All categories

3 years ago

Just need to know the first one

Mathematics

1 answer:

Wittaler [7]3 years ago

7 0

By solving the equations by elimination, we get x = -2 and y = 4.

Step-by-step explanation:

Step 1; 4x + 2y = 0, take this as equation 1 and

-4x -9y = -28, take this as equation 2.

Since the coefficient of x in equation 1 is 4 and the coefficient of x in equation 2 is -4, simply adding the two equations, we should be able to eliminate x and solve for y.

Step 2; Adding equation 1 and 2, we get

4x + 2y -4x -9y = 0 - 28,

2y - 9y = -7y = -28,

y = $\frac{-28}{-7}$ = 4.

Substituting the value of y in equation 1 we determine the value of x.

4x + 2y = 4x + (2 × 4) = 0, 4x = -8,

x = $\frac{-8}{4}$ = -2.

So for the given equation, x = -2 and y = 4.

You might be interested in

Find the measure of the angles

wel

Step-by-step explanation:

Make sure the bottom line of the angle points to 0. Then slowly go up until the other line hits a number. In this case, it's 40 degrees

8 0

2 years ago

Write the mixed number as an improper fraction.<br> -4 1/5

Sophie [7]

-(4 1/5)
5(4)+1 = 21
Thus the answer would be -21/5

4 0

3 years ago

Read 2 more answers

John bought 4 pounds of hot dogs for his party. How many ounces of hot dogs did John buy?

Sergio039 [100]

64 ounces

Because,

1 pound = 16 ounces

4 x 16 = 64 ounces.

4 0

3 years ago

Read 2 more answers

Which equation can be used to represent the statement?

Arte-miy333 [17]

You need to specify the statement needed to use the equation. Thank you. I will then answer it if needed.

3 0

3 years ago

A 500-gallon tank initially contains 220 gallons of pure distilled water. Brine containing 5 pounds of salt per gallon flows int

Wittaler [7]

Answer: The amount of salt in the tank after 8 minutes is 36.52 pounds.

Step-by-step explanation:

Salt in the tank is modelled by the Principle of Mass Conservation, which states:

(Salt mass rate per unit time to the tank) - (Salt mass per unit time from the tank) = (Salt accumulation rate of the tank)

Flow is measured as the product of salt concentration and flow. A well stirred mixture means that salt concentrations within tank and in the output mass flow are the same. Inflow salt concentration remains constant. Hence:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = \frac{d(V_{tank}(t) \cdot c(t))}{dt}$

By expanding the previous equation:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt} + \frac{dV_{tank}(t)}{dt} \cdot c(t)$

The tank capacity and capacity rate of change given in gallons and gallons per minute are, respectivelly:

$V_{tank} = 220\\\frac{dV_{tank}(t)}{dt} = 0$

Since there is no accumulation within the tank, expression is simplified to this:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt}$

By rearranging the expression, it is noticed the presence of a First-Order Non-Homogeneous Linear Ordinary Differential Equation:

$V_{tank} \cdot \frac{dc(t)}{dt} + f_{out} \cdot c(t) = c_0 \cdot f_{in}$ , where $c(0) = 0 \frac{pounds}{gallon}$ .

$\frac{dc(t)}{dt} + \frac{f_{out}}{V_{tank}} \cdot c(t) = \frac{c_0}{V_{tank}} \cdot f_{in}$

The solution of this equation is:

$c(t) = \frac{c_{0}}{f_{out}} \cdot ({1-e^{-\frac{f_{out}}{V_{tank}}\cdot t }})$

The salt concentration after 8 minutes is:

$c(8) = 0.166 \frac{pounds}{gallon}$

The instantaneous amount of salt in the tank is:

$m_{salt} = (0.166 \frac{pounds}{gallon}) \cdot (220 gallons)\\m_{salt} = 36.52 pounds$

3 0

3 years ago