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3 years ago

Which expression is equivalent to the following complex fraction?

Mathematics

1 answer:

Gwar [14]3 years ago

8 0

Answer:

(2x-1)/2x

Step-by-step explanation:

Given the function 1-(1/x÷2)

Using the rule of BODMAS

Solving the equation in bracket first, will give;

1/x÷2

= 1/x×1/2

= 1/2x

The equation then becomes

1-1/2x

Next is to look for the LCM of the resulting equation

1-1/2x

= (2x-1)/2x

The expression equivalent to the fraction is (2x-1)/2x

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Thanks if u help ✨:)

faltersainse [42]

Answer:

D.mode

Step-by-step explanation:

4 0

3 years ago

How is this solved using trig identities (sum/difference)?

GenaCL600 [577]

FIRST PART
We need to find sin α, cos α, and cos β, tan β
α and β is located on third quadrant, sin α, cos α, and sin β, cos β are negative

Determine ratio of ∠α
Use the help of right triangle figure to find the ratio
tan α = 5/12
side in front of the angle/ side adjacent to the angle = 5/12
Draw the figure, see image attached

Using pythagorean theorem, we find the length of the hypotenuse is 13
sin α = side in front of the angle / hypotenuse
sin α = -12/13

cos α = side adjacent to the angle / hypotenuse
cos α = -5/13

Determine ratio of ∠β
sin β = -1/2
sin β = sin 210° (third quadrant)
β = 210°

$cos \beta = -\frac{1}{2} \sqrt{3}$

$tan \beta= \frac{1}{3} \sqrt{3}$

SECOND PART
Solve the questions
Find sin (α + β)
sin (α + β) = sin α cos β + cos α sin β
$sin( \alpha + \beta )=(- \frac{12}{13} )( -\frac{1}{2} \sqrt{3})+( -\frac{5}{13} )( -\frac{1}{2} )$
$sin( \alpha + \beta )=(\frac{12}{26}\sqrt{3})+( \frac{5}{26} )$
$sin( \alpha + \beta )=(\frac{5+12\sqrt{3}}{26})$

Find cos (α - β)
cos (α - β) = cos α cos β + sin α sin β
$cos( \alpha + \beta )=(- \frac{5}{13} )( -\frac{1}{2} \sqrt{3})+( -\frac{12}{13} )( -\frac{1}{2} )$
$cos( \alpha + \beta )=(\frac{5}{26} \sqrt{3})+( \frac{12}{26} )$
$cos( \alpha + \beta )=(\frac{5\sqrt{3}+12}{26} )$

Find tan (α - β)
$tan( \alpha - \beta )= \frac{ tan \alpha-tan \beta }{1+tan \alpha tan \beta }$
$tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3} }{1+(\frac{5}{12}) ( \frac{1}{2} \sqrt{3})}$

Simplify the denominator
$tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3} }{1+(\frac{5\sqrt{3}}{24})}$
$tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3} }{ \frac{24+5\sqrt{3}}{24} }$

Simplify the numerator
$tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{6}{12} \sqrt{3} }{ \frac{24+5\sqrt{3}}{24} }$
$tan( \alpha - \beta )= \frac{ \frac{5-6\sqrt{3}}{12} }{ \frac{24+5\sqrt{3}}{24} }$

Simplify the fraction
$tan( \alpha - \beta )= (\frac{5-6\sqrt{3}}{12} })({ \frac{24}{24+5\sqrt{3}})$
$tan( \alpha - \beta )= \frac{10-12\sqrt{3} }{ 24+5\sqrt{3}}$

7 0

3 years ago

Jon and Anne had an equal amount of money. Jon spent $10. Anne spent $30. Now Jon has twice as much money as Anne. How much did

bulgar [2K]

They would have had $50 at the beginning

8 0

3 years ago

The graph of a proportional relationship contains the point (20, 4).

soldier1979 [14.2K]

Answer:

$y=\frac{1}{5}x$

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem we have

$point (20,4)$

Substitute the values and solve for k

$k=y/x$

$k=\frac{4}{20} =\frac{1}{5}$

therefore

the equation of the line is equal to

$y=\frac{1}{5}x$

6 0

3 years ago

Read 2 more answers

a ball is thrown straight up from the top of a 128 foot tall building with an initial speed of 32 feet per second. the height of

STatiana [176]

Factoring, you have
h(t) = -16(t^2 -2 -8) = -16(t -4)(t +2)

The ball hits the ground when h(t) = 0, so
0 = -16(t -4)(t +2)
t = 4 or -2

The positive solution is the one of interest.
It will take 4 seconds for the ball to hit the ground.

6 0

3 years ago