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The end behavior of the function is as x tends to infinity, f(x) tends to zero. It is power function.

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

The degree and the leading coefficient of a polynomial function given is determine the end behavior of the graph.

Given that function has a vertical asymptote at x = -5 and x = 3 , a point discontinuity at x = 2.

The end behavior of f(x) goes to 0 as x goes to negative infinity and f(x) goes to 0 as x goes to positive infinity.

The domain is (-inf, -5)U(-5, 2)U(2, 3) U (3,inf).

Hence, we can conclude that the end behavior of the function is as x tends to infinity, f(x) tends to zero.

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The amount of work done is Option A) 12 N/m

Work done is simply defined as the product of the magnitude of displacement, (d) and the component of the force that in the direction of displacement.

It measures energy transfer that occurs when an object is moved to a distance by an external force which is applied in the direction of the displacement.

Work done on a body is equivalent  to the increase in the energy of the body, because it transfers energy to the body.

The formula for work done is;

W = fd

Where, 'f' is the applied force and d is the distance

Substitute the values

Work done = 6(2)

Work done = 12 N/m

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9514 1404 393

Answer:

Step-by-step explanation:

The triangle is a right triangle, so the length of r can be found using the Pythagorean theorem.

  r = √(14.2² +7.15²) = √252.7625

  r ≈ 15.8985 ≈ 15.90 . . . meters

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The angles can be found from the tangent relation.

  Tan = Opposite/Adjacent

  tan(P) = 14.2/7.15

  P = arctan(14.2/7.15) ≈ 63.2738° ≈ 63.27°

Angle Q is the complement of angle P.

  Q = 90° -63.27° = 26.73°

The length of the real dinosaur's tail is 120 inches.

We know that the scale of the model is 1in : 15in, this means that each inch in the model represents 15 inches of the actual dinosaur.

So, if the tail of the model has a length of 8 inches, the length of the real tail will have 15 times that, so the length is given by the product:

8in*15 = 120in

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It will take the ball 2.12s to the nearest hundredth to hit the ground.

Quadratic formula is a formula that gives the solutions of the general quadratic equation ax² + bx + c = 0 and that is usually written in the form

x = (-b ± √(b2 − 4ac))/(2a)

From the question, the initial height, h, of the ball is 40 ft

When the ball hits the ground, the height, h, is zero

The equation h = - 16t² + 15t + 40 becomes

0 = - 16t² + 15t + 40

16t² - 15t - 40 = 0

Solving the quadratic equation by formula method for t,

t = (-b ± √(b² - 4ac)) / (2a)

Where, a = 16, b = -15, and c = -49

Substitute these values into the quadratic formula,

t = (15 ± √2785) / 32

Therefore, the possible values of t are:

t = (15 + √2785) / 32

t = (15 - √2785) / 32

Which implies t = 2.12 or t = - 1.18

Since time, t, cannot be negative, t = 2.12s to the nearest hundredth.

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Answer:

n = 1

Step-by-step explanation:

Represent the number with n.

Then:  reciprocal of this numer is 1/n.

1/2 added to this reciprocal comes to 1/n + 1/2, and this is equal to

2(1/n) - 1.

We must simplify this equation and solve for n:

Use the LCD 2n:

2 + n = 4 - 1, or 2 + n = 3, or n = 1.

Answer:

  2/3

Step-by-step explanation:

Let x represent the number. Then its reciprocal (the reciprocal of the original number) is 1/x

  1/2 + 1/x . . . . . 1/2 added to the reciprocal of a number

  2/x -1 . . . . . . . 1 less than twice the reciprocal of the original number

We want these expressions to be equal:

  \(\dfrac{1}{2}+\dfrac{1}{x}=\dfrac{2}{x}-1\\\\\dfrac{3}{2}=\dfrac{1}{x}\qquad\text{add 1-(1/x)}\\\\x=\dfrac{2}{3}\qquad\text{multiply by 2x/3}\)

The original number is 2/3.

The median of the given data set is 26.

In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.

Given the data set, we need to find the median.

So, let's arrange the numbers from smallest to largest in order to find the median.

\(\sf 15,20,22,26,28,35,36.\)

\(\text{Median}=\sf 26\)

Therefore, the median of the data set is 26.

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To graph the function g(x) = 7x + 10, we shift the graph of f(x) = 7x vertically by adding a constant term of +10. This means every y-coordinate on the graph increases by 10 units. The slope of the line remains the same at 7. The resulting graph is a straight line passing through (0, 10) with a slope of 7.

To graph the function g(x) = 7x + 10, you need to make the following change to the graph of f(x) = 7x:
1. Translation: The graph of f(x) = 7x can be shifted vertically by adding a constant term to the equation. In this case, the constant term is +10.
Here's how you can do it step by step:
1. Start with the graph of f(x) = 7x, which is a straight line passing through the origin (0,0) with a slope of 7.
2. To shift the graph vertically, add the constant term +10 to the equation. Now, the equation becomes g(x) = 7x + 10.
3. The constant term of +10 means that every y-coordinate of the points on the graph will increase by 10 units. For example, the point (0,0) on the original graph will shift to (0,10) on the new graph.
4. Similarly, if you take any other point on the original graph, such as (1,7), the corresponding point on the new graph will be (1,17) since you add 10 to the y-coordinate.
5. Keep in mind that the slope of the line remains the same, as only the y-values are affected. So, the new graph will still have a slope of 7.
By making this change, you will have successfully graphed the function g(x) = 7x + 10.

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The smallest number that will make it divisible by 11 is n = 2 and the number is A = 7,01,69,302

Given data ,

Let the missing number be represented as n

Now , the value of the original number is A = 7,01,69,30*​

where * represents = n

To make a number divisible by 11, the difference between the sum of the digits in the odd-numbered positions and the sum of the digits in the even-numbered positions must be a multiple of 11.

On simplifying the equation , we get

To make the difference between the sums a multiple of 11, we need to add the smallest digit to the end. The smallest digit is 8

Hence , the number that is divisible by 11 is 7,01,69,302

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The area of the composite figure is 122.5 square inches

Based on the problem statement, we have the following dimensions from the question

The area of the composite figure is the sum of individual areas

So, we have

Area = Isosceles right triangle + Rectangle + Another isosceles triangle

By applying the formulas, we have

Area = 0.5 * 11 * 11 + 14 * 4 + 0.5 * 4 * 3

Evaluate

Area = 122.5

Hence the area is 122.5 sq inches

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Answer:

B. More than 90

Step-by-step explanation:

Hope this helps!

D. I and IV are the quadrants the cosine function is positive

To determine in which quadrants the cosine function is positive, we need to consider the signs of cosine in different quadrants of the Cartesian coordinate system.

The unit circle is a useful tool to understand the behavior of trigonometric functions. In the unit circle, the x-coordinate represents the cosine value, while the y-coordinate represents the sine value. The cosine function is positive in the quadrants where the x-coordinate is positive.

Quadrant I is the top-right quadrant, where both the x and y coordinates are positive. In this quadrant, cosine is positive because the x-coordinate is positive.

Quadrant II is the top-left quadrant, where the x-coordinate is negative, but the y-coordinate is positive. In this quadrant, cosine is negative because the x-coordinate is negative.

Quadrant III is the bottom-left quadrant, where both the x and y coordinates are negative. In this quadrant, cosine is negative because the x-coordinate is negative.

Quadrant IV is the bottom-right quadrant, where the x-coordinate is positive, but the y-coordinate is negative. In this quadrant, cosine is positive because the x-coordinate is positive.

Based on this analysis, we can conclude that cosine is positive in Quadrant I and Quadrant IV. Therefore, the correct answer is D. I and IV.

It's important to note that this applies to the standard unit circle and the principal values of cosine. When considering periodicity and multiple revolutions around the unit circle, the positive regions of cosine will repeat every 360 degrees or 2π radians.

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Answer:

a c d

Step-by-step explanation:

One of the Possible values of length and width of the prism are 15 cm and 0.5 cm

In geometry, a prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy of the first, and n other faces, necessarily all parallelograms, joining corresponding sides of the two bases.

Given here: The volume of the prism is 2¹/₂=2.5 cm³

And the height is 1/3 cm

let the length and breadth of the prism is x and y respectively.

We know the volume of the prism as

1/3 × x×y=2.5

x×y=7.5

Thus possible values of length and breadth are the factors of 7.5

out of which one of the pair whose length is 15 cm and width 0.5 cm

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Answer: 32 sweets

[] The ratio 5:2 goes in the word "toys and sweets" as it is said in the sentence.

-> 5 toys for every 2 sweets

[] We know we will have 16 bags in total. She has exactly enough toys

-> 16 bags in total * 5 toys per bag = 80 toys

[] Because of this, we can multiply 2 by 16 to see how many sweets will be needed.

-> 16 bags in total * 2 sweets per bag = 32 sweets

Answer: Number 2

Step-by-step explanation: yes

The Sample space would be

        {(w,c), (w,e), (w,m), (o, c) (o,e), (o,m), (r,c), (r,e), (r,m)}

According to the question,

Colors for room are { w, o,r}

Entertainment center would be { c, e, m}

A set that consists of all possible outcomes and the result from a random experiment( real or conceptual) is called a sample set. The experiment of tossing a coin results in either of two possible outcomes; a head (H) or a tail (T). The sample space for this experiment is S= {H, T}. If we take a sample space by tossing two coins the result would be S={HH, HT, TH, TT}.

So, the Sample space would be

        {(w,c), (w,e), (w,m), (o, c) (o,e), (o,m), (r,c), (r,e), (r,m)}

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Answer:

\(t = 15.7\)

Step-by-step explanation:

Given

\(Principal = 25000\) --- P

\(Amount = 75000\) --- A

\(Rate = 7\%\) --- R

Required

Determine the time (t)

Using continuous growth formula:

We have

\(A = Pe^{rt}\)

Convert rate to decimal

\(Rate = 7\%\)

\(r = 0.07\)

Substitute values for A, P and r

\(75000 = 25000 * e^{0.07t}\)

Divide both sides by 25000

\(3 = e^{0.07t}\)

Rewrite the exponential function as logarithmic, we have:

\(ln3 = 0.07t\)

Reorder

\(0.07t = ln3\)

Divide both sides by 0.07

\(t = \frac{ln3}{0.07}\)

\(t = \frac{1.09861228867}{0.07}\)

\(t = 15.69\)

\(t = 15.7\)

Hence, the time is approximately 15.7 years

With such a larger sample size, the margin of error lowers (grows or decreases), whereas, at a higher confidence level, it increases (increases or declines).

             Margin of error \((E) = Z_c * {\frac{\sigma}{\sqrt{n}}}\)

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The probability of randomly forming the word "woord logic" is:Probability = 1 / (10! / (2!))

To calculate the probability of forming the word "woord logic" by randomly arranging the letters l, o, g, i, c, we need to consider the total number of possible arrangements and the number of arrangements that result in the desired word.

The word "woord logic" has 10 letters in total. Among these letters, there are 2 o's and the remaining letters appear only once.

The total number of possible arrangements is given by the factorial of the total number of letters:

Total arrangements = 10!

However, since the letter "o" appears twice, we need to divide by the factorial of the number of repeated letters:

Total arrangements = 10! / (2!)

To calculate the number of arrangements that result in "woord logic," we consider that the arrangement of "woord logic" is unique and distinct. Thus, there is only one arrangement that matches the desired word.Simplifying this expression would yield the exact probability.

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Answer:

x=5+-\(\sqrt\)25-48/6

Step-by-step explanation:

negative roots are not there

no real

Answer:

Step-by-step explanation:

This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.

Answer:

C

Step-by-step explanation:

\(\text{All other options contain rational numbers, such as} ~\sqrt{36} , \sqrt{25}, \sqrt{16}\)

Answer:

1/2

Step-by-step explanation:

8^x=2√2

Change 8 to have a base of 2.

2^3x=2^3/2

Both bases are the same, so you can set the exponents equal.

3x=3/2

x=1/2

Answer:

X = 10

Z = 67

Step-by-step explanation:

We see that the angles are formed by the intersection of two lines.

Angles z and  67° are vertically opposite angles and therefore they are equal to each other

z°= 67°

Angles z and (7x + 43) are supplementary angles. The sum of these angles add up to 180°

z + 7x + 43 = 180

67 + 7x + 43 = 180

7x + 110 = 180

7x = 180 -110 = 70

x = 70/7 = 10

Answer:

so the first picture is it graphed without solving it and the second graph is the answer to it graphed

Step-by-step explanation: