / 2 ) · side²

With each sides 15 inches long:  area  =  ( 3 · sqrt(3) / 2 ) · 15² 

You got a good start !

For the box that is in the Venn

  you are told     48 + x  =  3 (12+x)      

                           48 + x = 36 + 3x

                             12 = 2x

                               x = 6       for the box in the Venn   

THEN add up all of the numbers in the Venn       these are the farms that grow beets and /or potatoes    subtract this number from 100 to find the number for the lower left corner.....the number that do NOT grow potatoes or beets.

        AB + BC  =  AC

12 + (x + 157)  =  2x + 179

           x + 169  =  2x + 179

                  -10  =  x

Formula:  Distance  =  Rate x Time     --->     D  =  RT

Speed of boat in still water:  15 km/hr

Speed of the water current:  w

Distance downstream =  36 km                   Distance upstream =  36 km

Rate downstream       =  15 + w                  Rate upstream        =  15 - w

Time downstream       =  t                           Time upstream       =  t + 1

Formula downstream:  36  =  (15 + w)(t)    Formula upstream:  36  =  (15 - w)(t + 1)

                      36/(15 + w)  =  t                                        36/(15 - w)  =  t + 1

                                                                                  36/(15 - w) - 1  =  t

Putting these two equations together:  36/(15 + w)  =  36/(15 - w) - 1

Multiplying by (15 + w)(15 - w):              36(15 - w)  =  36(15 + w) - (15 + w)(15 - w)

                                                                540 - 36w  =  540 + 36w - (225 - w²)

                                                                        -72w  =  -225 + w²

                                                        w² + 72w - 225  =  0

                                                         (w + 75)(w - 3)  =  0

                         Either  w  =  -75 (discard)  or  w  =  3 km/hr

Being in Quadrant III, the x-values and y-values are both negative.

If you draw the reference triangle, the y-segment is -1 when the hypotenuse is 6. (Because sin(theta) = -1/6.)

Using the Pythagorean Theorem, we can find that the x-segment is - sqrt(35).

So the tan(theta) = -1 / -sqrt(35),

which makes the cot(theta) = sqrt(35).

Let

 \(\displaystyle x=y^{3},\)

then

\(\displaystyle 7y=y^{3}+6,\\ y^{3}-7y+6=0, \\ (y-1)(y^{2}+y-6)=0, \\ (y-1)(y-2)(y+3)=0,\)

etc. .

2 + 41 = 43

11 + 13 + 19 = 43

2 + 11 + 13 + 17 = 43

3 + 5 + 7 + 11 + 17 = 43

You are welcome :)

"...a. Find the probability that the number on the roll of the die is at most 3.
b. Find the probability that the number on the roll of the die is at least 5."

As follows:

Thank you so much Melody! 

Have you tried getting out your protractor and a ruler and drawing them. ?

You will not learn just by being given the answers.

I mucked around with this quite a bit before I came up with a solution.

First I did the division and found   \(f(x)=3(x^2+3)+\frac{3(-3x-5)}{x^2+x-2}\)

If I add    \(-3(x^2+3)\)

then the resulting expression will be  \(  \frac{3(-3x-5)}{x^2+x-2}\)

Now with this latest expression the degree of the numerator is 1 and the degree of the denominator is 2

As x tends to infinity both the numerator and the denominator tend to infinity also but the bottom is approaching infinity at a much faster rate (since the degree is higher.) so the expression will tend to 0 as x tends to infinity.

Hence    one solution is    \(g(x)=-3x^2-9\)

\(\displaystyle \lim_{x\rightarrow\infty}\;f(x)+g(x)=0^-\)

You could also tackle this as follows:

31x + 29y = 1125

30(x+y) + (x-y) = 1125

x+y = 37 + 15/30 - (x-y)/30

let x-y = 15, then

x + y = 37

(Can also find that x = 26, y = 11)

a=0.0970998

b=0.0336492

Use synthetic division to show that x is a zero of the third-degree polynomial equation. Then, the result to factor the polynomial completely. List all real zeros of the function.