You can reword the two equations as:
-5x-y=15 (Divide original value by 3)
-2x+6y=6
Then use elimination to find x:
-30x-6y=90 (Multiply by 6 to get y values to be same to cancel out)
-2x+6y=6
You're left with:
-32x=96. Which can then be solved to find x which is -3.
Then plug back in
-2x+6y=6
Now to: -2(-3)+6y=6.
Which reduces to 6+6y=6. So y=0.
To graph them, just reword the equations (yes once again) so that y is in front.
y=-5x-15 and y=(1/3)x+1
9514 1404 393
Answer:
1.1 quarts
Step-by-step explanation:
Let x represent the amount to be added, in quarts. Then the amount of anti-freeze in the resulting solution is ...
0.20(8) + 1.00(x) = 0.30(8 +x)
0.70x = 0.10(8) . . . . . . subtract 0.20(8)+0.30(x)
x = 8/7 . . . . . . . . . . . . . divide by the coefficient of x
x ≈ 1.142857 ≈ 1.1
About 1.1 quarts of pure antifreeze must be added.
If you notice the terms, they're
7, -21, 63, -189 and so forth.
7*-3 = -21 and -21 * -3 is 63 and so forth, meaning the "common ratio" is -3.
now, for a common ratio say "r", which is a fraction, namely less than ±1 and more than 0, or |r| < 1 , you do have a convergent sequence.
however this one notice, |-3| is 3, and that's greater than 1 clearly, therefore is divergent, meaning the summation has no finite value.
The assumptions of a regression model can be evaluated by plotting and analyzing the error terms.
Important assumptions in regression model analysis are
- There should be a linear and additive relationship between dependent (response) variable and independent (predictor) variable(s).
- There should be no correlation between the residual (error) terms. Absence of this phenomenon is known as auto correlation.
- The independent variables should not be correlated. Absence of this phenomenon is known as multi col-linearity.
- The error terms must have constant variance. This phenomenon is known as homoskedasticity. The presence of non-constant variance is referred to heteroskedasticity.
- The error terms must be normally distributed.
Hence we can conclude that the assumptions of a regression model can be evaluated by plotting and analyzing the error terms.
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