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16. Solve the equation. 8t+7 =-2 A {2} B. {8} C. {9} D ~1}...

Question

16. Solve the equation. 8t+7 =-2 A {2} B. {8} C. {9} D ~1}

16. Solve the equation. 8t+7 =-2 A {2} B. {8} C. {9} D ~1}



Answers

Solve each equation. Check your answer. $$ 2 b+4=-18-9 b $$

If two matrices are equal to each other and they have the same dimensions which they do, they're both two by two matrices, then every pair of corresponding entrances equal to each other. So we can take a lot of information from here, such as nine is equal to a squared. We also know that to be plus one is equal to nine. We know that negative five is equal to to a plus one. We know that 16 is equal to B squared. Well, the only variables here are A and B. And these are gonna be the two easiest ones to use. But when we solve A is going to be equal to the square root of nine, which is positive or negative three. Likewise, B is going to be equal to positive or -4. So then um that's not enough information. So let's use these two subtracting one to both sides. We see that B is equal to four. And for a uh if we subtract one to both sides, negative six is equal to two. A and A equals negative three. So it's the positive for in the negative three.

We need to find the value of being from the equation. Eight multiplied with B minus to plus three B is equal to minus nine multiplied with B minus one. So opening the apprentices and simplifying we'll get eight B minus 16 plus three. B is equal to minus 90 plus nine, which will become 11. B minus 16 is equal to minus 90 plus nine. That is, 11 B plus nine B is equal to 16 plus nine, which will give us 20. B is equal to 25 so be will be equal to 25 divided by 20 which will be which will be five divided by four. So therefore, our solutions said, comes out to be b equals five divided by four. Now we need to check on toe check. We're going to put be equal to five divided by four first in the left hand side so it will become it multiplayer with five debated by four minus two plus three multiplied with five divided by four, which will be equal toe eight multiplied with minus reiterated by four plus 15 divided by food, which is equal to minus nine. Divided by four. Next similar Livia Winter would be equal to five divided by four in the right hand side, so we'll get minus nine multiplied with five debated by four minus one, which is equal to minus nine multiplied with wonder rated by for witches minus nine, divided by four. Therefore, clearly the left hand side is equal to the united site, which means our solution, said bees. Equal toe five divided by four is therefore good it

And this problem we're being asked for which of the four answer choices gives us the solutions for this equation. So know this in this equation are radical is already by itself. So to get rid of the radical, we have to do the opposite of taking the square root, which is to square it. So what we're gonna do is we're gonna square both sides of the equation. Well, like I mentioned, when we square a square root, they cancel out and we're left with just luck where left with what's underneath the radical, which in this case is C squared minus 17. Now, on the right hand side, we have eight squared, which is 64. And now we have to solve for C. To do that, we're gonna add 17 to both sides. So we're gonna be left with c squared is equal to while 64 plus 17 is 81. And now what's the opposite of squaring? See? Well, that would be to take the square root. Well, whenever we take the square verte both sides, we have to take the positive or the negative of it. Well, the square with the C squared is just see. And now we have to find what plus or minus the square. The baby one is well, the square root of 81 is nine, so C could be plus or minus nine. So therefore see could be nine or C could be negative nine. And if you look in your answer choices, this would be the choices for choice D.

So for this, the first thing that we want to do is realize that for exponents we're dividing exponents, exponent efficient. You know that all we're going to be doing is taking that exponents numbers and then subtracting them if our base is the same. So if we had, like, two to the eggs over two to the why and we know that's maybe the same thing as true to the X minus y. And we know that that works for here because for a base we both out you have both of them was X So we know we just have to subtract them. Making X of a squared minus B squared is equal to X the sixteen. So then we know that if that's the case, exponents must be the same since the bases are the same. So we could say a squared minus B squared is equal to sixteen. And from here I can also utilize this equation to say that a plus B is equal to two. So then, in order to find a mind's be, we just have to use this and manipulate that. So then I'm just gonna go ahead and subtract, be from both sides. Giving me a is equal to two. Maina speaks and from here I'm going to use substitution to plug. Got right into there. So then I get to minus B the whole point of B squared minus B squared position to sixteen. If I expand this out using foil, remember to use Foyle, that's important here. So then I get four minus four b plus B squared minus B squared is equal to sixteen. But you have to notice that this positive B square in the negative B squared cancels out and I'm left with four minus for be a sequel to sixteen. From here, I'm going to go ahead and subtract four from both sides. Leaving with negative for B is equal to twelve. So from here, I just have to divide both sides by a negative for giving me B is equal to negative three. So I found my bees. That's good. But I still have to find my A. So at least if I want to know a minus B, I know it's gonna be a plus three because a minus note of three is the same thing as a plus three. Because the negatives I'm positive. So then I just had to plug that equation or that be value back into this one because that one is easier. So then I get a minus three is equal to chew. And if I said I had agreed to both sides, I get a is equal to five to, like, unplugging our A value right here. Five. When I get five plus three is equal to eight, so they must be our correct answer.


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