The graph of a linear equation is a straight line. The "solution" to a system of two linear equations is the point where the two lines cross. If the two lines are parallel, they never cross; hence parallel lines have no solution. Two lines are parallel if they have the same slope (the m value in y = mx+b). One of your equations is y = -2x + (you left the y-intercept out). The slope is -2. So any line with a slope of m = -2 will be parallel to this line and will not cross it. The second line also needs a different value of b, the y-intercept. Otherwise it is the same line and every point is a solution. So if your equation is:

y = -2x + 1

Then any equation of the form y = -2x + b, b≠1 will create a system with no solution. Hence the values of m and b are m = -2, b ≠ 1.

5 0

3 years ago

XD PLZ HELP ME I DONT UNDER STAND PLZ IM BEGGING

Natali [406]

Answer:

the volume for the second page is 607.5

Step-by-step explanation:

5 0

3 years ago

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Between x=2 and x=3, which function has a greater average rate of change than f(x)=2^x has?

maxonik [38]

Answer: f(3)

Step-by-step explanation:

First find the formula for the rate of change by taking the derivative of 2^x. Let f(x) equal some hypothetical y-value, then take the natural log of both sides.

$y=2^x\\\ln(y)=x \ln(2)$

Implicitly differentiate the left side and take the derivative of the right side

$\frac{y'}{y} =\ln(2)$

Multiply both sides by 'y' which was defined as 2^x

$y'=\ln(2)*2^x$

Plug in x = 2 and x = 3 to see which slope is larger

$y'=\ln(2)*2^2=4\ln(2)\\y'=\ln(2)*2^3=8\ln(2)$

4 0

3 years ago