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Naddik [55]
3 years ago
8

Solve this equation 4log√x - log 3x =log x^2​

Mathematics
1 answer:
ruslelena [56]3 years ago
5 0

Answer:

x =  \frac{1}{3}

Step-by-step explanation:

*Move terms to the left and set equal to zero:

4㏒(√x) - ㏒(3x) - ㏒(x²) = 0

*simplify each term:

㏒(x²) - ㏒(3x) - ㏒(x²)

㏒(x²÷x²) -㏒(3x)

㏒(x²÷x² / 3x)

*cancel common factor x²:

㏒(\frac{1}{3x})

*rewrite to solve for x :

10⁰ = \frac{1}{3x}

1 = \frac{1}{3x}

1 · x = \frac{1}{3x} · x

1x = \frac{1}{3}

*that would be our answer, however, the convention is to exclude the "1" in front of variables so we are left with:

x = \frac{1}{3}

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In the first equation in the system of equations, y represents the money collected from selling sweatshirts. In the second equat
NeTakaya

Answer:

The solution x = 229.89 ≅ 230 (since we cannot have a decimal number of sweatshirts)implies that, the money collected from selling sweatshirts equals the money used in producing sweatshirts when 230 sweatshirts have been sold or produced.

Step-by-step explanation:

Here is the complete question

In the first equation in the system of equations, y represents the money collected from selling sweatshirts. in the second equation, y represents the money spent to produce x sweatshirts with team logos on them for a professional sports league.

y=35x; y=-0.05(x-400)²+9,492

what does the solution of the system represent in this context?

Solution

The solution of the system is obtained when both equations are equal. That is y=35x = y=-0.05(x-400)²+9,492 .

So, 35x = -0.05(x-400)² + 9,492.

Expanding the right side, we have

    35x = -0.05(x² - 800x + 160000) + 9492

    35x = -0.05x² -800x × -0.05 + (-0.05) × 160000 + 9492

    35x = -0.05x² +40x - 8000 + 9492

    35x = -0.05x² +40x + 1492

Collecting all the terms to the left side, we have

0.05x² - 40x - 1492 + 35x = 0

0.05x² - 5x -1492 = 0

Using the quadratic formula,

x = \frac{-(-5) +/- \sqrt{(-5)^{2} - 4 X 0.05 X - 1492}  }{2X0.05}   = \frac{5 +/- \sqrt{25 + 298.4}  }{0.1} =  \frac{5 +/- \sqrt{323.4}  }{0.1}\\=  \frac{5 +/- 17.983 }{0.1}\\=  \frac{5 - 17.983 }{0.1}  or  \frac{5 + 17.983 }{0.1}\\= \frac{-12.983 }{0.1} or  \frac{22.983 }{0.1}\\= -129.83 or 229.83

We choose the positive answer x = 229.83. Since we cannot have a decimal number of sweatshirts, we approximate to the nearest whole number. So, x = 229.83 ≅ 230 sweatshirts.

The solution implies that the money collected from selling sweatshirts equals the money used in producing sweatshirts when 230 sweatshirts have been sold or produced.

We confirm that by plugging in x = 229.83 in both equations.

y = 35x = 35(229.83) = 8044.05 ≅ 8044.1

y=-0.05(x-400)²+9,492 = y=-0.05(229.83-400)²+9,492 = y=-0.05(-170.17)²+9,492 = y=-0.05(28,957.8289)+9,492 = -1447.8914 + 9492 = 8044.11 ≅ 8044.1

3 0
3 years ago
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How do I solve this problem <br> 15 = w + 4
vova2212 [387]

Answer:

w = 11

Step-by-step explanation:

<u>Step 1:  Subtract 4 from both sides</u>

15 = w + 4

15 - 4 = w + 4 - 4

11 = w

Answer: w = 11

3 0
3 years ago
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Help on number 8 please!
solmaris [256]

Answer:

ab/3

Step-by-step explanation:

I don't really know how to explain.

Μα†hway

hope this helps!

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2 years ago
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Complete the table with the number of sit-ups you have to do sunday so that the mean number of sit-ups per day is 100
marissa [1.9K]

The mean is the average of the numbers.

It is easy to calculate: add up all the numbers, then divide by how many numbers there are.

Let the number of sit-ups you have to do Sunday be x. Then the sum of all sit-ups is

100+65+120+150+90+0+x=525+x.

The number of days is 7.

Thus, the mean is

\text{mean}=\dfrac{525+x}{7}.

You know that the mean number of sit-ups per day is 100, equate these two means and solve the equation:

\dfrac{525+x}{7}=100,\\ \\525+x=700,\\ \\x=700-525,\\ \\x=175.

Answer: 175 sit-ups

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Find the simplify form of the expression. Give your answer in scientific notation:
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You multiply the 2 values together to get 1.5*10^12
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