Answer:
106 degrees
Step-by-step explanation:
Sides AB and CD are equal in length and sides AD and BC are parallel to each other. This tells us that angles B and C are equivalent. Knowing this, we can set up the following equation to solve for x:

Subtract both sides by 42

Subtract both sides by 2x

Divide both sides by 2

Now, to find angle ABC, or angle B, we can plug x back into its expression:

Therefore, the measure of angle ABC is 106 degrees.
I hope this helps!
Answer:
C
Step-by-step explanation:
A
(m² - 3m + 2) / (m² - m)
we see due to a little bit of experience with expressions and multiplications of expressions that
(m² - 3m + 2) = (m - 2)(m - 1)
(m² - m) = m(m - 1)
so,
(m - 2)(m - 1) / (m(m - 1)) = (m - 2) / m
so, that's not it.
B
(m² - 2m + 1) / (m - 1)
we see again
(m² - 2m + 1) = (m - 1)(m - 1)
so,
(m - 1)(m - 1) / (m - 1) = m - 1
so, that's not it.
C
(m² - m - 2) / (m² - 1)
we see again
(m² - m - 2) = (m - 2)(m + 1)
and
(m² - 1) = (m + 1)(m - 1)
so,
(m - 2)(m + 1) / ((m + 1)(m - 1)) = (m - 2) / (m - 1)
yes, that is the solution.
D
(2m² - 4m) / (2(m - 2))
2m(m - 2) / (2(m - 2)) = 2m/2 = m
no, that is not a solution.
Answer:
1. y = 1/4 and y = 1/4x+2
2. y - 1 = -x (x + 7) and y = -x and x + y = 3
-------
4. y = 3 and x = 6
5. y = 1/2x + 2 and y + 1 = -2x
6. Slope of <u>AB</u> = 2/3
Slope of BC = -3/2
AB is perpendicular to BC because 2/3(-2/3) = -1
ABC is a right triangle because it contains a right angle
Answer:
x=9
Step-by-step explanation:
hope this helps i think it's right 60=9x - 21 you add 21 to both sides and get 81 = 9x then divide 81 by 9 and get x=9
Answer:
The appropriate probability model for X is a Binomial distribution,
X
Bin (<em>n</em> = 5, <em>p</em> = 1/33).
Step-by-step explanation:
The random variable <em>X</em> can be defined as the number of American births resulting in a defect.
The proportion of American births that result in a birth defect is approximately <em>p</em> = 1/33.
A random sample of <em>n</em> = 5 American births are selected.
It is assumed that the births are independent, i.e. a birth can be defective or not is independent of the other births.
In this experiment the success is defined as a defective birth.
The random variable <em>X</em> satisfies all criteria of a Binomial distribution.
The criteria are:
- Number of observations is constant
- Independent trials
- Each trial has only two outcomes: Success and Failure
- Same probability of success for each trial
Thus, the appropriate probability model for X is a Binomial distribution, Bin (<em>n</em> = 5, <em>p</em> = 1/33).