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hint:

log(a * b) = log(a) + log(b)

= (x+3)³

See if you can make sense of this pic

Hello Babbeln,

Insert correct characters to make the P-Q formula.

\(x = -\frac{p}{} \pm \sqrt{\Big(\frac{}{2}\Big)^2-} \)

The right P-Q formula is like that:

\(x = -\frac{p}{2} \pm \sqrt{\Big(\frac{p}{2}\Big)^2-q}\)

What has been missed: 2, p, q.

Hope that was helpful.^^

Straight

Change in velocity / Change in time = acceleration

= (15-35) / 4     m/ s²

1/x  + 4/3

Each ball can go in 2 boxes, so the answer would be 2^5=32

Well 

the cap and glasses H region is fully INSIDE the S region.  That means that S includes the H (the hats)  as well as the sorts, shirts and sandals.   so    H is a subset of S.    That would be true.  

It looks to me like S stands for Summer and W stands for winter.  Caps and sunglasses are just a small part of the Summer clothing set.

Note:  S is not a subset of H because the S area is not inside the H area

Other examples.

A German Shepherd is a subset of all dogs.   Because all German shepherds are dog.

Trees are a subset of Plants because all trees are plants.

when two lines are parallel, their slopes are the same

hence h, in the equation y = hx + k, would be 12

to find k, you'd substitue point (-6, 4) into the existing equation:
y = 12x + k

4 = 12(-6) + k

4 = -72 + k

k = 76

so the value of k is 76

(the equation of the line would thus be y = 12x + 76)

Good job!

37/20 * 100% = 185%

Set h(t) = 6

6 = -4.9t^2 + 18t- .4

 0 = -4.9t^2 + 18t - 6.4     now use quadratic formula to solve for t.....

                                             you will get two 't' values ...the time above 6 m  will be the time between the two values

cos c = sin b

sin^2 + cos ^2 = 1

sin^2 = 1 - (3/25)^2

sin^2 = 616/625       sin b = cos c =   sqrt (616)  / 25      <====  simplify as needed......

The solutions are

$(\frac{\sqrt{93}}{3} + 5, -\frac{\sqrt{93}}{3} + 5)$
$(-\frac{\sqrt{93}}{3} + 5, \frac{\sqrt{93}}{3} + 5)$

Let 3x + y + xy = 115, x > 0, y > 0
Solving this gives us y  =  (115 -3x) / (1 + x)
So the point is (1, 56)
x = 1, y = 56

3 + 56 + 56 = 115

So the answer is x + y = 1 + 56 = 57

im not sure i understand

I'm sorry i mistiped I meant to say: How many solutions does the equation f(f(x))=6 have???

Graphing, the equation f(f(x)) = 4 only has the solution x = 2.  So the answer is 1 solution.

\(f(x)=2x-3 \quad and \quad g(f(x))=5-4x\qquad \qquad \\Find \;\; g(4)\\ f(x)=4\\ 5-4x=4\\ -4x=-1\\ x=0.25\\ g(4)=g(f(0.25))=5-4*0.25 = 1 \)

f(x)=1/x^2

See how it is developed here:

Hello Guest,

Write 37/20 as a percent

The fraction 37/20 is equal to 185%.

Hope that was helpful.^^

Straight

Find the equation whose graph is a parabola with vertex (2,4), vertical axis of symmetry, and contains the point (-1,-1).

Hello Guest!

\(f(x)=a (x-2)^2+4\\ a ((-1)-2)^2+4=-1\\ 9a=-5\\ \color{blue}a=-\frac{5}{9}\\ f(x)=-\frac{5}{9}(x^2-4x+4)+4\)

\(f(x)= -\dfrac{5}{9}x^2+\dfrac{20}{9}x+\dfrac{16}{9}\)

  !

3x + 50 + 70 = 180

3x = 60

x = 20

For a polynomial with rational coefficients, the the irrational roots come in pairs. 

If one root is 1 + sqrt(2), the other one must be 1 - sqrt(2). 

Similarly, if one root is 2 + sqrt(7), the other one must be 2 - sqrt(7). 

Now that the roots are found, you can find the factored form of the quartic. :))

=^._.^=

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