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3 years ago

What is the solution of the system of linear equations? y = 3x - 2 y - 2 = x

Mathematics

1 answer:

iris [78.8K]3 years ago

6 0

Answer:

x = 2 y = 4

Step-by-step explanation:

y = 3x - 2

x = y - 2

Plug in the equation of x into the first equation and solve for y.

y = 3x - 2

y = 3(y - 2) - 2 Multiply out

y = 3y - 6 - 2

y = 3y - 8 Add 8 to each side

y + 8 = 3y - 8 + 8 8 cancels on the right

y + 8 = 3y Subtract y from each side

y - y + 8 = 3y - y The y on the left cancels

8 = 2y Divide each side by 2

8/2 = 2y/2 2 on the right cancels because 2/2 = 1

8/2 = y

4 = y

Now plug your answer into the 2nd equation given to solve for x.

x = y - 2

x = 4 - 2

x = 2

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Answer:

The quality control facility operates for 10 hours each day.

Step-by-step explanation:

The given function models the number of cars that are put through a quality control test each hour at a car production factory.

The given function is

$c(t)= -t^2+8t+20$

We need to find the number of hours does the quality control facility operate each day.

Rewrite the given function it factored form.

$c(t)= -t^2+(10t-2t)+20$

$c(t)= (-t^2+10t)+(-2t+20)$

Taking out the common factors from each parenthesis.

$c(t)= -t(t-10)-2(t-10)$

$c(t)= (t-10)(-t-2)$

$c(t)=-(t-10)(t+2)$

The factored form of given function is c(t)=-(t-10)(t+2).

Equate the function equal to 0 to find the x-intercept.

$0=-(t-10)(t+2)$

$t-10=0\Rightarrow t=10$

$t+2=0\Rightarrow t=-2$

Number of hours cannot be negative. So from t=0 to t=10 quality control facility operate the cars.

Therefore the quality control facility operates for 10 hours each day.

7 0

3 years ago

Solve the following systems by Elimination

Alenkasestr [34]

Answer:

The solutions for both system of equations are as follows:

(5,2)
(2,-1)

Step-by-step explanation:

The first set of equations is:

$4x+6y=32\\3x-6y=3\\$

It can clearly be seen that the coefficients of y are already same in magnitude with different signs so we have to add both equations

So adding both equations, we get

$4x+6y+3x-6y = 32+3\\7x = 35\\\frac{7x}{7} = \frac{35}{7}\\x = 5$

Putting x=5 in equation 1

$4(5)+6y = 32\\20+6y = 32\\6y = 32-20\\6y = 12\\\frac{6y}{6} = \frac{12}{6}\\y = 2$

The solution is (5,2)

The second set of simultaneous equations is:

$-3x+5y=-113x+7y=-1$

We can see that the coefficients of x in both equations are same in magnitude with opposite signs so

Adding both equations

$-3x+5y+3x+7y = -11-1\\12y = -12\\\frac{12y}{12} = \frac{-12}{12}\\y = -1$

Putting y= -1 in first equation

$-3x+5(-1)=-11\\-3x-5=-11\\-3x=-11+5\\-3x=-6\\\frac{-3x}{-3} = \frac{-6}{-3}\\x = 2$

The solution is: (2,-1)

Hence,

The solutions for both system of equations are as follows:

(5,2)
(2,-1)

3 0

3 years ago

How to know how to solve properties of parallelograms

Archy [21]

Answer:

Opposite sides are corresponding (AB = DC).

Opposite angles are corresponding (D = B).

Consecutive angles are supplementary (A + D = 180°).

If one angle is right, then all angles are right.

The diagonals of a parallelogram hemisect each other.

Step-by-step explanation:

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3 years ago

A professor pays 25 cents for each blackboard error made in lecture to the student who pointsout the error. In a career ofnyears

arsen [322]

Answer:

The correct answer is "0.0000039110".

Step-by-step explanation:

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then,

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= $P(Y_{20}>1000)$

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= $P(Z>\frac{1000-800}{44.7214} )$

= $P(Z>\frac{200}{44.7214} )$

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By using the table, we get

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Step-by-step explanation:

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