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3 years ago

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Here is another riddle: The sum of two numbers is less than 2. If we subtract the second number from the first, the difference i

s greater than 1. What are the two numbers? The riddle can be represented by a system of inequalities. Write an inequality for each statement.

1 answer:

aivan3 [116]3 years ago

4 0

Answer:

Let x, y be the two numbers under consideration. Then, x+y<2 and x-y>1.

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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 <em>w</em> 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 <em>w</em> 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 <em>quadratic equation</em> 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

WILL GIVE BRAINLIEST

jok3333 [9.3K]

Answer:

J'(-2,5)

K'(-7,5)

M'(-3.5,2)

L'(5.5,2)

Step-by-step explanation:

Please refer to the image attached to this answer.

Trapezoid JKLM is reflected over the x-axis, what do we notice about the ordered pairs of the original figure and the ordered pairs of its reflection over the x-axis is described below.

Point J , K L and M , when reflected over x axis , there distance from the y axis remains the same in second quadrant. the x coordinate becomes negative however the y coordinates remains the same.

The coordinates will be as shown in the image attached.

3 0

3 years ago

Read 2 more answers

Solve the system of equations by elimination <br> 3x+4y=31<br> 2x-4y=-6

ANEK [815]

3x + 4y = 31
2x - 4y = -6

*The +4 and -4 in the center of the equation cancel out because 4-4 = 0*

3x = 31
2x = -6
------------

*add like terms*

3x + 2x = 5x

31 - 6 = 25

So now you should have this written on your paper ... > 5x = 25

*Divide by 5 on each side*

5x = 25
_ _
5 5

x = 5

5 0

3 years ago

Read 2 more answers

Show your work in the comments below and the answer choice ❤️

lawyer [7]

The answer is D, 2,520 cm³.

4 0

3 years ago

Solve the formula for the area of a parallelogram the height,

valkas [14]

Answer:

h=A/b

Step-by-step explanation:

Think of putting number in the place of the letter, for example

A is 4

b is 2

h is 2

4=2 x 2 then plug the numbers in the right spot

2=4/2 then see what can be rearranged or what is left to make the

equation true

5 0

3 years ago