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Ket [755]
2 years ago
6

20 points!!

Mathematics
1 answer:
ANEK [815]2 years ago
5 0

See below for the proof of the equation \frac{ax + by}{x + y} - \frac{ax - by}{x - y}= 2(a - b)

<h3>How to prove the equation?</h3>

The equation is given as:

\frac{ax + by}{x + y} - \frac{ax - by}{x - y}= 2(a - b)

Take the LCM

\frac{(ax + by)(x - y) -(ax - by)(x + y)}{(x + y)(x - y)}= 2(a - b)

Expand

\frac{ax^2 - axy + bxy - by^2 -ax^2 - axy + bxy + by^2}{(x + y)(x - y)}= 2(a - b)

Evaluate the like terms

\frac{-2axy + 2bxy }{(x + y)(x - y)}= 2(a - b)

Rewrite as:

\frac{-2axy + 2bxy }{x^2 - y^2}= 2(a - b)

Factorize the numerator

\frac{2(a - b)(x^2 - y^2)}{x^2 - y^2}= 2(a - b)

Divide

2(a - b)= 2(a - b)

Both sides are equal

Hence, the equation \frac{ax + by}{x + y} - \frac{ax - by}{x - y}= 2(a - b) has been proved

Read more about equations at:

brainly.com/question/2972832

#SPJ1

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I don't know how to do this :(
Lemur [1.5K]
Hello.

e is a mathematical constant, and it's like pi, it's irrational. It's approximately equal to 2.71828....

So, e^{\frac{3}{2}} = 4.4816... 
It's approximately equal to 4.5 which is choice 2.
8 0
2 years ago
Read 2 more answers
Find the measure of angle 1
nikklg [1K]

Answer:

Angle 1, 2, 4 = 45 degrees

Step-by-step explanation:

2x+15 = x+30

-15 both sides

2x = x+15

-x both sides

x = 15

Plug x = 15 into x+30 or 2x+15

15+30 = 45

2(15)+15 = 45

4 0
3 years ago
What is the slope of the line that passes through the points (-4, -2)(−4,−2) and (-4, -22) ?(−4,−22)? Write your answer in simpl
Anestetic [448]

The line is vertical, so the slope is infinite

Step-by-step explanation:

Given two points with coordinates (x_1, y_1) and (x_2,y_2), the slope of the line passing through the two points is given by the equation

m=\frac{y_2-y_1}{x_2-x_1}

In this problem, the coordinates of the two points are:

(x_1,y_1)=(-4,-2)

and

(x_2,y_2)=(-4,-22)

which means:

x_1=-4\\y_1=-2\\x_2=-4\\y_2=-22

Substituting all these values into the equation of m, we find the slope of the line:

m=\frac{-22-(-2)}{-4-(-4)}=\frac{-20}{0}=\infty

The slope is infinite: this is because the line is vertical.

Learn more about slope of a line:

brainly.com/question/4152194

brainly.com/question/12941985

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7 0
3 years ago
A group of 2 adults and 4 children spent $38 on tickets to a museum. A group of 3 adults and 3 children spent $40.50 on tickets
mrs_skeptik [129]

Answer:

adult $8.00

child $5.50

Step-by-step explanation:

Let the price of 1 adult ticket = x.

Let the price of 1 child ticket = y.

2x + 4y = 38

3x + 3y = 40.5

Multiply the first equation by 3. Multiply the second equation by -2. Then add them.

         6x + 12y = 114

(+)      -6x - 6y = -81

-----------------------------

                  6y = 33

y = 33/6

y = 5.5

2x + 4y = 38

2x + 4(5.5) = 38

2x + 22 = 38

2x = 16

x = 8

Answer:

adult $8.00

child $5.50

4 0
3 years ago
Read 2 more answers
30 POINTS FOR THE GENUIS WHO CAN ANSWER THIS!!
bearhunter [10]

Answer:

Answers are below in bold

Step-by-step explanation:

1) A = 1/2bh          Use this equation to find the area of each triangular base

A = 1/2(8)(6)         Multiply

A = 1/2(48)           Multiply

A = 12cm²           Area of each triangular base

2) A = L x W        Use this equation to find the area of the bottom rectangular face

A = 20 x 8          Multiply

A = 160 cm²       Area of the bottom rectangular face

3) A = L x W        Use this equation to find the area of the back rectangular face

A = 20 x 6          Multiply

A = 120 cm²       Area of the back rectangular face

4) A = L x W        Use this equation to find the area of the sloped rectangular face

A = 20 x 10         Multiply

A = 200 cm²      Area of the sloped rectangular face

5) To find the total surface area of the triangular prism, add together all of the numbers.

A = 12 + 12 + 160 + 120 + 200       Add

A = 504 cm²       Total area of the triangular prism

6 0
3 years ago
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