Answer:
176 books
Step-by-step explanation:
Let's call the number of fiction books 'F', and the number of non-fiction books 'N'. Then, we can write the following system of equations:
eq1:
eq2:
Using the 'F' value from the first equation, we have:
The total number of books is:
Answer:
The new points to the triangle will be:
Step-by-step explanation:
Because the reflection point is at , all x values will subtract their distances from
to get their new values. The y values remain the same.
The starting values are:
Point is 5 units away from
, so we'll subtract 5 from -1 to get the new x value:
, so
.
Point is also 5 unit away from
, so we'll subtract 5 from -1 to get the new x value:
, so
.
Point is 7 units away from
, so we'll subtract 7 from -1 to get the new x value:
, so
.
8x = 12
<h3>Explanation:</h3>Subtracting the first equation from the second, you get ...
... (5x +2y) -(3x +2y) = (7) -(5)
... 2x = 2 . . . . . the first answer choice is true
___
Multiplying this expression for x by 4, we get
... 8x = 8 . . . . . the second answer choice (8x=12) is false
___
Adding thee first equation to the second, you get ...
... (3x +2y) +(5x +2y) = (5) +(7)
... 8x +4y = 12
... 8 + 4y = 12 . . . . . . use the value of 8x just computed
... 4y = 4 . . . . . . . . . . subtract 8; the third answer choice is true
_____
<em>Alternate approaches</em>
In short, if you solve the system by any of the methods available, you find x=1 and y=1, so the second answer choice is clearly the correct one:
... 8x ≠ 12
By Cramer's method:
... x = (2·7-2·5)/(2·5-2·3) = 4/4 = 1
... y = (5·5-7·3)/4 = 4/4 = 1
By graphing, see attached.
By substitution (for 2y):
... 5x +(5-3x) =7 . . . . . using 2y=5-3x
... 2x = 2 . . . . . . subtract 5
... x = 1 . . . . . . . .divide by 2
... 5 -3·1 = 2y = 2 . . . . substitute x into the expression for 2y
... y = 1 . . . . . . . divide by 2
By matrix methods, see the second attachment. (x, y) = (1, 1), found in the rightmost column of the result.
