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3 years ago

(x+5)(x+4)(x-2)-(x^2+11x-9)(x+1)+5x^2

Mathematics

2 answers:

alina1380 [7]3 years ago

8 0

Answer:

(x+5)•(x+4)•(x-2)•(x2+11x-9)•(x+26)

STEP

Equation at the end of step 2

(((x+5)•(x+4)•(x-2))•(x2+11x-9))•(x+26)

STEP

Equation at the end of step 3

((x+5)•(x+4)•(x-2)•(x2+11x-9))•(x+26)

STEP

Trying to factor by splitting the middle term

4.1 Factoring x2+11x-9

The first term is, x2 its coefficient is 1 .

The middle term is, +11x its coefficient is 11 .

The last term, "the constant", is -9

Step-1 : Multiply the coefficient of the first term by the constant 1 • -9 = -9

Step-2 : Find two factors of -9 whose sum equals the coefficient of the middle term, which is 11 .

-9 + 1 = -8

-3 + 3 = 0

-1 + 9 = 8

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step

(x+5)•(x+4)•(x-2)•(x2+11x-9)•(x+26)

Step-by-step explanation:

Luda [366]3 years ago

6 0

(x+5)•(x+4)•(x-2)•(x2+11x-9)•(x+26)
STEP
2
:
Equation at the end of step 2

(((x+5)•(x+4)•(x-2))•(x2+11x-9))•(x+26)
STEP
3
:
Equation at the end of step 3

((x+5)•(x+4)•(x-2)•(x2+11x-9))•(x+26)
STEP
4
:
Trying to factor by splitting the middle term

4.1 Factoring x2+11x-9

The first term is, x2 its coefficient is 1 .
The middle term is, +11x its coefficient is 11 .
The last term, "the constant", is -9

Step-1 : Multiply the coefficient of the first term by the constant 1 • -9 = -9

Step-2 : Find two factors of -9 whose sum equals the coefficient of the middle term, which is 11 .

-9 + 1 = -8
-3 + 3 = 0
-1 + 9 = 8

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Equation at the end of step
4
:

(x+5)•(x+4)•(x-2)•(x2+11x-9)•(x+26)

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The northern lighthouse is approximately $24.4\; \rm mi$ closer to the boat than the southern lighthouse.

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By the law of sine, the length of a side in a given triangle would be proportional to the angle opposite to that side. For example, in the triangle in this question, $\angle {\rm B}$ is opposite to side $\rm NS$ , whereas $\angle {\rm S}$ is opposite to side ${\rm NB}$ . Therefore:

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(Round to at least one more decimal places than the values in the choices.)

Likewise, with $\angle {\rm N}$ is opposite to side ${\rm SB}$ , the following would also hold:

$\begin{aligned} \frac{\text{length of NS}}{\sin(\angle {\rm B})} = \frac{\text{length of SB}}{\sin(\angle {\rm N})} \end{aligned}$ .

$\begin{aligned} \frac{75\; \rm mi}{\sin(119^{\circ})} = \frac{\text{length of SB}}{\sin(40^{\circ})} \end{aligned}$ .

$\begin{aligned} & \text{length of SB} \\ =\; & (75\; \rm mi) \times \frac{\sin(40^{\circ})}{\sin(119^{\circ})} \\ \approx\; & 55.12\; \rm mi\end{aligned}$ .

In other words, the distance between the northern lighthouse and the boat is approximately $30.73\; \rm mi$ , whereas the distance between the southern lighthouse and the boat is approximately $55.12\; \rm mi$ . Hence the conclusion.

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