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Norma-Jean [14]
1 year ago
5

Select all that appear in the DOMAIN {(-8,-12),(4,-8), (2, -10),(-10.-16) -16 -12 -10 -8 -2-4

Mathematics
1 answer:
Yuri [45]1 year ago
3 0
Domain of a set of ordered pairs

We know the domain is the set of all x when is represented by ordered pairs: (x, y)

In this case {(-8,-12),(4,-8), (2, -10),(-10.-16) } we can observe that there are four x (the first number of each pair):

Domain = { -8, 4, 2, -10}

<h2>Domain = {-10, -8, 2, 4}</h2>

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Item 16 The variables x and y vary directly. Use the values to find the constant of proportionality, k. Then write an equation t
masya89 [10]

Answer:

k = 2

x = 2y

Step-by-step explanation:

If variables x and y vary directly, this is expressed as;

x ∝ y

x = ky

k is the proportionality constant

Let's assume the value of x and y since we are not given;

x = 20

y = 10

Substitute

20 = k(10)

10k = 20

k = 20/10

k = 2

Hence the constant of proportionality is 2

Substitute i=k = 2 into the equation x = ky

x = 2y

Hence an equation that relates x and y is x = 2y

<em>Note that the values here are assumed value, you can use the same method for any values of x and y</em>

4 0
3 years ago
1. Place these numbers in order from smallest to largest:
anyanavicka [17]

Answer:

Step-by-step explanation:

-3/8, - 3/4, - 3, - 2. 5, 1/4, 8/5 3.1, 6

6 0
3 years ago
If ray BD bisects angle CBE, ray BC is transparent to ray BA, angle CBD = (3x -1 ) degrees, and angle DBE = (7x - 13) degrees, f
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5 0
3 years ago
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 <em>x-</em>coordinate is measured in minutes since the tank began to be filled and the <em>y-</em>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 <em>m</em> is the slope/rate of change and (<em>x</em>₁, <em>y</em>₁) is a point.

We will substitute 0.1 for <em>m</em> 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 <em>y</em> represent how full the tank is and <em>x</em> represent the time in minutes since the tank began to be filled, we can substitute <em>y</em> for V(t) and <em>x</em> for <em>t</em>. Thus, our function is:

<em />\displaystyle V(t) = 0.1(t - 10) + 4.8<em />

<em />

The initial volume is when <em>t</em> = 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 <em>t</em>. 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.

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2 years ago
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