Which answer choice shows a solution set in which all values, when input for x, will be true?
1 answer:
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Answer:
See below.
Step-by-step explanation:
RSTV is a quadrilateral. We see that segments RV and RS are congruent. We also see that segments TV and TS are congruent. That makes quadrilateral RSTV a kite. A kite is a quadrilateral that has one set of congruent adjacent sides and a second set of congruent adjacent sides. One set of congruent adjacent sides may or may not be congruent to the second set of congruent adjacent sides. In this case they are not.
The diagonals of a kite are perpendicular which is shown in your figure with segment VS perpendicular to segment RT. The diagonals form 4 right triangles. The 4 right triangles are VRW, SRW, VTW, and STW.
Triangles VRW and SRW are congruent.
Triangles VTW and STW are congruent.
Let's work on the angles first.
Let's work on triangle VTW.
Angle VWT is a right angle.
m<VWT = 90
m<WVT = 42
m<VWT + m<VTW + m<WVT = 180
90 + 42 + m<WVT = 180
m<WVT + 132 = 180
m<WVT = 48
Triangle SWR is a right triangle.
m<RWS + m<RSW + m<SRW = 180
90 + m<RSW + 21 = 180
m<RSW + 111 = 180
m<RSW = 69
Triangles WVR and WSR are congruent with corresponding angles WVR and WSR.
m<WVR = m<WSR = 69
m<TVR = m<WVT + m<WVR
m<TVR = 48 + 69 = 117
m<TVR = 117
Now we deal with sides.
Let's look at triangle VWT.
Side VT is the hypotenuse.
m<VTW = 42 deg
VT = 15
For angle VTW, VW is the opposite leg, and VT is the hypotenuse.
The trig ratio that relates the opposite leg and the hypotenuse is the sine.
VW = 10
Since triangles RVW and RSW are congruent, corresponding sides VW and SW are congruent.
SW = VW = 10
Trianlge RSW is a right triangle with right angle RWS.
For angle WRS, SW is the opposite leg. RW is the adjacent leg.
RW = 26
We now know VW and RW. Using the Pythagorean theorem we can find RV.
(RW)^2 + (VW)^2 = (RV)^2
26^2 + 10^2 = (RV)^2
RV = 28
Perimeter:
Triangles RVT and RST are congruent, so we have:
RV = RS = 28
VT = ST = 15
perimeter = RS + RV + VT + ST
perimeter = 28 + 28 + 15 + 15
perimeter = 86
1. The 100 prisoner experiment: 100 prisoners are about to be executed (you can use paper stick figures to model 100 prisoners, or you can do about 10), but the warden has agreed to allow all prisoners to be commuted to a 6-month sentence if they can pass one game. The game states that 100 pieces of paper with each of the prisoner's numbers are to be randomly shuffled into boxes that have random prisoner's numbers (where the number on the paper does not match the number on the boxes.) Each prisoner is allowed to open 50 boxes to find their number such that they have a chance of finding their number. If you find your number, you are cleared to another room to wait. If you don't, then you've messed up huge. If even one prisoner does not find their number, all the prisoners die. If all of the prisoners find their numbers, they all get 6-month sentences instead. The chance of all the prisoners randomly finding their numbers is
, which is about a 0.0000000000000000000000000000008% chance. 30 zeros after the decimal placement. For reference, two people have a better chance of picking up the same grain of sand from any of the beaches in the world than finding their numbers randomly.
The Vickrey Auction can be modeled into an experiment by testing people's psychological thinking. You can do this with any of your friends. In a Vickrey auction, you put your bids into a closed letter. For an item, the highest bidder wins the auction, but does not pay what he or she put their bid under in the auction, but rather pays what the second bidder had bidded. It teaches people to be more honest, because if you bid the highest and win, you pay the second-highest bidder's payment, which could also be almost equally as high and could cost you a fortune for an undervalued item.
Another great experiment you can do is to measure the different unsynchronizations of analog clocks that are not close together. Scientists have measured atomic clocks that are just a millimeter apart that start ticking in different measures.
2. I select the 100-prisoner experiment.
3. A curved graph like -x^2 would fit perfectly.
4. A quadratic function would fit my experiment the best. The best graph to use would be . An equation with a large curve would be the best for this type of experiment to graph success and failure. More than three quarters of my graph wouls be full of failure and maybe a little more than 10% would be full of success if repeated over 100,000 times. I am not too sure though.