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3 years ago

Rewrite the fraction in the sentence below as a percentage.

Mathematics

1 answer:

klasskru [66]3 years ago

4 0

Answer:

42%

Step-by-step explanation:

To find the percentage of a fraction, you divide the numerator by the denominator and multiply by 100:

$\frac{21}{50}=21/50=0.42*100=42percent$

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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

Please help and answer the question properly.

RUDIKE [14]

Answer:

x = 15.65 and y = 5√2

Step-by-step explanation:

To get x and y we will use the Pythagoras theorem as shown

hyp^2 = adj^2 + opp^2

x^2 = 14^2+7^2

x^2 = 196 + 49

x^2 = 245

x = √245

x = 15.65

Similarly for y;

y2 = 5^2 + 5^2

y^2 = 25 + 25

y^2 = 50

y = √2*25

y = 5√2

Hence x = 15.65 and y = 5√2

6 0

2 years ago

Read 2 more answers

(+×9)(×-2) can some one solve it

marshall27 [118]

X2 - 2x + 9x - 18
X2 + 7x - 18

4 0

3 years ago

Evan typed 72 pages of notes one day. He typed 1 2 of the pages in the morning and 1 3 of the pages in the afternoon. He typed t

Korolek [52]

Answer:

60 pages

Step-by-step explanation:

Evan types a total of 72 pages a day.

In the morning he typed 1/2 pages or 72/2 = 36 pages.

In the afternoon he typed 1/3 pages or 72/3 = 24 pages.

Together, he typed 36 + 24 = 60 pages in the morning and afternoon.

7 0

3 years ago

Jeremy has 50 ft of fencing to enclose a rectangular-pen for his dog. He plans on using a side of his house for one side of the

kotykmax [81]

The dimensions such as length is 18 and width is 16 or length is 32 and width is 9 will produce an enclosed area of 288ft.

<h3>What is the dimension of length and width?</h3>

We know that,

P = l + 2w

50 = l + 2w

50 - 2w = l

A = l x w

288 = (50 - 2w)w

288 = 50w -2w²

2w² - 50w + 288

By dividing throughout by 2

w² - 25w + 144

This is in quadratic equation form.

By applying quadratic formula,

w = (-(-25) ± $\sqrt{(-25)^{2}-4*1*144$ ) / 2

w = (-(-25) ± 7)/2

w1 = (-(-25) + 7)/2

w1 = (25 + 7) / 2

w1 = 16

w2 = (-(-25) - 7)/2

w2 = (25 - 7) / 2

w2 = 9

By substituting the values in eq1,

A = l x w

if w = 16

288 = l x 16

l = 288/16

l = 18

if w = 9

288 = l x 9

l = 288/9

l = 32

The dimensions will be length is 18 and width is 16 or length is 32 and width is 9.

To learn more about area of rectangle refer to :

brainly.com/question/25292087

#SPJ1

3 0

1 year ago