Answer:
x = 17 and y = 8
Step-by-step explanation:
Since (6x + 3) and (8x - 31) are alternate interior angles, they are congruent.
Therefore, you can set them equal to each other and solve for x.
8x - 31 = 6x + 3
Combine like terms
2x = 34
Divide both sides by two
x = 17
Since (5y + 35) and (6x + 3) are consecutive interior angles, they add up to 180. Plug in 17 for x.
(5y + 35) + (6(17) + 3) = 180
Add like terms
5y + 140 = 180
5y = 40
y = 8
Answer:
44 degrees
Step-by-step explanation:
The angles x + 2 and x are complementary; they sum up to 90 degrees.
Thus, x + 2 + x = 90 degrees, or:
2x = 88, or
x = 44.
The value of x is 44 degrees.
Answer:
f(x) = 12x³ - 19x² + 17x - 17
Step-by-step explanation:
We can the numerator by multiplying the denominator by the quotient, and then adding the remainder.
We're given a denominator of 4x - 5
a quotient of 3x² - x + 3
and a remainder of -2
so the original numerator is:
(4x - 5)(3x² - x + 3) - 2
= 12x³ - 4x² + 12x - 15x² + 5x - 15 - 2
= 12x³ - 19x² + 17x - 17
Let's test that by dividing it by 4x -5 with long division:
That matches, so we know our answer's right, and:
f(x) = 12x³ - 19x² + 17x - 17
Answer:
0.5.
Step-by-step explanation:
Number of red marbles = 50
Yellow marble = 40
Green marble = 10
Total number of marble = 50+ 40 + 10 = 100
Probability of getting yellow marble =
= 0.4
Probability of getting green marble =
= 0.1
Probability of getting either red or green marble = 0.4 + 0.1 = 0.5
Hence, the required probability is equal to 0.5.