Category Essay

-8x-24=-8y  1=-1/3x+3/10y  Solution -8x + 8y = 24 (-1/3)x + (3/10)y = 1   Divide the first equation by -8 and multiply the second equation  by 30:                 x – y = -3…

2log(base 3)(x-4)+log(base 3)3=3 Solution Answer: x=7, 1 First, use the properties of logarithms to move the 2 up front. It can become an exponent: log3(x-4)2 + log33=3 Use properties of logarithms again to combine the two logs, since they have…

If x>0, simplify the expression below   sqrt((x)/(1-(x-1)/(x))) Solution IN the denominator of the complex fraction, the Least common denominator is X: 1 – (x-1)/x = (x-(x-1))/ x = (x – x +1)/x = 1/x SInce the 1/x is in…

The following table gives information on the amount of sugar (in grams) and the calorie count in one serving of a sample of 13 varieties of Kellogg’s cereal. Sugar (grams)4151211867271420313Calories12020014011012080190100120190190110120 1.     Which is the dependent variable and which is the independent…

Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 4; B: the numbers add to 2; C: at least one of the numbers is 5; and D: the numbers do not…

Directions: Given two reflections, determine a single transformation that could be used instead. Reflection over the line y = 3 followed by reflection over y= 8 Solution reflection over y = 3 is f(x,y) = (x,6 – y) reflection over…

explain why ³√-64 is real but √-64 is not Solution 3√(-64) = -4, since (-4)3 = -64   If x = √(-64), then x2 = -64.        If x is real, then x2≥0.        So, the equation…

Rod is paid an overtime rate of $25 per hour after he earns his basic wage of $600 per week. Write an equation in slope-intercept form for the total pay p if he works h hours of overtime. The monthly cost C of Marge’s phone plan…

Solution y = 2^x log_2(y) = x ln y / ln 2 = x <— change of base formula ln y = x * ln 2 y = e^(x * ln 2) = (e^(x))^ln2 or ln y = ln 2…

The current price of bunker fuel , (also known as heavy oil fuel ) costs $350 per metric ton. For a large cargo ship, approximately 0.1 metric tons of fuel is used for each mile sailing. 7) Calculate the approximate…