Solve the following system of equations: y = 5/4x - 2 y = -1/4x + 19 x = ? and y = ?

Mathematics

2 answers:

Dmitry [639]3 years ago

4 0

Answer:

1. y= 5 /4 x −2

2.x=−4y+76

Natalija [7]3 years ago

3 0

<h2>Answer:</h2>

We will use substitution to solve this system for x.

$y = \frac{5}{4}x - 2\\y = -\frac{1}{4}x + 19\\\\\frac{5}{4}x - 2 = -\frac{1}{4}x + 19\\\\\frac{3}{2}x - 2 = 19\\\\\frac{3}{2}x = 21\\\\x = 14$

Now, we will solve for y by pluging in what we got for x into one of the equations.

$y = \frac{5}{4}(14) - 2\\\\y = \frac{35}{2} - 2\\\\y = \frac{31}{2} = 15.5$

The solution is (14, 15.5).

You might be interested in

Select the rational expression that is equivalent to the given expression below. 4/x-3

Aliun [14]

To find the correct option we need to calculate each of the given options.
Option (1):
$\frac{x+2}{x-3} / \frac{4}{x+2} = \frac{x+2}{x-3} * \frac{x+2}{4} = \frac{(x+2)^2}{4(x-3)}$

Option (2):
$\frac{x+2}{x-3} * \frac{4}{x+2} = \frac{4}{x-3}$

Option (3):
$\frac{x+2}{x-3} - \frac{4}{x+2} = \frac{(x+2)^2-4(x-3)}{(x-3)(x+2)}$

option (4)
$\frac{x+2}{x-3} + \frac{4}{x+2} = \frac{(x+2)^2+4(x-3)}{(x-3)(x+2)}$

So, the correct answer is option (2)

7 0

3 years ago

Read 2 more answers

While Playing Yahtzee and rolling 5 dice, Mei gets the result shown at right (the numbers are 2, 4, 4, 4, and 1). Mei decides to

Elina [12.6K]

A. The probability is 1/36. There are 36 combinations of the first and second dice and only one of them is 2 - 4s.

B. 10/36. Ten of the options contain exactly 1 - 4.

C. The remaining 25/36 options do not include a 4.

5 0

3 years ago

Sam colors each tile in a 4 by 4 grid white or black. A coloring is called rotationally

DiKsa [7]

Answer:

65,280

Step-by-step explanation:

Consider the 4×4 grid ...

$\left[\begin{array}{cc}a&b\\d&c\end{array}\right]$

where each of a, b, c, d is a 2×2 array of tiles. Let's use the notation a' to represent the 2×2 array "a" rotated right 1/4 turn. For 90° rotational symmetry, we must have b=a', c=b'=a'', d=c'=b''=a'''. That is, once "a" is determined, the rest of the grid is determined. Since "a" consists of 4 tiles, each of which can be black or white, there are 2^4 = 16 patterns that have 90° rotational symmetry.

The same will be true of 270° rotational symmetry, for the same reason.

For 180° rotational symmetry, we must have c=a'' and d=b''. Then the combination of "a" and "b" together fully determines the grid. Together, "a" and "b" consist of 8 tiles, so there are 2^8 = 256 ways to pattern the grid so it will have 180° rotational symmetry. (Of those, 16 have 90° symmetry, and 16 have 270° symmetry. The sets are overlapping.)

The 16 tiles of the grid can be colored 2^16 = 65,536 different ways. As we have seen, 256 of those colorings result in 180° rotational symmetry. Then the number of colorings that have no rotational symmetry is ...

65,536 -256 = 65,280 . . . . colorings not rotationally symmetric

8 0

3 years ago

1. The formula for the volume of a cone is

Andre45 [30]

Answer:

$r=\sqrt{\frac{3V}{\pi\ h}}$