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2 years ago

10

Solve for x: 1 over 3 (2x − 8) = 4. (10 points) 2 6 10 10 over 3

1 answer:

LekaFEV [45]2 years ago

5 0

The answer is 10 if you see my work in the picture

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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

2 years ago

Please help!! Due tomorrow!!

Marysya12 [62]

The number of doughnuts in bags is 4 times the number of bags of doughnuts. So the number in B bags of doughnuts will be

... 4B

The number of doughnuts in cartons is 10 times the number of cartons of doughnuts, so the number in C cartons will be

... 10C

The total number of doughnuts (T) is the sum of those in bags and those in cartons:

... T = 4B +10C

3 0

3 years ago

Can somone give me the answer to 2 x 0

marshall27 [118]

Any number times 0 is going to equal 0

8 0

2 years ago

Read 2 more answers

J u l i a n has partially filled the p r i s m below with 16 unit cubes. How many more unit cubes will he need to completely fil

Wittaler [7]

add it

Step-by-step explanation:

11+20+25+36

8 0

2 years ago

Standard form of the equation that goes through (3, -1) with a slope of -1, please!

11111nata11111 [884]

Answer:

x+y=2

Step-by-step explanation:

Standard Form: ax+by=c

For most convenience start with slope-intercept form: y=mx+b

1. -1 = -1(3)+b - solve for b

b=2

y= -1x+2 (slope-intercept form)

2. Now convert to standard form

Add 1x to both sides:

1x+y=2

7 0

2 years ago