- 5x2 + 2x + 9= 0
factorize

Please check the explanation.

Step-by-step explanation:

Given the quadratic equation

5x²−2x−9 = 0

To factor the quadratic function 5x²−2x−9, we should solve the corresponding quadratic equation 5x²−2x−9 = 0.

Indeed, if x₁ and x₂ are the roots of the quadratic equation ax²+bx+c=0, then

ax²+bx+c = a(x-x₁)(x-x₂)

Now,

solving the quadratic function 5x²−2x−9 = 0

subtract 9 from both sides

Simplify

Divide both sides by -5

Add (-1/5)² to both sides

so solving

Add 1/5 to both sides

similarly solving

Add 1/5 to both sides

Thus, the roots are:

Conclusion:

Since the roots are irrational, we do not factor further.

Therefore, we leave 5x²−2x−9 as it is.

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)