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A rectangle has a length of (x+4) feet and a width of (+7) feet. The expression 2(x+4)+2(x+7) represents the perimeter of the re

Marta_Voda [28]

Answer:

(x+4)+(x+4)+(x+7)+(x+7)

4 0

2 years ago

Read 2 more answers

Explain how you know which method you should use to solve a rational equation.

notsponge [240]

Methods to solve rational equation:

Rational equation:

A rational equation is an equation containing at least one rational expression.

Method 1:

The method for solving rational equations is to rewrite the rational expressions in terms of a common denominator. Then, since we know the numerators are equal, we can solve for the variable.

For example,

$\frac{1}{2}=\frac{x}{2}\Rightarrow x=1$

This can be used for rational equations with polynomials too.

For example,

$\frac{1+x}{x-3}=\frac{4}{x-3}\Rightarrow(1+x)=4 \Rightarrow x=3$

When the terms in a rational equation have unlike denominators, solving the equation will be as follows

$\frac{x+2}{8}=\frac{3}{4}$

$\Rightarrow\frac{x+2}{1}=\frac{3\times8}{4}\Rightarrow{x+2}=2\times3$

$\Rightarrow{x+2}=6\Rightarrow x=6-2\Rightarrow x=4$

Method 2:

Another way of solving the above equation is by finding least common denominator (LCD)

$\frac{x+2}{8}=\frac{3}{4}$

Factors of 4: $1\times2\times2$

Factors of 8: $1\times2\times2\times2$

The LCD of 4 and 8 is 8. So, we have to make the right hand side denominator as 8. This is done by the following step,

$\Rightarrow\frac{x+2}{8}=\frac{3}{4}\times{2}{2}$

we get,

$\Rightarrow\frac{x+2}{8}=\frac{6}{8}$

On cancelling 8 on both sides we get,

$\Rightarrow(x+2)=6\rightarrow x=6-2\rightarrow x=4$

Hence, these are the ways to solve a rational equation.

7 0

2 years ago

A new cruise ship line has just launched 3 new ships: the Pacific Paradise, the Caribbean Paradise, and the Mediterranean Par

topjm [15]

Let the number of deluxe that Pacific has be x
the number that Caribbean has will be (x+18)
the number that Mediterranean has will be (3x-25)
total b=number of deluxe in the 3 ships will be:
x+(x+18)+(3x-25)
5x-7=928
5x=928+7
x=935/5
x=187
Hence the Pacific has 187, Caribbean has 187+18=205, Mediterranean has (3*187-25)
=534

6 0

2 years ago

Complete this statement: 16a2x2 + 20a²x + 12a2 - 4a?(

yaroslaw [1]

Answer:

the answer is 4aX(21+5ax)

Step-by-step explanation:the big x is a multiplication symbol

8 0

2 years ago

Show that n(n+1)(n+2) is divisible by 6 Solution (

vladimir2022 [97]

Proof by induction

Base case:

n=1: 1*2*3=6 is obviously divisible by six.

Assumption: For every n>1 n(n+1)(n+2) is divisible by 6.

For n+1:

(n+1)(n+2)(n+3)=

(n(n+1)(n+2)+3(n+1)(n+2))

We have assumed that n(n+1)(n+2) is divisble by 6.

We now only need to prove that 3(n+1)(n+2) is divisible by 6.

If 3(n+1)(n+2) is divisible by 6, then (n+1)(n+2) must be divisible by 2.

The "cool" part about this proof.

Since n is a natural number greater than 1 we can say the following:

If n is an odd number, then n+1 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.

If n is an even number" then n+2 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.

Therefore by using the method of mathematical induction we proved that for every natural number n, n(n+1)(n+2) is divisible by 6. QED.

6 0

2 years ago