Step-by-step explanation:
In that equation it tells you that your slope is 2/3. It also tells you that your y intercept is -4. (Remember slope is written in y=mx+b) So first you plot your y value. (Remember that y intercept is up and down and slope is rise/fall over run) So your first point should be located at -4. Now you can began putting in your slope. Since your slope is positive, go up two and go to the right 3 times (rise/run). That's how you graph your equation.
<u>Answer:</u>
The equation using a fractional exponent is
<u>Solution:</u>
Given, term is cube root of x square
In numerical terms cube root of x square can be written as ⇒ cube root of
We have to write the expression for above given term in the form of fractional exponent of x.
In , cube root is written in fractional form
Now, powers are multiplied
Finally x is in power of a fraction, so we got the required answer
Problem 7
<h3>Answer: Choice A) 7</h3>--------------------------------------
Work Shown:
p(x) = x^4+x^3-kx-x+6
If (x-2) is a factor of p(x), then x = 2 is a root of p(x). This is a special case of the remainder theorem.
This means p(2) = 0
Replace every x with 2 and solve for k
p(x) = x^4+x^3-kx^2-x+6
p(2) = 2^4+2^3-k(2)^2-2+6
p(2) = 16+8-4k-2+6
p(2) = 28-4k
0 = 28-4k .... replace p(2) with 0
4k = 28
k = 28/4
k = 7
The polynomial
p(x) = x^4+x^3-7x^2-x+6
has the factor (x-2)
============================================
Problem 8
<h3>Answer: D) 40</h3>--------------------------------------
Work Shown:
Check out the diagram below to see the synthetic division table. We're after the remainder which is highlighted in yellow.
An alternative is to use direct substitution
p(x) = 2x^4+4x^3-x^2-5
p(-3) = 2(-3)^4+4(-3)^3-(-3)^2-5 ... replace every x with -3
p(-3) = 2(81)+4(-27)-9-5
p(-3) = 162-108-9-5
p(-3) = 40
This helps confirm we got the right remainder and the right answer.
