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zvonat [6]
3 years ago
14

Which number line represents the solution set for the inequality 2x – 6 ≥ 6(x – 2) + 8?

Mathematics
2 answers:
mrs_skeptik [129]3 years ago
7 0
The answer is c on the edgenunity test
kari74 [83]3 years ago
4 0
Which number line represents the solution set for the inequality 2x – 6 ≥ 6(x – 2) + 8?

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I don't know if this is right... please someone help mee
worty [1.4K]
For the first circle, let's use the pythagorean theorem

\bf \textit{using the pythagorean theorem}\\\\
c^2=a^2+b^2\implies c=\sqrt{a^2+b^2}
\qquad 
\begin{cases}
c=hypotenuse\\
a=adjacent\\
b=opposite\\
\end{cases}
\\\\\\
c=\sqrt{8^2+15^2}\implies c=\sqrt{289}\implies c=17

now, it just so happen that the hypotenuse on that triangle, is actually 17, but we used the pythagorean theorem to find it, and the pythagorean theorem only works for right-triangles.

 so if the hypotenuse is actually 17, that means that triangle there is actually a right-triangle, meaning that the radius there, and the outside line there, are both meeting at a right-angle.

when an outside line touches the radius line, and they form a right-angle, the outside line is indeed a tangent line, since the point of tangency is always a right-angle with the radius.



now, let's check for second circle

\bf \textit{using the pythagorean theorem}\\\\
c^2=a^2+b^2\implies c=\sqrt{a^2+b^2}
\qquad 
\begin{cases}
c=hypotenuse\\
a=adjacent\\
b=opposite\\
\end{cases}
\\\\\\
c=\sqrt{11^2+14^2}\implies c=\sqrt{317}\implies c\approx 17.8044938

well, low and behold, we didn't get our hypotenuse as 16 after all, meaning, that triangle is NOT a right-triangle, and that outside line is not touching the radius at a right-angle, therefore is NOT a tangent line.



let's check the third circle

\bf \textit{using the pythagorean theorem}\\\\
c^2=a^2+b^2\implies c=\sqrt{a^2+b^2}
\qquad 
\begin{cases}
c=hypotenuse\\
a=adjacent\\
b=opposite\\
\end{cases}
\\\\\\
c=\sqrt{33^2+56^2}\implies c=\sqrt{4225}\implies c=\stackrel{33+32}{65}

this time, we did get our hypotenuse to 65, the triangle is a right-triangle, so the outside line is indeed a tangent line.
6 0
3 years ago
9y^2-6y+1=0<br> FIND Y PLEASE HELP STEP BY STEP
dlinn [17]

Answer:

y = 1/3

Step-by-step explanation:

<u>Step 1:  Factor</u>

9y^2 - 6y + 1 = 0

(3y - 1)(3y - 1) = 0

(3y - 1)^2 = 0

<u>Step 2:  Solve for y</u>

3y - 1 + 1 = 0 + 1

3y / 3 = 1 / 3

y = 1/3

Answer: y = 1/3

4 0
3 years ago
Solve the equation (for n )
myrzilka [38]

Hello! Hopefully I will be able to clarify and answer your equation in a way that can help you understand better. Here are the steps...

N + 6/-4 = 10

N + 6 = -40

N = -40 - 6

N= -46

Hope this helped!

7 0
3 years ago
Read 2 more answers
-2a4 + 8a– 9a<br> Find the degree of the polynomial
wlad13 [49]
Ajajjwususjdbdndkdlflfpc
8 0
2 years ago
How do you turn 0.45 into the simpilest form of a fraction
Paraphin [41]
All you need to do is put 45 over 100 to make it 45/100, then simplify down until you get your answer. The answer is 9/20 though. There may be better ways, but that's how I do it.
6 0
3 years ago
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