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3 years ago

Please solve and show work if you can!

Mathematics

2 answers:

sweet [91]3 years ago

8 0

$\frac{x+2}{2}\cdot\frac{4x+20}{x^2+6x+8}=\\
\frac{x+2}{2}\cdot\frac{2(2x+10)}{x^2+2x+4x+8}=\\
(x+2)\cdot\frac{2x+10}{x(x+2)+4(x+2)}=\\
(x+2)\cdot\frac{2x+10}{(x+4)(x+2)}=\\
\frac{2x+10}{x+4}$

skad [1K]3 years ago

4 0

$\frac{ x+2 }{2} \cdot \frac{ 4x+20 }{x^2+6x+8 } \\\\x^2+6x+8\neq 0\\ \\x^2+4x +2x+8 \neq 0 \\ \\ x(x+4)+2(x+4)\neq 0\\ \\(x+4)(x+2)\neq 0$

$x+4 \neq 0 \ \ \wedge \ \ x+2\neq 0\\ \\ x\neq -4 \ \ \wedge \ \ x\neq -2 \\ \\ D=R\setminus \left \{ -4,-2 \right \}$

$\frac{ x+2 }{2} \cdot \frac{ 4x+20 }{x^2+6x+8 } =\frac{\not( x+2 )^1}{\not2^1} \cdot \frac{ \not4^2(x+5) }{\not(x+2)^1(x+4) } =\frac{2(x+5)}{x+4}$

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Answer:

b; ∀x P(x) ∨ ¬P(x)

Step-by-step explanation:

Suppose that we have a proposition p

Such that p can be true or false.

We can define the negation of p as:

¬p

Such that, if p is false, then ¬p is true

if p is true, then ¬p is false.

Also remember that a proposition like:

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is true when, at least one, p or q, is true.

Then if we write:

p ∨ ¬p

Always one of these will be true (and the other false)

Then the statement is true.

And if the statement depends on some variable, then we will have that:

p(x) ∨ ¬p(x)

is true for all the allowed values of x.

from this, we can conclude that the statement that is always true is:

b; ∀x P(x) ∨ ¬P(x)

Where here we have:

For all the values of x, P(x) ∨ ¬P(x)

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3 years ago

3/5 of Jill's 30-page photo album is full. She wants to set aside 1/4 of the pages that are left for photos of her vacation. How

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3 years ago

Read 2 more answers

What is 2/3+3/6+5/9?

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Solution:
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3 years ago

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A family has two cars. The first car has a fuel efficiency of 15 miles per gallon of gas and the second has a fuel efficiency of

professor190 [17]

The fuel consumption of each of the cars during the week are as follows;

The first car consumes 20 gallons of fuel.

The second car consumes 30 gallons of fuel.

Reasons:

Fuel efficiency of the first car = 15 miles per gallon

Fuel efficiency of the second car = 35 miles per gallon

Combined distance traveled by the two cars in a week = 1,350 miles

The total gas consumption during the week = 50 gallons

Let x represent the number of gallons consumed by the first car, and let y

represent the number of gallons consumed by the second car, we get the

following system of simultaneous equations;

15·x + 35·y = 1,350...(1)

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Therefore;

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Which gives;

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From equation (2), we have;

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Therefore;

y = 50 - 20 = 30

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Learn more about word problems that lead to simultaneous equations here:

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