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Rus_ich [418]
3 years ago
13

How do I solve this?

Mathematics
1 answer:
Readme [11.4K]3 years ago
4 0

Answer:

  x ≈ -4.419

Step-by-step explanation:

Separate the constants from the exponentials and write the two exponentials as one. (This puts x in one place.) Then use logarithms.

  0 = 2^(x-1) -3^(x+1)

  3^(x+1) = 2^(x-1) . . . . . add 3^(x+1)

  3×3^x = (1/2)2^x . . . . .factor out the constants

  (3/2)^x = (1/2)/3 . . . . . divide by 3×2^x

Take the log:

  x·log(3/2) = log(1/6)

  x = log(1/6)/log(3/2) . . . . . divide by the coefficient of x

  x ≈ -4.419

_____

A graphing calculator is another tool that can be used to solve this. I find it the quickest and easiest.

_____

<em>Comment on alternate solution</em>

Once you get the exponential terms on opposite sides of the equal sign, you can take logs at that point, if you like. Then solve the resulting linear equation for x.

  (x+1)log(3) = (x-1)log(2)

  x=(log(2)+log(3))/(log(2)-log(3))

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How do I do this please help me I will give you thank even tho it’s not important Ahahah please help me
xxTIMURxx [149]

Answer:

(-2 , 5)

(-1 , 0)

(1 , -4)

(3 , 0)

(4 , -5)

Step-by-step explanation:

<u>First solve the equation:</u>

x² - 2x - 3

<em><u>Find two numbers with have a sum of -2 and a product of -3.</u></em>

-3 and 1

(x - 3)(x + 1)

Solve for x:

x - 3 = 0

x = 3

x + 1 = 0

x = -1

You know that the graph will cross the x-axis at -1 and 3.

(-1 , 0)

(3 , 0)

You know that the graph is positive.

<u>Complete the square to find the vertex</u>

x² - 2x - 3

(x - 1)² = x² - 2 + 1

x² - 2x - 3 = x² - 2 + 1 - 2 = (x - 1)² - 2

1 = 0

x = 1

Substitute into the original equation:

x² - 2x - 3 =

1² - (2 * 1) - 3 =

1 - 2 - 3 =

-4

(1 , -4)

<em><u>You can input any two numbers within -10 and 10. Such as -2 and 4.</u></em>

x² - 2x - 3 =

-2² - (2 * -2) - 3 =

4- -4- 3 =

5

(-2 , 5)

x² - 2x - 3 =

4² - (2 * 4) - 3 =

16 - 8 - 3 =

-5

(4 , -5)

4 0
3 years ago
What is the value of x? <br> -2/7x+6+1/7x=18 <br> x=
Alenkinab [10]
- \frac{2}{7} x + 6 + \frac{1}{7} x = 18

First, simplify \frac{2}{7} x to \frac{2x}{7} / Your problem should look like: -\frac{2x}{7} + 6 + \frac{1}{7} x = 18
Second, simplify \frac{1}{7} x to \frac{x}{7} / Your problem should look like: - \frac{2x}{7} + 6 + \frac{x}{7} = 18
Third, simplify - \frac{2x}{7} + 6 + \frac{x}{7} to - \frac{x}{7} + 6 / Your problem should look like: -\frac{x}{7} + 6 = 18
Fourth, regroup terms. / Your problem should look like: 6 - \frac{x}{7} = 18
Fifth, multiply both sides by 7. / Your problem should look like: 42 - x = 126
Sixth, subtract 42 from both sides. / Your problem should look like: -x = 126 - 42
Seventh, simplify 126 - 42 to 84. / Your problem should look like: -x = 84
Eighth, multiply both sides by -1. / Your problem should look like: x = -84

Answer: x = -84

4 0
3 years ago
The circle below is centered at the point (4-3) and has a radius of length 3. (4 What is its equation?
Dovator [93]

Step-by-step explanation:

3p88pf3368pdod5edee5owxu5wzoxut sjlylite

5 0
3 years ago
Which is the correct use of the distributive property?
sergiy2304 [10]

Answer:

42+18=6(7+3)

Step-by-step explanation:

6x7=42 and 6x3=18

4 0
3 years ago
Read 2 more answers
A person recently read that 84% of cat owners are women. How large a sample should the researcher take if she wishes to be 90% c
Lana71 [14]

Answer:

405

Step-by-step explanation:

To find sample size, use the following equation, where n = sample size, za/2 = the critical value, p = probability of success, q = probability of failure, and E = margin of error.

n=\frac{(z_{\frac{\alpha }{2} })^{2} *p*q  }{E^2}

The values that are given are p = 0.84 and E = 0.03.

You can solve for the critical value which is equal to the z-score of  (1 - confidence level)/2.  Use the calculator function of invNorm to find the z-score.  The value will given with a negative sign, but you can ignore that.

(1 - 0.9) = 0.1/2 = 0.05

invNorm(0.05, 0, 1) = 1.645

You can also solve for q which is 1 - p.  For this problem q = 1 - 0.84 = 0.16

Plug the values into the equation and solve for n.

n =\frac{(1.645)^2*0.84*0.16}{(0.03)^2}\\n= 404.0997333

Round up to the next number, giving you 405.

6 0
3 years ago
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