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3 years ago

Solve |3k-2|=2|k+12|

Mathematics

1 answer:

Stella [2.4K]3 years ago

7 0

Answer:

$k = 26$ or $k = -\dfrac{22}{5}$

Step-by-step explanation:

|3k - 2| = 2|k + 12|

$\dfrac{|3k - 2|}{|k + 12|} = 2$

$|\dfrac{3k - 2}{k + 12}| = 2$

$3k - 2 = 2(k + 12)$ or $3k - 2 = -2(k + 12)$

$3k - 2 = 2k + 24$ or $3k - 2 = -2k - 24$

$k = 26$ or $5k = -22$

$k = 26$ or $k = -\dfrac{22}{5}$

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Add 81/4 to both sides.

Step-by-step explanation:

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The exponential function f(x) = 3(5)x grows by a factor of 25 between x = 1 and x = 3. What factor does it grow by between x = 5

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Answer:

B) 25

Step-by-step explanation:

Given exponential function:

$f(x)=3(5)^x$

The growth factor between $x=1$ and $x=3$ is 25.

To find the growth factor between $x=5$ and $x=7$

Solution:

The growth factor of an exponential function in the interval $x=a$ and $x=b$ is given by :

$G=\frac{f(b)}{f(a)}$

We can check this by plugging in the given points.

The growth factor between $x=1$ and $x=3$ would be calculated as:

$G=\frac{f(3)}{f(1)}$

$f(3)=3(5)^3$

$f(1)=3(5)^1$

Plugging in values.

$G=\frac{3(5)^3}{3(5)^1}$

$G=\frac{(5)^3}{(5)^1}$ (On canceling the common terms)

$G=(5)^{(3-1)}$ (Using quotient property of exponents $\frac{a^b}{a^c}=a^{(b-c)}$ )

$G=(5)^{2}$

∴ $G=25$

Similarly the growth factor between $x=5$ and $x=7$ would be:

$G=\frac{f(7)}{f(5)}$

$f(7)=3(5)^7$

$f(5)=3(5)^5$

Plugging in values.

$G=\frac{3(5)^7}{3(5)^5}$

$G=\frac{(5)^7}{(5)^5}$ (On canceling the common terms)

$G=(5)^{(7-5)}$ (Using quotient property of exponents $\frac{a^b}{a^c}=a^{(b-c)}$ )

$G=(5)^{2}$

∴ $G=25$

Thus, the growth factor remains the same which is =25.

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tresset_1 [31]

Answer:

$y=-\frac{5}{3} x-\frac{42}{5}$

Step-by-step explanation:

Given the slope and another point, simply plug them into the point-slope formula to find your y-intercept.

$y-y1=m(x-x1)\\y-(-6)=\frac{3}{5} (x-4)\\y+6=\frac{3}{5} x-\frac{12}{5} \\y=\frac{3}{5} x-\frac{42}{5}$

Now that we've found your y-intercept, we have the original equation. To find the perpendicular equation, you need the opposite reciprocal of your slope.

To find the 'opposite,' change your slope's sign. Since your slope is positive $\frac{3}{5}$ , the opposite is $-\frac{3}{5}$ .