What is the solution to this 2b+9 when b=3

Write a series of rigid motions that transform pentagon ABCDE to pentagon A′B′C′D′E′

worty [1.4K]

Answer:

We need the following three rigid motions:

i) Reflection around y-axis, ii) Translation three units in the -y direction, iii) Translation four units in the -x direction.

Step-by-step explanation:

We need to perform three operations on pentagon ABCDE to create pentagon A'B'C'D'E':

i) Reflection around y-axis:

$(x',y') = (-x,y)$ (Eq. 1)

ii) Translation three units in the -y direction:

$(x'',y'') = (x', y'-3)$ (Eq. 2)

iii) Translation four units in the -x direction:

$(x''',y''') = (x''-4, y'')$ (Eq. 3)

We proceed to proof the effectiveness of operations defined above by testing point D:

1) $D(x,y) = (-1, 4)$ Given.

2) $(x',y') = (1,4)$ By (Eq. 1)

3) $(x'',y'') = (1, 1)$ By (Eq. 2)

4) $D'(x,y) = (-3,1)$ By (Eq. 3)/Result

7 0

3 years ago

What is the sum of the geometric sequence −4, 24, −144, ... if there are 8 terms?

Helga [31]

Answer:

The sum of 8 geometric sequence is 959780

Step-by-step explanation:

We are given

this sequence is geometric

-4 , 24 , -144

First term is -4

so, $a_1=-4$

now, we can find common ratio

$r=\frac{24}{-4}=-6$

we can use formula

$S_n=a_1(\frac{1-r^n}{1-r} )$

n=8

now, we can plug values

$S_8=-4(\frac{1-(-6)^{8}}{1+6} )$

now, we can simplify it

and we get

$S_8=959780$

4 0

3 years ago

Anne has 3 pairs of blue socks. If she randomly selects a pair of socks.what is the probability that it is a blue?

V125BC [204]

Answer:

I hate that clfufjwwjdkfkrifjeidoqodjfrjkejakxkdk

Step-by-step explanation:

5 0

3 years ago

What is the slope of the line that passes through the points (-4, -2)(−4,−2) and (-4, -22) ?(−4,−22)? Write your answer in simpl

Anestetic [448]

The line is vertical, so the slope is infinite

Step-by-step explanation:

Given two points with coordinates $(x_1, y_1)$ and $(x_2,y_2)$ , the slope of the line passing through the two points is given by the equation

$m=\frac{y_2-y_1}{x_2-x_1}$

In this problem, the coordinates of the two points are:

$(x_1,y_1)=(-4,-2)$

and

$(x_2,y_2)=(-4,-22)$

which means:

$x_1=-4\\y_1=-2\\x_2=-4\\y_2=-22$

Substituting all these values into the equation of m, we find the slope of the line:

$m=\frac{-22-(-2)}{-4-(-4)}=\frac{-20}{0}=\infty$

The slope is infinite: this is because the line is vertical.

Learn more about slope of a line:

brainly.com/question/4152194

brainly.com/question/12941985

#LearnwithBrainly

7 0

3 years ago

A school debate team has four girls and six boys. A total of four of the team members will be chosen to participate in the distr

alex41 [277]

Procedure:

1) calculate the number of diferent teams of four members that can be formed (with the ten persons)
2) calculate the number of teams tha meet the specification (two girls and two boys)
3) Divide the positive events by the total number of events: this is the result of 2) by the result in 1)

Solution

1) the number of teams of four members that can be formed are:

10*9*8*7 / (4*3*2*1) = 210

2) Number of different teams with 2 boys and 2 girls = ways of chosing 2 boys * ways of chosing 2 girls

Ways of chosing 2 boys = 6*5/2 = 15
Ways of chosing 2 girls = 4*3/2 = 6

Number of different teams with 2 boys and 2 girls = 15 * 6 = 90

3) probability of choosing one of the 90 teams formed by 2 boys and 2 girls:

90/210 = 3/7

7 0

3 years ago