Definition: A rigid transformation (also called an isometry) is a transformation of the plane that preserves length.
Four types of isometries:
1. Translation -- sliding a shape from one spot to another on the xy-plane;
2. Reflection -- creating a mirror image of a shape by reflecting a shape over a line, called the axis of reflection, on the xy-plane;
3. Rotation -- rotating a shape around a point, called the center of rotation, on the xy-plane;
4. Glide reflection -- a composite transformation which is a translation followed by a reflection in line parallel to the direction of translation.
Translations, reflections, and rotations don't change the shape or size of the shape being transformed, so we can see that these three types of transformations are isometric, the glide reflection doesn't change the shape or size of the shape being transformed, but changes orientation.
A composition or sequence of isometries occurs when two or more transformations are combined to form a new transformation. In a composition, one transformation produces an image upon which the other transformation is then performed (as for the glide reflection). The composition of isometries is always the isometry (preserves lengths).
Answer: correct choice is B.
Let's just make 15 students a group. how many groups are there if there r 135 student? 135/15 = 9 groups.
so if each group have 4 adults just multiply 9 by 4,
therefore there will be 36.adults.
The value of f(3) can be calculating by putting the variable x equal to 3 , x=3 which gives:
f(3)=81+3e-0.7*3=81+3e-2.1
But there is one more unknown in the equation e. e is a constant called Euler's number, after the Swiss mathematician Leonhard Euler.
e=2.7182818284590.....
Rounding to the nearest hundredth the thousandths place is used to determine whether the hundredths place rounds up or stays the same.
Rounding the Euler's constant to the nearest hundredths gives:
e=2.72
So, f(3)=81+3*2.72-2.1=81+8.16-2.1=87.06
Answer:
A real number
Step-by-step explanation:
a = interest rate of first CD
b = interest rate of second CD
and again, let's say the principal invested in each is $X.
![\bf a-b=3\qquad \implies \qquad \boxed{b}=3+a~\hfill \begin{cases} \left( \frac{a}{100} \right)X=240\\\\ \left( \frac{b}{100} \right)X=360 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \left( \cfrac{a}{100} \right)X=240\implies X=\cfrac{240}{~~\frac{a}{100}~~}\implies X=\cfrac{24000}{a} \\\\\\ \left( \cfrac{b}{100} \right)X=360\implies X=\cfrac{360}{~~\frac{b}{100}~~}\implies X=\cfrac{36000}{b} \\\\[-0.35em] ~\dotfill\\\\](https://tex.z-dn.net/?f=%5Cbf%20a-b%3D3%5Cqquad%20%5Cimplies%20%5Cqquad%20%5Cboxed%7Bb%7D%3D3%2Ba~%5Chfill%20%5Cbegin%7Bcases%7D%20%5Cleft%28%20%5Cfrac%7Ba%7D%7B100%7D%20%5Cright%29X%3D240%5C%5C%5C%5C%20%5Cleft%28%20%5Cfrac%7Bb%7D%7B100%7D%20%5Cright%29X%3D360%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cleft%28%20%5Ccfrac%7Ba%7D%7B100%7D%20%5Cright%29X%3D240%5Cimplies%20X%3D%5Ccfrac%7B240%7D%7B~~%5Cfrac%7Ba%7D%7B100%7D~~%7D%5Cimplies%20X%3D%5Ccfrac%7B24000%7D%7Ba%7D%20%5C%5C%5C%5C%5C%5C%20%5Cleft%28%20%5Ccfrac%7Bb%7D%7B100%7D%20%5Cright%29X%3D360%5Cimplies%20X%3D%5Ccfrac%7B360%7D%7B~~%5Cfrac%7Bb%7D%7B100%7D~~%7D%5Cimplies%20X%3D%5Ccfrac%7B36000%7D%7Bb%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C)
