Factor 81y+72. Write your answer as a product with a whole number greater than 1. help plz

Tju [1.3M]

Answer:

The answer would have to be B

7 0

2 years ago

A 2x2 square is centered on the origin. It is dilated by a factor of 3. What are the coordinated of the vertices of the square?

Alexxx [7]

Answer:

The vertices are:

A' = (-3, -3)

B' = (3, -3)

C' = (3, 3)

D' = (-3, 3)

The ratio of area of larger square to smaller square is 9:1

Step-by-step explanation:

Given:

A 2 x 2 square is centered at the origin.

So, the center of the square is (0, 0)

Since it is 2 x 2 square, the side of the square is 2 units.

So, the vertices of the 2 x 2 square are A (-1, -1), B(1, -1), C(1. 1), D(-1, 1)

The above square is dilated by a factor of 3.

Let's name the dilated square A'B'C'D'

To find the coordinates of the vertices of dilated square, we need to multiply each vertices of ABCD by 3.

A(-1, -1) = 3(-1, -1) = A'(-3, -3)

B(1, -1) = 3(1, -1) = B'(3, -3)

C(1, 1) = 3(1, 1) = C'(3, 3)

D(-1, 1) = 3(-1, 1) = D'(-3, 3)

To find the area of the small square

the side of the small square is 2 units

so the are of the small square is $2^2$ = 4 square units

To find the area of the larger square

lets find the side AB of the square using distance formula

=> $\sqrt{(x_2 -x_1)^2 +(y_2-y_1)^2}$

=> $\sqrt{(3 - (-3))^2 +(-3 - (-3))^2}$

=> $\sqrt{(3 +3)^2 +(-3 +3)^2}$

=> $\sqrt{(6)^2 +(0)^2}$

=> $\sqrt{36}$

=>6

AB =6 units

In a square all the sides will be equal

Now the area of the larger square will be

$6^2$

36 square units

The ratio of larger square to smaller square is

=>36 : 4

=>9 : 1

5 0

3 years ago

Suppose that $3000 is placed in an account that pays 16% interest compounded each year. Assume that no withdrawals are made from

Papessa [141]

Answer:

a) $3480

b) $4036.8

Step-by-step explanation:

The compound interest formula is given by:

$A(t) = P(1 + \frac{r}{n})^{nt}$

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

Suppose that $3000 is placed in an account that pays 16% interest compounded each year.

This means, respectively, that $P = 3000, r = 0.16, n = 1$