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andre [41]
3 years ago
9

Solve the inequality

Formula1" title=" \frac{2x}{x + 3} \leqslant 3" alt=" \frac{2x}{x + 3} \leqslant 3" align="absmiddle" class="latex-formula">
The solution set is

Mathematics
1 answer:
Fofino [41]3 years ago
3 0

Domain:x\neq-3\\\\\dfrac{2x}{x+3}\leq3\qquad\text{subtract 3 from both sides}\\\\\dfrac{2x}{x+3}-3\leq0\\\\\dfrac{2x}{x+3}-\dfrac{3(x+3)}{x+3}\leq0\\\\\dfrac{2x}{x+3}-\dfrac{3x+9}{x+3}\leq0\\\\\dfrac{2x-(3x+9)}{x+3}\leq0\\\\\dfrac{2x-3x-9}{x+3}\leq0\\\\\dfrac{-x-9}{x+3}\leq0\Rightarrow(x+3)(-x-9)\leq0\\\\x=-3,\ x=-9\\\\x\in(-\infty,\ -9]\ \cup\ (-3,\ \infty)

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seraphim [82]
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8 0
3 years ago
If ADAB<br> ACBA,<br> ZDAB = 35° and ZCBA = 8x + 3<br> A<br> D<br> x = [?]<br> X<br> C<br> B
bekas [8.4K]

Answer:

x=4

Step-by-step explanation:

We are given that the triangles are congruent.

Specifically, the order of the letters gives that the angles ∠DAB and ∠CBA are corresponding parts of the two congruent triangles.  Since corresponding parts of congruent triangles are themselves congruent, ∠DAB ≅ ∠CBA.  Thus, m∠DAB = m∠CBA.

Given the expressions for the two angles, we can substitute into the equation, and solve for the requested variable.

m\angle DAB=m\angle CBA\\(35)=(8x+3)\\(35)-3=(8x+3\!\!\!\!\!\!\!\!\!\!{--})-3 \!\!\!\!\!\!\!\!\!\! {--}\\32=8x\\\dfrac {32}{8}=\dfrac {8x\!\!\!\!\!\!\! {-}}{8\!\!\!\! {-}}\\4=x

6 0
2 years ago
Read 2 more answers
Decide all proper subsets of A { 8 ,7 ,6 ,5 ,4 ,3 ,2 ,1} = A 1- { 4 ,3 ,2 ,1} 2- { } 3- { 9 ,8 ,7 } 4- { 11 ,2} 5- { 5 }
NemiM [27]

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A, E

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8 0
3 years ago
Which statement is false?
Zarrin [17]
<span>Let's analyze our choices:
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2. When analyzing media, it is important to ask, "Does it work ". If a person told you that the sky is actually pink but Mary Poppins is actually a real person and just makes you think that the sky looks blue, and that they learned this because the news told them so, would you automatically believe them? Not really. :P Therefore option 2 is out of the way.
3. It is important to understand that media messages do not have a goal. HAH! People and messages always have a goal. I think we may have found our false statement, but just to be sure, let's take a look at our last statement.
4. People will perceive media messages differently. </span>Have you ever watched a debate and thought that one side did a better job than the other, and then your friend starts an argument with you as they think that's total baloney? This statement is true too.

This leaves the only false statement as 3. <span>It is important to understand that media messages do not have a goal.</span>

Did that answer your question?
7 0
4 years ago
6% sales tax on a pair of jeans selling for $19.99. What is the total cost? Round to the nearest tenth ​
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