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02.1 2 PointsThe negation of "For every ? > 0,@2 + y? > 0 for allly" is "There exists & 0 such that 22 + y? < 0 for all y"TrueFalse...

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02.1 2 PointsThe negation of "For every ? > 0,@2 + y? > 0 for allly" is "There exists & 0 such that 22 + y? < 0 for all y"TrueFalse02.2 2 PointsIf P, 9. and 7 are all false; then (p TrueVr is falseFalse

02.1 2 Points The negation of "For every ? > 0,@2 + y? > 0 for allly" is "There exists & 0 such that 22 + y? < 0 for all y" True False 02.2 2 Points If P, 9. and 7 are all false; then (p True Vr is false False



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In Exercises $112-115,$ determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$(2 y+7)^{2}=4 y^{2}+28 y+49$$

For this problem, it states is why plus seven equals zero. Then why equals seven? Um, we have to determine whether that statement is true or false, and it's a statement of false. We have to make the necessary changes to make it true. So we're giving why? But equals zero. And why equal? We know the answer is full. This statement is full. This is because if you cake seven and you plug it in for why you seven plus seven, which is 14 14 not equal zero. Okay. And in order to get the correct answer, we can go for why? So you get why plus seven equals zero, and we can subtract seven on both side. You'll get why equals negative seven. So why equals negative seven? Um, this is the correct or true, um, answer. So we could make this true. Um, by saying that why plus seven equals zero. Then why equals negative seven. So that the crew statement again? So it's wine a Southern people zero. In order for this statement to be true And why people negative seven. This is the truth

Okay. We want to determine if these four are true or false. Given the X is posted its great zero on wise negative. I less than zero. So here we've got a positive number. Take away a negative. Bogus. Be great In zero, we'll post it is great. Zero Ah nde When you take away negative Well, then it becomes a positive on two posters that together always great zero. So the first one's true. Next up, we've got a negative take away. A positive will be left in zero. Well, the negatives lesson zero on you taking away a positive. So you saw my adding on negatives you further into the natives. So Yep, that's fun. Hey, we've got the absolute value off Negative X. So the absolute value it will be left zero. So I think it would have been negative on the absolute value. Anything. It's always going to be like the positive version on it. So this is not true on now we've got the negative value off the absolute value off. Why I'm always left zero. Well, yes, it is. Because actually very wise is gonna be a positive. And then you're going to turn into negative because it's always going to be positive coming out of the absolute value on then. So you're always going to turn into a negative. So I've got three trees, have one false.

So this question asked us to determine if this expression is sure or false. So our first step is going. Teoh, distribute this negative sign to these three terms Here. Symbol gets six X squared minus seven X Y minus four minus six X squared minus seven X Y plus four. Um, we're trying to see if this equals zero. So now we're going to want to combine our like terms, so we notice that the six x where it's cancel out and our forces cancel out. But we're still left with 27 x wise, which means this answer simplifies to negative 14 x y, and it does not equal zero. So this answer is false.

All right, So this question asks us if the statement below is true. False were conditionally true. This statement might be true if the two matrices were equal. So to determine if to me, jerseys are equal, every entry in one has to be equal to the corresponding entry in the other. So I'm going to go through and look at each entry. First we have to pee. Plus one on the left would have to be equal to seven on the right. This is a conditional statement that will come back to in a minute. Next, we look at the second column in the first row, where negative five would have to be equal to negative five, which is true. Moving over. We have that nine would have to be equal two to minus que another conditional statement that will come back to in a minute. Living into the second row. We have that one equals one on the right and left. Next, we have another conditional statement that 12 would be have to equal three are. And in the third column, zero is equal to zero on the right, on the left, living down to our last row we have that Q plus five would have to equal negative to another conditional statement that nine would have to be equal to three p and that negative to our would have to be equal. It's a negative eight. So all of our entries that are kind of set in stone that have a finite value on the left and the right are all equal. So now we just need to meet these conditional statements in order for this to be conditionally true. So first looking at Pete, we have that P would be equal to three. And if we put that into her second statement, nine is equal to nine. So both of these statements are true when P is equal to three. Next. Moving on to Q. We get that Hugh is equal to negative seven to make this first date. And true. If you have negative seven plus five in the second statement, you get that negative to people's negative two, which is true. So when Q is equal to negative seven, both of those statements are conditionally true. Lastly, for our we have the articles four to make this top statement true, and we have that are times negative. Two equals negative eight on the bottom, so negative two times four equals negative eight negative eight is always equal to negative beat. So both of those statements are true when ours equals of four. Therefore all of the entries on the left are equal to the corresponding entries on the right, when P is equal to three, que is equal to negative seven and ours equal to four. Therefore, the statement is conditionally true as long as the thes three variables are set to the


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