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Final answer:

The rule for the function with the given points is f(x) = x^2 + 2/19, as derived from observing the relationship between x-values and their corresponding y-values where the y-values increase by the square of the x-value with a constant fractional part of 2/19.

Explanation:

To find the rule for the function represented by the set of points given, we need to look for a pattern in the y-values relating to the x-values. The provided points are (0,2/19), (1,1 2/19), (2,4 2/19), (3, 9 2/19), (4, 16 2/19), and (5, 25 2/19). Observing the differences between the y-values, it appears that the fractional part remains constant at 2/19, whereas the whole number part increases by the square of the x-value. Therefore, we can express the function rule as f(x) = x2 + 2/19.

Let's verify this by substituting the x-values from the points into our proposed rule:

As we can see, the values match perfectly, confirming that the rule of the function is indeed f(x) = x2 + 2/19.

number with closed dots on -1.5 and 1 with shading in between

The horse weighs 615 pounds.

Let's assume the rider's weight is x.

The horse's weight is 6 times the rider's weight plus 45 pounds: 6x + 45.

The total weight of the horse and rider is 710 pounds: 6x + 45 + x = 710.

Combining like terms: 7x + 45 = 710.

Subtract 45 from both sides: 7x = 665.

Divide both sides by 7: x = 95.

So, the rider weighs 95 pounds.

Substitute x = 95 back into the equation to find the horse's weight: 6(95) + 45 = 570 + 45 =

The horse weighs 615 pounds.

To solve this problem, we will set up an equation where [tex]\( h \)[/tex] represents the horse's weight and [tex]\( r \)[/tex] represents the rider's weight. According to the problem:

1. The horse's weight is 45 pounds more than six times the rider's weight, so we can express this as:

[tex]\[ h = 6r + 45 \][/tex]

2. The total weight of the horse and the rider is 710 pounds, so we have:

[tex]\[ h + r = 710 \][/tex]

Now we have a system of equations:

[tex]\[ h = 6r + 45 \][/tex]

[tex]\[ h + r = 710 \][/tex]

We can substitute the first equation into the second to solve for \( r \):

[tex]\[ (6r + 45) + r = 710 \][/tex]

[tex]\[ 7r + 45 = 710 \][/tex]

Now, we solve for[tex]\( r \)[/tex]:

[tex]\[ 7r = 710 - 45 \][/tex]

[tex]\[ 7r = 665 \][/tex]

[tex]\[ r = \frac{665}{7} \][/tex]

[tex]\[ r = 95 \][/tex]

Now that we have the rider's weight, we can find the horse's weight:

[tex]\[ h = 6r + 45 \][/tex]

[tex]\[ h = 6 \times 95 + 45 \][/tex]

[tex]\[ h = 570 + 45 \][/tex]

[tex]\[ h = 615 \][/tex]

To find -115 + (-35), simply add the two numbers as if they were positive, then add a negative sign, resulting in -150. It can be written as a fraction in simplest form as -150/1.

The operation in this question is addition. You are adding two negative numbers.

To add two negative numbers, simply add the numbers as though they were positive, then add a negative sign to the result. So, in this case, you would add 115 and 35 to get 150, then add a negative sign to your answer, resulting in -150.

This can be written as a fraction in simplest form as -150/1. It's also important to note that any number over 1 is simply the number itself, so -150/1 is essentially just -150.

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To solve the expression −115 + (−35), combine the numbers to get −150. The answer in simplest fractional form is −150/1.

Solving the Expression: −115+(−35)

To solve the expression −115 + (−35), follow these steps:

The final answer is −150/1.

Answer: The diver's new depth is 11.8 feet below the water's surface.

Step-by-step explanation:

Since we have given that

Depth below the water's surface = 15 feet

The diver swims up slowly at 0.5 feet per second for 4 seconds.

Number of miles he swims up is given by

[tex]0.5\times 4\\\\=2\ feet[/tex]

Number of miles he swims up for 3 more seconds at 0.4 feet per second.

So, Number of miles he swims up is given by

[tex]0.4\times 3\\\\=1.2\ feet[/tex]

So, the diver's new depth would be

[tex]-15+2+1.2\\\\=-15+3.2\\\\=-11.8\ feet[/tex]

Hence, the diver's new depth is 11.8 feet below the water's surface.

2x + 6 >-6

subtract 6 from both sides

2x > -12

divide both sides by 2

x > -6

The integer representation of '5 strokes above par' is '+5', while its opposite is '-5', representing '5 strokes under par'. The positive and negative signs indicate whether you are above or below the par in golf.

In the context of golf, '5 strokes above par' means that it took five more strokes than the par to complete a hole or course. We can express '5 strokes above par' as the integer +5. In this context, the positive sign in front of 5 indicates you are above par, which means it took you more swings to finish.

Conversely, the opposite of +5 is -5. This would mean '5 strokes under par,' suggesting that it took five fewer strokes than the par to finish the hole or course. Note that in golf, being under par is generally better as it means you needed fewer swings to complete the course.

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Answer:  there are 20 orange skittles and 10 red skittles in the bag.

Explanation:

Since we have given that

Let the number of red skittles be x

Let the number of orange skittles be 2x

According to question,

[tex]2x-x=10\\x=10[/tex]

So, there are 10 red skittles in the bag and

The number of orange skittles in the bag is given by

[tex]2x=2\times 10=20[/tex]

Hence, there are 20 orange skittles and 10 red skittles in the bag.

The number of red and orange Skittles in the bag are;

I. Red skittles, R = 10

II. Orange skittles, S = 20

To find the number of red and orange Skittles in the bag;

Translating the word problem into a mathematical (algebraic) expression, we would have;

[tex]R = S - 10[/tex]  ....equation 1.

[tex]S = 2R[/tex]  ....equation 2.

Substituting eqn 2 into eqn 1, we have;

[tex]R = 2R - 10\\\\2R - R = 10[/tex]

Red skittles, R = 10

To find the number of orange skittles;

[tex]S = 2[/tex] × [tex]10[/tex]

Orange skittles, S = 20

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Jessie ran the farthest on Monday when he ran 3.30 miles.

To determine on which day Jessie ran the farthest, we need to compare the distances he ran on each day. Let's list the distances:

From the list, we can see that Jessie ran the farthest on Monday when he ran 3.30 miles.

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The most basic figure in geometry is called a point. For example, point A which can also represent as .A. If we have a point, we usually we usually label it with a capital letter. If we have two points such as points X and Y, we can introduce our next figure in geometry which is called a line segment. For example, segment XY. A line segment is defined as a figure that is composed of two points which are called the endpoints and all the points in between. Segment XY can be represented as XY with a segment drawn over it.