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2 years ago

Solve 15k - 4 = 5k + 16

Mathematics

2 answers:

sveta [45]2 years ago

8 0

Answer:

Step-by-step explanation:

Solve 15k - 4 = 5k + 16

Subtract 5k from both sides

15k - 5k - 4 = 5k - 5k + 16

10k - 4 = 16

Add 4 to both sides

10k -4+4 = 16+4

10k = 20

Divide both sides by 10

10k/10 = 10/10

K = 2

I hope this was helpful, please mark as brainliest

dolphi86 [110]2 years ago

3 0

Answer:

k = 2

Step-by-step explanation:

Given

15k - 4 = 5k + 16 ( subtract 5k from both sides )

10k - 4 = 16 ( add 4 to both sides )

10k = 20 ( divide both sides by 10 )

k = 2

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Help please will mark brainliest!!!

solniwko [45]

Answer:

945

Step-by-step explanation:

8 0

2 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

Please solve the following questions!!

alexandr402 [8]

Answer:

3. The missing angle is 56°

4. x = 7

Step-by-step explanation:

We know sum of 3 angles in a triangle is 180°.

Looking at the top triangle, we can figure out the third angle. Let third angle be x:

85 + 35 + x = 180

120 + x = 180

x = 180 - 120

x = 60

<u>The angle "x" and the angle that is missing from the "bottom" triangle in the figure, are vertical angles, and hence, are EQUAL.</u>

So the bottom triangle now has 2 angles, 60 and 64 (given). Let the third angle be y(the one with a question mark). So we can write:

60 + 64 + y = 180

124 + y = 180

y = 180 - 124

y= 56

This is the missing angle.

10x - 5 AND 8x + 9 are vertical angles. They ARE EQUAL.

Thus we can write the equation:

(10x-5) = (8x+9)

10x-8x=9+5

2x=14

x=14/2

x=7

So x = 7

5 0

3 years ago

Bashir find some nickels and pennies under the couch cushions how much (money in dollars) does he have if he has 120 nickels and

s344n2d4d5 [400]

Answer:

Step-by-step explanation:

4 0

2 years ago

Add. Express your answer in standard form. (−3+5i)+(6+2i). Enter your answer in the box.

evablogger [386]

You add/subtract complex numbers simply by adding/subtracting real parts and imaginary parts.

So, the real part of this sum is the sum of the real parts:

$-3+6=3$

And the imaginary part of this sum is the sum of the imaginary parts:

$5i+2i=7i$

So, you have

$(-3+5i)+(6+2i) = 3+7i$

7 0

3 years ago