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fiasKO [112]
3 years ago
7

Malinda's family had walked 4/6 of a hiking trail. Owens family has walked 5/8 of another trail. Which family has walked farther

? Explain your answer.
Mathematics
1 answer:
Yuri [45]3 years ago
8 0
To answer this, we need to convert to the least common multiple.

The least common multiple of 2/3 and 5/8 is 24.

2 x 8 = 16 / 24

5 x 3 = 15 / 24

Malinda's family walked farther than Owen's family.
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How many ounces of a 35% alcohol solution must be mixed with 10ounces of 40% alcohol solution to make a 37% alcohol solution?
spayn [35]
First off, let's change the format of the percentage to decimal.. so 35% is just 35/100 or 0.35 and 40% is 40/100 or 0.4 and so on.

\bf \begin{array}{lccclll}
&amount&concentration&
\begin{array}{llll}
concentrated\\
amount
\end{array}\\
&-----&-------&-------\\
\textit{35\% sol'n}&x&0.35&0.35x\\
\textit{40\% sol'n}&10&0.40&4.00\\
-----&-----&-------&-------\\
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\end{array}

now, whatever "x" amount is, we know that x + 10 must add up to "y". x + 10 =  y, because both quantities added will give the mixture amount.

and whatever 0.35x + 4 = 0.37y, because both concentrated amounts must give the 37% of the mixture.

\bf \begin{cases}
x+10=\boxed{y}\\
0.35x+4=0.37y\\
----------\\
0.35x+4=0.37\left( \boxed{x+10} \right)
\end{cases}

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Read 2 more answers
The midpoint of GH is M( 6,-4). One endpoint is G(8,-2). Find the coordinates of endpoint H.
Finger [1]

Using the midpoint formula, the coordinates of endpoint H are (4, -6).

<h3>The Midpoint Formula</h3>

The midpoint formula is given as: (x_m, y_m) = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} )

<em>Where</em>,

(x_m, y_m) = coordinates of the midpoint

(x_1, y_1) = coordinates of the first point

(x_2, y_2) = coordinates of the second point

Given the following:

(x_m, y_m) = M( 6,-4)

(x_1, y_1) = G(8,-2)

(x_2, y_2) = H(?, ?)

Plug in the values into the midpoint formula

M(6, -4) = (\frac{8 + x_2}{2}, \frac{-2 + y_2}{2} )

Solve for the x-coordinate and y-coordinate separately

6 = \frac{8 + x_2}{2}

  • Multiply both sides

6 \times 2 = 8 + x_2\\\\12 = 8 + x_2\\\\12 - 8 = x_2\\\\4 = x_2\\\\\mathbf{x_2 = 4}

-4 = \frac{-2 + y_2}{2}\\\\-8 = -2 + y_2\\\\-8 + 2 = y_2\\\\-6 = y_2\\\\\mathbf{y_2 = -6}

Therefore, using the midpoint formula, the coordinates of endpoint H are (4, -6).

Learn more about midpoint formula on:

brainly.com/question/13115533

3 0
2 years ago
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