What is the difference between graphing the inequality y > x + 5 and y < x + 5

Mathematics

1 answer:

Zepler [3.9K]3 years ago

4 0

Answer:

The graph on the first equation y>x+5 will be shaded above the line. The graph on the second. equation y< x+5 will be shaded below the line.

When y is less than (y<), then the graph is shaded below the line. if y is greater than,( y>) then it will be shaded above the line.

Hope this helps! Give a heart and brainlest if so!

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Here’s my dilemma, I can accept a $1000 bill or play a game ten times. For each roll of the single die, I win $500 for rolling 1

Aloiza [94]

Answer:

you should accept the $1,000 bill

Step-by-step explanation:

Given the information:

$500 for rolling 1 or 2
$400 for rolling 3
lose $300 for rolling 4,5,6

P (rolling 1 or 2) = 1/6 + 1/6 = 2/6 = 1/3

P (rolling a 3) = 1/6

P (rolling 4 or 5 or 6) = 3/6 = 1/2

Hence, the expected value for 1 time is:

E = (1/3)*500 + (1/6)*400 - (1/2)*300

E = $166 + $66 - $150

E = $82

Expected value is linear so if you roll the die 10 times, expected value is: 10*82 = $820

The expected value is $82, meaning you should accept the $1,000 bill

5 0

3 years ago

The width of a rectangle is 6 kilometers less than twice its length. if its area is 108 square kilometers, find the dimensions

Art [367]

Hi there!

Answer:
length = 9 kilometres
Width = 12 kilometres

Let's solve this problem step by step!
To find our answer we need to set up and solve an equation.

Let the length of the rectangle be represented by x.
The width of the rectangle can therefore be expressed by 2x - 6.

The area of a rectangle can be found by using the formula:
A = width × length

Plug in the data from the formula
A = x (2x - 6).

Simplify using rainbow technique.
$x(2x - 6) = 2 {x}^{2} - 6x$

Now we've found the simplified expression that expresses the area of the rectangle. Therefore, we can now set up and start solve the equation.

$2 {x}^{2} - 6x = 108$
Subtract 108

$2 {x}^{2} - 6x - 108 = 0$
Divide by 2.

${x}^{2} - 3x - 54$
$(x - 9)(x + 6) = 0$
Rule AB = 0, gives A is 0 or B is 0.

$x - 9 = 0 \\ x = 9 \\ \\ x + 6 = 0 \\ x = - 6$

The length of the rectangle, which was represented by x, must be 9 (since it cannot be a negative number).

Length
$x = 9$
Width
$2x - 6 = 2 \times 9- 6 = 18 - 6 = 12$

Answer:
length = 9 kilometres
Width = 12 kilometres

~ Hope this helps you!

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3 years ago

A _______________________ is a comparison of two measurements in which the denominator has a value of one unit.

Galina-37 [17]

I think the answer is unit rate.

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3 years ago

What is the quadratic formula

LUCKY_DIMON [66]

Answer:

x = -b +or- the square root of (b^2-4ac) ALL / 2a

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