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3 years ago

Solve the simultaneous equations 6x + 5y = 32 2x + 5y = 12 V = y =

Mathematics

1 answer:

Anni [7]3 years ago

8 0

Answer: x = 5, y = 2/5

Step-by-step explanation:

We have the system of equations:

6*x + 5*y = 32

2*x + 5*y = 12

To solve it, we can start by isolating one of the variables in one of the equations.

Because in both of them we have the term 5*y, i will isolate 5*y in the second equation:

5*y = 12 - 2*x

Now let's replace it in the first equation:

6*x + (12 - 2*x) = 32

Now let's solve it for x

6*x + 12 - 2*x = 32

(6*x - 2*x) = 32 - 12 = 20

4*x = 20

x = 20/4 = 5

Now we know the value of x, we can replace it in the equation:

5*y = 12 - 2*x

to find the value of y.

5*y = 12 - 2*5

5*y = 2

y = 2/5

Then the solution of the system is x = 5, y = 2/5

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3 years ago

A triangle has a perimeter of 90 centimeters write and use a linear system

lawyer [7]

We are given sides of the triangle by expression

First side : n

Second side : m = 5n-5.

Third side : l = 5/4 m - n.

Perimeter is 90.

Therefore, first equation could be set :

n +m +l = 90 --------------equation(1)

Second equation would be

m = 5n-5 --------------equation(2)

Third equation would be

l = 5/4 m - n --------------equation(3)

Let us solve the system of equations by substitution.

Substituting m = 5n-5 and l = 5/4 m - n in first equation.

We get

n +5n-5 +5/4 m - n= 90

Now, substituting m = 5n-5 in above equation we get

n +5n-5 +5/4 (5n-5) - n= 90

5n + 25n/4 -5 - 25/4 =90

5n + 6.25n -5-6.25 = 90.

11.25n-11.25 = 90

Adding 11.25 on both sides, we get

11.25n-11.25+11.25 = 90+11.25

11.25n = 101.25.

Dividing both sides by 11.25, we get

n=9.

Plugging n=9 in 2nd equation.

m = 5(9)-5 = 45 -5 = 40.

Plugging n=9 and m=40 in first equation, we get

9 +40 +l = 90

49 +l = 90.

Subtracting 49 from both sides, we get

49-49 +l = 90-49

l = 41.

Therefore, sides are of lengths l = 41, m= 40 and n=9.

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3 years ago

You are traveling to Chicago for a job interview. You leave Toledo, Ohio, at 5:45 A.M. and arrive in Elkhart, Indiana, at 8:15 A

baherus [9]

The minimum speed will be calculated as follows:
Time taken from Toledo to Elkhart=(8.15-5.45)=2 1/2 hours
Distance=136 miles
thus the speed between Toledo and Elkhart= 136 miles/2.5=54.4 mph

Distance between Toledo and Chicago is 244 miles
Distance between Elkhart and Chicago=244-136=108 miles
time taken to travel between Elkhart and Chicago assuming that I left Elkhart at exactly 8:15 and reach at 10.30:
=10:30-8:15=2.25 hours
thus the speed will be:
speed=(108)/(2.25)=48 mph
Thus for us to get to Chicago by 10:30 a.m we should drive at 48 mph

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3 years ago

What percent of shrink is caused by employees

Alika [10]

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Step-by-step explanation:

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2 years ago

Prove that for all n in the naturals, n(n+1)(n+2) is divisible by 3

DerKrebs [107]

By induction:

It's true for $n=1$ , since $1\cdot2\cdot3$ clearly contains a factor of 3.

Suppose it's true for $n=k$ , that $k(k+1)(k+2)$ is divisible by 3. Then

$(k+1)(k+2)(k+3)=\dfrac{k(k+1)(k+2)(k+3)}k=\dfrac{3m(k+3)}k$

where $m$ is an integer. This reduces to

$\dfrac{3m(k+3)}k=3m+9\dfrac mk$

and both terms are clearly multiples of 3. We know that $\dfrac mk$ is an integer since we had set $m=k(k+1)(k+2)$ previously, which implies $m$ is a multiple of $k$ . So the statement is true.

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3 years ago