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adelina 88 [10]
3 years ago
14

The sentence , two less than the product of two and a number is greater than 5 times the opposite of the number, translates to w

hich mathematical statement
Mathematics
1 answer:
Kruka [31]3 years ago
8 0
It turns out: 2-2x>5y
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PLS HELP ILL GIVE BRAINLIEST
inysia [295]
<h3>Answer:   14x - 8</h3>

=======================================================

Explanation:

I'll use the quadratic formula to find the roots or x intercepts. This slight detour allows us to factor without having to use guess-and-check methods.

The equation is of the form ax^2+bx+c = 0

  • a = 12
  • b = -11
  • c = -5

This leads to...

x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-11)\pm\sqrt{(-11)^2-4(12)(-5)}}{2(12)}\\\\x = \frac{11\pm\sqrt{361}}{24}\\\\x = \frac{11\pm19}{24}\\\\x = \frac{11+19}{24} \ \text{ or } \ x = \frac{11-19}{24}\\\\x = \frac{30}{24} \ \text{ or } \ x = \frac{-8}{24}\\\\x = \frac{5}{4} \ \text{ or } \ x = -\frac{1}{3}

Now use those roots to form these steps

x = \frac{5}{4} \ \text{ or } \ x = -\frac{1}{3}\\\\4x = 5 \ \text{ or } \ 3x = -1\\\\4x - 5 =0 \ \text{ or } \ 3x+1 = 0\\\\(4x-5)(3x+1) = 0

Refer to the zero product property for more info.

Therefore, the original expression factors fully to (4x-5)(3x+1)

Use the FOIL rule to expand it out and you should get 12x^2-11x-5 again.

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

We did that factoring so we could find the side lengths of the rectangle.

I'm using the fact that area = length*width

  • L = length = 4x-5
  • W = width = 3x+1

The order of length and width doesn't matter.

From here, we can then compute the perimeter of the rectangle

P = 2(L+W)

P = 2(4x-5+3x+1)

P = 2(7x-4)

P = 14x - 8

6 0
2 years ago
Arrange the digits 1,2,3,4,5,6,7 so that when the numbers are added up, they will total 100.
GuDViN [60]
36 + 57  + 4 + 2 + 1 =   100   would do it.
6 0
3 years ago
Which of the following expressions is correct? Select one: a. marginal cost = (change in quantity of output)/(change in total co
Natasha_Volkova [10]

Answer:

b. average total cost = total cost/quantity of output

Step-by-step explanation:

The marginal cost is the additional cost of producing one more unit of output and it can be calculated by taking the change in total cost and dividing it by the change in quantity, its formula is:

  • <em>Marginal cost = change in total cost/ change in quantity</em>

The average total cost (sometimes referred to simply as average cost) is total cost divided by the quantity of output, its formula is:

  • <u><em>Average total cost = total cost / quantity of output</em></u>

The total cost is obtained adding together the fixed costs and the variable costs, its formula is:

  • <em>Total cost = fixed cost + variable cost</em>

The average variable cost is obtained when variable cost is divided by quantity of output, its formula is:

  • <em>Average variable = variable cost / quantity of output</em>

I hope you find this information useful and interesting! Good luck!

3 0
3 years ago
The ratio of the number of gallons of gasoline a car uses to the number of miles it travels is 15: 330. In miles per gallon (mpg
Murrr4er [49]

Answer:22mpg

Step-by-step explanation:

330miles/15gallons per mile = 22 mpg

3 0
3 years ago
Read 2 more answers
Can someone please help me with these questions!! Thanks,
fiasKO [112]

6a. 1 - 2sin(x)² - 2cos(x)² = 1 - 2(sin(x)² +cos(x)²) = 1 - 2·1 = -1

6c. tan(x) + sin(x)/cos(x) = tan(x) + tan(x) = 2tan(x)

6e. 3sin(x) + tan(x)cos(x) = 3sin(x) + (sin(x)/cos(x))cos(x) = 3sin(x) +sin(x) = 4sin(x)

6g. 1 - cos(x)²tan(x)² = 1 - cos(x)²·(sin(x)²)/cos(x)²) = 1 -sin(x)² = cos(x)²

8 0
3 years ago
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