When the expression x^2 + bx - 24 is factored completely, the difference of the factors is 11. Find both factors if it is known that b is negative. write the steps on the paper pleas
i need it asap

The two factors are (x + 3) and (x - 8)

Step-by-step explanation:

The given function is x² + b·x - 24

The difference between the factors = 11

The sign of coefficient b = Negative

Therefore, we have;

The factors as (x - c) and (x + d)

-b = d - c...(1)

d × (-c) = -24...(2)

(x + d) - (x - c) = 11

Which gives;

x + d - x  + c = 11

∴ d + c = 11...(3)

From equation (3), we have;

d = -24(-c) = 24/c

d = 24/c

Substituting the value of d in equation (3) gives;

d + c = 24/c + c = 11

24/c + c = 11

∴ c² + 24 = 11·c

c² + 24 - 11·c = 0

c² - 11·c + 24 = 0

(c - 8)·(c - 3) = 0

c = 8 or 3

From d + c = 11, we have, d = 3 or 8

Given that -b = d - c, therefore c > d and c = 8, d = 3

Therefore, the two factors are (x - 8) and (x + 3).

-13

step-by-step explanation:

f(x)=2x-5 for f(-4)

f(-4)   means let x=-4

f(-4) = 2(-4) -5

f(-4) =-8-5

      = -13

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3