Me
how many and what type of solution(s) does the equation have?
4p^2=12p-5

a. 1 rational solution
b. 2 irrational solutions
c. 2 non-real solutions
d. 2 rational solutions

  D.  2 rational solutions

Step-by-step explanation:

You can answer this question by (a) solving the equation, or (b) evaluating the discriminant.

In the latter case, ...

  4p^2 -12p +5 = 0 . . . . . . a=4, b=-12, c=5

The discriminant is ...

  b^2 -4ac = (-12)^2 -(4)(4)(5) = 64

This is a perfect square, so the roots are real and rational, choice D.

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Once you get the quadratic in the standard form above, you can see that the factors will be related to the factors of 20 that sum to -12. As soon as you find these integer factors of 20, you know the roots are rational.

  4p^2 -10p -2p +5 = 0 . . . . . . rewrite -12p using the factors -10 and -2

  2p(2p -5) -1(2p -5) = 0 . . . . . .factor by grouping

  (2p -1)(2p -5) = 0

The solutions are the values of p that make the factors zero, 1/2 and 5/2. Both are rational numbers.

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A graphing calculator shows you very quickly that the two roots are rational.

a. turk and mcalister

b. howard, mission, and market

c. yes. since streets end some do not cross yet are not parallel to others. example: mcalister and 5th

step-by-step explanation:

parallel lines are lines which do not intersect ever and look a lot like railroad tracks. turk, mcalister and golden gate are examples of these.

intersect are streets which cross each other and a car on one can reach the other. howard, mission, and market intersect with 6th.

skew lines are lines which neither intersect nor are parallel. these lines exist here because some streets end and never intersect another like mcalister and 5th.

-7/8

step-by-step explanation:

instead of subtracting you add the -6/8 and -1/8