Graph the inequality x>2

Mathematics

1 answer:

denis23 [38]3 years ago

5 0

Answer:

no problem :) have a nice day

Step-by-step explanation:

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The hypotenuse of the right triangle is 5 meter long. the shorter leg is 1 Meter shorter than the longer leg. find the side leng

Firlakuza [10]

Shorter leg = x

Longer leg = x +1

Length of the hypotenuse: 5 m

We can use the pythagorean theorem with the information given. Doing so, we have:

$\begin{gathered} a^2+b^2=c^2 \\ (x)^2+(x+1)^2=5^2\text{ (Replacing the values)} \\ x^2+x^2+2x+1=25\text{ (Raising both terms to the power of 2)} \\ x^2+x^2+2x=25-1\text{ (Subtracting 1 from both sides of the equation)} \\ 2x^2+2x=24\text{ (Adding like terms)} \\ 2x^2+2x\text{ }-24=0\text{ (Subtracting 24 from both sides of the equation)} \\ 2(x+4)(x-3)=0\text{ (Factoring)} \\ x1=-4\text{ (Since x=-4 makes the factor (x+4) equal to 0)} \\ x2=3\text{ (Since x=3 makes the factor (x}-3\text{) equal to 0)} \\ \text{ Since we need a positive solution x would be equal to 3} \end{gathered}$

So, the answers would be:

Shorter leg = 3 m

Longer leg = 4 m

Length of the hypotenuse: 5 m

6 0

1 year ago

Find the greatest common factor.<br> 42²x² + 42²x+ 40²<br> Enter the correct answer.

svlad2 [7]

Answer:

4a^2

Step-by-step explanation:

$4a^2x^2+4a^2x+4a^2= \\\\4a^2(x^2+x+1)$

Therefore, the largest common factor is 4a^2. Hope this helps!

3 0

3 years ago

Ron's recycle shop had an old paper-shredding machine. Business was good, so he bought a new paper-shredding machine. The old ma

levacccp [35]

Answer: 1 hour 20 minutes

Step-by-step explanation:

Given : The old machine could shred a truckload of paper in 4 hours.

Rate of work done by old machine = $\dfrac{1}{4}$

The new machine could shred the same truckload in 2 hours.

Rate of work done by new machine = $\dfrac{1}{2}$

Let 't' be the time taken by both of them working together , then we have the following equation:-

$\dfrac{1}{t}=\dfrac{1}{4}+\dfrac{1}{2}\\\\\Rightarrow\dfrac{1}{t}=\dfrac{1+2}{4}\\\\\Rightarrow\dfrac{1}{t}=\dfrac{3}{4}\\\\\Rightarrow t=\dfrac{4}{3}=1\dfrac{1}{3}\ \text{ hours}$