Identify one linear equation and one nonlinear equation, and state why it is linear or nonlinear. Thanks

Mathematics

1 answer:

alukav5142 [94]2 years ago

6 0

Equation (2) y = 2x - 5 is linear equation.

Equation with the highest power of x = 1 is a linear equation.

It is linear because it forms a straight line.

Equation (3) y = x² + 6 is not a linear equation.

Equation with the highest power of x = 2 is a curve, specifically a parabola curve.

It is not a linear equation because it is a curve.

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RoseWind [281]

Answer:

L = $\sqrt{52^2 + 30^2}$

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Step-by-step explanation:

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2 years ago

Ann is adding water to a swimming pool at a constant rate. The table below shows the amount of water in the pool after different

N76 [4]

Answer:

(a) As time increases, the amount of water in the pool increases.

11 gallons per minute

(b) 65 gallons

Step-by-step explanation:

From inspection of the table, we can see that as time increases, the amount of water in the pool increases.

We are told that Ann adds water at a constant rate. Therefore, this can be modeled as a linear function.

The rate at which the water is increasing is the rate of change (which is also the slope of a linear function).

Choose 2 ordered pairs from the table:

$\textsf{let}\:(x_1,y_1)=(8, 153)$

$\textsf{let}\:(x_2,y_2)=(12,197)$

Input these into the slope formula:

$\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{197-153}{12-8}=\dfrac{44}{4}=11$

Therefore, the rate at which the water in the pool is increasing is:

11 gallons per minute

To find the amount of water that was already in the pool when Ann started adding water, we need to create a linear equation using the found slope and one of the ordered pairs with the point-slope formula:

$y-y_1=m(x-x_1)$