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3 years ago

What is the solution to 0.4(12 – 3x) = 0.3(12x - 16)?

Mathematics

1 answer:

ser-zykov [4K]3 years ago

8 0

Answer:

You need to simplify 0.3(12x + -16) = 0.4(12 + -3x)

Step-by-step explanation:

Reorder the terms:

0.3(-16 + 12x) = 0.4(12 + -3x) (-16 * 0.3 + 12x * 0.3) = 0.4(12 + -3x) (-4.8 + 3.6x) = 0.4(12 + -3x) -4.8 + 3.6x = (12 * 0.4 + -3x * 0.4) -4.8 + 3.6x = (4.8 + -1.2x)

Solving -4.8 + 3.6x = 4.8 + -1.2x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.2x' to each side of the equation. -4.8 + 3.6x + 1.2x = 4.8 + -1.2x + 1.2x

Combine like terms: 3.6x + 1.2x = 4.8x -4.8 + 4.8x = 4.8 + -1.2x + 1.2x

Combine like terms: -1.2x + 1.2x = 0.0 -4.8 + 4.8x = 4.8 + 0.0 -4.8 + 4.8x = 4.8 Add '4.8' to each side of the equation. -4.8 + 4.8 + 4.8x = 4.8 + 4.8

Combine like terms: -4.8 + 4.8 = 0.0 0.0 + 4.8x = 4.8 + 4.8 4.8x = 4.8 + 4.8

Combine like terms: 4.8 + 4.8 = 9.6 4.8x = 9.6 Divide each side by '4.8'. x = 2

Simplifying x = 2

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4π cm = 12.57 cm

Step-by-step explanation:

180 degrees is half of a circle, so the length of the arc is half of the circumference.

length = (2πr)/2 = πr = 4π cm = 12.57 cm

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3 years ago

a dining set is priced at $785 . if the sales tax is 7 percent,what is the cost to purchase the dining set?round to the nearest

AleksAgata [21]

Price of the dining set = $785

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4 years ago

Read 2 more answers

Find the circumferences of the two circles circle a has a radius of 21 meters and circle b has a radius of 28 meters Is the rela

Feliz [49]

Answer:

The circumference for circle a is $\\ C = 131.9430$ m.

The circumference for circle b is $\\ C = 175.9240$ m.

The relationship between the radius of a circle and the circumference (the distance around the circle) is constant and is the same for all circles and can be written as $\\ \frac{C}{r} = 2\pi$ or, in a less familiar form, $\\ \frac{r}{C} = \frac{1}{2\pi}$ . The number $\\ \pi$ is constant for all circles and has infinite digits, $\\ \pi = 3.14159265358979....$ .

Step-by-step explanation:

The circumference of a circle is given by:

$\\ C = 2*\pi*r$ [1]

Where

$\\ C$ is the circle's circumference.

$\\ r$ is the radius of the circle.

And

$\\ \pi = 3.141592....$ is a constant value (explained below)

We can say that the distance around the circle is the circle's circumference.

The circumferences of the two circles given are:

Circle a, with radius equals to 21 meters ( $\\ r = 21m$ ).

Using [1], using four decimals for $\\ \pi$ , we have:

$\\ C = 2*\pi*r$

$\\ C = 2*3.1415*21$ m

$\\ C = 131.9430$ m

Then, the circumference for circle a is $\\ C = 131.9430$ m.

Circle b, with radius equals to 28 meters ( $\\ r = 28m$ ).

$\\ C = 2*3.1415*28$ m

$\\ C = 175.9240$ m

And, the circumference for circle b is $\\ C = 175.9240$ m.

We know that

$\\ 2r = D$

That is, the diameter of the circle is twice its radius.

Then, if we take the distance around the circle and we divided it by $\\ 2r$

$\\ \frac{C}{2r} = \frac{C}{D} = \pi$

This ratio, that is, the relationship between the distance around the circle (circumference) and the diameter of a circle is $\\ \pi$ and is constant for all circles. This result is called the $\\ \pi$ number, which is, approximately, $\\ \pi = 3.141592653589793238....$ (it has infinite number of digits).

We can observe that the relationship between the radius of a circle and the circumference is also constant:

$\\ \frac{C}{2r} = \frac{C}{D} = \pi$

$\\ \frac{C}{2r} = \pi$

$\\ \frac{C}{r} = 2\pi$

However, this relationship is $\\ 2\pi$ .

We can rewrite it as

$\\ \frac{r}{C} = \frac{1}{2\pi}$

And it is also constant.

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3 years ago

The car can hold up to 4 passengers. Write an inequality for the number of passengers that could be in the car at any given time

Blizzard [7]

Answer:

The equation relating the number of cars to the number of passengers is p = 4n

Step-by-step explanation:

Given that certain type of car has room for 4 passengers

To find: write an equation relating the number of cars to the number of passengers

Let "n" be the number of cars

Let "p" be the number of passengers

From given information,

Car has room for 4 passengers. Therefore, we can frame,

number of passengers = 4 ( number of cars )

p = 4 (n)

p = 4n

Thus the equation relating the number of cars to the number of passengers is p = 4n

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2 years ago