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2 years ago

How many solutions does this equation have? –2b − 9 = –b

Mathematics

1 answer:

RideAnS [48]2 years ago

6 0

Answer:

b= -3

b=3/2=1.500

Step-by-step explanation:

step 1 . b • (2b + 3) - 9 = 0

Step-2 : Find two factors of -18 whose sum equals the coefficient of the middle term, which is 3 .

-18 + 1 = -17

-9 + 2 = -7

-6 + 3 = -3

-3 + 6 = 3

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and 6

2b2 - 3b + 6b - 9

Step-4 : Add up the first 2 terms, pulling out like factors :

b • (2b-3)

Add up the last 2 terms, pulling out common factors :

3 • (2b-3)

Step-5 : Add up the four terms of step 4 :

(b+3) • (2b-3)

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3 years ago

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3 years ago

Find two positive numbers whose difference is 30 and whose product is 2584.

kvasek [131]

Answer:

$38$ and $68$ .

Step-by-step explanation:

Let $x$ be the smaller one of the two number.

$x$ must be a positive integer. The other number would be $(x + 30)$ .

The question states that the product of the two numbers is $2584$ . In other words:

$x\, (x + 30) = 2584$ .

Rearrange this equation and solve for $x$ :

$x^{2} + 30\, x - 2584 = 0$ .

The first root of this quadratic equation would be:

$\begin{aligned}x_{1} &= \frac{(-30) + \sqrt{30^{2} - 4 \times (-2584)}}{2} \\ &= \frac{(-30) + \sqrt{900 + 10336}}{2} \\ &= \frac{(-30) + \sqrt{11236}}{2} \\ &= \frac{(-30)}{2} + \sqrt{\frac{11236}{2^{2}}} \\ &= (-15) + \sqrt{2809} \\ &= (-15) + 53 \\ &= 38 \end{aligned}$ .

Similarly, the second root of this quadratic equation would be:

$\begin{aligned}x_{1} &= \frac{(-30) - \sqrt{30^{2} - 4 \times (-2584)}}{2} \\ &= (-15) - 53 \\ &= -68\end{aligned}$ .

Since the question requires that both numbers should be positive, $x > 0$ . Therefore, only $x = 38$ is valid.

Hence, the two numbers would be $38$ and $(38 + 30)$ , which is $68$ .

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3 years ago

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