9514 1404 393
Answer:
D.
Step-by-step explanation:
The wording "when x is an appropriate value" is irrelevant to this question. That phrase should be ignored. (You may want to report this to your teacher.)
When you look at the answer choices, you see that all of them are negative except the last one (D). When you look at the problem fraction, you see that it is positive.
The only reasonable choice is D.
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Your calculator can check this for you.
√12/(√3 +3) ≈ 3.4641/(1.7321 +3)
= 3.4641/4.7321 ≈ 0.7321 = -1 +√3
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If you want to "rationalize the denominator", then multiply numerator and denominator by the conjugate of the denominator. The conjugate is formed by switching the sign between terms.
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<em>Additional comment</em>
We "rationalize the denominator" in this way to take advantage of the relation ...
(a -b)(a +b) = a² -b²
Using this gets rid of the irrational root in the denominator, hence "rationalizes" the denominator.
We could also have multiplied by (3 -√3)/(3 -√3). This would have made the denominator positive, instead of negative. However, I chose to use (√3 -3) so you could see that all we did was change the sign from (√3 +3).
It works because even if the numbers are broken apart, you are still multiplying the numbers by their values, it's only different because once broken apart, it's in expanded form instead of standard form. It also makes multiplication easier since you don't have to deal with such large numbers.
Answer:
$53.83
Step-by-step explanation:
For David
David invested $340 in an account paying an interest rate of 2\tfrac{1}{8}2 8 1 % compounded continuously.
r = 2 1/8% = 17/8% = 2.125% = 0.02125
t = 17 years
P = $340
For Compounded continuously, the formula =
A = Pe^rt
A = Amount Invested after time t
P = Principal
r = interest rate
t = time
A = $340 × e^0.02125 × 17
A = $ 487.94
For Natalie
Natalie invested $340 in an account paying an interest rate of 2\tfrac{3}{4}2 4 3 % compounded quarterly.
r = 2 3/4 % = 11/4% = 2.75% = 0.0275
t = 17 years
P = $340
n = compounded quarterly = 4 times
Hence,
Compound Interest formula =
A = P(1 + r/n)^nt
A = Amount Invested after time t
P = Principal
r = interest rate
n = compounding frequency
t = time
A = $340 (1 + 0.0275/4) ^17 × 4
A = $ 541.77
After 17 years, how much more money would Natalie have in her account than David, to the nearest dollar?
This is calculated as
$541.77 - $ 487.94
= $53.83
Hence, Natalie would have in her account, $53.83 than David
Step-by-step explanation:
The axis of symmetry: is the line that makes the parabola split in exactly half and lines up with the vertex. For that parabola x=1 is the line of symetry.
The vertex is where the minimum of the graph is, on this graph you can eyeball it to be (1,-9)
The x-intercept is where y is 0 so that's where the lines intersex with the x-axis. (-2,0) and (4,0)
The y-intercept of the function is where x is 0 and where the parabola intersects with the y-axis. On this graph it would be (0,-8)
Hope that helps :)
X=58 the exterior angle is “D” 60degrees
