Answer:
see explanation
Step-by-step explanation:
given
f(x) =3x² - x - 4
To obtain roots set f(x) = 0, that is
3x² - x - 4 = 0
To factor consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 3 × - 4 = - 12 and sum = - 1
The factors are + 3 and - 4
Use these factors to split the x- term
3x² + 3x - 4x - 4 = 0 ( factor the first/second and third/fourth terms )
3x(x + 1) - 4(x + 1) = 0 ← factor out (x + 1)
(x + 1)(3x - 4) = 0
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
3x - 4 = 0 ⇒ 3x = 4 ⇒ x =
The roots are x = - 1 and x =
By the list provided that would give option 1
Answer:
ррооо
Step-by-step explanation:
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Answer: No this is not a linear function as the y values have different first differences.
Step-by-step explanation:
First we look at the x values. We start off and look at the second x value and subtract the first x value from it (That would be 1-0) and that equals to 1. Then we look at the third x value and subtract the second x value from it (2-1) and that equals to 1. Then we look at the fourth x value and subtract the third x value from it (That would be 3-2) and that is 1. Next we look at the fifth x value and subtract the fourth x value from it (That would be 4-3) and that is 1.
Now we look at the y values and do the same thing as with the x values. We start off and look at the second y value and subtract the first y value from it (That would be 1-0) and that equals to 1. Then we look at the third y value and subtract the second y value from it (4-1) and that equals to 3. Then we look at the fourth y value and subtract the third y value from it (That would be 9-4) and that is 5. Next we look at the fifth y value and subtract the fourth y value from it (That would be 16-9) and that is 7.
Even though the x values all have the same first differences, the y values do not and so this cannot be a linear function.
I hope this helps. Tell me if something doesn't make sense.
Answer:
Step-by-step explanation:
First, find the <em>rate of</em><em> </em><em>change</em><em> </em>[<em>slope</em>]:
Then plug these coordinates into the Slope-Intercept Formula instead of the <em>Point-Slope Formula</em> because you get it done much swiftly. It does not matter which ordered pair you choose:
1 = ⅖[6] + b
2⅖
−1⅖ = b
y = ⅖x - 1⅖ >> Line in <em>Slope-Intercept</em><em> </em><em>Form</em><em> </em>
If you need it written in <em>Standard Form</em>:
y = ⅖x - 1⅖
-⅖x -⅖x
_________
−⅖x + y = −1⅖ [We do not want fractions in our standard equation, so multiply by the denominator to get rid of it.]
−5[−⅖x + y = −1⅖]
2x - 5y = 7 >> Line in <em>Standard</em><em> </em><em>Form</em>
_______________________________________________
−3 = ⅖[−4] + b
−1⅗
−1⅖ = b
y = ⅖x - 1⅖ >> Line in <em>Slope-Intercept Form</em>
If you need it written in <em>Standard Form</em>:
y = ⅖x - 1⅖
-⅖x -⅖x
_________
−⅖x + y = −1⅖ [We do not want fractions in our standard equation, so multiply by the denominator to get rid of it.]
−5[−⅖x + y = −1⅖]
2x - 5y = 7 >> Line in <em>Standard</em><em> </em><em>Form</em>
** You see? I told you it did not matter which ordered pair you choose because you will ALWAYS get the exact same result.
I am joyous to assist you anytime.