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nataly862011 [7]
3 years ago
9

If a rectangle's length is y−2 and the width is 3y+2 write an expression for the perimeter and an expression for the area.

Mathematics
1 answer:
aalyn [17]3 years ago
3 0

Answer:

Area = 3y^2 - 4y - 4 units square.

Perimeter = 8y units.

Step-by-step explanation:

Area of a rectangle = length * width.

Perimeter of a rectangle = 2*(length + width).

It is given that length = y−2 units and width = 3y+2 units. To find the area and the area of the rectangle in terms of y, simply put the length and the width in the above area and perimeter equations.

Area = length * width = (y-2)*(3y+2).

Expanding the expression gives:

Area = 3y^2 + 2y - 6y - 4 = (3y^2 -4y - 4) units square.

Similarly,

Perimeter = 2*(length + width) = 2*(y-2 + 3y+2) = 2*4y = 8y units.

Therefore, the expression for the area and the perimeter of the given rectangle is (3y^2 - 4y - 4) units square and (8y) units respectively!!!

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Answer:

Step-by-step explanation:

You have to use the triangle inequality theorem:

12cm, 4cm, xcm

x > 4cm - 12cm

x > -8cm

x < 12cm - 4cm

x < 8cm

-8cm < x < 8cm

5 0
3 years ago
The radius of a sphere is 6 cm what is the volume
spayn [35]

Answer:

904.78

Step-by-step explanation:

A sphere with a radius of 6 units has a volume of 904.78 units

5 0
3 years ago
What is the solution to the liner equation <br><br> -12+3b-1=-5-b
Natalija [7]

Answer:

b=2

Step-by-step explanation:

-12+3b-1=-5-b

Combine like terms

-13 +3b = -5-b

Add b to each side

-13+3b+b = -5-b+b

-13+4b = -5

Add 13 to each side

-13+13 +4b = -5+13

4b = 8

Divide by 4

4b/4 = 8/4

b = 2

6 0
3 years ago
Read 2 more answers
Which ratio can be used to form a proportion with the given ratio? 3 to 4
quester [9]

As soon as I see the word "Which ...", I know that there's a list of choices that
goes along with this question, but you decided not to share them.  So there's
no way for me to help you choose the correct one.

In order to form a proportion with 3/4, you need another fraction (or ratio) that's
equal to 3/4 .  Look for a fraction whose numerator is 3/4 of its denominator. 

Here are a few examples:

-- 6 / 8
-- 24 / 32
-- 300 / 400
-- 12 million / 16 million
-- 3x / 4x
-- 15abc / 20abc
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6 0
3 years ago
Test the series for convergence or divergence (using ratio test)​
Triss [41]

Answer:

    \lim_{n \to \infty} U_n =0

Given series is convergence by using Leibnitz's rule

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given series is an alternating series

∑(-1)^{n} \frac{n^{2} }{n^{3}+3 }

Let   U_{n} = (-1)^{n} \frac{n^{2} }{n^{3}+3 }

By using Leibnitz's rule

   U_{n} - U_{n-1} = \frac{n^{2} }{n^{3} +3} - \frac{(n-1)^{2} }{(n-1)^{3}+3 }

 U_{n} - U_{n-1} = \frac{n^{2}(n-1)^{3} +3)-(n-1)^{2} (n^{3} +3) }{(n^{3} +3)(n-1)^{3} +3)}

Uₙ-Uₙ₋₁ <0

<u><em>Step(ii):-</em></u>

    \lim_{n \to \infty} U_n =  \lim_{n \to \infty}\frac{n^{2} }{n^{3}+3 }

                       =  \lim_{n \to \infty}\frac{n^{2} }{n^{3}(1+\frac{3}{n^{3} } ) }

                    = =  \lim_{n \to \infty}\frac{1 }{n(1+\frac{3}{n^{3} } ) }

                       =\frac{1}{infinite }

                     =0

    \lim_{n \to \infty} U_n =0

∴ Given series is converges

                       

                     

 

3 0
3 years ago
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