suppose that w and t vary inversely and that t=1/5 when w=4. write a function that models the inverse variation and find t when w=9
A. t= 1/5w; 4/45
B. t= 1/5w; 1/5
C. t= 1/20w; 1/80
D. t= 4/5w;4/45

To find the range of the function f(x) = 5x^2 + 4 for the given domain {-4, -2, 0, 1.5, 4}, evaluate the function for each value in the domain and find the minimum and maximum outputs. The range of the function is {4, 84}.

To find the range of the function f(x) = 5x^2 + 4 for the given domain {-4, -2, 0, 1.5, 4}, we need to evaluate the function for each value in the domain and find the minimum and maximum outputs.

The range of the function is the set of all possible outputs. In this case, the minimum output is 4 and the maximum output is 84. Therefore, the range of the function is {4, 84}.

Answer:

Any rational root of f(x) is a factor of 9 divided by a factor of 12.

Step-by-step explanation:

Given:

f(x) = 12x³– 5x² + 6x + 9

Required; Rational root of f(x)

The rational root theorem states that: each rational solution

x = p⁄q, written in lowest terms so that p and q are relatively prime

Where

p = factors of the constant

q = factors of the lead coefficient.

Given that

f(x) = 12x³– 5x² + 6x + 9

The constant is 9

And the lead coefficient is 12

The factor of these two are

9; ±1 , ±3, ±9

12: ±1, ±2, ±3, ±4, ±6, ±12

Then the rational root of f(x) is

factor of 9 divided by a factor of 12.

Possible Rational Roots

= (±1 , ±3, ±9) / (±1, ±2, ±3, ±4, ±6, ±12)

The correct statement according to the rational root theorem is

The rational root of f(x) is

factor of 9 divided by a factor of 12

The final price that is paid for the jacket is:

                    $ 48

The actual cost of jacket was: $ 100

The cost of the jacket was reduced by 40%

This means that the after reduction of 40% the jacket will cost:

[tex]100-\dfrac{40}{100}\times 100\\\\\\=100-40\\\\=60[/tex]

This means that the cost of jacket after 40% reduction is: $ 60

Also, there was a coupon that contains 20% off.

This means that the jacket will actually cost:

[tex]60-\dfrac{20}{100}\times 60\\\\\\=60-12\\\\\\=48[/tex]

                    The final price of jacket is:

                              $ 48

To find the common ratio of the given sequence, divide each term by the previous term. The common ratio is 0.75.

The given sequence is: 128, 96, 72, 54, ...

To find the common ratio, we need to determine the ratio between consecutive terms. We can do this by dividing each term by the previous term.

Ratio between the 2nd and 1st terms: 96/128 = 0.75

Ratio between the 3rd and 2nd terms: 72/96 = 0.75

Ratio between the 4th and 3rd terms: 54/72 = 0.75

Since the ratio is the same for all consecutive terms, we can conclude that the common ratio of this geometric sequence is 0.75.

The correct common ratio for the given sequence is [tex]\(\frac{3}{4}\) or 0.75.[/tex]

To find the common ratio of the sequence, we divide each term by the previous term and look for a consistent value:

1. For the second term, \(96\), divided by the first term, [tex]\(128\)[/tex], we get:

[tex]\[ \frac{96}{128} = \frac{3}{4} = 0.75 \][/tex]

2. For the third term, [tex]\(72\),[/tex] divided by the second term, [tex]\(96\),[/tex] we get:

[tex]\[ \frac{72}{96} = \frac{3}{4} = 0.75 \][/tex]

3. For the fourth term, [tex]\(54\),[/tex] divided by the third term, [tex]\(72\)[/tex], we get:

[tex]\[ \frac{54}{72} = \frac{3}{4} = 0.75 \][/tex]

The 5479th digit is 2.

One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components.

How many groups will be created, for instance, if 30 students need to be separated into groups of five for a sporting event? The division operation can be used to quickly and easily fix such issues. In this case, we must divide 30 by 5.

given:

8 digits written in that same order ( 8,7,6,5,4,3,2,1 ) over and over again

So, we have to find 5479th digit

= 5479/8

= 684 7/8

Now, The 684 quotient tells us how many complete times the sequence goes through the cycle of  8,7,6,5,4,3,2,1, and the 7 remainder tells us which member of the cycle is the 5479 digit.

Since the 7th member of the cycle is 2.

Hence, the 5479th digit is 2.

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Answer:

The Answer is Step 3. I took the test :)

Answer:

100

Step-by-step explanation:

To find the common difference, subtract the first term from the last term and divide by the number of terms minus 1.

To find the common difference of an arithmetic sequence given the first and last term, you can use the formula: common difference = (last term - first term) / (number of terms - 1). First, subtract the first term from the last term. Then, subtract 1 from the number of terms. Finally, divide the result of the subtraction by the number of terms minus 1 to find the common difference.

Answer:

the answer is d

Step-by-step explanation:

The vertex and the axis of symmetry are graphed incorrectly.

Answer: 48.7 degrees

Step-by-step explanation:

Let [tex]\theta[/tex] is the angle between the his sight line form with the side of the hotel,

Since, the building is of 5-story and a men having height 6 feet is in the fifth-story.

Thus, the total length from the eyes of the man and foot of the building = 6 + 12 × 5 = 6 + 60 = 66 feet

Also, the distance of the statue from the foot of the building = 75 feet.

Then by the below diagram,

[tex]tan\theta = \frac{75}{60+6}[/tex]

[tex]tan\theta = \frac{75}{66}[/tex]

[tex]\theta=48.6522227803\approx 48.7\text{ degree}[/tex]

The answer is 1/500 because it will always be the probability of the event occurring/total events

Answer:

Option A. July-August.

Step-by-step explanation:

Phillips family spent each month on groceries. The amount of money in each month is shown in a graph.

Approximate amount in each month was spent :

March : $450

April  : $400

May  :  $400

June  :  $500

July  :  $300

August : $ 500

Sep.  :  $480

Oct. : $420

From the graph given, there is a greatest month to month increase in spending occur in July to August (from $300 to $500).

So Option a. July-August is the correct answer.

The required rate of wingbeats per second is 92.

A Hummingbird moves its wings at a rate of 5520 wingsbeats a minute. Write this rate in wingbeats per second?

Rate of change is defined as the change in value with rest to the time is called rate of change.

given rate = 5520 wingsbeats a minute.
      now to convert it in seconds divide it by 60

= 5520/60
= 92 wingsbeats a second

Thus, The required rate wingbeats per second is 92.

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The quadratic equation 7x^2 + 4x - 8 = 14 does not have any real solutions.

The given equation is a quadratic equation of the form at² + bt + c = 0, where a = 7, b = 4, and c = -22. To find the solutions, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Substituting the values, we get:

x = (-4 ± √(4² - 4(7)(-22))) / (2(7))

Simplifying further, we get:

x = (-4 ± √(16 - 616)) / 14

x = (-4 ± √(-600)) / 14

The expression inside the square root is negative, which means there are no real solutions to the equation.

The given conditions suggest a second-degree polynomial of form p(x) = ax^2 + bx + c. By solving the given conditions a = 5, b = -3, and c = 3, yielding the polynomial p(x) = 5x^2 - 3x + 3.

The question is asking for a second-degree polynomial, which can generally be written in the form p(x) = ax^2 + bx + c. Given that p(1) = 5, that means a + b + c = 5. The derivative of p(x), p'(x) = 2ax + b, and p'(1) = 7, so 2a + b = 7. The second derivative, p''(x) = 2a, and p''(1) = 10, so 2a = 10 or a = 5. We can substitute a = 5 into the first two equations to find the values of b and c. So, b = -3 and c = 3. Therefore, the original function is p(x) = 5x^2 - 3x + 3.

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