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2 years ago

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Mathematics

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kiruha [24]2 years ago

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Which equation represents a linear function?

ipn [44]

Answer: y = lxl + 5. B) y = 1. 2 x + 3. C) y = x2 - 4. D) y = 3. 4 x2. Explanation: The solution ... y = x. B) y = |x|. C) y = x2. D) y = x. Explanation: A linear function has a degree of 1. ... 2. 4. B. x f(x). 1. 6. 2. 7. 3. 8. 4. 9. 5 10. C. x f(x). -2 -3. -1 -1. 0. 1. 1. 3. 2. 5. D. ... Since the x is cubed in y = −3x3, it graphs as a curve. y = 5 ...

Step-by-step explanation:

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2 years ago

Write an equation in slope-intercept form for the line that passes through the point ( -1 , -2 ) and is perpendicular to the l

mamaluj [8]

The equation in slope-intercept form for the line that passes through the point ( -1 , -2 ) and is perpendicular to the line − 4 x − 3 y = − 5 is $y = \frac{3}{4}x - \frac{5}{4}$

Solution:

The slope intercept form is given as:

y = mx + c ----- eqn 1

Where "m" is the slope of line and "c" is the y - intercept

Given that the line that passes through the point ( -1 , -2 ) and is perpendicular to the line − 4 x − 3 y = − 5

Given line is perpendicular to − 4 x − 3 y = − 5

− 4 x − 3 y = − 5

-3y = 4x - 5

3y = -4x + 5

$y = \frac{-4x}{3} + \frac{5}{3}$

On comparing the above equation with eqn 1, we get,

$m = \frac{-4}{3}$

We know that product of slope of a line and slope of line perpendicular to it is -1

$\frac{-4}{3} \times \text{ slope of line perpendicular to it}= -1\\\\\text{ slope of line perpendicular to it} = \frac{3}{4}$

Given point is (-1, -2)

Now we have to find the equation of line passing through (-1, -2) with slope $m = \frac{3}{4}$

Substitute (x, y) = (-1, -2) and m = 3/4 in eqn 1

$-2 = \frac{3}{4}(-1) + c\\\\-2 = \frac{-3}{4} + c\\\\c = - 2 + \frac{3}{4}\\\\c = \frac{-5}{4}$

$\text{ substitute } c = \frac{-5}{4} \text{ and } m = \frac{3}{4} \text{ in eqn 1}$

$y = \frac{3}{4} \times x + \frac{-5}{4}\\\\y = \frac{3}{4}x - \frac{5}{4}$

Thus the required equation of line is found

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2 years ago

Find lim ?x approaches 0 f(x+?x)-f(x)/?x where f(x) = 4x-3

Whitepunk [10]

If $f(x)=4x-3$ :

$\displaystyle\lim_{\Delta x\to0}\frac{(4(x+\Delta x)-3)-(4x-3)}{\Delta x}=\lim_{\Delta x\to0}\frac{4\Delta x}{\Delta x}=4$

If $f(x)=4x^{-3}$ :

$\displaystyle\lim_{\Delta x\to0}\frac{\frac4{(x+\Delta x)^3}-\frac4{x^3}}{\Delta x}=\lim_{\Delta x\to0}\frac{\frac{4x^3-4(x+\Delta x)^3}{x^3(x+\Delta x)^3}}{\Delta x}$

$\displaystyle=\lim_{\Delta x\to0}\frac{4x^3-4(x^3+3x^2\Delta x+3x(\Delta x)^2+(\Delta x)^3)}{x^3\Delta x(x+\Delta x)^3}$

$\displaystyle=\lim_{\Delta x\to0}\frac{-12x^2\Delta x-12x(\Delta x)^2-4(\Delta x)^3}{x^3\Delta x(x+\Delta x)^3}=-\frac{12}{x^4}$

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3 years ago

Select Equal or Not Equal to correctly classify each statement.

Black_prince [1.1K]

The first problem is true because with multiplication it doesn't matter which order it is in.

The second problem is false because you will get a different quotient depending on which numbers are on which side of the equation.

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3 years ago

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Write 24 over 40 in simplest form

dsp73

Three over five or 3/5

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