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3 years ago

The equation of a line is x + 5y = 12. What is the y-intercept of the line

1 answer:

4 0

Simple...

remember isolate the variable...

x+5y=12

x+5y=12
-x

5y=12-x

Now divide y 5....

$\frac{5y}{5} = -\frac{x}{5} + \frac{12}{5}$

The y-intercept would be....

$\frac{12}{5}$

Thus, your answer.

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Suppose two dice are tossed and the numbers on the upper faces are observed. Let S denote the set of all possible pairs that can

Thepotemich [5.8K]

Answer:

▪A = {(1,2) (1,4) (1,6) (2,2) (2,4) (2,6) (3,2) (3,4) (3,6) (4,2) (4,4) (4,6) (5,2) (5,4) (5,6) (6,2) (6,4)(6,6)}

▪C bar = {(2,2) (2,4) (2,6) (4,2) (4,4) (4,6) (6,2) (6,4) (6,6)}

▪A∩B = {(2,2) (2,4) (2,6) (4,2) (4,4) (4,6) (6,2) (6,4) (6,6)}

▪A∩B bar = {(1,2) (1,4) (1,6) (3,2) (3,4) (3,6) (5,2) (5,4) (5,6)}

▪A bar∪B = {(1,1) (1,3) (1,5) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (3,1) (3,3) (3,5) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (5,1) (5,3) (5,5) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)}

▪A bar∩C = {(1,1) (1,3) (1,5) (2,1) (2,3) (2,5) (3,1) (3,3) (3,5) (4,1) (4,3) (4,5) (5,1) (5,3) (5,5) (6,1) (6,3) (6,5)}

Step-by-step explanation:

S = {(1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)}

A = {(1,2) (1,4) (1,6) (2,2) (2,4) (2,6) (3,2) (3,4) (3,6) (4,2) (4,4) (4,6) (5,2) (5,4) (5,6) (6,2) (6,4)(6,6)} (second die is even)

B = {(1,1) (1,3) (1,5) (2,2) (2,4) (2,6) (3,1) (3,3) (3,5) (4,2) (4,4) (4,6) (5,1) (5,3) (5,5) (6,2) (6,4) (6,6)} (sum of the two numbers is even)

C = {(1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,3) (2,5) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,3) (4,5) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,3) (6,5)} (at least one in the pair is odd i.e one of the pair is odd or both are odd)

A bar = {(1,1) (1,3) (1,5) (2,1) (2,3) (2,5) (3,1) (3,3) (3,5) (4,1) (4,3) (4,5) (5,1) (5,3) (5,5) (6,1) (6,3) (6,5)} (the pairs that are not in A)

B bar = {(1,2) (1,4) (1,6) (2,1) (2,3) (2,5) (3,2) (3,4) (3,6) (4,1) (4,3) (4,5) (5,2) (5,4) (5,6) (6,1) (6,3) (6,5)} (the pairs that are not in B)

C bar = {(2,2) (2,4) (2,6) (4,2) (4,4) (4,6) (6,2) (6,4) (6,6)} (the pairs that are not in C)

▪A = {(1,2) (1,4) (1,6) (2,2) (2,4) (2,6) (3,2) (3,4) (3,6) (4,2) (4,4) (4,6) (5,2) (5,4) (5,6) (6,2) (6,4)(6,6)}

▪C bar = {(2,2) (2,4) (2,6) (4,2) (4,4) (4,6) (6,2) (6,4) (6,6)}

▪A∩B = {(2,2) (2,4) (2,6) (4,2) (4,4) (4,6) (6,2) (6,4) (6,6)} (intersection: the pairs that are common to both A and B)

▪A∩B bar = {(1,2) (1,4) (1,6) (3,2) (3,4) (3,6) (5,2) (5,4) (5,6)} (intersection: the pairs that are common to both A and B bar)

▪A bar∪B = {(1,1) (1,3) (1,5) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (3,1) (3,3) (3,5) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (5,1) (5,3) (5,5) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)} (union: all the pairs in A bar and B )

▪A bar∩C = {(1,1) (1,3) (1,5) (2,1) (2,3) (2,5) (3,1) (3,3) (3,5) (4,1) (4,3) (4,5) (5,1) (5,3) (5,5) (6,1) (6,3) (6,5)} (intersection: the pairs that are common to both A bar and C)

6 0

3 years ago

Consider the line y=4x-4.

erica [24]

9514 1404 393

Answer:

parallel: y = 4x -6
perpendicular: y = -1/4x +27/4

Step-by-step explanation:

If we want the new line to be written in slope-intercept form, we need to find the new value of the y-intercept. The equation of the line is ...

y = mx +b . . . . . . . for slope m and y-intercept b

Solving for b gives ...

b = y -mx . . . . . . . subtract mx from both sides.

The values of x and y come from the point we want the line to pass through. The value of m will be the same for the parallel line as for the given line: 4. For the perpendicular line, it will be the opposite reciprocal of this: -1/4.

<u>Parallel line</u>

b = 6 -4(3) = 6 -12 = -6

y = 4x -6

Perpendicular line

b = 6 -(-1/4)(3) = 6 +3/4 = 27/4

y = -1/4x +27/4

4 0

2 years ago

What is the equation in slope intercept form of the line that passes through the points (-4, 2) and (12, 6)

maksim [4K]

Answer:

search in anywhere

Step-by-step explanation:

or do it in calculator

or ask from your teacher

ans : A) y= 0.25x + 3

B) y= 0.25x - 4.5

C) y= 4x + 18

D) y= 4x - 42

7 0

2 years ago

In training for a swim meet, Logan swam 750 meters in 1/3 of an hour. His swimming partner Mila, swam 2/3 of Logan's distance in

Brut [27]

Answer:

speed of Logan is 37.5 m/minutes

speed of Milo is 33.33 meters per minutes

Speed of Logan is greater than speed of Milo

difference in speed = 37.5 - 33.33 = 4.17 meters per minutes

Step-by-step explanation:

we will calculate speed in meters per minutes

we know 1 hour = 60 minutes and

1 minutes = 60 seconds

speed = distance/time

____________________________________

For Logan

distance = 750 meters

time = 1/3 of hour = 1/3 *60 minutes = 20 minutes

speed = 750/20 = 37.5 meters per minute

__________________________________________________

For milo

distance = 2/3 of Logan's distance = 2/3 * 750 meters = 500 meters

time = 1/4 of hour = 1/4 *60 minutes =15 minutes

speed = 500/15 = 33.33 meters per minute

Thus, speed of Logan is 37.5 m/minutes

speed of Milo is 33.33 meters per minutes

Speed of Logan is greater than speed of Milo

difference in speed = 37.5 - 33.33 = 4.17 meters per minutes

Step-by-step explanation:

4 0

2 years ago

Using coupons, you spend $120 grocery shopping. This is 80% of the total retail price of the groceries. How much would you spend

mr Goodwill [35]

Answer: The correct answer is $150.

Step-by-step explanation: If you did not use the coupons while shopping you would have spent $150. The method to calculate this is to divide the amount that you paid by the percentage that you paid.

The formula that you need to use is $120/.8 = $150.

7 0

3 years ago