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Kay [80]
3 years ago
8

Find a rational number halfway in between the two numbers. 7/9 and 3/4​

Mathematics
1 answer:
AlekseyPX3 years ago
7 0

Answer: 55/126

Step-by-step explanation:

For this equation, the easiest way to solve is to change the denominators, or bottom halves, of both fractions to be the same thing. The easiest way to do this is to multiply themselves with a “funny form” of one. A funny form of one is just a way of representing “1” with numbers that aren’t 1. “2/2” is a funny form of one. log(x)/log(x) is a funny form of one, etc..

(3/7)x(9/9)=27/63

(4/9)x(7/7)=28/63

These fractions are very close. If you are willing to settle for an unsimplified fraction, the answer here would be 27.5/63. If you aren’t willing to settle for the unsimplified form, we can multiply both fractions by a funny form of one again, most easily 2/2, and find the median of the two fractions.

(27/63)x(2/2)=54/126

(28/63)x(2/2)=56/126

The median of these two fractions is 55/126.

55/126 is exactly halfway between 3/7 and 4/9.

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Suppose f(x) = mx + b. What is the inverse function in terms of m and b?
katrin2010 [14]

Answer:

f^(-1)(x) = (x-b)/m  or  x/m - b/m

Step-by-step explanation:

f(x) = y = mx + b

To find the inverse function, interchange x and y and solve for y, i.e.

x = my + b

my = x-b

y = (x-b)/m = x/m - b/m

7 0
2 years ago
2x+5y=12
anastassius [24]
Y = -3x - 1......so we sub in -3x - 1 in for y in the other equation

2x + 5y = 12
2x + 5(-3x - 1) = 12....now distribute the 5 through the parenthesis
2x - 15x - 5 = 12...add 5 to both sides
2x - 15x = 12 + 5..combine like terms
-13x = 17...divide both sides by -13
x = -17/13
now sub in -17/13 for x in the other equation
y = -3x - 1
y = -3(-17/13) - 1
y = 51/13 - 1
y = 51/13 - 13/13
y = 38/13

so the solution is (-17/13, 38/13)

8 0
3 years ago
About 2,200 years ago, one of the most famous mathematicians in history made a major discovery. The mathematician was Archimedes
cupoosta [38]
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8 0
3 years ago
What is 5x^2-7x-3=8 by solving using a graph???
Alinara [238K]
Hello!

Simplifying
5x2 + -7x + -3 = 8

Reorder the terms:
-3 + -7x + 5x2 = 8

Solving
-3 + -7x + 5x2 = 8

Solving for variable 'x'.

Reorder the terms:
-3 + -8 + -7x + 5x2 = 8 + -8

Combine like terms: -3 + -8 = -11
-11 + -7x + 5x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-11 + -7x + 5x2 = 0

Begin completing the square. Divide all terms by
5 the coefficient of the squared term:

Divide each side by '5'.
-2.2 + -1.4x + x2 = 0

Move the constant term to the right:

Add '2.2' to each side of the equation.
-2.2 + -1.4x + 2.2 + x2 = 0 + 2.2

Reorder the terms:
-2.2 + 2.2 + -1.4x + x2 = 0 + 2.2

Combine like terms: -2.2 + 2.2 = 0.0
0.0 + -1.4x + x2 = 0 + 2.2
-1.4x + x2 = 0 + 2.2

Combine like terms: 0 + 2.2 = 2.2
-1.4x + x2 = 2.2

The x term is -1.4x. Take half its coefficient (-0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
-1.4x + 0.49 + x2 = 2.2 + 0.49

Reorder the terms:
0.49 + -1.4x + x2 = 2.2 + 0.49

Combine like terms: 2.2 + 0.49 = 2.69
0.49 + -1.4x + x2 = 2.69

Factor a perfect square on the left side:
(x + -0.7)(x + -0.7) = 2.69

Calculate the square root of the right side: 1.640121947

Break this problem into two subproblems by setting
(x + -0.7) equal to 1.640121947 and -1.640121947.

Subproblem 1
x + -0.7 = 1.640121947

Simplifying
x + -0.7 = 1.640121947

Reorder the terms:
-0.7 + x = 1.640121947

Solving
-0.7 + x = 1.640121947

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = 1.640121947 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + x = 1.640121947 + 0.7
x = 1.640121947 + 0.7

Combine like terms: 1.640121947 + 0.7 = 2.340121947
x = 2.340121947

Simplifying
x = 2.340121947

Subproblem 2
x + -0.7 = -1.640121947

Simplifying
x + -0.7 = -1.640121947

Reorder the terms:
-0.7 + x = -1.640121947

Solving
-0.7 + x = -1.640121947

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = -1.640121947 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + x = -1.640121947 + 0.7
x = -1.640121947 + 0.7

Combine like terms: -1.640121947 + 0.7 = -0.940121947
x = -0.940121947

Simplifying
x = -0.940121947

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.340121947, -0.940121947}
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