Are these lines parallel, perpendicular, or neither. y=4x-1and 12x=3y+7

A tank and a pail contained a total of 962 ml of water. When 250 ml of water was poured from the pail to the tank, the amount of

Allisa [31]

By solving a system of equations, we will see that the pail originally contained 382.9 ml.

<h3>How to write the system of equations?</h3>

First, we need to define the variables, we will use:

T = amount of water in the tank.
P = amount of water in the pail.

First, we know that the total amount of water is 962 ml, then we have:

P + T = 962 ml.

We also know that if we pour 250 ml from the pail to the tank, the amount of water in the tank will be 12 times the amount of water in the pail, this is written as:

T + 250ml = 12*(P - 250ml)

Then the system of equations is:

P + T = 962 ml

T + 250ml = 12*(P - 250ml)

To solve this, first, we need to isolate one of the variables in one of the equations, I will isolate T in the first one:

T = 962 ml - P

Now we replace this into the other equation to get:

(962 ml - P) + 250ml = 12*(P - 250ml)

Now we can solve this for P.

962 ml + 250 ml - P = 12*P - 12*250 ml

1,212 ml - P = 12*P - 3,000 ml

1,212 ml + 3,000 ml = 12*P - P

(4,212 ml)/11 = P = 382.9 ml

So the pail originally contained 382.9 ml

If you want to learn more about systems of equations, you can read:

brainly.com/question/13729904

4 0

2 years ago

What's the solution of 6(3-2x)=54 ?

Nitella [24]

Answer:

X=-3

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

The graph of a proportional relationship passes through the points (0.5, 6) and (x,24). Find x.

laila [671]

Answer:

..................

Step-by-step explanation:

3 0

3 years ago

Please help!! :) Thank you!

Klio2033 [76]

Let's complete the square

f(x) = x^2 + 6x + 8

y = x^2 + 6x + 8

y-8 = x^2 + 6x

y-8+9 = x^2+6x+9 .... see note below

y+1 = (x+3)^2

y = (x+3)^2-1

note: I added 9 to both sides due to taking half of the 6, and then squaring that result.

We'll restrict x such that $x \ge -3$ to ensure that this function is one-to-one.

Now we need to swap x and y, and solve for y to get the inverse

y = (x+3)^2 - 1

x = (y+3)^2 - 1

x+1 = (y+3)^2

(y+3)^2 = x+1

y+3 = sqrt(x+1)

y = sqrt(x+1)-3

g(x) = sqrt(x+1)-3 is the inverse

The graph is shown below. The original function is in red. The inverse is in blue. The inverse is the result of reflecting the red curve over the dashed line y = x. So this explains why x and y swap places. Consequently, the domain and range also swap as well.

4 0

3 years ago

Eighty seven decreased by three times a number is greater than one hundred sixty five

Nata [24]

87-3x>165

-3x> (165-85)

-3x>80

80/-3 = -26.666

check;

87-3*(-26)=165

so x < -26

4 0

3 years ago