Suri's age is 4 less than 3 times her cousin's age. Suri is 17 years old. Which method can be used to find c, her cousin's age?

Without specific options available, I can provide guidance on where to focus your attention.

The end behavior of a function refers to how the graph behaves (upwards or downwards) as it nears positive or negative infinity within its domain. Essentially, we’re investigating the direction the graph tends towards on both sides.

In this scenario, as the value of x grows, the graph descends, while it ascends when x diminishes. Seek out a comparable occurrence.

If $24 is the price for the 5 used CDs, then your formula would be "24+5x" where x represents the count of additional CDs you buy.

24+5(6-5)

24+5(1)

24+5

=29

Thus, acquiring 6 CDs would cost $29

I hope that’s accurate, good luck^^

Answer:

Part 1) The equation is

Part 2) When x=40 m, the area of the schoolyard is A=2,800 m^2

Part 3) The valid domain consists of all real numbers exceeding zero and below 75 meters

Step-by-step explanation:

Part 1) Formulate an expression for A(x)

Let

x -----> the length of the rectangular school yard

y ---> the width of the rectangular school yard

It is known that

The perimeter for the fencing (taking the school wall as one side) is

thus

-----> this is equation A

The area of the rectangular school yard is

----> this is equation B

Substituting equation A into equation B yields

Change to function notation

Part 2) What is the area when x=40?

With x equal to 40 m

substitute the value into the expression from Part 1 to determine A

   

Part 3) What would be a suitable domain for A(x) in this scenario?

We understand that

A signifies the area of the rectangular school yard

x characterizes the length of the rectangular school yard

It follows that

This forms a vertical parabola opening downwards

The vertex indicates a maximum point

The x-coordinate of the vertex corresponds to the length that maximizes the area

The y-coordinate of the vertex denotes the maximum area

The vertex corresponds to (37.5, 2812.5)

Refer to the accompanying figure

Consequently,

The peak area achieved is 2,812.5 m^2

The x-intercepts are located at x=0 m and x=75 m

The domain for A is the range -----> (0, 75)

All real numbers greater than zero and less than 75 meters

Answer:

The composite function;

f(g(x) = 2x^2 + 15

Step-by-step explanation:

Given f(x) = 2x + 1 and g(x) = x^2 + 7;

we are tasked with calculating f(g(x))

This represents a composite function where we substitute g(x) into f(x)

Consequently, we find

f(g(x)) = 2(x^2 + 7) + 1

f(g(x)) = 2x^2 + 14 + 1

f(g(x)) = 2x^2 + 15

Answer:

The equation 0 = 3x² + 17x - 160 might be useful in determining the length.

Step-by-step explanation:

The area of the vegetable garden is specified as 170 ft².

Now, regarding the provided equations;

1) For 0 = 3x² + 2x + 180, applying the quadratic formula results in:

x = [-2 ± √(3² - 4(3 × 180)]/(2 × 3)

x = [-2 ± √(-2151)]/6

The square root value is negative, indicating no real solution for x.

Thus, this equation does not help find the length.

2) For the equation 0 = 3x² + 10x + 180, employing the quadratic formula, the square root value is also negative, hence there's no natural root for x. This means this equation can't be used to determine the length.

3) For 0 = 3x² + 17x - 160, the roots when using the quadratic formula yield -10.67 or 5. The value 5 is viable since it is a whole number. Considering the area is also a whole number, this equation can be applied to ascertain the length.

4) For 0 = 3x² - 160, simplifying gives;

3x² = 160

x² = 160/3

x = ±√(160/3)

x = ±7.303

Since the area is a whole number but this length isn't, this equation may not accurately determine the length.