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ACT Math February - Problems 11-15 (Form 1267C)

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we're going to work through problems 11 through 15 from the February act tutoring sessions for math number 11 says in Triangle the sum of the measures of angle a and angle B is 47 degrees what is the measure of angle C when this problem we have to know three angles in any triangle have a sum of 180 so if the first two together equal 47 I've got to find what is the angle just going to make 47 in the third angle equal 180 so I can just take 280 and subtract from that 47 degrees  it's going to give me what angle C is equal to in this difference here gives me 100 in 33 degrees to my answers one of the answer option D find move number 12 number 12 says in the school cafeteria students choose their lunch from three sandwiches three soups for salads and two drinks how many different lunches possible for a student who chooses chooses exactly one sandwich one soup one salad and one drink or some kind of combination they want to know how many different combinations of a sandwich is supercell in a drink Kansas to Dan have these are all independent horses and where that means is the sandwich they choose has no impact on the soup they choose which has no impact on the salad and has no impact on the drink also since our drink on one of each it has no impact on how many options you have for each each of the categories so no problem like this multiply all of these numbers together so we would take the number sandwiches  and then multiply that by the number of soups how about the number of salads and then finally X the number of drinks tattoo we multiply all these and it gives me the number of combinations of the students have how many different combinations I could have choosing one of each of these which gives us a product 72 swing are there are 72 different lunches that student can made for picking one from each category play number 13 says for two consecutive integers the result of adding the smaller integer and triple the larger integer 79 what are the two integers we can solve this some multiple different ways the way that some people might want to start the problem it's a setup some equations or represent what this problem is saying and then we can use a different approach actually find out what the answer is where's with two consecutive integers we've a larger one and a smaller room with sensor consecutive we could save the larger one L  minus smaller one which is s is equal to one and we know that because their consecutive if you look at your answer choices they're all consecutive set alarm to 1 minus the smaller when are always in give you one 19-18 is 120 - 19 is one and so on the other can we have Davis's the result of adding the smaller integer which is us Plus  triple the law your integers I would say that is 3 times cell  is 79  Haslett again what's the result of adding the smaller integer s plus three times the larger integer is equal to 79 so I really want to focus on this equation solving a system of equations which you can do I can really just look at these choices and figure out which of these choices the bigger number being l small a number mean which of these choices will make this second equation true for example if I would check problem or answer choice how do you say 18 + 3 * 19 K and if I put them in the calculator three times 19 which gives me 50 + 18  that's going to give me 75 that is not equal to 79 answer Choice a is not correct sound get a bee or bee is the S is 19 + 3 * tell which is 3 * 20 + 10 + 3 * 20 gives us 60 and if I added that 19 what is 9 18 + 60  any grocery night so that means it makes equation true so I'm done my answer has to be introduced B my number 14 says they function known as f of x is defined as f of x equals do you have 8 x squared what is the function of -32 this problem is a lot like number two that we did earlier never remember number who was hired by a citizen easier problem the number 14 but it really ask us to do the same thing this just gives it to us as a function what is tonicity was it wants us to take this negative three that's in the problem and plug it into the function 4X so I'm going to start with negative 8 I'm replacing x with negative three  close parentheses in squared now I do have the option of plugging straight in the calculator exactly how descendants of parentheses have to be there and everything or I can just use order of operations and solve it so to show you -3 raised to the second power that's negative three times negative 3 gives me a positive 9 so I still have this negative 8 outside now times a positive non  85 * together that gives me a product of -72 should the same thing your cow quarter would have given you you if you just plug this then so that means my answer has to be answered choice at Vice listen to 15 over the last one for this video it says if 3 to the X power equals 54 then which of the following must be true suggest all these scenarios let's figure out what the different values of X could be so for example 3 to the one power is equal to 3 3 to the second power is equal to 9 I want to do this until what fun what numbers found the answer 5430 cubed X32 3 * 3 is equal to 27  Sam still not to 54 young then I do 3 to the 4th what's 3 * 3 * 3 * 3 and it gives us 81 now let's stop for a second it says if it's three did I start equals 54 that means it falls somewhere between this area so 3 to the third power is too small through the 4th Powers too big so once what do we know about X for this to be true I know X has to be somewhere between 3 and 4 so which of our Roxanne says of x Falls between 3 and 4  and that has to be insert option C says 3 must be less than x X must be listening for

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ACT Math February - Problems 11-15 (Form 1267C)

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