Write the ratio 1.5:9 in simplest form.

you are given an 8-gallon jug filled with water and also two empty jugs: one that holds 5 gallons and other that holds 3 gallons

Yanka [14]

Answer:

Step-by-step explanation:

We will use following steps to measure exactly 4 gallons of water with the help of 5 gallons and 3 gallons empty jugs.

1). Fill 3 gallons jug completely.

2). Pour this 3 gallons of water into 5 gallons jug. Now we have 3 gallons of water in 5 gallons jug and 3 gallons jug empty.

We can add 2 gallons of water in the empty space of 5 gallons jug more.

3). Fill the 3 gallons jug with the water again.

4). Pour this water into 5 gallons jug which can hold 2 gallons of water more.

Now we have 5 gallons of jug filled fully and 1 gallon water remaining in the 3 gallons jug.

5). Empty the 5 gallons jug completely.

6). Pour the remaining 1 gallon of remaining water in 3 gallons jug into 5 gallons jug.

7). Fill the 3 gallons jug completely and pour it into 5 gallon jug.

8). Finally we have 4 gallons of water in the 5 gallons jug.

8 0

3 years ago

find the area of a parrellelogram whose base is of length 25 cm and the corresponding altitude is of length 8.4 cm

Free_Kalibri [48]

Answer:

Check the above photo and do the sum

6 0

2 years ago

Factor the polynomial, x2 + 5x + 6

patriot [66]

Answer:

Choice b.

$x^{2} + 5\, x + 6 = (x + 3)\, (x + 2)$ .

Step-by-step explanation:

The highest power of the variable $x$ in this polynomial is $2$ . In other words, this polynomial is quadratic.

It is thus possible to apply the quadratic formula to find the "roots" of this polynomial. (A root of a polynomial is a value of the variable that would set the polynomial to $0$ .)

After finding these roots, it would be possible to factorize this polynomial using the Factor Theorem.

Apply the quadratic formula to find the two roots that would set this quadratic polynomial to $0$ . The discriminant of this polynomial is $(5^{2} - 4 \times 1 \times 6) = 1$ .

$\begin{aligned}x_{1} &= \frac{-5 + \sqrt{1}}{2\times 1} \\ &= \frac{-5 + 1}{2} \\ &= -2\end{aligned}$ .

Similarly:

$\begin{aligned}x_{2} &= \frac{-5 - \sqrt{1}}{2\times 1} \\ &= \frac{-5 - 1}{2} \\ &= -3\end{aligned}$ .

By the Factor Theorem, if $x = x_{0}$ is a root of a polynomial, then $(x - x_0)$ would be a factor of that polynomial. Note the minus sign between $x$ and $x_{0}$ .

The root $x = -2$ corresponds to the factor $(x - (-2))$ , which simplifies to $(x + 2)$ .
The root $x = -3$ corresponds to the factor $(x - (-3))$ , which simplifies to $(x + 3)$ .