All categories

2 years ago

What is the solution to the system of equations?

Mathematics

1 answer:

asambeis [7]2 years ago

4 0

Plug the second equation (the one already solved for y) into the first equation

2x - (2x + 3) = 7

2x - 2x - 3 = 7

-3 = 7

Since the 2x's canceled out and left a false statement, this system of equations has no solution.

Hope this helps!

You might be interested in

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

3 years ago

a 20 cm nail just fits inside a cylindrical can. three identical spherical balls need to fit entirely within the can. what is th

DIA [1.3K]

The maximum radius of each ball is 3.33 cm.

<h3>What is a Cylinder?</h3>

A cylinder is a three-dimensional figure which is made of two parallel circular bases separated at a certain distance by a curved surface of the same radius as that of the bases.

A 20 cm nail perfectly fits the cylinder.

So the height of the cylinder = 20cm.

A sphere is a three-dimensional geometrical figure analogous to a circle. All the points of the sphere are at the same distance from the center.

If 3 spheres have to be fitted inside the cylinder,

The sum of the diameter of the spheres will be equal to the height of the cylinder.

The spherical balls are identical and so will have the same diameter

Let the maximum diameter of the sphere that can fit in the cylinder is d cm

Then,

d + d + d = 20

3d = 20

d = 20/3 = 6.67 cm

r = 3.33 cm

The maximum radius that the spheres can have to fit in the cylinder is 3.33 cm.

To know more about Cylinder

brainly.com/question/16134180

#SPJ1

5 0

1 year ago

Activity 2: Time is gold!

Svet_ta [14]

Answer:

time is gold ............

3 0

1 year ago

Read 2 more answers

Rewrite 105,000 in scientific notation.

Damm [24]

Your answer is B) 1.05 x 10 5

6 0

3 years ago

Of 100 staff member of school 48 drank coffee 25 drank both tea and coffee and every one drinks either coffee or tea . How staff

aivan3 [116]

Answer:

Step-by-step explanation:

Number of member of staff that drank tee = total number of member of staff - number that drank coffee - number that drank both tea and coffee

100 - 48 - 25 = 27 members of staff

7 0

3 years ago