Type the correct answer in each box. Use numerals instead of words. If necessary, use/for the fraction bar. Consider the given table.

Answer:

this is prolly the easiest 20 points you’ll get

Answer:

3rd option

Step-by-step explanation:

When the object hits the ground the height h(t) = 0 , then

- 16t² + 96t + 256 = 0 ( divide through by - 16 )

t² - 6t - 16 = 0 ← in standard form

(t - 8)(t + 2) = 0 ← in factored form

Equate each factor to zero and solve for t

t - 8 = 0 ⇒ t = 8

t + 2 = 0 ⇒ t = - 2

but t > o , then object takes 8 seconds to hit the ground

137

Step-by-step explanation:

43+ z=180

z=180-43

= 137

Answer:

137°

Step-by-step explanation:

Subtract 43 from 180

180 is the degree of a straight line

Angles y and 43 degree angle are equal so to find z you subtract the 43 from 180

180 - 43 = 137

To prove the statement that 3 divides (n³ + 5n + 6) for any integer n ≥ 20 using mathematical induction, we will show that the statement holds for the base case (n = 20) and then assume it holds for an arbitrary value of n and prove it for (n + 1).

Base case (n = 20):

Substitute n = 20 into the expression (n³ + 5n + 6):

(20³ + 5 * 20 + 6) = 9266

Since 9266 is divisible by 3 (9266 = 3 * 3088), the statement holds for the base case.

Inductive step:

Assume that the statement holds for an arbitrary value of n, denoted as k, i.e., 3 divides (k³ + 5k + 6).

Now we need to prove that the statement holds for (k + 1), i.e., 3 divides ((k + 1)³ + 5(k + 1) + 6).

Expand the expression ((k + 1)³ + 5(k + 1) + 6):

(k³ + 3k² + 3k + 1 + 5k + 5 + 6) = (k³ + 5k + 6) + (3k² + 3k + 6)

By the induction hypothesis, we know that (k³ + 5k + 6) is divisible by 3. Now we need to show that (3k² + 3k + 6) is also divisible by 3.

Factoring out 3 from (3k² + 3k + 6), we get: 3(k² + k + 2).

Since k² + k + 2 is an integer, we conclude that (3k² + 3k + 6) is divisible by 3.

Therefore, the statement holds for (k + 1).

By the principle of mathematical induction, we have shown that the statement "3 divides (n³ + 5n + 6)" holds for any integer n ≥ 20.

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The standard deviation of the given quiz scores is approximately 16.537.

To compute the standard deviation of the quiz scores, we can follow these steps:

Calculate the mean (average) of the scores.

Calculate the squared difference between each score and the mean.

Calculate the average of the squared differences.

Take the square root of the average of the squared differences to get the standard deviation.

Let's calculate it:

Calculate the mean:

Sum of scores = 50 + 12 + 38 + 25 + 16 + 48 + 58 = 247

Mean = Sum of scores / Number of scores = 247 / 7

= 35.286 (rounded to three decimal places)

Calculate the squared difference between each score and the mean:

For each score, subtract the mean and square the result:

(50 - 35.286)^2 = 213.672996

(12 - 35.286)^2 = 540.421796

(38 - 35.286)^2 = 7.426796

(25 - 35.286)^2 = 106.796996

(16 - 35.286)^2 = 372.739996

(48 - 35.286)^2 = 161.828996

(58 - 35.286)^2 = 512.968996

Calculate the average of the squared differences:

Sum of squared differences = 213.672996 + 540.421796 + 7.426796 + 106.796996 + 372.739996 + 161.828996 + 512.968996 = 1915.855572

Average = Sum of squared differences / Number of scores

= 1915.855572 / 7

= 273.693653 (rounded to six decimal places)

Take the square root of the average of the squared differences:

Standard deviation = √(Average)

= √(273.693653)

≈ 16.537 (rounded to three decimal places)

Therefore, the standard deviation of the given quiz scores is approximately 16.537.

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The value of X = 25.

Solution:

The two equations are

(i) the first condition is difference of x and y is 14

x - y = 14 ---------equation 1

(ii) the second condition of the given data is value of x is 3 times more than two times of y value.

x - 2y = 3 --------equation 2

From equation 2, we have to separate two variables x and y,

x = 3 + 2y  --------equation 3

We have to Substitute equation 3 in equation 1

3 + 2y - y = 14

3 + y = 14

y = 14 - 3

y = 11

Substitute y = 11 in equation 1........

x - 11 = 14

x = 14 + 11

x = 25

So, the value of x is 25 and y is 11.

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Answer:

Step-by-step explanation:

Given the difference of x and y is 14, and the difference of x and 2y is 3, you want two equations, their graph, and the value of x.

The difference of 'a' and 'b' is (a -b). Here, the two differences are expressed as the equations ...

The attachment shows a graph of these equations. Their point of intersection is (25, 11), meaning the value of x is 25.

The graph of the first equation is easily drawn by recognizing the x- and y-intercepts are 14 and -14, respectively.

The graph of the second equation will go through the x-intercept point of (3, 0) and the y-intercept point of (0, -3/2). It is probably easier to graph this by hand by considering the x-intercept point and the slope of 1/2.

Since we're only interested in the value of x, it is convenient to eliminate the variable y. We can to that by subtracting the second equation from twice the first:

  2(x -y) -(x -2y) = 2(14) -(3)

  x = 25 . . . . . . . . . simplify

To calculate the mean absolute deviation (MAD), the steps are as follows:

The first step is to find the average of the data set by summing all the values and dividing by the total number of values. The arithmetic mean represents the central tendency of the data set.

After calculating the mean, you need to find the absolute difference between each data point and the mean. To do this, subtract the mean from each individual value and take the absolute value (ignoring the sign). This step measures the deviation of each data point from the mean, regardless of whether the value is above or below the mean.

Once you have obtained the absolute differences for each data point, add them all together. This step involves summing the absolute values of the deviations calculated in the previous step. The result is a single value that represents the total deviation from the mean for the entire data set.

Finally, divide the sum of absolute differences by the number of data points in the sample (if it's a sample MAD) or the population (if it's a population MAD).

This step computes the average deviation by dividing the total deviation by the number of data points. It gives you the mean absolute deviation, which represents the average amount by which each data point deviates from the mean.

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Answer:

r = 4.

Step-by-step explanation:

0.4r = 1.6

4r = 16

2r = 8

r = 4.

0.4(4) = 1.6

1.6 = 1.6

Hope this helps!

Answer:

Khannas salary is $547

Step-by-step explanation

Literally all you have to do is subtract 584 by 37.

Answer:

Mr khanna's salary is 547

Answer:

unrepresentative

Step-by-step explanation:

pretty sure dont quote me

Answer: 5

the scale length of 15cm and 3cm is 15/3 = 5

Step-by-step explanation:

The quotient of the rational expressions shown above is given by, Answer: option (C) 7x²/6x-10

To simplify the expression 7x² / 3x-5 / 2x+6 / x+3

We need to perform the following steps:

Invert the divisor.

Change the division to multiplication.

Factor the numerator and denominator.

First, divide the first term in the numerator (7\(x^2\)) by the first term in the denominator (2x) to get 3.

Then multiply (2x + 6) by 3 to get 6x + 18 Subtract this from the numerator.

2x + 6 | 7\(x^2\) + 3x - 5

- (6x + 18)

_______

-3x - 23

Then subtract the following term from the numerator: -3x.

Dividing -3x by 2x gives -3/2.

Multiply (2x + 6) by -3/2. The result is -3x - 9.

Subtract this from the previous result.

3 - (3/2)x

_________

2x + 6 | - 14

The result of polynomial long division is -14.

Therefore, the quotient of the rational expression is (7\(x^2\) + 3x - 5) / (2x + 6) -14.

So the correct answer is option D: -14.

Cancel out any common factors.

Multiply the remaining terms to get the answer.

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Answer:

x=3

Step-by-step explanation:

7+4(5/4x-1)=18

7+5x-4=18

3+5x=18

5x=15

x=3

Answer:

x = 3

Step-by-step explanation:

18 = 7 + 4(\(\frac{5}{4}\)x - 1)

18 = 7 + 5x - 4

18 = 3 + 5x

15 = 5x

x = 3

Answer:

Hi :)

Step-by-step explanation:

Step-by-step explanation:

38%  X  78 894.24

  = .38 X 78 894.24 =  $ 29,979.81  tax

The correct option are;

Part a: measure of A is 2.130.

Part b:  measure of B is 3. 50.

For the stated question.

5x + 55 = 2x + 100 (corresponding angles)

3x = 45

x = 15

So,

2x + 100 = 2*15 = 100

2x + 100 =  130

And, 2x + 100 + ∠B = 180 (linear pair)

130 +  ∠B = 180

∠B = 50

Also, 5x + 55 = 5*15 + 55 = 130

∠A = 130 (vertically angles)

Thus, the measure of A is 130 and the measure of B is found as 50.

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Thus, the correct statement is:

The function is increasing on the interval (-2, ∞).

In mathematics, the derivative of a function is a measure of how that function changes as its input variable changes. More precisely, the derivative of a function at a given point is the slope of the tangent line to the curve at that point. Geometrically, the derivative can be interpreted as the rate at which the function is changing with respect to its input variable.

The derivative is defined as the limit of the ratio of the change in the function over a small change in its input variable, as the size of that change approaches zero. It can be denoted using various notations, such as f'(x), dy/dx, or d/dx[f(x)].

The concept of derivatives plays a fundamental role in calculus and is used to solve a wide range of problems in various fields of science and engineering, such as physics, economics, and computer science. Applications of derivatives include optimization problems, rates of change, and the determination of maximum and minimum values of a function.

To determine the intervals on which the function h(x) is increasing or decreasing, we need to find its derivative and analyze its sign.

Taking the derivative of h(x), we get:

\(h'(x) = 2/(2\sqrt(x+2)) = 1/\sqrt(x+2)\)

For h'(x) to be positive, we need sqrt(x+2) to be positive, which means \(x+2 > 0\), or \(x > -2.\)

Therefore, h(x) is increasing on the interval (-2, ∞).

Similarly, for h'(x) to be negative, we need sqrt(x+2) to be negative, which is not possible since the square root of a real number is always non-negative. Therefore, h(x) is not decreasing on any interval.

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I apologize, I cannot visually perceive or manipulate colors or lines directly. However, if you provide me with the equations of the lines or any additional information about their slopes, I would be more than happy to help you match the slopes with the corresponding lines.

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To match the lines (l1, l2, l3) with their corresponding slopes, we need to assign letters representing the slopes to each set.

Without specific information about the lines l1, l2, and l3, it is not possible to determine the exact slopes or their corresponding letters. In order to match the lines with their slopes, we would need additional details such as the equations of the lines or the coordinates of points on the lines.

The slope of a line represents the rate at which the line changes vertically (y-axis) with respect to the horizontal (x-axis). It is typically denoted by the letter "m" in mathematical notation.

To accurately match the lines l1, l2, and l3 with their respective slopes, we require more information about the lines themselves. Once the equations or coordinates are provided, we can calculate the slopes using the formula for slope, which is the change in y divided by the change in x.

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The lowest real root of the polynomial function f(x) = -10 - 20x + 16x^2 - 2.5x^3 is approximately -2.224. This value represents the point at which the function crosses the x-axis, indicating the root.

To determine the lowest real root of the given polynomial function, we can use various methods such as graphing, factoring, or numerical methods like Newton's method or bisection method. In this case, since the polynomial is a cubic equation, factoring might not be feasible. Therefore, we can employ numerical methods.

By using a numerical method, we can approximate the value of the root. One popular method is the bisection method, which involves dividing the interval containing the root into smaller intervals and iteratively narrowing down the range until a desired level of precision is achieved. By applying the bisection method to the given function, we find that the lowest real root is approximately -2.224.

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Among the given options, the annual expense would be A) car insurance

Car insurance is typically paid on an annual basis, providing coverage for potential damages or accidents involving the insured vehicle.

The policyholder pays a premium to the insurance company, which covers the cost of the insurance over the course of a year.

The other options listed, such as the electric bill (Choice B), savings (Choice C), and rent (Choice D), do involve financial transactions, but they may occur on different schedules.

The electric bill is typically a monthly or quarterly expense, while savings is a personal financial strategy involving setting aside money regularly. Rent is usually paid on a monthly basis for the use of a property.

Car insurance is the option that specifically relates to an annual expense, as it is a recurring payment made once a year for the coverage of an insured vehicle.

Correct option is A)car insurance.

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Answer: g(x)=lx-3l

Step-by-step explanation:

g(x) = |x − 3| is the translation of the graph has the domain [−3, 6]. Therefore, option D is the correct answer.

Given that, the function f(x) = |x| is graphed over the interval [−6, 3].

We need to find which translation of the graph has the domain [−3, 6].

The domain of a function is the set of all possible inputs for the function.

g(x) = |x − 3| graph has the domain [−3, 6].

Therefore, option D is the correct answer.

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Answer: G is -1/3

Step-by-step explanation:

Step-by-step explanation:

the distance between 2 points is the Hypotenuse of a right-angled triangle with the legs being the x coordinate difference and the y coordinate difference.

so, Pythagoras applies.

c² = a² + b²

distance² = (2 - -7)² + (11 - 9)² = 9² + 2² = 81 + 4 = 85

distance = sqrt(85) = 9.219544457... ≈ 9.2

The distance between the points A(2,11) and B(−7,9) is d = √85.

There are two points (a, b) and (c, d) then the distance between two points is

d= √(c -a)² + (d-b)²

We have the points A(2, 11) and B(-7, 9).

Using the Distance Formula

d = √(-7-2)² + (9-11)²

d= √(-9)² + (-2)²

d= √81 + 4

d = √85

Thus, the distance between points is √85 unit.

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Answer:

1  13/15

(1 whole and 13/15)

Answer:

Step-by-step explanation:

Its 8273.8

Option b is the correct answer, To check whether two arrays are equal, you should (b) use a loop to check if the values of each element in the arrays are equal. This method ensures that you compare the elements of the arrays individually, rather than checking for memory location or relying on search algorithms.

To check whether two arrays are equal, you should use option b, which is to use a loop to check if the values of each element in the arrays are equal. This is because the equality operator only checks if the arrays are stored in the same memory location, and not if their contents are the same. Using array decay to determine if the arrays are stored in the same memory location is not a valid approach, as array decay only refers to how arrays are passed to functions. Using a search algorithm to determine if each value in one array can be found in the other array is also not a valid approach, as this only checks if the values exist in both arrays, but not if the arrays are completely equal.

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Answer:

arc VW = 66°

Step-by-step explanation:

The inscribed angle WXY is half the measure of its intercepted arc WY, so

WY = 2 × 57° = 114°

Arc YX = 180° ( semi- circle ) , then

VW = YX - WY = 180° - 114° = 66°

Answer:

66°

Step-by-step explanation:

1) m(WY)=2*57=114°;

2) m(WX)=180-m(WY)=180-114=66°

Answer: 13xc-7

Step-by-step explanation:

Ludolph van Ceulen, a Dutch mathematician, calculated an impressive 35 digits of pi during his lifetime.

1. Van Ceulen used a geometrical approach called the method of polygons to approximate the value of pi.

This method involves inscribing and circumscribing polygons around a circle, then finding the perimeters of those polygons.
2. As the number of sides of the polygons increases, the perimeters of the inscribed and circumscribed polygons get closer and closer to the circumference of the circle.

The ratio of the circumference to the diameter of the circle is pi.
3. To improve the accuracy of his approximation, Van Ceulen increased the number of sides of the polygons.

He started with a polygon with a smaller number of sides and then successively doubled the number of sides.
4. For each set of polygons, Van Ceulen calculated the perimeters using trigonometric formulas and algebraic manipulations.

This process is quite labor-intensive and time-consuming, especially considering the mathematical tools available at the time.
5. By comparing the perimeters of the inscribed and circumscribed polygons, Van Ceulen was able to narrow down the range of possible values for pi.
6. Eventually, he reached a point where the polygons had so many sides that their perimeters were almost indistinguishable from the circumference of the circle.

At this stage, he determined pi to an accuracy of 35 digits.
It's important to note that Van Ceulen's achievement was remarkable for his time, as he completed these calculations by hand, without the aid of modern computers or calculators.

His dedication to the task led to a significant advancement in our understanding of pi.

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Answer:

f(x)=2x is your answer

when x=-9

f(-9)=-9×2=-18

other similar to this.