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# A shadow box is a type of picture frame that allows you to put your treasures on display. (answer)

If I read the problem correctly, the cardboard is to be shaped into a box by cutting squares off of each corner and these turned up to make a box.   If this is the case, isn't the volume = x(22-2x)(16-2x) and the value of x to maximize the volume would be the derivative = 0?   If...

# Whats -6(4-3x)-5x= ?x + ? (answer)

-6(4-3x)-5x = -24+18x-5x = 13x-24

# Can Someone Factor these (answer)

1)  First, look for greatest common factor.   Note:  each term of x3 - 2x2 - 8x contains an x, therefore, this equals x(x2 - 2x - 8), found by dividing each term by x.   We now need to factor x2 - 2x - 8.  What 2 factors of 8(1) subtract to equal 2? ...

# on the right is an illustration of a tap root. what is the function of the small root hairs that branch off the main root? (answer)

I believe the hairs are searching for water.

# I need to have the combination for this question and the conclusion (answer)

It sounds like you need 3 combinations of 8 reds and 1 combination of 6 whites.   8C3 + 6C1 =8!/(3!5!) + 6!/(1!5!) = 56 + 6 = 62.  Does this make sense?

# An ice cream cone is shaped like a hemisphere on top of a cone. If the radius of the base of the cone is 3.5 cm and the height is 8.5 cm, find the volume of the (answer)

OK.  We need to find the volume of a cone and semicircle and add together.   Let Vs = volume of semicircle.  Vs =½ (4/3)πr3 ,  and Vc = volume of a cone.  Vc = (1/3)πr2h.   If r = 3.5 and h = 8.5, plug these values  in and, voila, there is your...

# Solve tan 2x - cot x = 0 (answer)

Use the following identities:  cot x = 1/tanx. and tan 2x = (2tanx)/(1-tan2x)   The equation then becomes (2tanx)/(1-tan2x) - 1/(tanx) = 0   Add 1/(tanx) to each side:  (2tanx)/(1-tan2x) = 1/(tanx).   Multiply each side by tanx*(1-tan2x):  2tan2x...

# (x -2)2 if the value = -8 (answer)

If the problem is (x-2)2 = -8,  then |x-2| = 2i√2, and x-2 = 2i√2 and x-2 = -2i√2.   So the answers are x = 2+2i√2, and x = 2-2i√2.

# Find the average or mean slope of the function on this interval (answer)

The Mean Value Thm states:  If f(x) is continuous over [a, b], and f'(x) is defined over (a, b), where a<<b, then there is a c such that f'(c) = (f(b) - f(a))/(b - a).  Try this and you should have your answer.   Therefore:  f'(c) = -14c,  and (f(5)-f(4))/(5-(-4))...

# vertex of the parabola #1 (answer)

Hi, Carlos.   There are two ways to approach this problem.  We need to put this equation into a different form.   f(x) = a(x-h)2 + k, so the vertex will be the point (h, k).   One way is to complete the square:  f(x) = (x2 - 8x +   ...

# I need to check this equation (answer)

Remember, if this is an inequality, if you divide by a negative number, the inequality changes.   Therefore, -9x + 9 >= 4 x - 8  becomes -13x >= -17.   Divide by -13, and the answer becomes:  x<= 17/13.

I don't see an equation.  However, if your equation is in the form:  1x2 + bx  = 0, in order to make sure the equation is a perfect square, divide b by 2, square it, and add to both sides.   Example:  x2 + 6x = 0,  b = 6, b/2 = 6/2 = 3,  so (b/2)2...

# top level will always have 2 blocks. How many levels can her pyramid have if Alicia has 200 blocks? (answer)

How about the sum 2+3+4+...+(n+1) = 200?

a)  The vertical asymptote is the value of x such that x-q = 0(i.e. when the f(x)-> ∞.      Therefore, x = q.        The horizontal asymptote is the value of f(x) when x-> ∞.       Therefore, y = 3 (the...

# if the denominator is not a power of ten how can I change the fraction to a decimal (answer)

You can just divide the denominator into the numerator.  eg.  3/4 = .75.

# I have another question (answer)

Again we have a perfect square.   Same process:  y2 - 2/3y + 1/9 = 0     (How do we know that this is a perfect square?   Take 1/2 of 2/3 = 1/3,  square  that and we get 1/9)   y2 - 2/3y + 1/9 = 0   (y -...

# I have a question (answer)

Note that the left side is a perfect square.  If we rewrite the left side as a square, all that is needed to do is take the square root of each side.   x2 + 10x + 25 = 81   (x+5)2 = 81   √(x + 5)2 = √81   |x + 5| = 9   Therefore, ...

# How do you factor 6x2-19x+10 (answer)

Another approach:  6x2 - 19x + 10   Try to find 2 numbers whose product is 60  (the product of the coefficient of x2 and 10, the constant), and whose sum is 19.  Try 15 and 4.   Rewrite to get 6x2 - 15x - 4x + 10   Factor by grouping: ...

# Can someone help me with a differential equation problem? (answer)

Using the equation,  y(t) = yoekt,  where y(t) is the value of y at time t, yo is the value of y at time  t = 0, and k is the rate at which y increases as a function of time.   Therefore, yo = 10,000 and k = .02.   a)  y(0) = 10,000e0.02*0 = 10,000(1)...

# .: Let R={3,4,5,6,7,8,9} ,S={1,3,5} and T={ 2,4,6,8} a) R n S b) R – T c) S ? T (answer)

a.  R ∩ S = {3, 5}   b.  R - T = {3, -2, 5, 7, 9}   c.  ???