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Nastasia [14]
3 years ago
5

Express the sum in the simplest form.

Mathematics
1 answer:
attashe74 [19]3 years ago
3 0
The last option, 2.
Because the 2 terms have a common denominator, we can add them together on the same fraction. This gives us 2y+4 / y+2. We notice that the left is twice each co-effecient of the right, so after simplifying, we get 2 / 1.
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How can you find the LCM of two rational expressions if the polynomials cannot be factored?
Leviafan [203]

Answer:

To find the LCD of two rational expressions, we factor the expressions and multiply all of the distinct factors. For instance, if the factored denominators were (x+3)(x+4) ( x + 3 ) ( x + 4 ) and (x+4)(x+5) ( x + 4 ) ( x + 5 ) , then the LCD would be (x+3)(x+4)(x+5) ( x + 3 ) ( x + 4 ) ( x + 5 ) .

7 0
2 years ago
$2000 was borrowed for 4 years with an interest rate of 3% compounded annually. What is the total amount owed at the end of the
kompoz [17]

Answer:

\$2,251.02  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

A=P(1+\frac{r}{n})^{nt}  

where  

A is the total amount owed  

P is the amount of money borrowed

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

t=4\ years\\ P=\$2,000\\ r=3\%=3/100=0.03\\n=1  

substitute in the formula above  

A=2,000*(1+\frac{0.03}{1})^{1*4}  

A=2,000*(1.03)^{4}  

A=\$2,251.02  

4 0
3 years ago
Read 2 more answers
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Pavlova-9 [17]

Answer:

whats the question

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
How to write numbers in standard form?
Rama09 [41]
Standard form is just another way of saying "how to write a number in a regular form".


Ex. Standard form is any number. 

4
65
234
1,865
234,908
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6 0
3 years ago
Three spherical balls with radius r are contained in a rectangular box. two of the balls are each touching 5 sides of the rectan
olganol [36]

Answer:

The volume of the space between the balls and the rectangular box is 4r^{3}(6 - \pi)

Step-by-step explanation:

The attachment below shows the description of the rectangular bow and the three spherical balls.

From the description,  

  • Two of the balls are each touching 5 sides of the rectangular box, say the 5 sides touched by one of the balls are sides 1,2,3,4, and 5; then the other ball will touch sides 2,3,4,5, and 6).  
  • The middle ball also touches four sides of the rectangular box, These four sides touched by the middle ball will be sides 2,3,4, and 5.

This means the balls are tightly fitted into the rectangular box.

Each of the balls has a radius r

Hence, The volume of one of the balls is given by the volume of a sphere

Volume of a sphere = \frac{4}{3} \pi r^{3} \\

The volume occupied by one of the balls is \frac{4}{3} \pi r^{3} \\

∴ The volume occupied by the three spherical balls will be

3 × \frac{4}{3} \pi r^{3} \\

= 4\pi r^{3}

The volume occupied by the three spherical balls 4\pi r^{3}

For the rectangular box,

The volume of a rectangular box = l w h

Where l\\ is the length

w is the width and

h is the height

Since the balls are tightly packed,

The width of the rectangular box will be the diameter of the balls

diameter of the balls = 2r

∴ w = 2r

The height of the rectangular box will also be the diameter of the balls

∴ h = 2r

The length of the rectangular box will be 3 times the diameter of the balls

∴l = 3 × 2r = 6r

Hence,

The volume of a rectangular box = 6r × 2r × 2r

= 24r³

The volume of the space between the balls and the rectangular box is given by

Volume of the space between the balls and the rectangular box =

volume of the rectangular box -  volume occupied by the three spherical balls

Volume of the space between the balls and the rectangular box= 24r³ - 4πr³

=  24r³ - 4πr³

= 4r³(6 - π)

5 0
3 years ago
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