Can someone really help me please

The length of a rectangle is three times it’s width. The area of the rectangle is 48 square centimeters. Find the measures of th

denis-greek [22]

---------------------------------------------------------------------------------
Define length and width
---------------------------------------------------------------------------------
Let the width be x
Width = x
Length = 3x

---------------------------------------------------------------------------------
Form equation and solve for x
---------------------------------------------------------------------------------
x(3x) = 48
3x² = 48
x² = 48 ÷ 3
x² = 16
x = √16
x = 4

---------------------------------------------------------------------------------
Find length and width
---------------------------------------------------------------------------------
Width = x = 4
Length = 3x = 3(4) = 12

---------------------------------------------------------------------------------
Answer: Width = 4cm, Length = 12cm
---------------------------------------------------------------------------------

7 0

3 years ago

Find the center and radius of the circle whose equation is x2 + y2 - 6x-2y+4= 0

marin [14]

Answer:

The center of the circle = (3, 1)

The radius of a circle is given as r = √6

Step-by-step explanation:

The equation of a circle is given as:

( x - a)² + (y - b)² = r²

where ( a , b) = center of the circle

r = radius of the the circle

In the question above, we are given the equation of a circle as

x² + y² - 6x - 2y + 4= 0

In order to find the center and radius of this circle we would use completing the square method to solve it

Step 1

Collect the like terms

x² - 6x + y² - 2y + 4= 0

Step 2

Complete the square for both x and y

x² - 6x + (-6/2)² + y² - 2y + (-2/2)² = - 4 +(- 6/2)² + (-2/2)²

x² - 6x + (-3)² + y² - 2y + (-1)² = -4 + (3)² + (1)²

x² - 6x + 9 + y² - 2y + 1 = -4 + 9 + 1

(x² - 6x + 9) + (y² - 2y + 1 )= -4 + 9 + 1

(x² - 3x - 3x +9) + ( y² - y - y +1) = 6

x(x - 3) -3( x - 3) + y( y - 1) - 1( y - 1) = 6

(x - 3) (x -3) +(y - 1) ( y - 1) = 6

(x - 3)²(y - 1)² = 6

Since,

The equation of a circle is given as:

( x - a)² + (y - b)² = r²

where ( a , b) = center of the circle

r = radius of the the circle

The equation of the the circle for the above question is calculated as:

(x - 3)²(y - 1)² = 6

where ( a , b) = center of the circle = (3, 1)

r = radius of the the circle

r² = 6

r = √6

8 0

3 years ago

Plot the four points on the number line below -1/3 1 2/3 2/3 1 1/3

navik [9.2K]

Answer:

Step-by-step explanation:

6 0

3 years ago

What simple interest rate would allow $6000 to grow to an amount of $14550 in 10 years?

Harman [31]

Answer:

$\boxed{ \bold{ \huge{ \boxed{ \sf{ \: 14.25 \: \% \: }}}}}$

Step-by-step explanation:

Given,

Principal ( P ) = $ 6000

Amount ( A ) = $ 14550

Time ( T ) = 10 years

Rate ( R ) = ?

Finding the Interest

The sum of principal and interest is called an amount.

From the definition,

$\boxed{ \sf{Amount = \: Principal + Interest}}$

plug the values

⇒ $\sf{14550 = 6000 + Interest}$

Swap the sides of the equation

⇒ $\sf{6000 + Interest = 14550}$

Move 6000 to right hand side and change its sign

⇒ $\sf{Interest = 14550 - 6000}$

Subtract 6000 from 14550

⇒ $\sf{Interest = \: 8550 \: }$

Interest = $ 8550

Finding the rate 

${ \boxed{ \sf{Rate = \frac{Interest \times 100}{Principal \times Time}}}}$

plug the values

⇒ $\sf{ Rate = \frac{8550 \times 100}{6000 \times 10} }$

Calculate

⇒ $\sf{Rate = \frac{855000}{60000} }$

⇒ $\sf{Rate = 14.25 \: \% \: }$

Hope I helped!

Best regards!!

8 0

3 years ago

Determine if the linear system

zubka84 [21]

Answer:

b. The system is not in echelon form because the system is not organized in descending "stair step" pattern so that the index of the leading variables increases from the top to bottom.

Step-by-step explanation:

The given linear system has a equation which is not in echelon form. The echelon is a system which divides the data into rigid hierarchal groups. The given linear equation in not in echelon form as the leading variables are increased from top to bottom indicating descending stair step pattern.

4 0

3 years ago