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3 years ago

A line has the equation 3x–4y–12=0. Write the equation in slope-intercept form.

Mathematics

2 answers:

algol133 years ago

8 0

Answer:

y=3/4x−7/4

Step-by-step explanation:

rjkz [21]3 years ago

5 0

The slope-intercept form: y = mx + b

$3x-4y-12=0\ \ \ |+4y\\\\3x-12=4y\\\\4y=3x-12\ \ \ |:4\\\\y=\dfrac{3}{4}x-3$

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What is the inverse one to one function of f(x) = square root of x-2???

alexira [117]

$f(x) = \sqrt{x - 2} \\y = \sqrt{x - 2} \\y^{2} = (\sqrt{x - 2})^{2} \\y^{2} = x - 2 \\x^{2} = y - 2 \\x^{2} + 2 = y \\x^{2} + 2 = f^{-1}(x)$

6 0

3 years ago

Given that 3x+2y=5a+b and 4x-3y=a+7b, solve for y-x in terms of a and b.

Eduardwww [97]

Answer:

y - x = - 2 b

Step-by-step explanation:

Given-

3 x + 2 y = 5 a + b...................(i)

4 x - 3 y = a + 7 b.....................(ii)

Multiply by 3 and 2 in equation (i) & (ii) respectively-

Add equation (iii) & (iv)-

9 x + 6 y = 15 a + 3 a...................(iii)

8 x - 6 y = 2 a + 14 b ...................(iv)

17 x = 17 a + 17 b

x = a + b

Put x = a + b in equation (i)-

2 y = 5 a + b - 3 a - 3 b

2 y = 2 a - 2 b

y = a - b

∴ y - x = a - b - ( a + b )

y - x = a - b - a - b

y - x = - 2 b

3 0

3 years ago

If 1/3 is 0.333 then 3/3 is 0.999 that means 1 doesnt actually equal 1

sergejj [24]

Answer:

Correct

Step-by-step explanation:

When you type 1/3 into a calculator it should give you something along the lines of .333333334. If you continue to round, eventually you will get 1.

7 0

3 years ago

Read 2 more answers

A North American river otter wants to cross the North Saskatchewan river. It can swim at a speed of 2.75 m/s. In that location,

insens350 [35]

Answer:

Step-by-step explanation:

time to cross will be the distance divided by the velocity in that direction.

a) t = d/v = 45/2.75 = 16.363636... 16.4 s

In the same time that the otter is swimming cross stream, the stream is also moving perpendicularly at its own pace.

b) d = vt = 2.5(16.36) = 40.9090... 40.9 m

As velocity is a vector, An observer on the bank would see the velocity as the vector addition of the cross stream and down stream velocities

c) v = √(2.75² + 2.5²) = 3.716517... 3.72 m/s magnitude

θ = arctan2.5/2.75 = 42.2736... 42.3° downstream of a line straight across

7 0

3 years ago

Which is the inverse of the function a(d)=5d-3? And use the definition of inverse functions to prove a(d) and a-1(d) are inverse

Drupady [299]

Answer:

$a'(d) = \frac{d}{5} + \frac{3}{5}$

$a(a'(d)) = a'(a(d)) = d$

Step-by-step explanation:

Given

$a(d) = 5d - 3$

Solving (a): Write as inverse function

$a(d) = 5d - 3$

Represent a(d) as y

$y = 5d - 3$

Swap positions of d and y

$d = 5y - 3$

Make y the subject

$5y = d + 3$

$y = \frac{d}{5} + \frac{3}{5}$

Replace y with a'(d)

$a'(d) = \frac{d}{5} + \frac{3}{5}$

Prove that a(d) and a'(d) are inverse functions

$a'(d) = \frac{d}{5} + \frac{3}{5}$ and $a(d) = 5d - 3$

To do this, we prove that:

$a(a'(d)) = a'(a(d)) = d$

Solving for $a(a'(d))$

$a(a'(d)) = a(\frac{d}{5} + \frac{3}{5})$

Substitute $\frac{d}{5} + \frac{3}{5}$ for d in $a(d) = 5d - 3$

$a(a'(d)) = 5(\frac{d}{5} + \frac{3}{5}) - 3$

$a(a'(d)) = \frac{5d}{5} + \frac{15}{5} - 3$

$a(a'(d)) = d + 3 - 3$

$a(a'(d)) = d$

Solving for: $a'(a(d))$

$a'(a(d)) = a'(5d - 3)$

Substitute 5d - 3 for d in $a'(d) = \frac{d}{5} + \frac{3}{5}$

$a'(a(d)) = \frac{5d - 3}{5} + \frac{3}{5}$

Add fractions

$a'(a(d)) = \frac{5d - 3+3}{5}$

$a'(a(d)) = \frac{5d}{5}$

$a'(a(d)) = d$

Hence:

$a(a'(d)) = a'(a(d)) = d$

7 0

3 years ago