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3 years ago

8^x+3=16^x−1 solve the exponential equation ...?

1 answer:

6 0

Let us write down the equation clearly and in a proper manner. This will help in solving the equation very easily.

8^(x + 3) = 16^(x - 1)
(2^3)^(x + 3) = (2^4)^(x - 1)
(2)^3(x + 3) = (2)^4(x - 1)
Then
3(x + 3) = 4(x - 1)
3x + 9 = 4x - 4
4x - 3x = 9 + 4
x = 13

I hope the procedure is clear enough for you to understand. I also hope that this is the answer that has actually come to your desired help.

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Homework: Algebra Re<br> Find the slope and the y-intercept<br> 6x-7y=15

umka21 [38]

Answer:

the slope is 6/7 the y-intercept is (0, - $\frac{15}{7}$ )

Step-by-step explanation:

I'm not 100% sure sorry lol.

3 0

3 years ago

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7. Olivia purchases gifts for her mom and

viktelen [127]

Answer:

Variable- it doesnt really matter. Im just going to use X.

Equation- $16.35 + x = $39.75.

The solution is $23.40

Step-by-step explanation: Basically you reverse the equation so it says $39.75 - $16.35 = x . Then you just subtract.

5 0

2 years ago

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Lydia graphed ADEF at the coordinates D (-2,-1), E (-2, 2), and F (0,0). She thinks ADEF is a right triangle. Is Lydia's asserti

Setler79 [48]

The true statement is (c) No; the slopes of segment EF and segment DF are not opposite reciprocals.

<h3>Right triangles </h3>

Right triangles have a pair of perpendicular lines

Coordinates

The coordinates are given as:

D = (-2,-1)
E = (-2,2)
F = (0,0)

<h3>Slopes</h3>

Start by calculating the slopes of lines DF and EF using:

$m = \frac{y_2 -y_1}{x_2 -x_1}$

So, we have:

$m_{DF} = \frac{0 + 1}{0 +2}$

$m_{DF} = \frac{1}{2}$

Also, we have:

$m_{EF} = \frac{0 -2 }{0+2}$

$m_{EF} = \frac{-2 }{2}$

$m_{EF} = -1$

For the triangle to be a right triangle, then the calculated slopes must be opposite reciprocals.

i.e.

$m_1 = -\frac{1}{m_2}$

By comparison, the slopes of both lines are not opposite reciprocals.

Hence, the true statement is (c)

Read more about right triangles at:

brainly.com/question/17972372

7 0

2 years ago

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Find x: 1) 2x= 1/8 2)3x multiplied by 9= 81

Rainbow [258]

$= 2x = \frac{1}{8 } \\ = x = \frac{1}{2 \times 8} \\ = x = \frac{1}{16}$ $3x \times 9 = 81 \\ 3x = \frac{81}{9} \\ x = \frac{9}{3} \\ x = 3$

Heres your answer girlfriend ♥️♥️

Have you followed me when I answered your last question???

6 0

3 years ago

Why the derivative of (x^2/a^2) = (2x/a^2)?

Neko [114]

I assume you're referring to a function,

$f(x) = \dfrac{x^2}{a^2}$

where <em>a</em> is some unknown constant. By definition of the derivative,

$\displaystyle f'(x) = \lim_{h\to0}{f(x+h)-f(x)}h$

Then

$\displaystyle f'(x) = \lim_{h\to0}{\frac{(x+h)^2}{a^2}-\frac{x^2}{a^2}}h \\\\ f'(x) = \frac1{a^2} \lim_{h\to0}{(x+h)^2-x^2}h \\\\ f'(x) = \frac1{a^2} \lim_{h\to0}{(x^2+2xh+h^2)-x^2}h \\\\ f'(x) = \frac1{a^2} \lim_{h\to0}{2xh+h^2}h \\\\ f'(x) = \frac1{a^2} \lim_{h\to0}(2x+h) = \boxed{\frac{2x}{a^2}}$

8 0

2 years ago