The answer is III only, or D.
We can start to solve this by knowing what the HL theorem means. The HL theorem, like its name implies, shows says that if a hypotenuse and leg of a triangle are congruent to the hypotenuse and leg of a different triangle, then the triangles are congruent. The only triangle that we see a hypotenuse congruent in is in figure III. In figure II, those congruent sides are both legs while in figure I we just see 2 congruent angles. Now in figure III, we can also see that two legs are congruent because of the reflexive property. That means that the answer is III, or D.
<span><span>f<span>(x)</span>=8x−6</span><span>f<span>(x)</span>=8x-6</span></span> , <span><span>[0,3]</span><span>[0,3]
</span></span>The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.<span><span>(−∞,∞)</span><span>(-∞,∞)</span></span><span><span>{x|x∈R}</span><span>{x|x∈ℝ}</span></span><span><span>f<span>(x)</span></span><span>f<span>(x)</span></span></span> is continuous on <span><span>[0,3]</span><span>[0,3]</span></span>.<span><span>f<span>(x)</span></span><span>f<span>(x)</span></span></span> is continuousThe average value of function <span>ff</span> over the interval <span><span>[a,b]</span><span>[a,b]</span></span> is defined as <span><span>A<span>(x)</span>=<span>1<span>b−a</span></span><span>∫<span>ba</span></span>f<span>(x)</span>dx</span><span>A<span>(x)</span>=<span>1<span>b-a</span></span><span>∫ab</span>f<span>(x)</span>dx</span></span>.<span><span>A<span>(x)</span>=<span>1<span>b−a</span></span><span>∫<span>ba</span></span>f<span>(x)</span>dx</span><span>A<span>(x)</span>=<span>1<span>b-a</span></span><span>∫ab</span>f<span>(x)</span>dx</span></span>Substitute the actual values into the formula for the average value of a function.<span><span>A<span>(x)</span>=<span>1<span>3−0</span></span><span>(<span>∫<span>30</span></span>8x−6dx)</span></span><span>A<span>(x)</span>=<span>1<span>3-0</span></span><span>(<span>∫03</span>8x-6dx)</span></span></span>Since integration is linear, the integral of <span><span>8x−6</span><span>8x-6</span></span> with respect to <span>xx</span> is <span><span><span>∫<span>30</span></span>8xdx+<span>∫<span>30</span></span>−6dx</span><span><span>∫03</span>8xdx+<span>∫03</span>-6dx</span></span>.<span><span>A<span>(x)</span>=<span>1<span>3−0</span></span><span>(<span>∫<span>30</span></span>8xdx+<span>∫<span>30</span></span>−6dx)</span></span><span>A<span>(x)</span>=<span>1<span>3-0</span></span><span>(<span>∫03</span>8xdx+<span>∫03</span>-6dx)</span></span></span>Since <span>88</span> is constant with respect to <span>xx</span>, the integral of <span><span>8x</span><span>8x</span></span> with respect to <span>xx</span> is <span><span>8<span>∫<span>30</span></span>xdx</span><span>8<span>∫03</span>xdx</span></span>.<span><span>A<span>(x)</span>=<span>1<span>3−0</span></span><span>(8<span>∫<span>30</span></span>xdx+<span>∫<span>30</span></span>−6dx)</span></span><span>A<span>(x)</span>=<span>1<span>3-0</span></span><span>(8<span>∫03</span>xdx+<span>∫03</span>-6dx)</span></span></span>By the Power Rule, the integral of <span>xx</span> with respect to <span>xx</span> is <span><span><span>12</span><span>x2</span></span><span><span>12</span><span>x2</span></span></span>.<span>A<span>(x)</span>=<span>1<span>3−0</span></span><span>(8<span>(<span><span>12</span><span>x2</span><span>]<span>30</span></span></span>)</span>+<span>∫<span>30</span></span>−6dx<span>)</span></span></span>
This is tricky because we are given the interest rate for the year but the problem is figureing the interest for 6 months or 1/2 year. We will have to double the difference before solving for the yearly interest.
572.60 - 560.00 = 12.60 interest added for 6 months x 2 = 25.20 for 12 months
(This problem assumes the interest will stay the same the next 6 months)
We need to find what percent 25.20 is to our original balance.
25.20/560 = x / 100
2520 = 560x
x = 4.5 percent interest
Check .045 x 560.00 = 25.20 interest in one year (or 12.60 in 6 months)
So fuctions mean
if
f(x)=x+2 then if you put in 3 for x then
f(3)=3+2=5 so
if x=years after 2000
in 2020 then
2020-2000=20 so x=20
subsitute
f(20)=9204e^0.022(20)
e could be:
1. common base of logarithms (memorised to 15 decmals) 2.718281828459045
2. a computer notation exg if you have 3e11 that means 3 times 10^11
if it is 1
9240 times (2.718281828459045^(0.022 times 20))=( simplify exponent first) 9240 times (2.718281828459045^0.44)=9204 times 1.5527072185113=14291.1 or rounded to 14291
if it is 2
9204 times 10^(0.022 times 20)=9204 times 10^(0.44)=9204 times 254.491 rounded to 254
so the answer dependes on what e represents,
if e is:
1. common base of logarithms (memorised to 15 decmals) 2.718281828459045, then answer is 14291
2. a computer notation exg if you have 3e11 that means 3 times 10^11 =254
