3 to the -2 power is basically 3x-3, which is -9, and -5 to the -3 power is (-5)(-5)(-5) which is equal to -125. hope that helped you out, bud!
9514 1404 393
Answer:
- P₂ and x are both supplementary to N₁
- Q₁
- R = 90° -x
- ΔSMP ≅ ΔSMR ∴ PS ≅ SR
Step-by-step explanation:
1. Angles P₂ and N₁ are opposite angles of inscribed quadrilateral PMNQ, so are supplementary. Angles N₁ and N₂ form a linear pair, so are supplementary. Angles supplementary to the same angle (N₁) are congruent, hence P₂ = x ≅ N₂
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2. ΔPMQ is isosceles, so angle Q₁ is also congruent to x.
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3. In ΔPMQ, the sum of angles is 180°, so ...
M₁ +2x = 180°
Dividing by 2 gives ...
M₁/2 +x = 90°
Angle M₁ subtends arc PQ of circle M. Angle R inscribed in circle M subtends the same arc, so ...
R = (M₁/2)
R = 90° -x
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4. From the above, we know that angles N₂ and R are complementary (total 90°), so angle S₂ = 90°. Segment MS will only intersect chord PR at right angles at the midpoint of that chord.
Hence S is the midpoint of PR and PS = SR.
Answer:
6.84 ≤ x ≤ 37.39
Step-by-step explanation:
we have
-----> equation A
we know that
The company wants to keep its profits at or above $225,000,
so
-----> inequality B
Remember that P(x) is in thousands of dollars
Solve the system by graphing
using a graphing tool
The solution is the interval [6.78,39.22]
see the attached figure
therefore
A reasonable constraint for the model is
6.84 ≤ x ≤ 37.39
This equation has some nested grouping symbols on the left-hand side. As usual, I'll simplify from the inside out. I'll start by inserting the "understood" 1 in front of that innermost set of parentheses:
3 + 2[4x – (4 + 3x)] = –1
3 + 2[4x – 1(4 + 3x)] = –1
3 + 2[4x – 1(4) – 1(3x)] = –1
3 + 2[4x – 4 – 3x] = –1
3 + 2[1x – 4] = –1
3 + 2[1x] + 2[–4] = –1
3 + 2x – 8 = –1
2x + 3 – 8 = –1
2x – 5 = –1
2x – 5 + 5 = –1 + 5
2x = 4
x = 2
It is not required that you write out this many steps; once you get comfortable with the process, you'll probably do a lot of this in your head. But until you reach that comfort zone, you should write things out at least this clearly and completely.
Always remember, by the way, that you can check your answers in "solving" problems by plugging the numerical answer back in to the original equation. In this case, the variable is only in terms on the left-hand side (LHS) of the equation; my "check" (that is, my evaluation at the solution value) looks like this:
LHS: 3 + 2[4x – (4 + 3x)]:
3 + 2[4(2) – (4 + 3(2))]
3 + 2[8 – (4 + 6)]
3 + 2[8 – (10)]
3 + 2[–2]
3 – 4
–1
Since this is what I was supposed to get for the right-hand side (that is, I've shown that the LHS is equal to the RHS), my solution value was correct.
O_o Whhhhaaaaat?? How does that make sense.
