There are two approaches: 1. The direct way is to subtract 28 from 58 to determine the number of blue cars, then divide that number by the total number and multiply by 100% to find the percent of blue cars. i.e. 58 - 28 = 30. 30/58 times 100%. 2...

## Kevin C.'s Resources

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

I believe the hairs are searching for water.

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?

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...

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...

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.

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))...

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 + ...

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...

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...

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

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 -...

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, ...

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: ...

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)...

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

DeMoivre's Theorem states: (a+bi)n = (r cisθ)n = rn cis(nΘ) r cisθ means r (cosΘ + isinΘ) where r = √(a2 + b2) and θ = arctan(b/a) evaluated in the correct quadrant. So, in your example, a=1 and b=-1, so r = √2, and, since a and b are equal in...