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3 years ago

Write In (4/9) in terms of In 2 and In 3.

1 answer:

7 0

Answer

A) 2 ln 2 - 2 ln 3

Explanation

Using the laws of logarithms:

ln (x/y) = ln (x) - ln (y)

ln (4/9) = ln (4) - ln (9)

This can be written as

ln (2^2) - ln (3^2)

Another law is:

ln (n^m) = m ln(n)

So finally:

2ln (2) - 2ln 3

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Explain how you could convert 152 cups into gallons.

Mila [183]

Answer: There are 16 cups in every gallon so we could divide 152 by 16 and get our number of gallons which would give us 9.63 or a little over 9 and a half gallons.

Step-by-step explanation:

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3 years ago

The value of the exponent in (22)−5 is

lyudmila [28]

Answer:

Let's calculate:

22-5

• Remove minus in the exponent and invert the base:

= (1/22)5

• Expand the multiplication:

= (1/22) * (1/22) * (1/22) * (1/22) * (1/22)

• Find your result:

= 1/5153632 ≈ 0.000000194038

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3 years ago

Describe and correct the error in writing the phrase as an expression?

lesantik [10]

Answer:

12 < x

Step-by-step explanation:

In writing 12 less than a number x, the expression, 12 - x is wrong because "less than" is not the same thing as "minus" (-). Rather, the sign, "<" should have been used as follows:

12 < x.

4 0

3 years ago

(Hehe...Please ignore the markings)

inysia [295]

Answer:

See below:

Step-by-step explanation:

Problem 1:

Multiply Equation 1 by 4, keep Equation 2 the same.

x+y=8, multiply each term by 4:

4*x=4x, 4*y=4y, 8*4=32

so, the equivalent system is: 4x+4y=32 and x-y=2

Solve the system of equations:

x-y=2 becomes x=y+2

plug into 4x+4y=32 to solve for y

4(y+2)+4y=32---> 4y+8+4y=32--->8y=24---> y=3

Plug into x-y=2---> x-3=2---> x=5

Problem 1 Answer:

Equivalent system: 4x+4y=32, x-y=2; solution: x=5, y=3

Problem 2:

Keep Equation 1 the same. Add 1 and 2.

To add an equation, add the left sides together, and then the rights.

so: x+y=8 + x-y=2 gives us: 2x=10

solve for x ---> 2x/2=10/2--->x=5

plug x into x+y=8--->5+y=8--->y=3

Problem 2 answer:

Equivalent system: x+y=8, 2x=10; solution:x=5, y=3

Problem 3:

Subtract Equation 2 from 1, and keep 2 the same.

To subtract an equation, subtract the left sides, then the rights. We are subtracting 1 from 2, so its 2-1.

x-y=2 - x+y=8 gives us: -2y=-6

Solve for y by dividing by -2-->-2y/-2=-6/-2---> y=3

Plug into x-y=2---> x-3=2---> x=5

Problem 3 answer:

Equivalent system: -2y=-6, x-y=2; solution: x=5, y=3

Problem 4:

Multiply the sum of Equation 1 and 2 by a factor of 3. Keep equation 2 the same.

First we add 1 and 2: (we did this earlier) ---> 2x=10 ---> now we multiply it all by 3---> 2x*(3)=10*(3)---> this gives us: 6x=30---> now divide by 6 to solve for x: 6x/6=30/6 gives us: x=5

Now, solve for y by plugging x into equation 2: x-y=2---> 5-y=2--->y=3

Problem 4 answer:

Equivalent system: 6x=30, x-y=2; solution: x=5, y=3

______

Quick Tip: One thing inherent of Equivalent systems is that they have the same set of solutions. Thus, we know the systems are equivalent when they have the same set of solutions for x and y. Moreover, you don't need to solve every time after you attempt to find an equivalent system, instead, just plug in the values found in problem 1 to each new set of equations to test if they are equivalent.

If we find x=5 and y=3 for x+y=8 and x-y=2, then all we have to do is plug them in to 6x=30 and -2y=-6 to see if they are equivalent.

6(5)=30 ---> true

-2(3)=-6 ---> true

3 0

3 years ago

PLS HELP WILL MARK YOU BRAINLIEST, NO FAKE ANSWERS!!

Makovka662 [10]

Answer:

1. if x + 5 = 12, then x = 7

:Subtraction property of equality

2. If x + y = 20, and y = 5, then x + 5 = 20.

:Substitution property of equality

3. If 2x3 = 11, then 11 = 2x - 3.

:Symmetric property of equality

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2 years ago