The waiter places a bowl of soup in front of Igor. In a counterclockwise direction, he passes the soup to Elan who then passes it to Abbey. Which two rotations about the center of the table describe passing the soup?
A) first 80° and then 80°
B) first 120° and then 120°
C) first 144° and then 144°
D) first 160° and then 160°

Answers

Answer 1

Answer: $\alpha=(360^o)/(12)=30^o\n\nIgor-Elan\to4\cdot30^o=120^o\n\nElan-Abbey\to4\cdot30^o=120^o\n\nAnswer:C$

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If f(x)=-5x-1 and g (x)= √x-6 what is (f º g)(7)

Answers

$(fog)(7) = -6$

Step-by-step explanation:

The function composition is achieved by putting the second function in first function in place of independent variable.

Given functions are:

$f(x) = -5x-1\ng(x) =√(x-6)$

In order to find (fog)(x) we will put function g in function f in place of x

$(fog)(x) = -5(g(x)) -1\n= -5√(x-6)-1$

Since we have to find (fog)(7)

Putting 7 in place of x

$= -5√(7-6) - 1\n=-5√(1)-1\n= -5(1) -1\n= -5-1\n=-6$

Hence,

$(fog)(7) = -6$

Keywords: Functions, composition

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John and Julie are planning to have a new house built the architect designs a house instant them the blueprints skilled at the art architect used on the blueprints is 2 1/2 inches equals 10 feet the living room what are the actual dimensions of 12‘ x 16‘ what are the dimensions on the blueprints

Answers

Answer:

3"x4

Step-by-step explanation:

The symbol for a foot is "ft", sometimes denoted by a prime(') , also, the inch is denoted by a double prime(").

Given

2 1/2inces (2.5") blue print represents 10ft living room

We are told that the dimension of the room on the blueprint is

12'x16'

Let us convert 12' to inches

2.5" represents 10'

X ' will be 12'

Cross multiplying

X=(2.5*12)/10

X=3"

Let us convert 16' to inches

2.5" represents 10'

Y ' will be 16'

Cross multiplying

Y=(2.5*16)/10

Y=4"

the dimension of the blue print is

3"x4"

For questions 1-7, use the following functions to answer the questions: f(x)x^2+5x g(x)=3x-4/2

Answers

Answer:

f(4) = (4)² + 5(4) = 36.

g(9) = [3(9) - 4]/2 = 23/2.

f(-3) = (-3)² + 5(-3) = -6.

g(-6) = [3(-6) - 4]/2 = -11.

Set f(x) = 14.

=> x² + 5x = 14

=> x² + 5x - 14 = 0

=> (x + 7)(x - 2) = 0

=> x = -7 or x = 2.

Set g(x) = -28.

=> (3x - 4)/2 = -28

=> 3x - 4 = -56

=> 3x = -52

=> x = -52/3.

Answer:

11.5

-11

-2, 7

-17.333 / - 17⅓

Step-by-step explanation:

f(4) = 4² + 5(4) = 16+20 = 36

g(9) = 3(9)-4 ÷ 2 = 23÷2 = 11.5

f(-3) = (-3)²+5(-3) = 9 - 15 = 6

g(-6) = 3(-6)-4 ÷ 2 = - 22 ÷ 2 = - 11

f(x) = 14

x² - 5x = 14

x² - 5x - 14 = 0

(x+2) (x-7) = 0

x = - 2 or x = 7

g(x) = -28

$(3x - 4)/(2) = - 28$

3x - 4 = - 56

3x = - 52

x = - 52/3 = - 17 ⅓

Dennis is getting balloons for his grandfather's birthday party. He wants each balloon string to be 9 feet long. At the party store, string is sold by the yard. If Dennis wants to get 69 balloons, how many yards of string will he need?

Answers

Answer:

207

Step-by-step explanation:

9ft=3yrds

3x69=207

Which correctly gives the location of the point (18, 0)? A. x-axis B. y-axis C. Quadrant I D. Quadrant II

Answers

it would be A cuz 18,0 are in the x-axis not quadrant

2. Juan worked 2.5 hours and earned $37.00. Lisa was paid $42.00 for 3 hours of work. Which of the following statements is true?

Answers

The true statement about the juan and lisa is Juan made a higher rate of pay than Lisa.

Juan made a lower rate of pay because he made less money.

This statement is false. Juan and Lisa made a similar rate of pay per hour ($14.80 and $14.00 respectively).

Lisa made a better rate of pay because she made more money.

This statement is false. The total earnings do not determine the rate of pay; the hourly rate does.

Lisa said she made a better rate of pay because her rate was $14 an hour.

This statement is false. Lisa's actual rate was $14.00 per hour, not $14.00 as stated.

Juan said he made a better rate of pay because he was paid $14.80 an hour.

This statement is true. Juan's hourly rate was $14.80, which is higher than Lisa's rate of $14.00 per hour.

To calculate the rate of pay, we divide the money earned by the hours worked.

Juan's rate of pay is $37.00 / 2.5 hours = $14.80 per hour.

Lisa's rate of pay is $42.00 / 3 hours = $14.00 per hour.

Therefore, Juan made a higher rate of pay than Lisa.

Answer: Juan said he made a better rate of pay because he was paid $14.80 an hour.

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The following question may be like this:

Juan worked 2.5 hours and earned $37.00. Lisa was paid $42.00 for 3 hours of work. Which of the following statements is true?

Juan made a lower rate of pay because he made less money.

Lisa made a better rate of pay because she made more money.

Lisa said she made a better rate of pay because her rate was $14 an hour.

Juan said he made a better rate of pay because he was paid $14.80 an hour.

Answer:

2. Juan worked 2.5 hours and earned $37.00. Lisa was paid $42.00 for 3 hours of work. Which of the following statements is true?

Lisa said she made a better rate of pay because her rate was $14 an hour.

Answer: Juan said he made a better rate of pay because he was paid $14.80 an hour.

Juan made a lower rate of pay because he made less money.

Lisa made a better rate of pay because she made more money.

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Order the following masses from least to greatest: 500 g, 50 kg, 5,000 mg

Whats ten hundredths in standard form

a taxi driver charges a fixed rate of r to pick up a passenger.in addition, the taxi driver charges a rate of m for each mile driven.write a formula to represent t, the total amount this taxi driver will charge for a trip of n miles