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3 years ago

Find the solution x/5-1/5=x/3+1/4

Mathematics

1 answer:

insens350 [35]3 years ago

8 0

Answer:

x = - 27/8

Step-by-step explanation:

¹²⁾x/5 - ¹²⁾1/5 = ²⁰⁾x/3 + ¹⁵⁾1/4

12x - 12 = 20x + 15

- 12 - 15 = 20x - 12x

- 27 = 8x

x = - 27/8

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2 years ago

There are 6 times as many dogs as cats. If total the total number of dogs and cats is 21, how many dogs are there?

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3 years ago

If a punch bottle says 20% fruit juice,and it is a 200 milliliter bottle, how many milliliters of fruit juice is in the bottle?

padilas [110]

Answer:

There are 40 milliliters of fruit juice in the bottle

Step-by-step explanation:

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2 years ago

Find the longer leg of the triangle.

Paha777 [63]

Answer:

Choice A. 3.

Step-by-step explanation:

The triangle in question is a right triangle.

The length of the hypotenuse (the side opposite to the right angle) is given.
The measure of one of the acute angle is also given.

As a result, the length of both legs can be found directly using the sine function and the cosine function.

Let $\text{Opposite}$ denotes the length of the side opposite to the $30^{\circ}$ acute angle, and $\text{Adjacent}$ be the length of the side next to this $30^{\circ}$ acute angle.

$\displaystyle \begin{aligned}\text{Opposite} &= \text{Hypotenuse} \times \sin{30^{\circ}}\\ &=2\sqrt{3}\times \frac{1}{2} \\&= \sqrt{3}\end{aligned}$ .

Similarly,

$\displaystyle \begin{aligned}\text{Adjacent} &= \text{Hypotenuse} \times \cos{30^{\circ}}\\ &=2\sqrt{3}\times \frac{\sqrt{3}}{2} \\&= 3\end{aligned}$ .

The longer leg in this case is the one adjacent to the $30^{\circ}$ acute angle. The answer will be $3$ .

There's a shortcut to the answer. Notice that $\sin{30^{\circ}} < \cos{30^{\circ}}$ . The cosine of an acute angle is directly related to the adjacent leg. In other words, the leg adjacent to the $30^{\circ}$ angle will be the longer leg. There will be no need to find the length of the opposite leg.