Learn how to solve quadratic equations like x^2 =36 or (x-2)^2=49. ... Not all quadratic equations are solved by immediately taking the square .
We have to select all of the transformations that could change the location of the asymptotes of a cosecant of secant function.
So given function can be written as:
y=csc( sec(x))
First we need to determine the location of asymptote which is basically a line that seems to be touching the graph of function at infinity.
From attached graph we see that Asymptotes (Green lines) are vertical.
So Vertical shift or vertical stretch will not affect the location of asymptote because moving up or down the vertical line will not change the position of any vertical line.
only Left or right side movement will change the position of vertical asymptote. Which is possible in Phase shift and period change.
Hence Phase shift and Period change are the correct choices.
Make a proportion to get the answer the proportion will be
to give you the answer of 37.5
The middle section is n(n+1)
The top row is n+2
The bottom row is 2n+1
So the rule for the total number of tiles will be the sum of the above rules...
s(n)=n(n+1)+n+2+2n+1
s(n)=n^2+n+n+2+2n+1
s(n)=n^2+4n+3
22.
pythagorean theorem says legs a and b and hypotenuse c of a right triangle are related via the equation c²=a²+b². in other words, adding the sum of the squares of the legs get you the square of the hypotenuse
if the hypotenuse is 4 meters long, c = 4.
if one leg is 3 meters long, we can choose either a or b to be 3. it does not really matter. let us choose a = 3. now we have to find b.
if we have c²=a²+b², we can solve for b.
subtract a² both sides to get c²-a²=b², and then square root both sides to get
b = √(c²-a²)
plugging in our info we get
b = √(4²-3²) = √(16 -9) = √7
so the answer is √7 meters for 22
23
two triangles are similar, then the proportion of their sides are the same. the propotion between the smaller triangles' hypotenuse and 2cm leg is 5cm/3cm.
notice how the bigger triangle just have a doubled hypotenuse. therefore, the bigger triangle's x and y are just the corresponding smaller triangle values doubled.
x = 6 and y = 8
