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elena-14-01-66 [18.8K]
2 years ago
15

Help please!!!!!!!!!

Mathematics
2 answers:
marshall27 [118]2 years ago
7 0
A) 4x=32, x=8
b)4=32x, x=4/32 or 1/8
c)10x=26, x= 26/10 or 13/5
d)26=100x, x=26/100 or 13/50
kvasek [131]2 years ago
6 0

Answer:

a=8

b=⅛

c= 2.6

d= 0.26

that's all the answers

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The difference between the two roots of the equation 3x^2+10x+c=0 is 4 2/3 . Find the solutions for the equation.
andrezito [222]

Answer:

Given the equation: 3x^2+10x+c =0

A quadratic equation is in the form: ax^2+bx+c = 0 where a, b ,c are the coefficient and a≠0 then the solution is given by :

x_{1,2} = \frac{-b\pm \sqrt{b^2-4ac}}{2a} ......[1]

On comparing with given equation we get;

a =3 , b = 10

then, substitute these in equation [1] to solve for c;

x_{1,2} = \frac{-10\pm \sqrt{10^2-4\cdot 3 \cdot c}}{2 \cdot 3}

Simplify:

x_{1,2} = \frac{-10\pm \sqrt{100- 12c}}{6}

Also, it is given that the difference of two roots of the given equation is 4\frac{2}{3} = \frac{14}{3}

i.e,

x_1 -x_2 = \frac{14}{3}

Here,

x_1 = \frac{-10 + \sqrt{100- 12c}}{6} ,     ......[2]

x_2= \frac{-10 - \sqrt{100- 12c}}{6}       .....[3]

then;

\frac{-10 + \sqrt{100- 12c}}{6} - (\frac{-10 + \sqrt{100- 12c}}{6}) = \frac{14}{3}

simplify:

\frac{2 \sqrt{100- 12c} }{6} = \frac{14}{3}

or

\sqrt{100- 12c} = 14

Squaring both sides we get;

100-12c = 196

Subtract 100 from both sides, we get

100-12c -100= 196-100

Simplify:

-12c = -96

Divide both sides by -12 we get;

c = 8

Substitute the value of c in equation [2] and [3]; to solve x_1 , x_2

x_1 = \frac{-10 + \sqrt{100- 12\cdot 8}}{6}

or

x_1 = \frac{-10 + \sqrt{100- 96}}{6} or

x_1 = \frac{-10 + \sqrt{4}}{6}

Simplify:

x_1 = \frac{-4}{3}

Now, to solve for x_2 ;

x_2 = \frac{-10 - \sqrt{100- 12\cdot 8}}{6}

or

x_2 = \frac{-10 - \sqrt{100- 96}}{6} or

x_2 = \frac{-10 - \sqrt{4}}{6}

Simplify:

x_2 = -2

therefore, the solution for the given equation is: -\frac{4}{3} and -2.


3 0
2 years ago
In 2014, the population of China was 1.39 billion. Compare China’s 2014 population to the world population with a ratio. Write y
pychu [463]

Answer:

Faction of population = 1.39 / 7.2

Percentage of population = 19.3% (Approx.)

Step-by-step explanation:

Given:

China's population in 2014 = 1.39 billion (Approximately)

Find:

Compare China's population to world population

Computation:

World's population in 2014 = 7.2 billion (Approximately)

Faction of population = China's population in 2014 / World's population in 2014

Faction of population = 1.39 / 7.2

Percentage of population = [China's population in 2014 / World's population in 2014]100

Percentage of population = [1.39/7.2]100

Percentage of population = [0.193]100

Percentage of population = 19.3% (Approx.)

6 0
3 years ago
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