All categories

3 years ago

9. If the diagonal of a square is 12 centimeters, the area of the square is

Mathematics

1 answer:

SVEN [57.7K]3 years ago

6 0

Answer:

D. 72 cm²

Step-by-step explanation:

The area of a square is given by ;

Area= l² where l = length

Given that the diagonal is 12 cm, let assume length of the square to be l

Apply the Pythagorean relationship where a=b=l

l² + l² = 12²

2 l² = 144

l²= 144/2

l²= 72

l =√72 =8.485 cm

⇒length of the square= l= 8.485 cm

⇒Area of the square= l² = 8.485² = 72 cm²

You might be interested in

Mr. Jones is reading a mystery book to his sixth-grade English class. He reads 4 pages in 12 minutes.

kompoz [17]

4, 8, 12, 16 I can’t see your table but I think these are the answers. :)

5 0

3 years ago

Read 2 more answers

Simplify 4z2 + z2 + 6a.

podryga [215]

5z^2 + 6a is the simplified expression

5 0

3 years ago

Some types of algae have the potential to cause damage to river ecosystems. Suppose the accompanying data on algae colony densit

Phantasy [73]

Answer:

$y=-2.95836 x +234.56159$

Step-by-step explanation:

We assume that th data is this one:

x: 50, 55, 50, 79, 44, 37, 70, 45, 49

y: 152, 48, 22, 35, 43, 171, 13, 185, 25

a) Compute the equation of the least-squares regression line. (Round your numerical values to five decimal places.)For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

So we can find the sums like this:

$\sum_{i=1}^n x_i =50+ 55+ 50+ 79+ 44+ 37+ 70+ 45+ 49=479$

$\sum_{i=1}^n y_i =152+ 48+ 22+ 35+ 43+ 171+ 13+ 185+ 25=694$

$\sum_{i=1}^n x^2_i =50^2 + 55^2 + 50^2 + 79^2 + 44^2 + 37^2 + 70^2 + 45^2 + 49^2=26897$

$\sum_{i=1}^n y^2_i =152^2 + 48^2 + 22^2 + 35^2 + 43^2 + 171^2 + 13^2 + 185^2 + 25^2=93226$

$\sum_{i=1}^n x_i y_i =50*152+ 55*48+ 50*22+ 79*35+ 44*43+ 37*171+ 70*13+ 45*185+ 49*25=32784$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=26897-\frac{479^2}{9}=1403.556$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=32784-\frac{479*694}{9}=-4152.22$

And the slope would be:

$m=-\frac{-4152.222}{1403.556}=-2.95836$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{479}{9}=53.222$

$\bar y= \frac{\sum y_i}{n}=\frac{694}{9}=77.111$

And we can find the intercept using this:

$b=\bar y -m \bar x=77.1111111-(-2.95836*53.22222222)=234.56159$

So the line would be given by:

$y=-2.95836 x +234.56159$

7 0

3 years ago

What is the perimeter of the fifth square in this pattern?

torisob [31]

The first square has side lengths of 4 units(because the square root of 16 is 4). The second square has side lengths of 8 units. The third square has side lengths of 12 units. As you can tell, the side lengths increase by 4. So the fourth square will have side lengths of 16 units, and the fifth square will have side lengths of 20 units. The question wants the perimeter, so the answer is 20*4(sum of 4 sides of equal lengths) which is 80 units.

5 0

3 years ago

AB = 3 + x

strojnjashka [21]

Answer:

Option A) 4, 2

Step-by-step explanation:

We are given that quadrilateral ABCD is a parallelogram with sides:

$AB = 3 + x\\DC = 4x\\AD = y + 1\\BC = 2y$