(05.02) a system of equations is shown below: 5x + 2y = 3 (equation 1) 2x − 3y = 1 (equation 2) a student wants to prove that if equation 2 is kept unchanged and equation 1 is replaced with the sum of equation 1 and a multiple of equation 2, the solution to the new system of equations is the same as the solution to the original system of equations. if equation 2 is multiplied by 1, which of the following steps should the student use for the proof? (4 points) select one: a. show that the solution to the system of equations 7x − y = 4 and 2x − 3y = 1 is the same as the solution to the given system of equations b. show that the solution to the system of equations 2x + 5y = 3 and 3x − 2y = 1 is the same as the solution to the given system of equations c. show that the solution to the system of equations 9x + 4y = 5 and 7x − y = 4 is the same as the solution to the given system of equations d. show that the solution to the system of equations −4x + 9y = 5 and 2x − 3y = 1 is the same as the solution to the given system of equations

Ihave my work put down already! but my teacher have said that number 2 and 3 are messed ! ill give the highest amount of points for she said "great start on this activity! for full credit, resubmit and try again on whether mass is conserved for reactions #2 and #3, i know you got this! " conservation of mass activity worksheet instructions: observe and analyze the interactions between the substances pictured in the slide show. compare the properties of substances before and after each interaction. you will submit your completed worksheet for grading. data table on the table below, record your observations before and after the interactions and explain how mass was conserved. describe the changes in properties that prove a chemical reaction occurred. the first row is an example. 3 observations before interaction observations after interaction how was mass conserved? proof of a chemical reaction example: sugar + heat the sugar is in tiny white particles in a pile. heat is not seen but is implied by the heat source. the pile of sugar in the pot has a mass of 100 grams. there is a solid, light brown mass at the bottom of the pot. it has a mass of 100 grams. the mass of the sugar is the same in melted form as it is in solid crystal form. there was not a chemical reaction. sugar did not change composition. it only melted. melting point is a physical property, and this is a physical change. steel wool + oxygen (fire) steel wool is like a cloth but is electrical and has a mass of 6 grams, until heat is touched. when heat is applied to steel wool, heat such as batteries attract to steel wool, it starts to heat up until it is hot enough to make fire. well mass cannot be created or destroyed, it depends on the mass of a substance, i’m going to say that there is a chemical reaction because of how fire burns and reacts, if it was a stove of sugar like the example said, it only melted so its only physical change, so i consider steel wood and fire basically a chemical reaction and a change. egg + heat eggs are simple and are from chickens, some eggs can be white or brown but there is no difference, one egg is about 40 grams or more. one egg carries a substance that overweighs the egg. when the egg is cracked, the egg is weighed less than before it is weighing at at least 5 or 6. the mass of it is changed because it was originally from an egg shell that carried it, with that, the shell weighs less, and the egg is now being cooked and heated which should make the weight in general of the egg about 8 grams or 10. this would be called physical change and it would not be called a chemical change at all. water + heat water is a normal substance which can be drinkin’ or could be boiled and for all kinds of things, but lets say we have a cup of water, which is about 60 grams. if we take the water, and put it in the pot, it would still be the same amount grams because we only poured it out a cup that almost weighs the same as a pot. now lets say if we boil the water, when we boil water for too long it starts to heat up and soon evaporates into steam or smoke, so it has boiled down to about 20 – 30 grams. the water is now being heated so that means that it will boil and lessen the weight which is now 20 – 30. this would be called thermal change and it would be called a physical change because of the water evaporating. zinc is like a rock that weighs at ab out 10 grams. hydrogen chloride weighs at least 6 grams. hydrogen gets bubbly after interaction with zinc which should now weigh it at about 4 or 3 grams. they equal the same amount of mass, they are both mass products. it’s a chemical because for example, think of paint and vinegar, we all know it bubbles up and its like a volcano, so this would be called a chemical change. sodium hydroxide + copper sulfate sodium hydroxide is clear and copper sulfate is blue, they both have different weighs. blue is 57 grams and the clear one is 0 grams. the only thing that changes is that it is a different color. besides so, the sodium sulfate weighs now at 47 grams and the copper sits at 20, now that they have interacted. they equal the same after being together. i will say this is chemical change as well as chemical reactant.

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In δabc, m∠acb = 90°, cd ⊥ ab and m∠acd = 45°. find: a find cd, if bc = 3 in