All categories

3 years ago

Express as a single power of 2

Mathematics

1 answer:

den301095 [7]3 years ago

6 0

When you multiply powers, they add, and when you divide them they subtract.
So I would first add the 2^a + 2^b +2^c to get 2^(a+b+c)
Then, divide by 2^(a+b). Because when you divide powers they subtract, you will be taking away the (a+b) from the (a+b+c) and you will be left with c on its own.
The answer is 2^c

You might be interested in

Solve 10 + 6(–9 – 4x) = 10(x – 12) + 8.

Luden [163]

Answer: x = 2

Step-by-step explanation:

first, we remove the parentheses.

10 - 54 - 24x = 10x - 120 + 8

then, we just calculate that out.

-44 - 24x = 10x - 112

next, we move the terms.

-24x - 10x = -112 + 44

then, we collect the like terms and calculate it.

-34x = -68

finally, we divide both sides.

x = 2

3 0

3 years ago

Use Laplace transform methods to solve the differential equation: The initial conditions are f(0) = 0 and <img src="https://tex.

Llana [10]

Answer:

Step-by-step explanation:

$\frac{d^2 y}{dt^2} +12\frac{dy}{dt} +32y = 10e^{-2t}$ where f(x) is replaced by y

Take Laplace on both sides

$s^2 Y -s(0)-0 +12s Y-0+32Y = \frac{10}{s+2} \\Y(s^2+12s+32) = \frac{10}{s+2}\\Y = \frac{10}{(s+2)(s+4)(s+8)}$

We can resolve into partial fraction to get Y = L(y)

Let this equals

$\frac{A}{s+2} +\frac{B}{s+4} +\frac{C}{s+8} \\10 = A(s+4)(s+8) + B(s+2)(s+8) +Cs+4)(s+2) \\$

Solving we get

s=-9

24C = 10 or C =5/12

s=-2: A=10/12=5/6

s=-4: B = -5/4

Taking inverse Laplace

$y(t) = \frac{-5e^{-4t} }{4} + \frac{5e^{-8t} }{12} +\frac{-5e^{-2t} }{6}$

6 0

3 years ago

How to do -7x-3x+2=8x-8

zavuch27 [327]

If you would like to solve the equation - 7 * x - 3 * x + 2 = 8 * x - 8, you can calculate this using the following steps:

- 7 * x - 3 * x + 2 = 8 * x - 8
- 7 * x - 3 * x - 8 * x = - 8 - 2
- 18 * x = - 10 /(-18)
x = 10 / 18
x = 5/9

The correct result would be 5/9.

7 0

3 years ago

Read 2 more answers

E) 3 - 2x = 15 what is x

Anestetic [448]

3 - 2x = 15

-2x = 15 - 3

-2x = 12

x = 12 ÷ 2

x = 6

3 0

3 years ago

Read 2 more answers

How do you write in slope intercept with only the rate of change and one point. Like rate of change is -5 and the point is (3,0)

Simora [160]

Answer:

A linear equation in the slope-intercept form is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Now, we know that the rate of change (the slope) is -5

Then we just replace a by -5

y = -5*x + b

Now we also know that this line passes through a point, and the point is (3, 0)

This means that the point (3, 0) is a solution for the line equation, so when x = 3, we also have y = 0.

Replacing these values in our equation we get:

0 = -5*3 + b

0 = -15 + b

15 = b

Now we know the value of b, so we can replace it in the line equation to get:

y = -5*a + 15

Which is the complete equation of the line.

5 0

3 years ago