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3 years ago

Determine the point of intersection of the lines x + y = 4 and 2x + 3y = 12

Mathematics

1 answer:

tangare [24]3 years ago

6 0

Answer:

(2,2)

Step-by-step explanation:

x=4-y

2 ( 4 - y )+ 3y= 12

2y = 12 -8

y= 2

substitute y in first eq. :

x=4 - 2

x= 2

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PLZ HELP/...... :) :?

alexdok [17]

Answer:

3 gallons of diesel weight = 22.2 pounds

The constant of variation = 7.4

The quantities vary directly

Step-by-step explanation:

Given:

5 gallons of gas weights = 37 pounds

To find

a) the weight of 3 gallons of gas.

b) if the quantities vary directly or inversely.

c) the constant of variation.

Solution:

Applying unitary method to find weight of 3 gallons of gas.

If 5 gallons weight = 37 pounds

Then, 1 gallon will weight = $\frac{37}{5}$ =7.4 pounds

Thus, 3 gallons will weight = $3\times 7.4$ = 22.2 pounds

Listing out the data we have:

1 gallon = 7.4 pounds

3 gallons = 22.2 pounds

5 gallons = 37 pounds

From the data, we find out that as the number of gallons of gas increases the weight of gas also increases. This shows that these quantities are directly proportional to each other.

The unit rate of the quantities is called the constant of variation.

Unit rate: 7.4 pounds per gallon

Thus, the constant of variation = 7.4

8 0

3 years ago

A coin weighs 4/15 ounces. A different coin weighs 1/15 ounces. How much do the two coins weigh together? Write your answer as a

olchik [2.2K]

Answer:

1/3

Step-by-step explanation:

4/15 + 1/15 = 5/15

simplified its 1/3

7 0

3 years ago

Someone please help with this and explain your answer!!! I will give brainliest if correct!

Radda [10]

Answer:

the answer is a.

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Please help me!!!!!!!

hammer [34]

Answer:no

Step-by-step explanation:

3 0

3 years ago

Help me out with this

elena55 [62]

Let's follow the transformations that happen to A, to get to A' and A''.

Point A is at (-5, -2)

It moves to (-5, 2) which is where A' is located. Note the x coordinate stays the same while the y coordinate flips from negative to positive. This must mean we applied a reflection over the x axis.

That rule in general is $(x, y) \rightarrow (x,-y)$

------------------------------------

Now compare A'(-5,2) and A''(1,4). We can shift A' 6 units to the right and then 2 units up so we move from A' to A''.

Algebraically this is stated as $(x,y) \rightarrow (x+6, y+2)$

Whatever the x coordinate is, add 6 to it. For the y coordinate, we add on 2.

Applying that rule to B'(-1,2) gets us to

$(-1,2) \rightarrow (-1\textbf{+6}, 2\textbf{+2}) = (5,4)$

which is the proper location of B''

The same applies to moving C' to C''

$C' = (-5, 0) \rightarrow (-5\textbf{+6}, 0\textbf{+2}) = (1, 2) = C''$

-------------------------------------------

In summary, we started off by reflecting over the x axis. Then we applied the translation rule of "shift to the right 6 units, shift up 2 units".

In terms of algebra, combining the rules $(x,y) \rightarrow (x,-y)$ and $(x,y) \rightarrow (x+6, y+2)$ will have us end up with $(x,y) \rightarrow (x+6, -y+2)$

3 0

4 years ago