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3 years ago

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The denominator of a rational number is greater than its numerator by 7. If the numerator is increased by 6 and the denominator

is decreased by 5, the new rational number obtained is 3/2. Find the original rational number.

1 answer:

ollegr [7]3 years ago

8 0

Answer:

6/13

Step-by-step explanation:

6 + 6 = 12 3

---- ---- = ---

13 - 5 = 8 2

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Answer:

The product of given $-4 \cdot \left[\begin{array}{ccc}8\\-1\\-5\\9\end{array}\right]$ is $\left[\begin{array}{ccc}-32 \\4\\20\\-36\end{array}\right]$

Step-by-step explanation:

Consider the given product of a constant and a matrix.

$-4 \cdot \left[\begin{array}{ccc}8\\-1\\-5\\9\end{array}\right]$

To do product we multiply scalar -4 with each element of the matrix given,

$-4 \cdot \left[\begin{array}{ccc}8\\-1\\-5\\9\end{array}\right]= \left[\begin{array}{ccc}-4 \times 8 \\-4 \times -1\\-4 \times -5\\-4 \times 9\end{array}\right]$

On solving further , we get,

$\left[\begin{array}{ccc}-4 \times 8 \\-4 \times -1\\-4 \times -5\\-4 \times 9\end{array}\right]=\left[\begin{array}{ccc}-32 \\4\\20\\-36\end{array}\right]$

Thus, the product of given $-4 \cdot \left[\begin{array}{ccc}8\\-1\\-5\\9\end{array}\right]$ is $\left[\begin{array}{ccc}-32 \\4\\20\\-36\end{array}\right]$

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What is the midpoint of the segment shown below? (5,4) (5,-3)

Monica [59]

The midpoint is (5, ¹/₂).

<h3>Further explanation</h3>

The midpoint is the coordinates of a point right in the middle of a line segment or two endpoints.

The Midpoint Formula $\boxed{\boxed{ \ M = \bigg( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \bigg) \ }}$

So, abscissa and ordinate of the midpoint are the averages of both endpoints. i.e., (x₁, y₁) and (x₂, y₂).

Given (x₁, y₁) = (5, 4) and (x₂, y₂) = (5, -3).

Let's calculate the midpoint.

$\boxed{ \ M = \bigg( \frac{5 + 5}{2}, \frac{4 + (-3)}{2} \bigg) \ }$

$\boxed{ \ M = \bigg( \frac{10}{2}, \frac{1}{2} \bigg) \ }$

$\boxed{ \ M = \bigg( 5, \frac{1}{2} \bigg) \ }$

We get the midpoint between the two endpoints, that is, (5, ¹ / ₂).

<h3>Learn more</h3>

Finding a line that is not parallel to either the x-axis or the y-axis and passes through a point brainly.com/question/4691222
Finding the equation, in slope-intercept form, of the line that is parallel to the given line and passes through a point brainly.com/question/1473992
A line segment is a piece of a line with two endpoints brainly.com/question/909890

Keywords: the midpoint, the line segment, endpoints, in the middle, between, average, abscissa and ordinate, the coordinates

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