Brandy is trying to factor the quadratic $3x^2 - x - 10.$ she starts by assuming that the quadratic factors as \[3x^2 - x - 10 = (x + b)(3x + d),\]for some integers $b$ and $d.$ after some work, brandy successfully factors the quadratic. find the ordered pair $(b, d).$

(B , D) = (-2,5)

Step-by-step explanation:

The given quadratic expression is

compare the given expression with

so we have

now and

we need to find two numbers such that their product is -30 and sum is -1

-6 and 5 are such numbers

so we have

grouping first two terms and last two terms

factor out 3x from first two terms and 5 from last two terms

       ( factor out (x-2))

hence B =-2 and D= 5

(B,D)= (-2,5)

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.

< coa = 150 ( given)

as ba and bc are tangents

so oc and oa is perpendicular to cb and ab respectively because in circle normal passes through centre

so in quadrilateral oabc

< coa + < oab + < ocb + < abc = 360

150 +90+90 + < abc = 360

330 + < abc = 360

< abc = 360 -330 = 30

so < abc = 30

⭐dhruv⭐