Answer:
D. (12,3)
Step-by-step explanation:
From the graphical diagram attached below ; we would realize that the x-coordinate is in the positive direction and the y-coordinate is in the negative direction.
Initially, the location of S = 12 to the horizontal x axis from the graphical diagram. So, if the trapezoid RSTU is rotated 90° clockwise about the origin to produce trapezoid R'S'T'U, we will have :
S' = 3
Thus; the (x,y) coordinate of R'S'T'U = (12,3)
Answer:
m = 2
Step-by-step explanation:
Given:
x = 4
y = 6m - 2
a = 8
b = 5
Required:
Value of m
SOLUTION:
x and y are segments of a chord divided when it intersects another chord that also has segments a and b.
According to the Intersecting chords theorem,
Thus:
Solve for m
The value of m = 2
Answer: The required answers are
(a) 69, (b) 21, (c) 21 and (d) 0.
Step-by-step explanation: We are given that the set A has 48 elements and the set B has 21 elements.
(a) To determine the maximum possible number of elements in A ∪ B.
If the sets A and B are disjoint, that is they do not have any common element. Then, A ∩ B = { } ⇒ n(A ∩ B) = 0.
From set theory, we have
So, the maximum possible number of elements in A ∪ B is 69.
(b) To determine the minimum possible number of elements in A ∪ B.
If the set B is a subset of set A, that is all the elements of set B are present in set A. Then, n(A ∩ B) = 21.
From set theory, we have
So, the minimum possible number of elements in A ∪ B is 21.
(c) To determine the maximum possible number of elements in A ∩ B.
If the set B is a subset of set A, that is all the elements of set B are present in set A. Then, n(A ∩ B) = 21.
So, the maximum possible number of elements in A ∩ B is 21.
(d) To determine the minimum possible number of elements in A ∩ B.
If the sets A and B are disjoint, that is there is no common element in the sets A and B . Then, n(A ∩ B) = 0.
So, the maximum possible number of elements in A ∩ B is 0.
Thus, the required answers are
(a) 69, (b) 21, (c) 21 and (d) 0.
Let, total number of T-shirts are x.
Number of blue T-shirts = (2/3)x = 2x/3 .
Number of blue shirts on sale = (3/5)(2x/3) = 2x/5 .
Number of medium sized blue shirts on sale = (1/5)(2x/5) = 2x/25 .
Fraction of the shop's T-shirts are blue T-shirts that are on sale and are size medium = = 2/25 . ( Number of medium sized blue shirts on sale divided by total number of T-shirts )
Hence, this is the required solution.
Answer:
x=12
Step-by-step explanation:
This is a right triangle, so the Pythagorean theorem can be used. The Pythagorean theorem states that where C is the hypotenuse and a and b are legs. In this question, we are given a and C. So, plugin 13 for C and 5 for a and solve for b. Once you rearrange the equation you get,
. Next, solve what is under the root to get,
. Finally, square root 144 for the final answer b=12.