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2 years ago

Factorise 12 raised 2 minus 7x + 1

Mathematics

1 answer:

professor190 [17]2 years ago

6 0

Answer:

(4x - 1)(3x - 1).

Step-by-step explanation:

I think you mean 12x^2 - 7x + 1

= 12x^2 - 4x - 3x + 1

= 4x(3x - 1) -- 1(3x - 1)

= (4x - 1)(3x - 1).

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A football field has these measurements. What is the area of the football field?

kotegsom [21]

Answer:

6,360 yd.

Step-by-step explanation:

To find area you multiply length times width (l*w)

120 times 53

6,360 yd

Hope I helped!! :)

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7 0

2 years ago

Read 2 more answers

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

2 years ago

Susan's art class is 8 hours long. How long is her class in minutes?

PilotLPTM [1.2K]

Answer: 480 minutes

Step-by-step explanation:

8 hours x 60 minutes in a hour = 480

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2 years ago

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Evaluate each expression by replacing the variable with 8. Show each step. (8 marks) 2n - 6

monitta

Answer:

Step-by-step explanation:

2n-6

n=8

2(8)-6

16-6

4 0

2 years ago

If a bag contains 12 quarters, 6 dimes, and 18 nickles, what is the part-to-whole ratio of nickles to all coins?

zepelin [54]

Answer:

18/36 or 1/2

Step-by-step explanation:

There are 18 nickels, which is the numerator.

You add all the numbers together to get the denominator, which is 12+6+18=36.

Then, you put the two values in a fraction - 18/36

and simplify, to get you 1/2.

3 0

2 years ago

Factorise 12 raised 2 minus 7x + 1​

Factorise 12 raised 2 minus 7x + 1