<span>(x, y)→(x − 8, y − 7) is the correct translation. Take point D for example. The coordinate of D is (2, 5). The coordinate of D' (after translation) is (-6, -2). Since 2-8=-6, 5-7=-2, only the first choice is correct. You can also try other points and see why only this is the right translation.</span>
Answer:
George has 8x+2=26 bottles of soap what is x
Step-by-step explanation:
Answer:
80%
Step-by-step explanation:
75% + 20% - 15% = 80%
The probability is 80%
Answer:
Step-by-step explanation:
Two lines are given to us which are perpendicular to each other and we need to find out the value of a . The given equations are ,
Step 1 : <u>Conver</u><u>t</u><u> </u><u>the </u><u>equations</u><u> in</u><u> </u><u>slope</u><u> intercept</u><u> form</u><u> </u><u>of</u><u> the</u><u> line</u><u> </u><u>.</u>
and ,
Step 2: <u>Find </u><u>the</u><u> </u><u>slope</u><u> of</u><u> the</u><u> </u><u>lines </u><u>:</u><u>-</u>
Now we know that the product of slope of two perpendicular lines is -1. Therefore , from Slope Intercept Form of the line we can say that the slope of first line is ,
And the slope of the second line is ,
Step 3: <u>Multiply</u><u> </u><u>the </u><u>slopes </u><u>:</u><u>-</u><u> </u>
Multiply ,
Multiply both sides by a ,
Divide both sides by -1 ,
<u>Hence </u><u>the</u><u> </u><u>value</u><u> of</u><u> a</u><u> </u><u>is </u><u>9</u><u> </u><u>.</u>
Notation
The inverse of the function f is denoted by f -1 (if your browser doesn't support superscripts, that is looks like f with an exponent of -1) and is pronounced "f inverse". Although the inverse of a function looks like you're raising the function to the -1 power, it isn't. The inverse of a function does not mean the reciprocal of a function.
Inverses
A function normally tells you what y is if you know what x is. The inverse of a function will tell you what x had to be to get that value of y.
A function f -1 is the inverse of f if
<span><span>for every x in the domain of f, f<span> -1</span>[f(x)] = x, and</span><span>for every x in the domain of f<span> -1</span>, f[f<span> -1</span>(x)] = x</span></span>
The domain of f is the range of f -1 and the range of f is the domain of f<span> -1</span>.
Graph of the Inverse Function
The inverse of a function differs from the function in that all the x-coordinates and y-coordinates have been switched. That is, if (4,6) is a point on the graph of the function, then (6,4) is a point on the graph of the inverse function.
Points on the identity function (y=x) will remain on the identity function when switched. All other points will have their coordinates switched and move locations.
The graph of a function and its inverse are mirror images of each other. They are reflected about the identity function y=x.
