Can someone please help me on this problem :)

Mathematics

1 answer:

ozzi3 years ago

5 0

Answer:

y = 10

Step-by-step explanation:

It is given that the 2 triangles are similar,

hence we can write the following relationship based on the length of each side.

3/(3+6) = x / (x+y)

3/9 = x / (x+y)

1/3 = x / (x+y)

(x+y) = 3x -----------(1)

By observing the hypotenuse of both triangles, we can see that

(x + y) = 15 -----------(2)

we can substitute this into equation (1) above to get:

15 = 3x

x = 15/3 = 5 (substitute this back into eq (2) to find y)

(x + y) = 15

(5+y) = 15

y = 15-5

y = 10

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Suppose we want to choose 5 colors, without replacement, from 8 distinct colors.1. If the order is relevant, how many can be don

Charra [1.4K]

(1) From the information given, if we want to choose 5 colors from 8 distinct colors and the order in which the selection is made is relevant, then what we have is a permutation.

The formula is given as;

$nP_r=\frac{n!}{(n-r)!}$

This formula means we need to select/arrange r items out of a total of n items and the anwer derived would be the total number of arrangements possible.

Therefore, we would have;

$\begin{gathered} nP_r\Rightarrow_8P_5 \\ _8P_5=\frac{8!}{(8-5)!}\Rightarrow\frac{8!}{3!} \\ _8P_5=\frac{8\times7\times6\times\ldots1}{3\times2\times1}\Rightarrow\frac{40320}{6} \\ _8P_5=6720 \end{gathered}$

Therefore, if the order is relevant, this selection can be done in 6,720 ways.

(2) If the order is NOT relevant, then what we need to calculate is a combination and the formula is;

$_nC_r=\frac{n!}{(n-r)!r!}$

The formula can now be applied as follows;

$\begin{gathered} _nC_r\Rightarrow_8C_5 \\ _8C_5=\frac{8!}{(8-5)!\times5!} \\ _8C_5=\frac{8!}{3!\times5!}\Rightarrow\frac{8\times7\times6\times\ldots1}{(3\times2\times1)\times(5\times4\times\ldots1)} \\ _8C_5=\frac{40320}{6\times120} \\ _8C_5=56 \end{gathered}$

If the order is not relevant, then the selection can be done in 56 ways.

3 0

11 months ago

Find the value of x 117,145,133,140,119,125

andreev551 [17]

Answer:

here u go hope this is right

Step-by-step explanation:

x + 779 = 900

x = 900- 779

x = 121

4 0