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3 years ago

What is the difference?

Mathematics

1 answer:

Crazy boy [7]3 years ago

6 0

Answer:

<h2>D. $\frac{x^{2}+3x-12 }{(x-5)(x+3)(x+7)} \\$ or StartFraction x squared + 3 x minus 12 Over (x + 3) (x minus 5) (x + 7) EndFraction</h2>

Step-by-step explanation:

Given the expression $\frac{x}{x^{2}-2x-15 } - \frac{4}{x^{2} + 2x - 35 }$ , the dfference is expressed as follows;

Step1: First we need to factorize the denominator of each function.

$\frac{x}{x^{2}-2x-15 } - \frac{4}{x^{2} + 2x - 35 }\\= \frac{x}{x^{2}-5x+3x-15 } - \frac{4}{x^{2} + 7x-5x - 35 }\\= \frac{x}{x(x-5)+3(x-5) } - \frac{4}{x( x+ 7)x-5(x +7) }\\= \frac{x}{(x-5)(x+3) } - \frac{4}{(x-5)(x +7) }\\\\$

Step 2: We will find the LCM of the resulting expression

$= \frac{x}{(x-5)(x+3) } - \frac{4}{(x-5)(x +7) }\\= \frac{x(x+7)-4(x+3)}{(x-5)(x+3)(x+7)} \\= \frac{x^{2}+7x-4x-12 }{(x-5)(x+3)(x+7)} \\= \frac{x^{2}+3x-12 }{(x-5)(x+3)(x+7)} \\$

The final expression gives the difference

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Jamie ordered 200 business cards and paid $23. She ordered 500 business cards a few months later and paid $35. Write and solve a

Gnesinka [82]

Answer:

To purchase 700 business cards, Jamie needs to pay $43.

Step-by-step explanation:

We are given that Jamie ordered 200 business cards and paid $23 in total.

We are also given that Jamie ordered 500 business cards and paid $35.

We can use the rate of change formula to find the average change.

$\displaystyle \bullet \ \ \ \frac{\triangle y}{\triangle x}$

This can also be represented with:

$\displaystyle \bullet \ \ \ \frac{y_2-y_1}{x_2-x_1}$

Therefore, we need to identify our variables.

In every relationship, there is a dependent variable and an independent variable.

The independent variable is the variable that an experimenter adjusts in order to receive an altered effect from an output.
The dependent variable is the variable that adjusts based on the changes made to the independent variable.

We change the amount of business cards that are purchased, which in turn, changes the price.

The y-variable is assigned to the dependent variable and the x-variable is assigned to the dependent variable.

Therefore, if we use the coordinate system:

(200, 23)
(500, 35)

Now, we can name our coordinates. We use this system:

(x₁, y₁)
(x₂, y₂)

This means that we can name our points:

x₁ = 200
y₁ = 23
x₂ = 500
y₂ = 35

Revisiting the rate of change formula, we can insert these values.

$\displaystyle \frac{y_2-y_1}{x_2-x_1}$

$\displaystyle \frac{35 - 23}{500-200}\\\\\frac{12}{300}=\frac{1}{25}$

Next, we need to find the y-intercept of our line. We can do this by using one coordinate pair from above and our slope.

The slope-intercept equation is:

$\bullet \ \ \ y = mx + b$

We already know m:

$\displaystyle \bullet \ \ \ \frac{1}{25}$

We also know x and y (we take them from of the coordinate pairs):

$\bullet \ \ \ x = 200$

$\bullet \ \ \ y = 23$

Now, we can substitute these values into the equation and solve for b.

$\displaystyle [y = mx + b]\\\\23 = \frac{1}{25}(200) + b\\\\23 = 8 + b\\\\23 - 8 = 8 - 8 + b\\\\15 = b\\\\b = 15$

Now, we can set up our linear equation.

$\displaystyle y = \frac{1}{25}x + 15$

Therefore, in order to find the price of 700 business cards, we make x in the equation equal 700 and then solve.

$\displaystyle y = \frac{1}{25}(700)+15\\\\y = 28 + 15\\\\y = 43$

Therefore, the price of 700 business cards is equal to $43.

3 0

2 years ago

Please answer correctly !!!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!!

cestrela7 [59]

Answer:

x = √47

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Trigonometry

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

Step-by-step explanation:

Step 1: Define

We have a right triangle. We can use PT to solve for the missing side length.

Step 2: Identify Variables

Leg a = 5

Leg b = x

Hypotenuse c = √72

Step 3: Solve for x

Substitute [PT]: 5² + x² = (√72)²
Exponents: 25 + x² = 72
Isolate x term: x² = 47
Isolate x: x = √47

8 0

2 years ago

Solve 5X30 draw a picture

emmasim [6.3K]

150 is your correct answer

3 0

2 years ago

Read 2 more answers

Can you please help me with 1-12? Thank you

Marysya12 [62]

Answer:

1. 18.84 in

2. 56.52 cm

Step-by-step explanation:

The circumference of a circle is the distance around the circle. Its found using the formula C = πd or C=2πr. The variable d represents the diameter or the distance from one edge of the circle to the other through the cent. The variable r represents the radius of a circle or the distance from one edge to the center. Use the formula by substituting a diameter or radius then simplify.

1. C = πd = π(6) = 3.14(6) = 18.84 in

2. C = 2πr = 2(3.14)(9) = 56.52 cm

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3 years ago

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diamong [38]

Answer:

Step-by-step explanation:

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