LINEAR INEQUALITIES ! Jason needs to rent a hall to host a party. A particular rental hall charges a flat fee, with an additional charge per person, excluding the host. The cost per person to rent the hall is listed in the table below.

Number of People Total Cost
(in $)
( 1 50)
(2 55)
(3 60)
(4 65)

Which of the following inequalities can be used to determine how many friends Jason can invite to the party if he wants to spend less than $100?

Answer:

the answer is the 2nd graph your welcome:)

Step-by-step explanation:

A function is the relationship between two variables such that each input has exactly one output

The function which is negative for the interval [-1, 1] is the function represented by the second graph

The reason the second graph is the correct option is as follows:

The output values of a function are the y-values of the function. A function is negative over an interval if its y-values are negative in the interval

The given interval is [-1, 1], which is the interval from x = -1, to x = 1

From the given graphs, the graph of the function that is negative over the interval [-1, 1] which is the second graph

a·x² + b·x + c = 0

At x = 0, y = -2

At x = 1, y = 0

At x = -1, y = 0

At x = 2, y = 2

Solving the above gives; The equation of the function is f(x) = x² - 2

The graph of the function is attached

Learn more about graphs of function here:

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Final answer:

John's weight dropped by 12.5%.

Explanation:

To calculate the percent by which John's weight dropped, we need to find the difference between his initial weight and final weight, and then divide that difference by his initial weight. We can then multiply the result by 100 to express it as a percentage.

Initial weight = 168 pounds
Final weight = 147 pounds

Difference = 168 - 147 = 21 pounds

Percent drop = (Difference / Initial weight) x 100

Percent drop = (21 / 168) x 100 = 12.5%

Therefore, John's weight dropped by 12.5%.

Final answer:

To calculate the percent by which John's weight dropped, subtract his final weight from his initial weight, and divide the difference by his initial weight, then multiply by 100. John's weight dropped by 12.5%.

Explanation:

To calculate the percent by which John's weight dropped, you need to find the difference between his initial weight and his final weight, then divide that difference by his initial weight and multiply by 100.

So, John's weight dropped by 12.5%.

Answer:

  -4

Step-by-step explanation:

Use your knowledge of multiplication facts.

  [tex]\sqrt[3]{-64}=\sqrt[3]{(-4)^3}=-4[/tex]

__

Your calculator may be able to do this for you.

Answer:

C. [tex]\frac{2}{5}[/tex]

Step-by-step explanation:

Let x be the number which is more than 0.35 but less than 0.41,

⇒ 0.35 < x < 0.41

[tex]\implies \frac{35}{100}< x < \frac{41}{100}[/tex]

[tex]\implies \frac{7}{20} < x < \frac{41}{100}[/tex]

∵ Only [tex]\frac{2}{5}[/tex] is between [tex]\frac{7}{20}[/tex] and [tex]\frac{41}{100}[/tex],

Hence, option C is correct.

6 pots

6 pots

6 pots

6 pots

Jackson walks 5/12 miles farther than Thomas to work. So, Jackson walks approximately [tex]\( \frac{5}{12} \)[/tex] miles farther than Thomas.

To find out how much farther Jackson walks to work than Thomas, we need to subtract the distance Thomas walks from the distance Jackson walks.

Thomas walks 1 1/4 miles, which is equivalent to 5/4 miles. Jackson walks 1 2/3 miles, which is equivalent to 5/3 miles.

To subtract fractions, we need a common denominator, which in this case is 12. So, 5/3 is equivalent to 20/12, and 5/4 is equivalent to 15/12.

Now, subtracting, we get 20/12 - 15/12 = 5/12 miles.

Therefore, Jackson walks 5/12 miles farther than Thomas.

Answer:

  -8 or +7

Step-by-step explanation:

Let x represent the number. The the problem statement tells us ...

  x² + x = 56

  x² +x -56 = 0 . . . . . subtract 56 to put into standard form

  (x +8)(x -7) = 0 . . . . factor

Solutions to the equation are values of x that make the factors zero:

  x = -8 . . . or . . . x = +7

The number could be -8 or +7.

_____

Check

For x = -8, the square is (-8)² = 64. Adding -8 to that gives 64-8 = 56.

For x = 7, the square is 7² = 49. Adding 7 to that gives 49+7 = 56.

Answer:

[tex]\left\{\begin{matrix}x+y\geq 2\\ x< y\\ y> \frac{1}{2}\end{matrix}\right.[/tex]

Step-by-step explanation:

Let  x represents the number of hours spent practicing his backhand

Let y represents the number of hours practicing his serve.

Since we are given that Tim practices his backhand and his serve at least 2 hours each day i.e. he practices his backhand and serves for two hours or more than two hours

⇒ x+y≥2 --(a)

We are also given that He works less on his backhand than his serve

⇒x < y --(b)

And we are also given that he practices his serve more than 1/2 hour daily.

⇒ y > 1/2 --(c)

Thus the inequalities are :

[tex]\left\{\begin{matrix}x+y\geq 2\\ x< y\\ y> \frac{1}{2}\end{matrix}\right.[/tex]

Thus the Option C is correct .

To find the perimeter of a polygon with vertices, calculate the sum of the lengths of all the sides of the polygon by taking the distance between each pair of consecutive vertices and adding them together.

To find the perimeter of a polygon with vertices, you need to calculate the sum of the lengths of all the sides of the polygon. The perimeter is the distance around the polygon. You can do this by taking the distance between each pair of consecutive vertices and adding them together. For example, if you have a triangle with vertices A, B, and C, you would calculate the length of AB, BC, and AC, and then add these lengths together to find the perimeter of the triangle.

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#SPJ12

Answer:

two pair of opposite equal angles

bisecting diagonals

two pair of opposite parallel sides