Simplify this expression.

Mathematics

2 answers:

olchik [2.2K]3 years ago

7 0

Answer:

(y^2+3y-28)/(4y^2-15y-4)

Step-by-step explanation:

(4y-1)(y-3)(2y+3)(y+3)(y+7)(y-3)/(2y+3)(y-4)(4y+1)(4y-1)(y-3)(y+3)

= (y+7)(y-3)/(y-4)(4y+1)

= (y^2+3y-28)/(4y^2-15y-4)

ANEK [815]3 years ago

6 0

Answer:

(y+7)/(4y+1).

Step-by-step explanation:

If we factor all the polynomials we get:

(4y-1)(y-3) . (2y+3)(y+3) . (y-4)(y+7)

-------------- ---------------- -------------

(2y+3)(y-4) (4y-1)(4y+1) (y-3)(y+3)

we see that (4y-1), (y -3), (2y+3), (y+3) and (y - 4) are in the numerators and denominators so we can cancel them out.

This leaves us with:

(y + 7)

--------

(4y + 1)

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Sergeeva-Olga [200]

Answer: 114.37 ft

Step-by-step explanation:

If we model this situation as a right triangle, where the hypotenuse is the length of the ladder ( $110 ft$ ), the opposite leg is the height the ladder will reach $h$ , and the adjacent leg is the distance between the base of the ladder and the building ( $28 ft$ ); we have two options:

1) Using trigonometric functions, since we are given the angle $\theta=75\°$

2) Using the Pithagorean Theorem

Any of the options will give a similiar result. So, let's choose the Pithagorean Theorem:

$(hypotenuse)^{2}=(opposite-leg)^{2}+(adjacent-leg)^{2}$

$(110 ft)^{2}=(h)^{2}+(28 ft)^{2}$

Isolating $h$ :

$h=\sqrt{(110 ft)^{2}-(28 ft)^{2}}$

$h=106.37 ft$

Adding to this height the extra height of $8 ft$ (since the base of the ladder is at this distance above the ground, perhaps held by a firefighter truck):