The table shows the outputs y for different inputs x:
Input (x) 5 6 7 8
Output (y) 2 5 8 11
Part A: Do the data in this table represent a function? Justify your answer. (3 points)
Part B: Compare the data in the table with the relation f(x) = 2x + 13. Which relation has a greater value when x = 7? (2 points)
Part C: Using the relation in Part B, what is the value of x if f(x) = 75?

Let X be the expected number of distinct types of coupons in the collection of k coupons X = X1 + X2 + ……. + Xx.  

Answer:

answer is d

Step-by-step explanation:

Kaia will pay a $1,500 deductible and the remaining 20% not covered by insurance after the deductible, totaling to $1,680 for her braces.

To calculate how much Kaia will need to pay for her braces, we need to take into account her insurance deductible and the percentage her insurance will cover after that deductible is paid. Kaia's braces cost $2,400, so let's break it down step-by-step:

Kaia pays her insurance deductible, which is $1,500. So, $2,400 - $1,500 = $900 remains.

Her insurance then covers 80% of the remaining $900. To calculate this, we use 80% of $900: ($900 x 0.80) = $720.

Since the insurance pays $720 of the remaining cost, Kaia is left with 20% of $900 to pay out of her pocket. To calculate this, we take 20% of $900: ($900 x 0.20) = $180.

Therefore, Kaia will need to pay $1,500 (deductible) plus $180, for a total of $1,680.

Answer:

The density of silver is 10.49 g/cm3.

Step-by-step explanation:

Physical properties are those that can be observed without any change in the identity of the element in question. In this case, the physical property that is mentioned is density. Other examples include color and hardness. On the other hand, chemical properties describe how a substance can change into a different substance. This would include characteristics such as flammability and corrosion resistance.

ds=√1+(dydx)2dx=√1+14(x4−2+1x4)dx

=√14(x4+2+1x4)dx=√122(x2+1x2)2dx

=12(x2+1x2)dx

The daily population growth function is P=25,000((1.0095)1/365.25)t, and the daily growth rate is approximately 1.000026 or an increase of about 0.0026% per day.

The city population growth function given, P=25,000(1.0095)t, is an exponential function. To identify the daily growth rate, we need to rewrite this function in terms of days. As there are approximately 365.25 days in a year, we substitute this into the formula for t. Hence, the daily population growth function becomes P=25,000(1.0095)t/365.25.

To find the approximate daily growth rate, we solve for the base of the exponent. Using the fact that (ab)c = abc, we can rewrite the function as P=25,000((1.0095)1/365.25)t.

Thus, the daily growth rate of the population is approximately the value of (1.0095)1/365.25, which calculates to about 1.000026, or an increase of about 0.0026% per day.

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After combining like terms, the polynomial simplifies to 5x^3 - 18x - 27. It cannot be factored using basic techniques due to the lack of common factors and its incompatibility with simple factoring patterns.

To factor the polynomial 2x^3 + 3x^3 - 18x - 27, we first combine like terms and then look for common factors or patterns that we can use to factor the polynomial.

Combining Like Terms

Combining the cubic terms, we get 5x^3. Therefore, the polynomial simplifies to 5x^3 - 18x - 27.

Factoring

We look for a greatest common factor (GCF) among the terms. In this case, there are no common factors other than 1.

Since there is no obvious way to factor by grouping, and the polynomial does not fit the patterns for difference of cubes or sum of cubes, we'd have to consider other methods such as Rational Root Theorem or synthetic division to find if the polynomial has rational roots and can be factored further. However, those methods are more complex and require trial and error or a systematic approach that typically isn't covered until more advanced algebra classes or college algebra.

Conclusion

Without additional methods, we conclude that the polynomial 5x^3 - 18x - 27 cannot be factored over the rationals using basic factoring techniques commonly taught in high school algebra.

To factor the expression 2x^3 + 3x^3 - 18x - 27, we can group the terms with common factors and factor out those common factors.

To factor the expression 2x^3 + 3x^3 - 18x - 27, we can group the terms with common factors. The first two terms, 2x^3 and 3x^3, have a common factor of x^3. The last two terms, -18x and -27, have a common factor of -9. Factoring out these common factors, we get:

2x^3 + 3x^3 - 18x - 27 = x^3(2 + 3) - 9(2 + 3) = x^3(5) - 9(5) = 5x^3 - 45

So, the factored form of the expression is 5x^3 - 45.

Answer To Questions :

3 3/4

The area of the rectangle board, including the wooden border, is 280 cm².

The student's question pertains to finding the new area of the rectangle board after adding a 2 cm wooden border around it. Initially, the board has dimensions of 16 cm in length and 10 cm in width. To account for the new wooden border, we add 2 cm to each side of the board. This means that the new length will be 16 cm + 4 cm (2 cm for each side of the length) and the new width will be 10 cm + 4 cm (2 cm for each side of the width).

The calculation will be as follows:

New Length = 16 cm + 4 cm = 20 cm

New Width = 10 cm + 4 cm = 14 cm

Area = New Length * New Width

Area = 20 cm * 14 cm

Area = 280 cm²

Therefore, the area of the rectangle board with a 2 cm border added around it will be 280 cm².

Answer:

Option C

output=0.5(input)+1.5

Step-by-step explanation:

Let

y------> the output

x------> the input

we have

[tex]A(-1,1), B(5,4)[/tex]

Find the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute the values

[tex]m=\frac{4-1}{5+1}[/tex]

[tex]m=\frac{3}{6}=0.5[/tex]

Find the equation of the line

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=0.5[/tex]

[tex]A(-1,1)[/tex]

substitute

[tex]y-1=0.5(x+1)[/tex]

[tex]y=0.5x+0.5+1[/tex]

[tex]y=0.5x+1.5[/tex]

remember that

y=output

x=input

substitute

output=0.5(imput)+1.5

The graph which represent a graph of a function is:

        Graph A and Graph C

We know that a graph of a function satisfies the vertical line test i.e. any line passing through the domain and parallel to y-axis should intersect the curve exactly once i.e. corresponding to each x-value there is exactly one y-value.

Hence, from the figure attached to the answer we see that the Graph which is a function is:

            Graph A and Graph C

Graph A represents a function.

A function is a relation in which each input has only one output. In other words, for every x-value, there can only be one y-value. To determine if a graph represents a function, we can use the vertical line test. If a vertical line intersects the graph at more than one point, then the graph does not represent a function. Looking at the given graphs, Graph B and Graph D do not pass the vertical line test, as there are vertical lines that intersect these graphs at multiple points. Therefore, the correct answer is Graph A.