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2 years ago

Solve the equation for y. 6y+x=8

Mathematics

1 answer:

iVinArrow [24]2 years ago

6 0

Answer:

The correct answer is $\bold{y = -\frac{1}{6}x+\frac{4}{3}}$ .

Step-by-step explanation:

We want to solve for y in the given equation. We can do this by rearranging the equation and using operational techniques to simplify.

$6y + x = 8 \ $\tex Subtract x from both sides of the equation.$

$6y + x - x = 8 - x \ $\tex Carry out the operation.$

$6y = 8 - x \ $\tex Rearrange so the equation lists the variables first and the constants second.$

$6y = -x + 8 \ $\tex Create a coefficient for the x-variable (this is -1).$

$6y = -1x + 8 \ $\tex Divide by 6 on both sides of the equation in order to isolate the y-variable.$

$\frac{6y}{6}=\frac{-1x}{6} + \frac{8}{6} \ $\tex Carry out this operation by simplifying the fractions and dividing out the operations accordingly.$

$y = -\frac{1}{6}x+\frac{4}{3} \ $\tex Be sure to verify that all fractions and terms are simplified as far as they can be and that the equation is written in proper syntax.$

Because we have the y-variable isolated from the rest of the equation, we are done!

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Let C(n, k) = the number of k-membered subsets of an n-membered set. Find (a) C(6, k) for k = 0,1,2,...,6 (b) C(7, k) for k = 0,

vladimir1956 [14]

Answer:

(a) $C(6,0) = 1$ , $C(6,1) = 6$ , $C(6,2) = 15$ , $C(6,3) = 20$ , $C(6,4) = 15$ , $C(6,5) = 6$ , $C(6,6) = 1$ .

(b) $C(7,0) = 1$ , $C(7,1) = 7$ , $C(7,2) = 21$ , $C(7,3) = 35$ , $C(7,4) = 35$ , $C(7,5) = 21$ , $C(7,6) = 7$ , $C(7,7)=1$ .

Step-by-step explanation:

In this exercise we only need to recall the formula for C(n,k):

$C(n,k) = \frac{n!}{k!(n-k)!}$

where the symbol $n!$ is the factorial and means

$n! = 1\cdot 2\cdot 3\cdot 4\cdtos (n-1)\cdot n$ .

By convention 0!=1. The most important property of the factorial is $n!=(n-1)!\cdot n$ , for example 3!=1*2*3=6.

(a) The explanations to the solutions is just the calculations.

$C(6,0) = \frac{6!}{0!(6-0)!} = \frac{6!}{6!} = 1$

$C(6,1) = \frac{6!}{1!(6-1)!} = \frac{6!}{5!} = \frac{5!\cdot 6}{5!} = 6$

$C(6,2) = \frac{6!}{2!(6-2)!} = \frac{6!}{2\cdot 4!} = \frac{5!\cdot 6}{2\cdot 4!} = \frac{4!\cdot 5\cdot 6}{2\cdot 4!} = \frac{5\cdot 6}{2} = 15$

$C(6,3) = \frac{6!}{3!(6-3)!} = \frac{6!}{3!\cdot 3!} = \frac{5!\cdot 6}{6\cdot 6} = \frac{5!}{6} = \frac{120}{6} = 20$

$C(6,4) = \frac{6!}{4!(6-4)!} = \frac{6!}{4!\cdot 2!} = frac{5!\cdot 6}{2\cdot 4!} = \frac{4!\cdot 5\cdot 6}{2\cdot 4!} = \frac{5\cdot 6}{2} = 15$

$C(6,5) = \frac{6!}{5!(6-5)!} = \frac{6!}{5!} = \frac{5!\cdot 6}{5!} = 6$

$C(6,6) = \frac{6!}{6!(6-6)!} = \frac{6!}{6!} = 1$ .

(b) The explanations to the solutions is just the calculations.

$C(7,0) = \frac{7!}{0!(7-0)!} = \frac{7!}{7!} = 1$

$C(7,1) = \frac{7!}{1!(7-1)!} = \frac{7!}{6!} = \frac{6!\cdot 7}{6!} = 7$

$C(7,2) = \frac{7!}{2!(7-2)!} = \frac{7!}{2\cdot 5!} = \frac{6!\cdot 7}{2\cdot 5!} = \frac{5!\cdot 6\cdot 7}{2\cdot 5!} = \frac{6\cdot 7}{2} = 21$

$C(7,3) = \frac{7!}{3!(7-3)!} = \frac{7!}{3!\cdot 4!} = \frac{6!\cdot 7}{6\cdot 4!} = \frac{5!\cdot 6\cdot 7}{6\cdot 4!} = \frac{120\cdot 7}{24} = 35$

$C(7,4) = \frac{7!}{4!(7-4)!} = \frac{6!\cdot 7}{4!\cdot 3!} = frac{5!\cdot 6\cdot 7}{4!\cdot 6} = \frac{120\cdot 7}{24} = 35$

$C(7,5) = \frac{7!}{5!(7-2)!} = \frac{7!}{5!\cdot 2!} = 21$

$C(7,6) = \frac{7!}{6!(7-6)!} = \frac{7!}{6!} = \frac{6!\cdot 7}{6!} = 7$

$C(7,7) = \frac{7!}{7!(7-7)!} = \frac{7!}{7!} = 1$

For all the calculations just recall that 4! =24 and 5!=120.

6 0

2 years ago

Someone please help me! 15 points

Genrish500 [490]

Answer:

g . 47.6 degrees.

Step-by-step explanation:

g. The 3 towns form a right angled triangle and

tan A = BC/BA

= 105 / 96

A = 47.6 degrees.

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3 years ago

David earns $8 per hour he works 40 hours each week how much does he earn in 6 weeks

dem82 [27]

Answer:

$1920

Step-by-step explanation:

First, find out how much he earns in one week-so $8 times 40 = 320. Then multiply 320 by 6 to get how much earns in 6 weeks which is $1920.

(hope this helps :P)

5 0

2 years ago

Read 2 more answers

I need help omg thanks !

coldgirl [10]

Answer:

Option C.

Step-by-step explanation:

If you subtract each value from the next one, you see the differences are different. Therefore, it is not linear. Now divide each value by the previous value. You get 1.7 each time.

Answer: Option C.

6 0

3 years ago

What is the solution to the systems of equations? y= 2/3x + 3 x=-2

Romashka [77]

Answer:

y = 8/3

Step-by-step explanation:

x = -2

y = 2/(3*-2) + 3

y = 2/-6 + 3

y = -1/3 + 3

y = -1/3 + 9/3

y = 8/3

8 0

2 years ago