Solve A = (1/2)(b1 + b2)h
Multiply both sides by 2: 2A = (b1 + b2)h
Divide both sides by b1 + b2: 2A/(b1 + b2) = h
Write y = (-2/3)x - 7 in standard form
Multiply both sides by 3: 3y = -2x - 21
Add 2x to both sides: 2x + 3y = -21
Write in slope-intercept form: 5x + 2y = -6
Subtract 5x from both sides: 2y = -5x - 6
Divide both sides by 2: y = (-5/2)x - 3
Each 20-sided die has 10 odd-numbered sides and 10 even-numbered sides.
To show exactly two even numbers, you must also show two odd numbers.
The probability of showing an even number is 1/2; the probability of showing an odd number is also 1/2.
There are 6 combinations that show two even numbers and two odd numbers:
6 x (1/2)2 x (1/2)2 = 6/16 = 3/8
a) Let x = number of hot dogs sold for the month
Let m = amount of money made from hot dog sales
m = 3.25(x - 4)
b) m = 3.25(55 - 4) = 165.75
c) Let x = number of hamburgers sold for the month
Let m = amount of money made from hamburger sales
m = 4.75(x - 2)
d) Since the number of hamburgers sold is probably not the same as the number of hot dogs sold, the work shown is
You need to use different variable for the number of hamburgers sold than for the number of hot dogs sold.
A possible equation is: m = 3.25(x - 4) + 4.75(y - 2)
where x = number of hot dogs sold for the month
y = number of hamburgers sold for the month
m = amount of money made from the sales of both hamburgers and hot dogs.
To find the y-intercept of 7x + 2y = -12, replace the x-term with 0:
7x + 2y = -12 ---> 7(0) + 2y = -12 ---> 0 + 2y = -12 ---> 2y = -12 ---> y = -6
To find the x-intercept of -3x - 5y = 21, replace the y-term with 0:
-3x - 5y = 21 ---> -3x - 5(0) = 21 ---> -3x - 0 = 21 ---> -3x = 21 ---> x = -7
Projected profit = projected revenues - projected costs
Projected profit = (3x + 22,050) - (2x - 1,560)
= 3x + 22,050 - 2x + 1,560
= x + 23,610
The probability of rolling a 1 is 1/6.
The probability of rolling anything but a 1 is 5/6.
You want one 1 and nine not 1s: (1/6) x (5/6)9.
Since there are ten different places the 1 could be rolled, you need to multiply the answer in the above line by10.
Therefore, the probability of exactly one die, out of ten, shows a 1 is: 10 x (1/6) x (5/6)9 = 10 x 1 953 125 / 60 466 176
= 19 531 250 / 60 466 176
= 0.323 (approximately)
Solve: 2x-1 + 2x-4 + 2x-2 = 6,5555...
6,55555... = 6 + 5/9 = 54/9 + 5/9 = 59/9
The terms: 2x-1, 2x-4, and 2x-2 can all be written in terms of 2x-4:
2x-1 = 2x-4+3 = 2x-4·23 = 2x-4·8
2x-4 = 2x-4·1
2x-2 = 2x-4+2 = 2x-4·22 = 2x-4·4
Therefore, the problem can be re-written as:
2x-4·8 + 2x-4·1 + 2x-4·4 = 59/9
Factoring out the term 2x-4:
2x-4(8 + 1 + 4) = 59/9
2x-4(13) = 59/9
Dividing by 13:
2x-4 = (59/9) / 13
2x-4 = 59/117
Taking the log of both sides:
log( 2x-4 ) = log(59/117)
(x-4)·log(2) = log(59/117)
Dividing by log(2):
x - 4 = log(59/117) / log(2)
x = log(59/117) / log(2) + 4
x = 3.012278...
If the length of the base of an isosceles triangle is 'a' and the length of each of the two congruent sides is 'b', then the distance between the orthocenter (the point of intersection of the altitudes) and the circumcenter (the point of intersection of the perpendicular bisectors of the sides) can be found using the formula: | (b2 - a2) / sqrt( 4·b2 - a2 ) |.
I calculated this formula using analytic geometry.
Since Loc can mow the lawn in 20 minutes, his rate is 1 lawn / 20 minutes or 1/20th of the lawn per minute.
Since Reza can mow the lawn in 30 minutes, his rate is 1 lawn / 30 minutes or 1/30th of the lawn per minute.
Loc mows for 5 minutes before he his joined by Reza. In these 5 minutes, he can mow (1/20)·(5) = 5/20th = 1/4th of the lawn.
Now, there is only 3/4th of the lawn to finish.
Assuming that the time they mow together is x, we can create this equation:
Amount done by Loc + Amount done by Reza = Total Amount
(1/20)(x) + (1/30)(x) = 3/4
Multiplying both sides by 60:
60(1/20)(x) + 60(1/30)(x) = 60(3/4)
3x + 2x = 45
5x = 45
x = 9 [It will take them 9 minutes, working together, to finish the lawn.]
Adding 9 to the 5 minutes that Loc mows alone = 14 minutes after Loc starts ---> 1:14 pm
For the lines, x = a and x = -a, with a > 0: the graph will be a pair of vertical lines, one passing through the point (a,0) and the other passing through the point (-a,0). There will be no 'solution' beccause there is no point of intersection.
For the lines, y = b and y = -b, with b > 0: the graph will be a pair of horizontal lines, one passing through the point (0,b) and the other passing through the point (0, -b). There will be no 'solution' because there is no point of intersection.
A line segment starting at point A(2, -2) extends through point B(14, 4) to point C.
If the length from B to C is 1/3rd the length from A to B, what are the coordinates of point C?
The x-distance from A to B is 12 because 14 - 2 = 12.
The y-distance from A to B is 6 because 4 - -2 = 6.
Since 1/3rd of 12 is 4, the x-value of point C must be 4 more than the x-value of point B ---> 14 + 4 = 18.
Since 1/3rd of 6 is 2, the y-value of point C must be 2 more than the y-value of point B ---> 4 + 2 = 6.
Therefore, the coordinates of point C are (18, 6).
The probability of choosing a red marble from bag A: (1/3) x (35/100) = 7/60
The probability of choosing a red marble from bag B: (2/3) x (55/100) = 22/60
The probability of getting a red marble is 29/60.
Getting that red marble from bag A is 7/60 / 29/60 = 7/29.
Getting that red marble from bag B is 22/60 / 29/60 = 22/29.