Simplify the following expression 4[7+2/3-2(3/5)]

1 answer:

vladimir2022 [97]2 years ago

3 0

Answer: Add 7+ $\frac{2}{3}= \frac{7}{1} + \frac{2}{3} = \frac{7.3}{1.3} + \frac{2}{3} = \frac{21.2}{3} = \frac{23}{3}$ For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(1, 3) = 3. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 1 × 3 = 3. In the next intermediate step the fraction result cannot be further simplified by canceling.

In words - seven plus two thirds = twenty-three thirds.

Multiple: 2 * $\frac{3}{5} = \frac{2.3}{1.5} = \frac{6}{5}$ Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(6, 5) = 1. In the next intermediate step the fraction result cannot be further simplified by canceling.

In words - two multiplied by three fifths = six fifths.

Subtract = $\frac{23}{3} - \frac{6}{5} = \frac{23.5}{3.5} - \frac{6.3}{5.3} = \frac{115}{15} - \frac{18}{15} =\frac{115 - 18}{15}$ For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(3, 5) = 15. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 5 = 15. In the next intermediate step the fraction result cannot be further simplified by canceling.

In words - twenty-three thirds minus six fifths = ninety-seven fifteenths.

Multiple: 4 Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(388, 15) = 1. In the next intermediate step the fraction result cannot be further simplified by canceling.

In words - four multiplied by ninety-seven fifteenths = three hundred eighty-eight fifteenths.

Step-by-step explanation:

hope this helps

You might be interested in

Divide 33 photos into two groups so the ratio is 4 to 7.

MrRissso [65]

33 divided by 2= 16.5

3 0

3 years ago

Marine biologists have determined that when a shark detectsthe presence of blood in the water, it will swim in the directionin w

siniylev [52]

Solution :

a). The level curves of the function :

$C(x,y) = e^{-(x^2+2y^2)/10^4}$

are actually the curves

$e^{-(x^2+2y^2)/10^4}=k$

where k is a positive constant.

The equation is equivalent to

$x^2+2y^2=K$

$\Rightarrow \frac{x^2}{(\sqrt K)^2}+\frac{y^2}{(\sqrt {K/2})^2}=1, \text{ where}\ K = -10^4 \ln k$

which is a family of ellipses.

We sketch the level curves for K =1,2,3 and 4.

If the shark always swim in the direction of maximum increase of blood concentration, its direction at any point would coincide with the gradient vector.

Then we know the shark's path is perpendicular to the level curves it intersects.

b). We have :

$\triangledown C= \frac{\partial C}{\partial x}i+\frac{\partial C}{\partial y}j$

$\Rightarrow \triangledown C =-\frac{2}{10^4}e^{-(x^2+2y^2)/10^4}(xi+2yj),$ and

$\triangledown C$ points in the direction of most rapid increase in concentration, which means $\triangledown C$ is tangent to the most rapid increase curve.