Find the value of r so the line passes through each pair of points has the give slopes
1 answer:
Answer:
Step-by-step explanation:
First, let's start with what we have. If we use here's what we can put in:
Then we can use one of the given points to find the y-intercept. Since the only complete one is (12,10), we'll use that.
So now we have .
Now we can use our other point with the missing y-value and solve for y.
So the missing value is 64.
Hope this helps!
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Start by writing the system down, I will use to represent
Substitute the fact that into the first equation to get,
Simplify into a quadratic form (),
Now you can use Vieta's rule which states that any quadratic equation can be written in the following form,
which then must factor into
And the solutions will be .
Clearly for small coefficients like ours , this is very easy to figure out. To get 5 and 6 we simply say that
.
This fits the definition as and
.
So as mentioned, solutions will equal to but these are just x-values in the solution pairs of a form
.
To get y-values we must substitute 3 for x in the original equation and then also 2 for x in the original equation. Luckily we already know that substituting either of the two numbers yields a zero.
So the solution pairs are and
.
Hope this helps :)
The two-way table is attached.
We know that 63 people took the survey, and 22 of them were left-handed. This means that 63-22=41 of them are right handed.
Out of the 63 total, 37 are left brain dominant; this means that 63-37=26 are right brain dominant.
Of the 26 that are right brain dominant, 21 are right handed; this means 26-21=5 are left handed.
Of the 22 left-handed people, 5 are right brain dominant; this means 22-5 = 17 are left brain dominant.
Of the 37 left brain dominant people, 17 are left handed; this means 37-17=20 are right handed.
We know that 63 people took the survey, and 22 of them were left-handed. This means that 63-22=41 of them are right handed.
Out of the 63 total, 37 are left brain dominant; this means that 63-37=26 are right brain dominant.
Of the 26 that are right brain dominant, 21 are right handed; this means 26-21=5 are left handed.
Of the 22 left-handed people, 5 are right brain dominant; this means 22-5 = 17 are left brain dominant.
Of the 37 left brain dominant people, 17 are left handed; this means 37-17=20 are right handed.