Is each line parallel, perpendicular or neither parallel or nor perpendicular to the line -x+4y=20? ? !

It's best to start by getting your equation into slope intercept form y=mx+b, where m is the slope

Given -x+4y=20, solve for y

4y=x+20

y=(1/4)x+5

If two lines are parallel, they will have the same slope. If two lines are perpendicular, they will have opposite reciprocal slopes (2/3 and -3/2, for example).

Solving for y, the first equation is y=(1/4)x+2. This has the same slope as the given equation, so the two are parallel.

The second equation is y=-4x-1, with -4 being the opposite reciprocal of 1/4. These two are perpendicular.

The third equation has slope -1/4, which is opposite but not the reciprocal, so it falls into the neither category.

The final equation also has slope -4, again the opposite reciprocal of 1/4. This line is perpendicular.

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!

c-   36

taxicab circle radius 9 has 4(9) = 36 points