Your equations are correct: f(x) = ($4.40)x + $50 g(x) = ($3.90)x + $90 x represents the number of mugs you purchase and f(x) and g(x) represent your cost. (c) x = 120 mugs f(120) = ($4.40)(120) +...
Your equations are correct: f(x) = ($4.40)x + $50 g(x) = ($3.90)x + $90 x represents the number of mugs you purchase and f(x) and g(x) represent your cost. (c) x = 120 mugs f(120) = ($4.40)(120) +...
The money is divided into 1 + 3 + 1/2 = 4 1/2 parts. The smallest part is the 1/2 part, which equals $42.50. (1/2)/(41/2) = $42.50/x 1/9 = $42.50/x x = ($42.50)*9 = $382.50
The results of a survey showed that 3 out of 10 people had voted for Lucky Luke. If there were 40,000 votes: a) what is the ratio of those who voted for Lucky Luke to those who did not? (3/10)/(7/10) = 3/7 b) How many voted for Luke? 3/10 = x/40,000. Solve for...
Let x = the numerator. The denominator exceeds the numerator by 7, so it's x+7. The full fraction is: x/(x+7) If 3 is added to the numerator and 1 is subtracted from the denominator, it's equal to 4/5 ...
∫(2√x)/(√x) dx Note that √x = x1/2. Now let u = x1/2: du = (1/2)x-1/2 dx = (1/2u) dx. Hence 2u du = dx. Now substitute: ∫(2u/u) 2u du = 2 ∫ 2u du Note that 2u = eln(2^u) = euln(2) ...
I assume the expression is 1/(x2+y). In math division by zero is undefined. So when you have a rational expression like this, the expression will be undefined when the denominator is zero. The denominator is (x2+y), so we need to know the values of x and y that can make...
Let x = the unknown number(s). (x + 6)2 = 169 x2 + 12x + 36 = 169 x2 + 12x - 133 = 0 (x+19)(x-7) = 0 x = -19 and 7
Use the "vertex form" of the quadratic equation: y = a(x-h)2 + k where (h,k) is the location of the vertex. In this problem (h,k) is given as (3,-4) so: y = a(x-3)2 - 4 To...
2x + x + 4 = -17 Subtract 4 from both sides: 2x + x + 4 - 4 = -17 - 4 Combine like terms: 3x = -21 Divide both sides by 3: ...
(3x5y3)3 (5xy7)2 = 33(x5)3(y3)3(5)2*(x)2(y7)2 = 27x15y925x2y14 = (27*25)(x15+2)(y9+14) = 675x17y23
y= x3 - 11x2 + 24x + 5 dy/dx = d(x3)/dx - d(11x2)/dx + d(24x)/dx + d(5)/dx dy/dx = 3x2 - 22x + 24
The Coulomb Force is an inverse square force; that is, it's proportional to 1/r2 where r is the distance between the particles. F = (1/4piε0)*q1q2/r2 so when you cut the distance in half, the force increases by a factor of four: 1/(1/2)2 = 1/(1/4) = 4.
A direct variation equation has the general form: y = kx where k is the constant of variation. Since k is given as -8, the direct variation equation in this problem is: y = -8x For...
Let x = the unknown number The number divided by 4: x/4 equals 6: = 6 x/4 = 6 Multiply both sides by 4: x = 6*4 x = 24
log3(9/√3) = log3(32/31/2) Now use the log rule log(a/b) = log(a) - log(b) = log3(32) - log3(31/2) = 2 - 1/2 = 3/2
Assuming that 17,561,600 is the number of workers in 2008, then the equation would be: W(t) = (322,560)*t + 17,561,600 Where t is the number of years since 2008. In 2018, t = 2018-2008 = 10. Plug t= 10 into the above equation...
P(t) = P0*ekt Where: P(t) = the population at time t P0 = the initial population k = the exponential growth rate t = time e = Euler's Number ≅ 2.718 If the population doubles when t = 62 years, then P(t=62) = 2P0. ...
2x - 2y = -3 -4x + 4y = 6 Multiply the first equation by 2: 2*(2x - 2y = -3) = 4x - 4y = -6 Now add this to the second equation: 4x - 4y = -6 -4x + 4y = 6 ----------------- ...
Percent Increase = (100%)* (Final Amount)/(Starting Amount) = (100%)*(1,900,000)/(200,000) ...
f(x) = (4x-6)/√(8-x) In math, division by zero is undefined. So any value of x that makes the denominator of f(x) equal zero will make f(x) undefined. All such values of x are excluded from the domain of f(x). The denominator of f(x) is √(8-x), and √(8-x) = 0 when...