Factor the trinomial. You many need to check the discriminant to make sure it can be factored. SHOW YOUR WORK.

1 answer:

6 0

Check the discriminant (always a good idea).

b^2 - 4ac
b = -19
c = -15
a = 10

(-19)^2 - 4(10)(-15)
361 + 600
961

Yes it can be factored, but if you like, you could use the quadratic formula.
x = [- (-19) +/- sqrt(961)]/(2 * 10)
x = [19 +/- 31 ] / 20
x = (19 + 31/20
x = (50)/20
x = 5/2

x = [19 - 31] / 20
x = [- 12]/20
x = -3/5

Getting the factors is a little tricky.
(x - 5/2)(x + 3/5) = 0
The first factor is found by putting
x - 5/2 in that form and multiplying through by 2
1/2 (2x - 5) The 1/2 comes from multiplying by 2.

The second factor is
1/5 (5x + 3)

So the equation will look like
1/2(2x - 5)1/5(5x + 3) = 0 If you multiply by 2 you get
(2x - 5)1/5(5x + 3) = 0 and now multiply by 5 you get
(2x - 5) (5x + 3)

Check
2x*5x - 25x + 6x - 15
10x^2 - 19x - 15 = 0

So everything works out.

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True or false? A correct answer is worth (2 pts). Explain how you know for the additional (2 pts). Using complete sentence for (

PtichkaEL [24]

answer (in words)

FALSE. the coordinate pair (5, 2) is not a solution to the equation $2x+3y=10$ . in order to figure out whether or not the statement is true or false, plug the $x$ and $y$ values from the coordinate pair (5, 2) into the given equation, $2x+3y=10$ . if both sides of the equation end up equal, the coordinate pair is a solution to the equation. if not, the coordinate pair is not a solution to that equation.

(i hope i explained that well enough, i'm better at explaining it algebraically as opposed to putting it into words lol)

answer (algebraic/steps for solving)

first, plug in 5 for $x$ in the equation $2x+3y=10$ .

$2x+3y=10$ ⇒ $2(5)+3y=10$

then plug in 2 for $y$ .

$2(5)+3y=10$ ⇒ $2(5)+3(2)=10$

now your equation is $2(5)+3(2)=10$ . all that's left to do is to simplify. you can do this in whatever order you'd like, but i'll start with multiplying 2 · 5.

$2(5)+3(2)=10$ ⇒ $10 + 3(2) = 10$

multiply 3 · 2.

$10 + 3(2) = 10$ ⇒ $10 + 6 = 10$

add 10 + 6.

$10 + 6 = 10$ ⇒ $16=10$

16 and 10 are not equal, therefore (5, 2) is not a solution to the equation $2x+3y=10$ . in order for a coordinate pair to be the solution to an equation, both sides of the equation need to end up equal after solving and simplifying.

i hope this helps! have a great rest of your day <3

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mestny [16]

The ratio would be 3:4, or however you write ratios.

Hope this helped! :)

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