A. Multiplication Property of Equality

The length of a rectangle is 6 more than twice the width. if the area is 40 cm^2, find the length and breadth of the rectangle

ra1l [238]

Answer: 3.217 & 12.434

Step-by-step explanation:

If we use w to represent the width, the length will be 6 more than 2 times w.

Hence, the length is $2w+6$ .

The area of a rectangle would be its length times its width, so let's make an equation to represent it's area.

$A=w(2w+6)$

We can also substitute 40 in for A as it's given in the question.

$40 = w(2w+6)$

Distributing w by multiplying it by both terms in the parentheses, we get

$40 = 2w^2+6w$

We can make the equation simpler by dividing both sides by 2.

$20 = w^2+3w$

Subtracting both sides by 20 will make the left-hand side 0.

$0=w^2+3w-20$

Now that we have put this quadratic equation into standard form (ax²+bx+c), we can find its solutions using the quadratic formula.

For reference, the quadratic formula is

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

In this case, a is 1, b is 3, and c is -20.

Substituting, we get

$w=\frac{-3\pm\sqrt{3^2-4(1)(-20)}}{2(1)}$

$w= \frac{-3\pm\sqrt{9+80}}{2}$

$w=\frac{-3+\sqrt{89}}{2}\hspace{0.1cm}or\hspace{0.1cm}\frac{-3-\sqrt{89}}{2}$

Since the second solution results in a negative number, it cannot be the length of w.

$w=\frac{-3+\sqrt{89}}{2}\approx3.217$

The width/breadth of the rectangle is 3.217 cm.

To calculate the length, let's substitute the width into the expression for the length:

$l=2(3.217)+6$

$l=12.434$

The length of this rectangle is 12.434 cm.

6 0

1 year ago

Write a formula for this sequence: 8,-1,-10,-19

Romashka [77]

This is an arith. sequence, and the common difference is -9.

a(n+1) = a(n)-9, with a(1)=8. Thus, if we look at the first term, we see 8; subracting 9 from 8 produces the second term (-1).

4 0

3 years ago

WHAT THE HECC IS THIS

anyanavicka [17]

Answer:

h(x)

Step-by-step explanation:

to solve for an inverse, you swap the x and the y and then solve for y

f(x) = 4x^3-8

y = 4x^3 - 8

x = 4y^3 - 8 swap the x and y

now solve for y:

x + 8 = 4y^3

(x + 8)/4 = y^3

1/4x + 8/4 = y^3

1/4x + 2 = y^3

y = $\sqrt[3]{1/4x + 2}$

4 0

2 years ago

How many cubes will it take to fill the bottom layer of this rectangular prism?

Alik [6]

The bottmo layer should be the same as the top layer sinc it is all squares

count the top
6 squares
answer is 6 squares

7 0

3 years ago

Determine whether the random variable is discrete or continuous. a. The number of statistics students now reading a book. b. The

andrey2020 [161]

Answer:

Continuous random variables: c and e

Discrete random variables: a, b, d

Step-by-step explanation:

We have to identify whether the random variable is discrete or continuous.

A discrete variable is a variable whose value is obtained by counting.
A continuous random variable X takes all values in a given interval of numbers.
Thus, a continuous variable can have values in decimals but a discrete random variable cannot take values in decimals.

a. The number of statistics students now reading a book.

Discrete random variable since number of students cannot take decimal values.

b. The number of textbook authors now sitting at a computer.

Discrete random variable since number of textbooks cannot be expressed in decimals but counted.

c. The exact time it takes to evaluate 27 plus 72.

It is a continuous random variable as it may take all values within an interval of time.

d. The number of free dash throw attempts before the first shot is made.

It is a discrete random variable since the number of throws can always be whole number.

e. The time it takes to fly from City Upper A to City Upper B.

Time is a continuous random variable.

6 0

3 years ago