Answer:
The answer is below
Step-by-step explanation:
The equation of a linear function is given as:
y = mx + b;
where y, x are variables, m is the rate of change and b is the initial value of variable y.
A) Since there is B bacteria in the Petri dish at 12:00 midnight and the number of bacteria increases after midnight by 25 every hour. Let h represent the time in hours and T represent the total number of bacteria, therefore the equation is:
T = 25h + B
B) Given that B = 5, h = 6, hence:
T = 25(6) + 5 = 150 + 5 = 155 bacteria
C) The equation of the graph is:
T = 25h + 5
The graph was plotted using geogebra online graphing.
Answer:

Step-by-step explanation:
Hi there!
<u>What we need to know:</u>
- Linear equations are typically organized in slope-intercept form:
where <em>m</em> is the slope and <em>b</em> is the y-intercept - Parallel lines always have the same slope (<em>m</em>)
<u>Determine the slope (</u><em><u>m</u></em><u>):</u>
<u />
<u />
The slope of the given line is
, since it is in the place of <em>m</em> in y=mx+b. Because parallel lines always have the same slope, the slope of a parallel line would also be
. Plug this into y=mx+b:

<u>Determine the y-intercept (</u><em><u>b</u></em><u>):</u>

To find the y-intercept, plug in the given point (6,14) and solve for <em>b</em>:

Therefore, the y-intercept of the line is 22. Plug this back into
:

I hope this helps!
Answer:
<em>Jane traveled 8 miles farther then her trainer</em>
Step-by-step explanation:
<u>The Pythagora's Theorem</u>
In any right triangle, the square of the measure of the hypotenuse is the sum of the squares of the legs. This can be expressed with the formula:

Where
c = Hypotenuse or largest side
a,b = Legs or shorter sides
Jane's path from the Health Club to the end of her route describes two sides of a right triangle of lengths a=16 miles and b=12 miles.
Her total distance traveled is 16 + 12 = 28 miles
Her trainer goes directly from the Health Club to meet her through the hypotenuse of the triangle formed in the path.
We can calculate the length of his route as:


c = 20 miles
The difference between their traveled lengths is 28 - 20 = 8 miles
Jane traveled 8 miles farther then her trainer
Answer ⇒ 
Step-by-step explanation:

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5x can be written as x + x + x + x + x