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2 years ago

Line g is shown on the graph.

1 answer:

5 0

The equation of the line g that passes through points (-3, 2) and (0, 5), in slope-intercept form, is: y = x + 5.

<h3>How to Write the Equation of a Line in Slope-intercept Form?</h3>

Given the coordinates of two points that lie on a straight line on a graph, the equation that represents the line in slope-intercept form can be expressed as, y = mx + b, where:

Slope = m = change in y / change in x

y-intercept = b (the value of y when x = 0).

The coordinates of the two points on line g is given as:

(-3, 2) = (x1, y1)

(0, 5) = (x2, y2).

Find the slope (m) of the line:

Slope (m) = (5 - 2)/(0 - (-3))

Slope (m) = 3/3

Slope (m) = 1.

Y-intercept (b) = 5

Substitute m = 1 and = 5 into y = mx + b:

y = x + 5

The equation of the line in slope-intercept form is: y = x + 5.

Learn more about the slope-intercept equation on:

brainly.com/question/1884491

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3 years ago

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The number of bacteria in a refrigerated food product is given by N ( T ) = 22 T 2 − 123 T + 40 , 6 < T < 36 , where T is

antoniya [11.8K]

Answer:

$N(T(t)) = 1408t^2 - 385.6t - 105.52$

Time for bacteria count reaching 8019: t = 2.543 hours

Step-by-step explanation:

To find the composite function N(T(t)), we just need to use the value of T(t) for each T in the function N(T). So we have that:

$N(T(t)) = 22 * (8t + 1.7)^2 - 123 * (8t + 1.7) + 40$

$N(T(t)) = 22 * (64t^2 + 27.2t + 2.89) - 984t - 209.1 + 40$

$N(T(t)) = 1408t^2 + 598.4t + 63.58 - 984t - 169.1$

$N(T(t)) = 1408t^2 - 385.6t - 105.52$

Now, to find the time when the bacteria count reaches 8019, we just need to use N(T(t)) = 8019 and then find the value of t:

$8019 = 1408t^2 - 385.6t - 105.52$

$1408t^2 - 385.6t - 8124.52 = 0$

Solving this quadratic equation, we have that t = 2.543 hours, so that is the time needed to the bacteria count reaching 8019.

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