Which is the simplified expression for 3^-4*2^3*3^2/2^4*3^-3

What value of X makes the equation true? 12x-15=16-3x

gogolik [260]

X= 2 1/15 or 31/15.

4 0

3 years ago

Which of the inequalities represents the statement, "two times a number x, less 15, is greater than or equal to 4 times the numb

Damm [24]

The choices are:

A)
2x - 15 ≤ 4y

B)
2x - 15 ≥ 4y

C)
15 - 2x ≤ 4y

D)
15 - 2x ≥ 4y

Therefore, the best and most correct answer among the choices provided by the question is the fourth choice "15 - 2x ≥ 4y". I hope my answer has come to your help. God bless and have a nice day ahead!

5 0

3 years ago

Read 2 more answers

The graph of a sinusoidal function has a minimum point at (0,3)(0,3) and then intersects its midline at (5π,5)

bekas [8.4K]

Answer: F(x) = 2*sin(x/10 +(3/2)*pi) + 5

Step-by-step explanation:

The information that we have is that:

We have a minimum at (0, 3)

the midline is at (5*pi, 5)

This is a sinusoidal function, so we can write one generic one as:

F(x) = A*sin(c*x + p) + B.

where A and B are constants, c is the frequency and p is a phase

First, the minimum of the sine function is when sin(x) = -1, and this happens at (3/2)*pi

We know that this minimum is at x = 0.

sin(c*0 + p) = -1

Then p = 3/2*pi.

So our function is:

F(x) = A*sin(c*x +(3/2)*pi) + B.

Now, we know that F(0) = 3, so:

3 = A*sin(c*0 +(3/2)*pi) + B = -A + B.

now we can use the other hint, the midpoint of the sine function is when sin(x) = 0, and this happens at x = 0 and x = pi, particularlly as we here have a phase of 3/2*pi, we should find x = 2*pi.

then:

c*5*pi + (3/2)*pi = 2*pi

c*5 + 3/2 = 2

c*5 = 2 - 3/2 = 1/2

C = 1/2*5 = 1/10

So our function is

F(x) = A*sin(x/10 +(3/2)*pi) + B

and we know that when x = 5*pi, F(5*pi) = 5, so:

5 = F(x) = A*sin(5*pi/10 +(3/2)*pi) + B

5 = B

and we aready knew that:

- A + B = 3

-A + 5 = 3

A = 5 - 3 = 2

So our equation is:

F(x) = 2*sin(x/10 +(3/2)*pi) + 5

8 0

4 years ago

In one year, the Perseid meteor shower had a meteor appear every 1 1/5 minutes on average. That same year, the Leonid meteor sho

RoseWind [281]

Answer:

325,452 more meteors fell during the Perseid meteor shower

Step-by-step explanation:

An year has 365 days.

Each day has 24 hours.

Each hour has 60 minutes.

Minutes in an year:

365*24*60 = 525600

Persoid:

$1 + \frac{1}{5} = 1 + 0.2 = 1.2$

One each 1.2 minutes. How many during an year?

1 meteor - 1.2 minutes.

x meteors - 525600 minutes.

$1.2x = 525600$

$x = \frac{525600}{1.2}$

$x = 438000$

438,000 meteors fell during the Persoid shower.

Leonid:

$4 + \frac{2}{3} = 4.67$

One each 4.67 minutes. How many during an year.

1 meteor - 4.67 minutes.

x meteors - 525600 minutes.

$4.67x = 525600$

$x = \frac{525600}{4.67}$

$x = 112548$

112,548 meteors fell during the Leonid Shower.

How many more meteors fell during the Perseid meteor shower?

438,000 - 112,548 = 325,452

325,452 more meteors fell during the Perseid meteor shower

5 0

3 years ago

X^2 -9X = 0. Factor and use the Zero property to solve

Veseljchak [2.6K]

The first step of factoring is to try to factor out a common factor.
The terms x^2 and -9x have the factor x in common.
Factor out x from both terms.

x^2 - 9x = 0

x(x - 9) = 0

Now you have a product of fully factored terms equaling zero, so you can apply the zero product property to solve.

x = 0 or x - 9 = 0

x = 0 or x = 9

Answer: x = 0 or x = 9

5 0

3 years ago