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3 years ago

Which of the following represents the translation of M (8,-2) along vector<-5, 1 > and its reflection

Mathematics

1 answer:

Ulleksa [173]3 years ago

4 0

Step-by-step explanation:

M(8.-2), M'(x,y) , $$$\overrightarrow{v}$ =(-5,1)

$$$\overrightarrow{MM'} = $$\overrightarrow{v}$

--> x - 8 = -5 --> x= 3

---> y+2 = 1 --> y =-1

so M'(3,-1) and its reflection y-axis is (-3,-1)

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A certain organization recommends the use of passwords with the following format: vowel commavowel, consonant comma consonant c

zimovet [89]

The password format is = inpray93

vowel , consonant, consonant, consonant, vowel, consonant, number, number.

There are 21 consonants, 5 vowels and 10 number choices (0-9)

Since, there are 21 consonants and repetition is allowed so for 2nd, 3rd, 4th, and 6th positions 21 choices are available. For 1st and 5th positions, 5 choices are available and for 7th and 8th position there are 10 choices (0 to 9).

Passwords are not case sensitive which means upper case and lower case letters are same.

So, the number of passwords can be =

$5\times21\times21\times21\times5\times21\times10\times10$

= 486202500

Part (b) question is not given. But it can be opposite to the first part i.e when the password letters are case sensitive.

This means all the letters are different.

So, number of passwords will be =

$10\times42\times42\times42\times10\times42\times10\times10$

= 31116960000

4 0

3 years ago

Fill in the blanks

katen-ka-za [31]

1 - 9
2 - 87
3 - -2
4 - -9
that’s the answers for them :), have a great day !! :)

5 0

2 years ago

What is the equation of the quadratic graph with a focus of (3, 1) and a directrix of y = 5?

lbvjy [14]

Answer:

The equation of the quadratic graph is f(x)= - (1/8) (x-3)^2 + 3 (second option)

Step-by-step explanation:

Focus: F=(3,1)=(xf, yf)→xf=3, yf=1

Directrix: y=5 (horizontal line), then the axis of the parabola is vertical, and the equation has the form:

f(x)=[1 / (4p)] (x-h)^2+k

where Vertex: V=(h,k)

The directix y=5 must intercept the axis of the parabola at the point (3,5), and the vertex is the midpoint between this point and the focus:

Vertex is the midpoint between (3,5) and (3,1):

h=(3+3)/2→h=6/2→h=3

k=(5+1)/2→k=6/2→k=3

Vertex: V=(h,k)→V=(3,3)

p=yf-k→p=1-3→p=-2

Replacing the values in the equation:

f(x)= [ 1 / (4(-2)) ] (x-3)^2 + 3

f(x)=[ 1 / (-8) ] (x-3)^2 + 3

f(x)= - (1/8) (x-3)^2 + 3

4 0

3 years ago

Kim wants to know how many families in her small neighborhood of 70 homes would participate in a neighborhood sports event. She

tatuchka [14]

Answer:

Yes, this is a valid inference because she took a random sample of the neighborhood.

Step-by-step explanation:

As her survey was non bias and completely random and she found that 15% of the families would participate in the event. She claims that 15% of the neighborhood families would be expected to participate in the sports event. So, yes, this is a valid inference because she took a random sample of the neighborhood.

7 0

3 years ago

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A math class is having a discussion on how to determine if the expressions 4 x minus x + 5 and 8 minus 3 x minus 3 are equivalen

dedylja [7]

Answer:

They are NOT equivalent

Step-by-step explanation:

4x-x+5 and 8-3x-3

<u>simplify</u>

3x+5 and 5x-3

5 0

3 years ago

Read 2 more answers