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3 years ago

The graph represents which system of inequalities?

Mathematics

1 answer:

Lena [83]3 years ago

4 0

your answer is option 3.

you can also deduce it by option.

as in graph one line is dotted and one is solid that means 1 equation must have equality sign for solid line and one equation should not have equal sign for dotted line.

using this we can see only 3rd option has that.

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3 years ago

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3 years ago

What is the true solution to the equation below 2 log3(6x)-log3(4x)=2 log 3(x+2)

Tanya [424]

Answer: The answer is (C) C. x=1 and x=4.

Step-by-step explanation: We are given to find the true solution of the following equation involving logarithms:

$2\log_36x-\log_34x=2\log_3(x+2).$

We will be using the following properties of logarithms in the solution.

$(i)~a\log b=\log a^b,\\\\(ii)~\log a-\log b=\log\dfrac{a}{b}.$

The solution is as follows:

$2\log_36x-\log_34x=2\log_3(x+2)\\\\\Rightarrow \log_3(6x)^2-\log_34x=\log_3(x+2)^2\\\\\\\Rightarrow \log_3\dfrac{36x^2}{4x}=\log_3(x^2+4x+4)\\\\\\\Rightarrow 9x=x^2+4x+4\\\\\Rightarrow x^2-5x+4=0\\\\\Rightarrow (x-4)(x-1)=0\\\\\Rightarrow x-4=0,~~~x-1=0\\\\\Rightarrow x=4,~~~x=1.$

Since we can find the logarithm of a positive integer only, and both the solutions x = 1 and 4 satisfy this condition after substituting in the given equation, so both the solutions are TRUE.

Thus, the correct option is (C).

6 0

3 years ago

Read 2 more answers

True or false? if two triangles are congruent, then they can be moved so that they line up perfectly

Mnenie [13.5K]

<span>Yes they both will overlap each other perfectly meaning they will line up perfectly </span>

5 0

3 years ago

Read 2 more answers

Determine if the problem below has a mistake or not. Identify the mistake and explain how to correct it.

pochemuha

Answer:

The problem has a mistake in it. The mistake is found in line 3. The person who solved the problem subtracted 6 from both sides when they should have added 6.

x = 1

Step-by-step explanation:

4x-2=8-6x

10x-2=8

10x=10

x= 1

4 0

3 years ago