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3 years ago

Which expression is equivalent to the following complex fraction?

Mathematics

1 answer:

just olya [345]3 years ago

5 0

Answer:

$\mathbf{=\frac{2x-1}{2x}}$

Step-by-step explanation:

$1-\frac{1}{x}\div2$

To divide a fraction by a number just reciprocate the number which is there after division sign as done here. If there is one more fraction then reciprocate the fraction.

$=1-\frac{1}{x}\times\frac{1}{2}$

$=1-\frac{1}{2x}$

∴ $=\frac{2x-1}{2x}$

(NOTE : <em>Reciprocating means interchanging the numerator and denominator of that fraction</em>.)

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6 cousins inherited a total of 58 of their great aunt's assets which they divided evenly what fraction of their great aunt's ass

mina [271]

Answer:

9 1/9 per cousin

Step-by-step explanation:

if the aunt has 58 items to be distributed to 6 cousins, we would set a fraction of 58/6. performing that is 9 with 4/6 left over.

since there is 6 cousins, there will be 2/3 divided by 6 = 2/18, or 1/9

4 0

3 years ago

Triangle DEF has vertices located at D (2, 1), E (3,5), and F (6,2).

IRINA_888 [86]

Answer:

(A)

Length of DE = √17

EF = √18

DF = √17

(B) Slope of DE = 4

EF = 1

DF = 1/4

Step-by-step explanation:

See attached image.

3 0

3 years ago

f(x) is a quadratic function with x-intercepts at (−1, 0) and (−3, 0). If the range of f(x) is [−4, [infinity]) and g(x) = 2x^2

iren2701 [21]

Answer with Step-by-step explanation:

We are given that function f(x) which is quadratic function.

x -intercept of function f(x) at (-1,0) and (-3,0)

x-Intercept of f means zeroes of f

x=-1 and x=-3

Range of f =[-4, $\infty$ )

g(x)= $2x^2+8x+6=2(x^2+4x+3)$

$g(x)=0$

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

$x^2+4x+3=0$

$x^2+3x+x+3=0$

$x(x+3)+1(x+3)=0$

$(x+1)(x+3)=0$

$x+1=0\implies x=-1$

$x+3=0\implies x=-3$

Therefore, x-intercept of g(x) at (-1,0) and (-3,0).

Substitute x=-2

$g(-2)=2(-2)^2+8(-2)+6=8-16+6=-2$

$g(x)=2(x^2+4x)+6$

$g(x)=2(x^2+2\times x\times 2+4-4)+6=2(x^2+2\times x\times 2+4)-8+6$

$g(x)=2(x+2)^2-2$

By comparing with the equation of parabola

$y=a(x-h)^2+k$

Where vertex=(h,k)

We get vertex of g(x)=(-2,-2)

Range of g(x)=[-2, $\infty$ )

Zeroes of f and g are same .

But range of f and g are different.

Range of f contains -3 and -4 but range of g does not contain -3 and -4.

f and g are both quadratic functions.

3 0

3 years ago

owenn goes on a camping trip with his family cabin rentals are $430 for the week, kayak rentals are $7 per hour and paddle board

Hatshy [7]

Answer:

430 + 16h

Step-by-step explanation:

They are staying for a week ($430)

They are renting both a kayak ($7 per hour) and paddle board ($9 per hour), without defining the amount of hours. Create a variable, for example H for hours.

To create the expression, take the $430, the $7 per hour and $9 per hour, or 430 + 16h.

5 0

3 years ago

The mass of the particles that a river can transport is proportional to the sixth power of the speed of the river. A certain riv

katrin2010 [14]

Answer:

7.25

Step-by-step explanation:

200m/s^6 = m/3^6

s^6 = 200*3^6

s = 3*200^(1/6) = 7.25 mi/hr

Hope I helped!

8 0

4 years ago