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3 years ago

The area of a square is 32 more than its perimeter. find the length of a side.

Mathematics

1 answer:

Eva8 [605]3 years ago

6 0

Answer:

The length of a side of the square is 8 unit.

Step-by-step explanation:

Suppose, the length of a side of the square is $a$ unit.

Formula for perimeter of square: $P=4(side) = 4a$

Formula for area of square: $A=(side)^2 = a^2$

Given that, the area is 32 more than the perimeter. So, the equation will be......

$a^2= 4a+32$

Moving all terms to the left side, we will get.....

$a^2-4a-32=0$

Now, factoring out the left side.......

$a^2-8a+4a-32=0\\ \\ a(a-8)+4(a-8)=0\\ \\ (a-8)(a+4)=0$

Using 'zero-product property', we will get......

$a-8=0\\ a=8\\ \\ and\\ \\ a+4=0\\ a=-4$

(Negative value is ignored as the side length can't be in negative)

So, the length of a side of the square is 8 unit.

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SOMEONE PLEASE HELP ME ASAP PLEASE !!!

Ede4ka [16]

Answer:

530.66

Step-by-step explanation:

The way we find the area of the circle we use the radius of the circle for this one it's 13cm squared * pi or 3.14

For this circle we do 3.14 * 13^2

First we have to square 13: 13^2 = 169

Then we multiply 169 by 3.14: 3.14 * 169 = 530.66

Then we do to the nearest hundredth which is the same as the previous answer: 530.66

3 0

4 years ago

Read 2 more answers

Amelia and Elliott are collecting empty soda cans for recycling. Amelia has 13 less than 5 times the cans that Elliott has. Toge

sleet_krkn [62]

ANSWER

Find out the how many cans does each one have.

To proof

As given

Amelia and Elliott are collecting empty soda cans for recycling

Amelia has 13 less than 5 times the cans that Elliott has.

let us assume that the Elliott has can be =x

Amelia can = 5x -13

Total can = 257 cans

than the equation becomes

x + 5x - 13 = 257

6x = 257 +13

6x = 270

x = 45

Elliott has can be = 45cans

Amelia can = 5 × 45 - 13

= 212cans

Hence proved

5 0

4 years ago

Item 5

sveticcg [70]

Answer:

$94.50

Step-by-step explanation:

6 0

3 years ago

Which ordered pairs are solutions to the inequality 2x+y>−4?

alexgriva [62]

Answer:

The ordered pairs are (5,-12), (-1,-1).

Step-by-step explanation:

Given : Inequality $2x+y>-4$

To find : Which ordered pairs are solutions to the inequality ?

Solution :

We put the given options the point which satisfied the equation is the solution.

Inequality $2x+y>-4$

1) (5,-12)

$2(5)+(-12)>-4$

$10-12>-4$

$-2>-4$

It is true.

2) (-1,-1)

$2(-1)+(-1)>-4$

$-2-1>-4$

$-3>-4$

It is true.

3) (-3,0)

$2(-3)+(0)>-4$

$-6+0>-4$

$-6>-4$

It is false.

4) (4,-12)

$2(4)+(-12)>-4$

$8-12>-4$

$-4>-4$

It is false.

Therefore, The ordered pairs are (5,-12), (-1,-1).

4 0

4 years ago

If caffeine reduces by about 10% per hour, how many hours h does it take for the amount of caffeine in a body to

Mila [183]

Answer:

7 hours

Step-by-step explanation:

Since, the final amount of caffeine formula would be,

$A=P(1-r)^t$

Where,

P = Initial value,

r = rate per period,

t = number of periods,

Here, r = 10% = 0.10, t = h, A = $\frac{P}{2}$

$\frac{P}{2}=P(1-0.10)^h$

$\frac{1}{2}=(0.90)^h$

Taking log both sides,

$log 0.5 = log 0.90^h$

$log 0.5 = h log 0.90$

$\implies h = \frac{log 0.5}{log 0.9}=6.57881347896\approx 7$

Hence, after 7 hours the amount of caffeine in a body to reduce by half.

3 0

3 years ago