What is the value of (-3/4)^-4

Mathematics

1 answer:

frez [133]4 years ago

6 0

Answer:

256/81

Step-by-step explanation:

a⁻ᵇ = 1/aᵇ

(a/c)ᵇ = aᵇ / cᵇ

1/(c/d) = d/c

then:

(-3/4)⁻⁴ = 1/(-3/4)⁴ = 1/(-3⁴/4⁴) = 1/(81/256) = 256/81

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Find the equation of a line perpendicular to y=-2x+4 that contains the point (0,3).

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Slope-intercept form: y = mx + b

(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)

For lines to be perpendicular, their slopes have to be negative reciprocals of each other. (flip the sign +/- and the fraction(switch the numerator and the denominator))

For example:

Slope = 2 or $\frac{2}{1}$

Perpendicular line's slope = $-\frac{1}{2}$ (flip the sign from + to -, and flip the fraction)

Slope = $-\frac{2}{5}$

Perpendicular line's slope = $\frac{5}{2}$ (flip the sign from - to +, and flip the fraction)

y = -2x + 4 The slope is -2, so the perpendicular line's slope is $\frac{1}{2}$

Now that you know the slope, substitute/plug it into the equation:

y = mx + b

$y=\frac{1}{2} x+b$ Since they gave you the point (0, 3), which is the y-intercept, you can just plug 3 into "b". Another way to find b is plugging in the point on the line (0, 3) into the equation, then isolate/get the variable "b" by itself