The real solutions the equation as given in the task content; x² = 225 are; +25 and -25.
<h3>What are the real solutions of the equation as given in the task content?</h3>
It follows from the task content that the real solutions of the equation as given in the task content can be determined as follows;
x² = 225
x = ± 15
Therefore, the real solutions of the equation are; +25 and -25.
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First, Use the slope equation to find the slope of the line passing thru these two points:
m=rise/run
Here, the rise is 13-3, or 10, and the run is 7-2, or 5. Thus, the slope, m, is 10/5, or 2: m=2.
We want the slope-intercept form, so let's begin with its general form:
y=mx+b. Substitute the slope 2 for m: y=2x+b. Now choose either of the given points. Arbitrarily I am choosing (2,3). Then x=2 and y=3.
Substituting these values into y=2x+b: 3 = 2(2) + b, or b= 3 -4, or b = -1.
Then the equation of this line, in slope-intercept form, is y = 2x - 1.
There's a really easy way to convert any units to other units.
Right now, we have the fraction (4 miles) / (2 hours).
We want to find a fraction that's exactly equal to that one,
but has the units of (miles/minute) or maybe (feet/minute).
Just take the original fraction, and multiply it by some other
fractions.
Each fraction you multiply it by must have the value of ' 1 ' so
you don't change the value of the original fraction. But it can
have different units, that cancel with other units to eventually
give you the units you want.
(4 miles / 2 hours) times (1 hour / 60 minutes)
The second fraction is equal to ' 1 ', because the top and the bottom
have the same value ... 1 hour is the same thing as 60 minutes.
Multiply the fractions: (4 miles x 1 hour) / (2 hour x 60 minutes)
Now you can cancel 'hour' from the top and the bottom, and you have
(4 miles x 1) / (2 x 60 minutes)
= (4 miles) / (120 minutes)
= (4 / 120) mile/minute = 0.0333... mile / minute .
Let's do it again, go a little farther, and get an answer that
might mean more and feel more like an answer.
(4 miles) / (2 hours) x (5280 feet / mile) x (1 hour / 60 minutes)
The 2nd and 3rd fractions both have the value of ' 1 ', because
the top is equal to the bottom.
Multiply all three fractions:
(4 miles x 5280 feet x 1 hour) / (2 hours x 1 mile x 60 minutes)
You can cancel both 'mile' and 'hour' out of the top and bottom,
and look what you have left:
(4 x 5280 feet x 1) / (2 x 1 x 60 minutes)
= (4 x 5280) / (2 x 60) feet / minutes
= (21,120 / 120) feet/minute = 176 feet per minute
