Answer: 
Step-by-step explanation:
Given
The rug is 4 feet longer than its width
Suppose the length of the width is x
Length is given by x+4
So, the product of length and width is equal to the area of the rug
![\Rightarrow x\left(x+4\right)=A\quad\quad [\text{A=Area of rug}]](https://tex.z-dn.net/?f=%5CRightarrow%20x%5Cleft%28x%2B4%5Cright%29%3DA%5Cquad%5Cquad%20%5B%5Ctext%7BA%3DArea%20of%20rug%7D%5D)
Answer:
Step by step explanation:
We have been given that measure of angle A is fifty five degrees, the measure of angle B is eighty degrees and the measure of angle C is x.
Since we know that sum of measures of all the three angles of any triangle equals to 180 degrees.
Let us set sum of measures of all angles of our triangle equal to 180 degrees.
Upon substituting our given values in our equation we will get,
Therefore, the measure of angle x equals to 45 degrees.
Answer
n║m
Step-by-step explanation:
Hope this is helpful!
Answer:
m<ADC = 107
Step-by-step explanation:
You need to know three things to solve this problem.
1) Opposite angles of an inscribed quadrilateral are supplementary.
2) The measure of an inscribed angle is half the measure of its subtended arc.
3) The sum of the measures of all the arcs of a circle is 360 deg.
From 1) we get:
m<A + m<C = 180
72 + m<C = 180
m<C = 108
From 2) we get:
m<C = (1/2)m(arc)BAD
108 = (1/2)[m(arc)AB + m(arc)AD]
216 = m(arc)AB + 122
m(arc)AB = 94
From 3) we get:
m(arc)AB + m(arc)BC + m(arc)CD + m(arc)DA = 360
94 + 120 + m(arc)CD + 122 = 360
m(arc)CD = 24
From 2) we get:
m<ADC = (1/2)m(arc)ABC
m<ADC = (1/2)[m(arc)AB + m(arc)BC]
m<ADC = (1/2)[94 + 120]
m<ADC = 107
There are 12 marbles in total. 4 of them are white.
The probability of getting a white marble on the first try is 4/12 or 1/3.
The probability of getting a second white marble in a row? Since you already pulled out a white marble on the first attempt, there are now 3 white marbles and 11 marbles in total. So the probability of getting a white marble at this point is 3/11.
Thus the probability of doing this back to back is 1/3 * 3/11 or 3/33 or 1/11.
The answer is B.
