If n(A) = P and n(B)=q then n(AxB) is (a ) p (b ) q ( c ) p+q ( d ) pq

1 answer:

6 0

By way of example, suppose A = {1, 2, 3} and B = {a, b, c}. Then the Cartesian product of A and B is

A × B = {{1, a}, {1, b}, {1, c}, {2, a}, {2, b}, {2, c}, {3, a}, {3, b}, {3, c}}

That is, each element in A gets a pairing with each element in B, and for each pairing you have n(A) choices for the first element and n(B) choices for the second element.

So if n(A) = p and n(B) = q, then n(A × B) = pq.

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Which inequality represents the values of x that ensure triangle ABC exists? a triangle with side lengths of 6.5 units, 3.5 unit

nikdorinn [45]

Answer:

1 < x < 7.5

Step-by-step explanation:

This problem can be solved using given below property of triangle.

Sum of two sides is always greater than third side of triangle.

Difference of two sides is always lesser than third side of triangle.

_______________________________________________

Given

sides length

6.5 units

3.5 units

Third side is 2.5 + x

using the property, Sum of two sides is always greater than third side of triangle.

6.5 + 3.5 > 2.5 +x

=>10 >2.5 + x

=>2.5 + x< 10

=> x< 10 -2.5

=> x < 7.5

using the property, Difference of two sides is always lesser than third side of triangle.

6.5 - 3.5 > 2.5 +x

=>3.5 > 2.5 +x

=> 2.5 +x > 3.5

=> x > 3.5 - 2.5

=> x > 1

combining both we have

1 < x < 7.5

out of the given option none is 1 < x < 7.5

hence, correct answer will be 1 < x < 7.5 and wrong option can be claimed by student.

8 0

2 years ago

Read 2 more answers

Find the perimeter of the parallelogram with these vertices.

blondinia [14]

Check the picture below.

so we can say that two sides are "4" each in length, since opposite sides are equal, let's find how long the slanted sides are.

$~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-4}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[3 - (-4)]^2 + [5 - 2]^2}\implies d=\sqrt{(3+4)^2+3^2} \\\\\\ d=\sqrt{49+9}\implies d=\sqrt{58} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\Large Perimeter}}{4~~ + ~~4~~ + ~~\sqrt{58}~~ + ~~\sqrt{58}\implies 8+2\sqrt{58}}$