Simplify (-8z+4) + (7z-7)
1 answer:
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<em><u>Question:</u></em>
Marty and Ethan both wrote a function, but in different ways.
Marty
y+3=1/3(x+9)
Ethan
x y
-4 9.2
-2 9.6
0 10
2 10.4
Whose function has the larger slope?
1. Marty’s with a slope of 2/3
2. Ethan’s with a slope of 2/5
3. Marty’s with a slope of 1/3
4. Ethan’s with a slope of 1/5
<em><u>Answer:</u></em>
Marty’s with a slope of 1/3 has the larger slope
<em><u>Solution:</u></em>
<em><u>Given that Marty equation is:</u></em>
<em><u>The point slope form is given as:</u></em>
Where, "m" is the slope of line
On comapring both equations,
<em><u>Ethan wrote a function:</u></em>
Consider any two values from the table we have;
(0, 10) and (2, 10.4)
<em><u>The slope is given by formula:</u></em>
From above two points,
Therefore,
Thus we get,
Therefore, Marty’s with a slope of 1/3 has the larger slope
Answer:
x⁴+2x³ +3x²+6x +12 r.
Step-by-step explanation:
You can do this through synthetic division. It is a shorthand way of dividing polynomials.
First you need to make your divisor equal to zero so you can solve for what goes into the division box:
x - 2 = 0 → x = 2
The next step is to arrange your polynomials in descending powers. All missing terms, you will put in a zero.
x⁵ - x³ + (-5) → x⁵ + 0x⁴- x³ + 0x² + 0x + (-5)
Now you can proceed to synthetic division. Make an upside down division box with the divisor outside and the coefficients of the dividend listed, along with their sign. Leave a space below the divident
+2 | +1 0 -1 0 0 -5
|<u> </u>
Next you bring down the first coefficient:
+2 | +1 0 -1 0 0 -5
|<u> </u>
+1
Then you multiply it by the divisor and write the product under the next coefficient:
+2 | +1 0 -1 0 0 -5
|<u> +2 </u>
+1
Next add the column and put the sum below it:
+2 | +1 0 -1 0 0 -5
|<u> +2 </u>
+1 +2
Then multiply again and repeat until you reach the last coefficient:
+2 | +1 0 -1 0 0 -5
|<u> +2 +4 +6 +12 +24 </u>
+1 +2 +3 +6 +12 +19
Now that you have your results, add in the x and their powers. The powers will start with the highest power but 1 less than the dividend. Since the dividend's highest power is 5, then the quotient's highest power will be 4. Then write it in descending order :
+1x⁴ +2x³ +3x² +6x +12 +19
Now the last coefficient is your remainder. So your results will be:
x⁴+2x³ +3x²+6x +12 r.