By some properties of logarithms, rewrite the equation as
so that
(<em>a</em> - 2<em>b</em>)² = <em>ab</em>
Expand the left side:
<em>a</em> ² - 4<em>ab</em> + 4<em>b</em> ² = <em>ab</em>
Rearrange terms to get a quadratic equation in <em>a</em>/<em>b</em> :
<em>a</em> ² - 5<em>ab</em> + 4<em>b</em> ² = 0
<em>b</em> must be greater than 0, otherwise log(<em>b</em>) doesn't exist, and the same goes for <em>a</em>. So we can divide by <em>b</em> ² to get
<em>a</em> ²/<em>b</em> ² - 5<em>a</em>/<em>b</em> + 4 = 0
Factorize and solve for <em>a</em>/<em>b</em> :
(<em>a</em>/<em>b</em> - 4) (<em>a</em>/<em>b</em> - 1) = 0
==> <em>a</em>/<em>b</em> = 4 or <em>a</em>/<em>b</em> = 1
However, if <em>a</em>/<em>b</em> = 1, then <em>a</em> = <em>b</em> makes <em>a</em> - 2<em>b</em> = -<em>b</em>. But we must have <em>b</em> > 0, so we omit the second solution and end up with
<em>a</em>/<em>b</em> = 4
Answer:
The answer is A.
You can graph the two inequaltiy just like you would graph slope intercept from. Just think of the inequality sign as an equal sign. :)
Step-by-step explanation:
Answer:
The last choice is the one you want.
Step-by-step explanation:
Simply take the x coordinate and subtract 4, then do the same with the y coordinate since the vector movement is <-4, -4>. The first coordinate F is <4,0>. Subtract 4 from both of those coordinates and end up at <0, -4>. The second coordinate G is <1, 3>. Subtract 4 from both of those and end up at <-3, -1>. The third coordinate H is <2, 6>. Subtract 4 from both of those and end up at <-2, 2>. The last coordinate I is <4, 2>. Subtract 4 from both of those and end up at <0, -2>.
It is pretty easy to eliminate the wrong answers by trying the answers in the equations.
a. 7 times 30 is way more than 4
c. 6 times 226 is way more than 172, even after subtracting 64
d. 7 times -74 is way less than 4
The appropriate choice is
... b. x=4, y=30
You can check it with your graphing calculator.
_____
Since you have an expression for y, you can substitute that into the second equation:
... -2x + 6(2+7x) = 172 . . . . substitute for y
... 40x = 160 . . . . . . . . . . . . eliminate parentheses, subtract 12, collect terms
... x = 4 . . . . . . this is sufficient to help you locate the correct answer
Answer:
4x+5y=15
Step-by-step explanation:
Btw brainliest me plss
