Answer:
A) f^-1(x)=(x-8)^3+2
Step-by-step explanation:
To find the function inverse, switch the x with y and solve for y.
![y=\sqrt[3]{x-2}+8 \\\\x=\sqrt[3]{y-2}+8\\\\(x-8)^3 = y-2\\\\ (x-8)^3 + 2 = y](https://tex.z-dn.net/?f=y%3D%5Csqrt%5B3%5D%7Bx-2%7D%2B8%20%5C%5C%5C%5Cx%3D%5Csqrt%5B3%5D%7By-2%7D%2B8%5C%5C%5C%5C%28x-8%29%5E3%20%3D%20y-2%5C%5C%5C%5C%20%28x-8%29%5E3%20%2B%202%20%3D%20y)
Answer:
Step-by-step explanation:
The k is indicative of movement either up or down, while h is indicative of movement that is either right or left. The blue graph moves both to the right and down to get to the position of the red graph. On the blue graph, locate the point (0, 1). That point moves from a y-location of 1 to a y-location of -2, meaning that it moves down 3 units; therefore, the value of k is -3.
Answer:
1.35cm
Step-by-step explanation:
Given the scale of the map
1cm = 100km
For 135km;
x cm = 135 km
Divide both equations
1/x = 100/135
100x = 135
x = 135/100
x = 1.35cm
Hence the map distance will be 1.35cm
The regression equation to predict the number of cans sold on a day that is 90°F will be 871.
<h3>What is the linear system?</h3>
A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
A convenience store manager notices that sales of soft drinks are higher on hotter days, so he assembles the data in the table, shown above. Use technology to find the equation of the least-squares regression line.
Then the regression line will be passing through (55, 340) and (84, 780). Then we have
y - 340 = 15.17(x - 55)
Then the regression equation to predict the number of cans sold on a day that is 90°F will be
y - 340 = 15.17 (90 - 55)
y = 871
More about the linear system link is given below.
brainly.com/question/20379472
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Answer:
Step-by-step explanation:
Because we have 3 unknowns, we need to come up with 3 equations. If the total number of animals is 440 and that number is made up of a combination of goats (g), ducks (d), and chickens (c) the first equation is
g + d + c = 440
The next equation is found in the fact that the number of ducks is one-quarter the number of chickens:
and solving for c gives us that
c = 4d
The last equation says that of the total number of animals, 440, half the goats and half the ducks got away, leaving only 320 animals behind. The last equation, the tricky one, is:
and simplifying that:
and because nobody hates fractions more than I do, I'm going to get rid of them by multiplying everything by 2 to get:
-g - d = -240
We've got these equations now, but what I'm going to do is to sub in what c equals (c = 4d) for c in the first equation:
g + d + 4d = 440 and
g + 5d = 440 and pair that with the one right above:
-g - 1d = -240 and use elimination to solve. The g's cancel each other out, leaving us with 4d = 200 and d = 50. So there were 50 ducks originally. Now we will sub that in to solve for c:
c = 4d so
c = 4(50) and
c = 200. Now we will sub both those values into the very first equation we put together to solve for g:
g + 200 + 50 = 440 and
g + 250 = 440 so
g = 190.
Add them all together just to be sure we have the 440 that we were told we had in the beginning (and we do, so we're all done!)