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3 years ago

14

Show the steps to solve the inequality. Then graph the solution set.

1 answer:

antoniya [11.8K]3 years ago

5 0

$-7x+32$

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Find an m > 0 such that the the equation x^4−(3m+2)x^2+m^2=0 has four real solutions that form an arithmetic sequence.

Aleonysh [2.5K]

Answer:

The value of m is 6.

Step-by-step explanation:

Here, the given equation,

$x^4-(3m+2)x^2+m^2=0$

$x^4+0x^3-(3m+2)x^2+0x+m^2=0$

Let the roots of the equation are a-3b, a-b, a+b and a + 3b, ( they must be form an AP )

Thus, we can write,

$a-3b+a-b+a+b+a+3b=\frac{\text{coefficient of }x^3}{\text{coefficient of }x^4}$

$=\frac{0}{1}=0$

$\implies a=0----(1)$

$(-3b)(-b)+(-b)(b)+(b)(3b)+(3b)(-3b)+(-b)(3b)+(-3b)(b)=\frac{\text{coefficient of }x^2}{\text{coefficient of }x^4}}$

$=\frac{-3m-2}{1}$

$3b^2-b^2+3b^2-9b^2-3b^2-3b^2=-3m-2$

$-10b^2=-3m-2$

$\implies b^2=\frac{3m+2}{10}-----(2)$

$(-3b)(-b)(b)(3b)=\frac{\text{Constant term}}{\text{coefficient of}x^4}= m^2$

$9b^4=m^2$

$9(\frac{3m+2}{10})^2=m^2$

$9(\frac{9m^2+4+12m}{100})=m^2$

$81m^2+36+108m=100m^2$

$-19m^2+108m+36=0$

$19m^2-108m-36=0$

$19m^2-114m+6m-36=0$

$19m(m-6)+6(m-6)=0$

$(19m+6)(m-6)=0$

$\implies m=-\frac{6}{19}\text{ or }m=6$

But m > 0,

Hence, the value of m is 6.

4 0

3 years ago

The level of the tide in a harbor changed from 9 1/4 ft to 4 1/2 ft above sea level over a period of 3 1/4 hr

kumpel [21]

Answer:

The answer is " $\bold{- \frac{19}{13} \ / hour}$ "

Step-by-step explanation:

Please find the complete question in the attached file.

Calculating the difference of $9 \frac{1}{4}\ and \ 4 \frac{1}{2}$ dividing the value by $3 \frac{1}{4}$

$\to 4 \frac{1}{2} - 9 \frac{1}{4}\\\\ \to \frac{9}{2} - \frac{37}{4}\\\\ \to \frac{18-37}{4} \\\\ \to -\frac{19}{4}\\\\\to -\frac{19}{4} \div \frac{13}{4}= -\frac{19}{4} \times \frac{4}{13} = -\frac{19}{13}\\$

3 0

3 years ago

What is the midpoint of AB?

spayn [35]

Answer: Point G.

Step-by-step explanation:

Count the number of spaces between points A and B. Then divide that number by 2 and count that many spaces from one point.

14/2=7

I hope this helps!! Pls mark brainliest :)

6 0

2 years ago

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Plzzzz help meim almost out of time thank uuuuu

Masja [62]

Answer: line 2

Explanation: hope this helps

7 0

3 years ago

Choose the most appropriate name for the function described below. The postage required to mail a box depends on its weight

Stells [14]

Answer:

Postage(weight) or p(w)

Step-by-step explanation:

6 0

4 years ago

Read 2 more answers