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3 years ago

What property would you use to solve m+6=-4

Mathematics

1 answer:

Marrrta [24]3 years ago

8 0

You would subtract 6 from both sides in order to get m by itself. When you do this you get m=-10

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A tank is filled at a constant rate. 10 minutes after filling is started, the tank contains 4.8L of water. After 35 minutes the

Mashcka [7]

Answer:

Part A)

0.1 liters per minute.

Part B)

There was initially 3.8 liters of water.

$\displaystyle V(t) = 0.1(t - 10) + 4.8$

Part C)

562 minutes.

Step-by-step explanation:

A tank is filled at a constant rate. After 10 minutes, the tank contains 4.8 L of water and after 35 minutes, the tank contains 7.3 L of water.

Part A)

We can represent the current data with two points: (10, 4.8) and (35, 7.3). The x-coordinate is measured in minutes since the tank began to be filled and the y-coordinate is measured in how full the tank is in liters.

To find the rate at which the tank is being filled, find the slope between the two points:

$\displaystyle m = \frac{\Delta y}{\Delta x} = \frac{(7.3)-(4.8)}{(35)-(10)} = \frac{2.5}{25} = 0.1$

In other words, the rate at which the tank is being filled is 0.1 liters per minute.

Part B)

To find the function of the volume of the tank, we can use the point-slope form to first find its equation:

$\displaystyle y - y_1 = m( x - x_1)$

Where m is the slope/rate of change and (x₁, y₁) is a point.

We will substitute 0.1 for m and let (10, 4.8) be the point. Hence:

$\displaystyle y - (4.8) = 0.1(x - 10)$

Simplify:

$\displaystyle y = 0.1(x-10) + 4.8$

Since y represent how full the tank is and x represent the time in minutes since the tank began to be filled, we can substitute y for V(t) and x for t. Thus, our function is:

$\displaystyle V(t) = 0.1(t - 10) + 4.8$

The initial volume is when t = 0. Evaluate:

$\displaystyle V(0) = 0.1 ((0) - 10) + 4.8 = 3.8$

There was initially 3.8 liters of water.

Part C)

To find how long it will take for the tank to be completely filled given its maximum capacity of 60 liters, we can let V(t) = 60 and solve for t. Hence:

$60 = 0.1(t - 10) + 4.8$

Subtract:

$55.2 = 0.1(t - 10)$

Divide:

$552 = t - 10$

Add. Therefore:

$t = 562\text{ minutes}$

It will take 562 minutes for the tank to be completely filled.

8 0

3 years ago

In ΔDEF, what is sin D, in simplified form?

Igoryamba

Answer: second option.

Step-by-step explanation:

You must apply $sin\alpha=\frac{opposite}{hypotenuse}$

Then, given the right triangle and the angle D, the opposite side and the hypotenuse of the triangle are the following:

$opposite=20\\hypotenuse=25$

Therefore, when you substitute values, you have:

$sinD=\frac{20}{25}$

Reduce the fraction, then you obtain:

$sinD=\frac{4}{5}$

5 0

3 years ago

Read 2 more answers

Solve the system of equations using the addition method 2a+3b=-1 ; 3a+5b=-2

Alexeev081 [22]

Answer:

Then, a=-1 and b=-1

Step-by-step explanation:

We need to solve the following system of equations using the adition method:

2a+3b=-1 (i)

3a+5b=-2 (ii)

First, we multiply the equation (i) by -3 and the equation (ii) by 2, so we get:

-6a-9b=3

6a+10b=-4

Adding the two equations we have:

-6a-9b=3

6a+10b=-4

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

0 + b = -1

Then b=-1. Now, let's substitute the value of b into equation (i):

2a+3b=-1

2a + 3(-1) = -1

2a -3 = -1

2a = 2

a = 1

Then, a=-1 and b=-1

3 0

4 years ago

Read 2 more answers

Find A intersection B.

Alecsey [184]

A: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
B: {-2, -1, 1, 4, 7, 11}

A ∩ B = {1, 4, 7, 11}

So the answer is B.

Intersection of two or more sets cointains only common elements.

3 0

3 years ago

What is the answer to 12 times 3

Virty [35]

12 times 3 is equal to 36 so 36 is your answer

5 0

3 years ago

Read 2 more answers