Answer:
An irrational number is a number that has no pattern and has no end. For example 3 divided by 7 is an irrational number because of the lack of pattern and never-ending decimal.
7. x=3 is the midpoint between the roots. The other root is x = 2*3 -(-5) = 11.
8a) f(x) = (x +3)^2 -49. The vertex is (-3, -49). The roots are -10, 4.
8b) y = (x+4)^2 -1. The vertex is (-4, -1). The roots are -5, -3.
8c) f(x) = 2(x +3)^2 -34. The vertex is (-3, -34). The roots are -3±√17.
Answer:
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The missing piece of information in the proof is that m∠DOA and m∠BOC are vertical opposite angles.
<h3>How to find vertically opposite angles?</h3>
We want to prove that m∠BOC = 90°.
We are given that m∠AOB is a right angle triangle. Thus;
m∠BOC must also be equal to 90°
Now, since m∠BOC and m∠AOB are right angles, then it means that we must equally say that m∠DOA and m∠BOC are vertical opposite angles and they are as such equal.
Thus, the missing piece of information in the proof is that m∠DOA and m∠BOC are vertical opposite angles.
Read more about vertical opposite angles at; brainly.com/question/24425517
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Carla can babysit for 5 hours and tutor for 7 hours or babysit for 8 hours and tutor for 5.5 hours
<h3>How to graph the inequality?</h3>
Let x represents hours babysitting and y represents hours tutoring
So, we have:
Earnings = Rate of babysitting * x + Rate of tutoring* y
This gives
Earnings = 5x + 10y
He wants to earn at least $95.
This means that:
5x + 10y ≥ 95
See attachment for the graph of the inequality
From the attached graph, two possible solutions are: (5, 7) and (8, 5.5)
This means that Carla can babysit for 5 hours and tutor for 7 hours or babysit for 8 hours and tutor for 5.5 hours
Read more about inequalities at:
brainly.com/question/25275758
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