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3 years ago

Which is the simplified rational expression for 4p-3/3p+1+2p+5/3p+1?

Mathematics

1 answer:

Anvisha [2.4K]3 years ago

5 0

Answer:

$\frac{4p-3}{3p+1}+\frac{2p+5}{3p+1}=2$

Step-by-step explanation:

we are given

$\frac{4p-3}{3p+1}+\frac{2p+5}{3p+1}$

we can see that

denominators of both terms are 3p+1

So, both has same denominators

so, we can combine numerators

and we get

$\frac{4p-3}{3p+1}+\frac{2p+5}{3p+1}=\frac{4p-3+2p+5}{3p+1}$

now, we can combine like terms

$\frac{4p-3}{3p+1}+\frac{2p+5}{3p+1}=\frac{4p+2p-3+5}{3p+1}$

$\frac{4p-3}{3p+1}+\frac{2p+5}{3p+1}=\frac{6p+2}{3p+1}$

now, we can factor out common term

$\frac{4p-3}{3p+1}+\frac{2p+5}{3p+1}=\frac{2(3p+1)}{3p+1}$

we can see that 3p+1 is on both top and bottom

so, we can cancel it

and we get

$\frac{4p-3}{3p+1}+\frac{2p+5}{3p+1}=2$

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a cell phone company plans to market a new smartphone. they have already sold 612 units durning the first week of the campaign.

Vadim26 [7]

The first term is 612.

The common ratio is 1.08 and

The recursive rule is $a_{n} = a^{n-1} \times r$

Step-by-step explanation:

the question to the problem is to write the values of the first term, common ratio, and expression for the recursive rule.

The first term :

In geometric sequence, the first term is given as $a_{1}$ .

⇒ $a_{1} = 612$

Now, the geometric sequence follows as 612, 661, ........

The common ratio (r) :

It is the ratio between two consecutive numbers in the sequence.

Therefore, to determine the common ratio, you just divide the number from the number preceding it in the sequence.

⇒ r = 661 divided by 612

⇒ r = 1.08

To find the recursive rule :

A geometric series is of the form a,ar,ar2,ar3,ar4,ar5........

Here, first term $a_{1} = a$ and other terms are obtained by multiplying by r.

Observe that each term is r times the previous term.
Hence to get nth term we multiply (n−1)th term by r .

The recursive rule is of the form $a_{n} = a^{n-1} \times r$

This is called recursive formula for geometric sequence.

We know that r = 1.08 and $a_{1}$ = 612.

To find the second term $a_{2}$ , use the recursive rule $a_{n} = a^{n-1} \times r$

⇒ $a_{2} = a^{2-1}\times r$

⇒ $a_{2} = a^{1}\times r$

⇒ $a_{2} = 612\times 1.08$

⇒ $a_{2} = 661$

3 0

4 years ago

An astronaut who weighs 85 kilograms on earth weighs 14.2 kilograms on the moon. How much would a person weigh on the moon if th

STatiana [176]

Answer:

Weight on the moon=x=15.87 kilograms

Step-by-step explanation:

This can be expressed as;

Weight on earth=Constant×Weight on moon

where;

Weight on moon=14.2 kilograms

Constant=k

Weight on Earth=85 kilograms

Replacing in the expression above;

85=14.2×k

k=(85/14.2)=5.986

If the person weighs 95 kilograms on Earth;

Weight on the earth=Constant×Weight on moon

where;

Weight on the moon=x

Constant=5.986

Weight on the earth=95 kilograms

Replacing;

95=5.986×x

x=95/5.986=15.87

Weight on the moon=x=15.87 kilograms

4 0

3 years ago

What is the product of 9 and -7?

kolezko [41]

Answer:

The product of 9 and -7 is -63

Step-by-step explanation:

Hope This Helped!

3 0

3 years ago

A rectangular prism. The rectangular base has a length of 5 centimeters and width of 4 centimeters. What are the dimensions of t

AVprozaik [17]

Answer:

dimension is 5cm * 4 cm

Step-by-step explanation:

As the plane is parallel to the base, the ratio between plane's length and width is equal to the ratio of that of the base. -> similar shape.

Moreover, it also divided the rectangular prism into 2 smaller rectangular prism. hence the plane is identical to the base. Hence, same dimension.

see photo

3 0

3 years ago

I NEED HELP PLEASE !

MrRa [10]

Answer:

x = 4, -2 1/2

Step-by-step explanation:

factors:

(2x + 5) (x - 4)

set each factor equal to zero:

2x + 5 = 0

2x = -5

x = -5/2

x - 4 = 0

x = 4

6 0

3 years ago