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3 years ago

Systems of linear equations iready quiz

Mathematics

1 answer:

saw5 [17]3 years ago

7 0

Answer:

<h2>One solution.</h2>

Step-by-step explanation:

The given question is

<em>Does the following system have One Solution, No Solution, or Infinite Solutions. </em>

<em />

To solve this system, we just need to multiply the first equation by -1, and then sum those equations.

$-y = -4x - 8\\y = -5x + 3$

$0=-9x-5\\5=-9x\\x=-\frac{5}{9}$

Then, we use this value to find the other one

$y=4x+8\\y=4(-\frac{5}{9} )+8\\y=-\frac{20}{9}+8\\y =\frac{-20+72}{9} \\y=\frac{52}{9}$

As you can observe, the system of equations have a unique solution.

Therefore, the answer is one solution.

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3 years ago

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Answer:

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3 years ago

A fence for a rectangular garden with one side against an existing wall is constructed by using 60 feet of fencing. What is the

Y_Kistochka [10]

Step-by-step explanation:

A fence for a rectangular garden with one side against an existing wall is constructed by using 60 feet of fencing.

Perimeter of rectangle (3 sides)= 60 feet

Let 'x' be the width of the wall

$Perimeter = 2(length)+2(width)\\60=2(length)+2x\\\\60-2x=2(length)\\\frac{60-2x}{2} =length\\Length =30-x$

Formula for the area of the rectangle is

$Area=length \cdot width\\A=length(x)$

Replace the length we got using perimeter

$A=(30-x)(x)\\A(x)= 30x-x^2$

To find out the maximum are we take derivative

$A'(x)= 30-2x\\0=30-2x\\-30=-2x\\x=15$

find out second derivative to check whether x=15 is maximum

$A''(x)=-2$

second derivative is negative

So, Maximum area at x=15

To find maximum area we plug in 15 for x in A(x)

$A(x)=30x-x^2\\A(15)=30(15)-15^2\\A(15)=225$

So, maximum area is 225 square feet

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3 years ago

A line is parallel to the x-axis and passes through (-5,4) write the equation of that line, the slope, and the slope of a line p

-Dominant- [34]

A line parallel to the x-axis is horizontal and thus any point on the line has a fixed y-coordinate. So the given line that passes through (-5, 4) has equation y = 4 with slope 0.

A line perpendicular to this one would be vertical. Its slope would be undefined (or infinite, depending on convention), so that any point on it has a fixed x-coordinate. If this line also passes through (-5, 4), then its equation would be x = -5.

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3 years ago