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3 years ago

What property is illustrated in this equation?

Mathematics

1 answer:

Lerok [7]3 years ago

8 0

In the equation given, the Distributive Property is being demonstrated.

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What is the formula of finding the volume of a triangular prism?

rewona [7]

Answer:

Step-by-step explanation:

Let A represent the area of the triangular base and h the height of the prism. Then the volume of this triangular prism is V = (1/3)(A)(h).

7 0

3 years ago

(03.05 MC) Solve the rational equation x divided by 2 equals x squared divided by quantity x minus 2 end quantity, and check for

ycow [4]

Answer:

x = 0 and x = -2 are solutions of the given rational equation.

Step-by-step explanation:

We must solve the following rational equation:

$\frac{x}{2} = \frac{x^{2}}{x-2}$

Now we present the procedure:

1) $\frac{x}{2} = \frac{x^{2}}{x-2}$ Given

2) $x\cdot (x-2) = 2\cdot x^{2}$ Compatibility with multiplication/Existence of the multiplicative inverse/Definition of division/Modulative property.

3) $x^{2}-2\cdot x = 2\cdot x^{2}$ Distributive property/ $a^{b}\cdot a^{c} = a^{b+c}$

4) $x^{2} + 2\cdot x = 0$ Compatibility with addition/Existence of the additive inverse/Modulative property/Reflexive property

5) $x \cdot (x+2) = 0$ Distributive property/ $a^{b}\cdot a^{c} = a^{b+c}$

6) $x = 0\, \lor\, x = -2$ Result

Now we check the rational equation with each root:

x = 0

$\frac{x}{2} = \frac{x^{2}}{x-2}$

$\frac{0}{2} = \frac{0^{2}}{0-2}$

$0 = \frac{0}{-2}$

$0 = 0$

x = 0 is a solution of the rational equation.

x = -2

$\frac{x}{2} = \frac{x^{2}}{x-2}$

$\frac{-2}{2} = \frac{(-2)^{2}}{-2-2}$

$-1 = -1$

x = -2 is a solution of the rational equation.

4 0

3 years ago

Currently a product has a gear ratio of 17:5, driver:driven. If the company wants to change the product to have the same gear ra

Sedbober [7]

Answer:

10 teeth must go on the driven gear

Step-by-step explanation:

Let the number of teeth be x

In order for the new product to maintain the same ratio as the old the ratio must remain the same. This means that

17:5 = 34:x

$\frac{17}{5} = \frac{34}{x}\\Now\ let\ us\ cross-multiply\\17 \times x = 5 \times 34\\17x = 170\\dividing\ both\ sides\ by\ 17 \\x = \frac{170}{17} \\x = 10$

∴ 10 teeth must go on the driven gear

hence ratio = 34:10

8 0

2 years ago

2, -6, 18, __, 162, __, ...

Semmy [17]

Answer:

-54, 162, -486

Step-by-step explanation:

You multiply the number in front by -3.

2*-3=-6

-6*-3=18

18*-3=-54

-54*-3=162

162*-3=-486

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7 0

3 years ago

Lilia is saving money for dance lessons. She already has $10. Each week she is going to save $5. Write an equation, in slope-int

katrin [286]

The equation which represents the amount of money, y, that Lilia will save in x weeks is;

y =$5x + $10.

<h3>Slope-intercept form of linear equations</h3>

The slope-intercept form of linear equations usually takes the form;

y = mx + c

According to the information given;

Lilia already has $10.

Therefore, the y-intercept of the equation is; $10.

And since she saves $5 each week;

The slope of the equation is; $5.

By substitution, the required equation is;

y =$5x + $10.

Read more on slope-intercept form of equations;

brainly.com/question/1884491

4 0

2 years ago