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Mazyrski [523]
3 years ago
15

Select the correct answers (there are more than one that are correct)​

Mathematics
1 answer:
Liono4ka [1.6K]3 years ago
4 0

Answer:

its really good luck for you know what is not my phone

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Yesterday morning, at 6:00 AM, water started leaking from a tank at a constant rate. The tank contained8,496liters of water at 6
GREYUIT [131]

A linear equation can be written as:

y = a*x + b

where a is the slope and b is the y-intercept.

If we know that the line passes through the points (x₁, y₁) and (x₂, y₂) the slope is:

a = \frac{y_2 - y_1}{x_2 - x_1}

The answers are:

a) y = (-12 L/min)*t + 9,000 L

b) 6,840 L

a) Here we know that we can model this situation with a linear equation, we know that the leak starts at 6:00 am, then we define t = 0 as 6:00 am

We know that at 6:42 am  (at t = 42 mins) the tank has 8,496 liters.

And at 7:15 am (at t = 75 mins) the tank has 8,100 liters.

Then we have two points of the line:

(42 mins, 8,496 liters)

(75 mins, 8,100 liters)

Then the slope is:

a = \frac{8,100 liters - 8,496 liters }{75 mins -42 mins } = -12 L/min

So the line will be something like:

y = (-12 L/min)*t + b

To find the value of b, which is the initial volume of water in the tank, we use the point (75 mins, 8,100 liters)

This means that if t = 75 mins, then we have y = 8,100 L

So we can replace these two on the above equation:

8,100 L = (-12 L/min)*75 mins + b

8,100L = -900L + b

8,100L + 900L = b = 9,000 L

Then the linear equation is:

y = (-12 L/min)*t + 9,000 L

b) Now we want to know how much water is in the tank at 9:00 am.

Notice that 9:00 am is 3 hours after 6:00 am, our t = 0.

Then  9:00am is equivalent to t = 180 mins.

So to know the volume of water that there is in the tank at 9:00 am, we just need to evaluate the linear function at t = 180 mins.

y = (-12 L/min)*180 mins + 9,000 L = 6,840 L

If you want to learn more, you can read:

brainly.com/question/24594539

7 0
3 years ago
Select the equivalent expression.
Free_Kalibri [48]

Answer:

\frac{7^{15}}{3^{30}}

Step-by-step explanation:

The given expression is:

(\frac{3^{-6}}{7^{-3}})^{5}

Moving the expression to the other side in the fraction changes its sign to opposite. A numerator with negative exponent, when written in denominator will have the positive exponent. Using this rule, we can write:

(\frac{3^{-6}}{7^{-3}})^{5}\\\\ = (\frac{7^{3}}{3^{6}} )^{5}

The exponent 5 can be distributed to both numerator and denominator as shown:

(\frac{7^{3}}{3^{6}} )^{5}\\\\ = \frac{(7^{3})^{5}}{(3^{6})^{5}}

The power of a power can be written as a product. i.e.

\frac{(7^{3})^{5}}{(3^{6})^{5}}\\\\ =\frac{7^{15}}{3^{30}}

So, the expression similar to the given expression and with positive exponents is: \frac{7^{15}}{3^{30}}

6 0
3 years ago
Read 2 more answers
ou push a large crate with a force of 100 N to the right . What force could your friend apply in order to cause a balanced force
mina [271]

Answer:

100 N to the left

Step-by-step explanation:

They have to be equal and opposite to balance, so they will need a force of 100 N to the left

7 0
3 years ago
Paul bought a soft drink and a sandwich for $9.90. What equation may be used to find the price of each item if the sandwich cost
UNO [17]

Answer:

D

Step-by-step explanation:

The other ones don't make sense. The answer is 3.5x+x=9.90

8 0
3 years ago
Which of the following pairs of functions are inverses of each other?
aliina [53]
Answer:

A or C

Step by Step Explanation:

7 0
3 years ago
Read 2 more answers
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