Angle KMQ and angle RNL are on apposite sides of the transversal and between above and below (exterior to) the parallel lines, so they are alternate exterior angles. Theorem - Alternate exterior angles formed by parallel lines and a transversal have the same measure.
For this case we convert the mixed numbers to fractions:
Now we add the fractions:
We find the least common multiple of the denominators. The l.c.m is 8, then we divide by each denominator and multiply the result by each numerator.
8,375
Thus, the punch recipe implies 8.375 gallons. If we convert to a mixed number we have:
gallons
Answer:
gallons
When we are to divide the line segment such that the ratio is 1:2, there are actually 3 parts of the segment. First, we determine the distance between the coordinates and divide the distance by 3. Then, we add the quotient to the x-coordinate.
x-coordinate: (2 - 9) / 3 = -7/3
y-coordinate: (6 - 3 ) / 3 = 1
Adding them to the coordinates of a,
x - coordinate: (9 - 7/3) = 20/3
y - coordinate: (3 + 1) = 4
Thus, the coordinates are (20/3, 4).
Answer:
Equation ----> 2(c - 40)
c = -40
Step-by-step explanation:
2(c - 40)
= (2c) - (80)
= 2c - 80
= 
+ 
c = -40
<h3>Given</h3>
Two positive numbers x and y such that xy = 192
<h3>Find</h3>
The values that minimize x + 3y
<h3>Solution</h3>
y = 192/x . . . . . solve for y
f(x) = x + 3y
f(x) = x + 3(192/x) . . . . . the function we want to minimize
We can find the x that minimizes of f(x) by setting the derivative of f(x) to zero.
... f'(x) = 1 - 576/x² = 0
... 576 = x² . . . . . . . . . . . . multiply by x², add 576
... √576 = x = 24 . . . . . . . take the square root
... y = 192/24 = 8 . . . . . . . find the value of y using the above equation for y
The first number is 24.
The second number is 8.
