Given:
The expression is:
![-\dfrac{1}{4}-\left(\dfrac{2}{5}+\dfrac{3}{7}\right)](https://tex.z-dn.net/?f=-%5Cdfrac%7B1%7D%7B4%7D-%5Cleft%28%5Cdfrac%7B2%7D%7B5%7D%2B%5Cdfrac%7B3%7D%7B7%7D%5Cright%29)
To find:
The expression that is equivalent to the given expression.
Solution:
We have,
![-\dfrac{1}{4}-\left(\dfrac{2}{5}+\dfrac{3}{7}\right)](https://tex.z-dn.net/?f=-%5Cdfrac%7B1%7D%7B4%7D-%5Cleft%28%5Cdfrac%7B2%7D%7B5%7D%2B%5Cdfrac%7B3%7D%7B7%7D%5Cright%29)
Using the distributive property, we get
![=-\dfrac{1}{4}-\dfrac{2}{5}-\dfrac{3}{7}](https://tex.z-dn.net/?f=%3D-%5Cdfrac%7B1%7D%7B4%7D-%5Cdfrac%7B2%7D%7B5%7D-%5Cdfrac%7B3%7D%7B7%7D)
Taking LCM, we get
![=\dfrac{-35-56-60}{140}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B-35-56-60%7D%7B140%7D)
![=\dfrac{-151}{140}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B-151%7D%7B140%7D)
Therefore, the expression
is equivalent to the given expression expression.
Note: There are more than one equivalent expressions.
Answer:
<D is congruent to <B
Step-by-step explanation:
They both have the 3 lines indicated on them
Answer:
3240°
Explanation:
The formula for calculating the sum of the interior angles of a polygon is (n-2)x180 where n refers to the number of sides. Because we know that the polygon has 20 sides, the equation would be (20-2)x180. The answer would be 3240°.
Answer:
This can be done in 3645 ways
Step-by-step explanation:
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
![P_{(n,x)} = \frac{n!}{(n-x)!}](https://tex.z-dn.net/?f=P_%7B%28n%2Cx%29%7D%20%3D%20%5Cfrac%7Bn%21%7D%7B%28n-x%29%21%7D)
In this problem, we have that:
1 Beethoven symphony, from a set of 9.
1 Mozart concerto, from a set of 27.
1 string quartets, from a set of 15.
So
![P_{(9,1)}*P_{(27,1)}*P_{(15,1)} = \frac{9!}{(9-1)!}*\frac{27!}{(27-1)!}*\frac{15!}{(15-1)!} = 3645](https://tex.z-dn.net/?f=P_%7B%289%2C1%29%7D%2AP_%7B%2827%2C1%29%7D%2AP_%7B%2815%2C1%29%7D%20%3D%20%5Cfrac%7B9%21%7D%7B%289-1%29%21%7D%2A%5Cfrac%7B27%21%7D%7B%2827-1%29%21%7D%2A%5Cfrac%7B15%21%7D%7B%2815-1%29%21%7D%20%3D%203645)
This can be done in 3645 ways