Solve the given equation by completing the square.

x^2 + 8x = 38

Fill in the values of a, b, and cto complete the solutions.

Answer:

1/2e^bx^2-1/3x^3a+C

Step-by-step explanation:

Answer:

62%

Step-by-step explanation:

10 000 ÷ 100 = 100

620 ÷ 100

= 62%

The angle between the stick and the base of the box is 77. 9 degrees

To determine the angle between the stick and the base, we have to know the trigonometric identities.

These identities are;

From the information given, we have;

sin A = FB/AB

Given that;

GB = 14.5cm

AB = 18. 6cm

substitute for the length of the sides, we have;

sin A = 14.5/18. 6

Divide the values, we have;

sin A = 0. 7796

Find the inverse sine

A = 77. 9 degrees

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#5

Since the elevation of the picture is

We need to change it in decimal, then divide the numerator of the fraction by the denominator of the fraction

Then the elevation in decimal is

The correct option is  B) increase.

To decrease sample error, a pollster must increase the number of respondents. The larger the sample size, the more representative it is likely to be of the target population, leading to a lower margin of error.

When conducting surveys or polls, it is essential to obtain responses from a diverse and random group of individuals. By increasing the number of respondents, the pollster can capture a broader range of perspectives, which helps to reduce sampling bias and increase the accuracy of the results.

For example, let's say a pollster wants to understand the political preferences of voters in a particular city. If they only survey 50 people, the sample may not accurately reflect the larger population, and the margin of error could be high. However, if they survey 500 or even 1000 people, the results are more likely to provide a reliable estimate of the overall population's preferences.

Therefore, to decrease sample error, pollsters should increase the number of respondents in their surveys or polls. This approach helps to ensure a more accurate representation of the population's views and minimize the potential for misleading or biased results.

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Perimeter of rectangle is 208p² - 160p + 272 centimeters

Given:

Width of rectangle = (10p+6)(10p+6) centimeters

Length of rectangle = (2p-10)(2p−10) centimeters

Find:

Perimeter of rectangle

Computation:

Width of rectangle = (10p+6)(10p+6)

Width of rectangle = 100p² + 120p + 36

Length of rectangle = (2p-10)(2p−10)

Length of rectangle = 4p² - 40p + 100

Perimeter of rectangle = 2(l + b)

Perimeter of rectangle = 2[(4p² - 40p + 100) + (100p² + 120p + 36)]

Perimeter of rectangle = 2[104p² - 80p + 136]

Perimeter of rectangle = 208p² - 160p + 272 centimeters

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Moving on to step 20, you need to take a screenshot issues of the tools menu. This can usually be accessed by clicking on the "Tools" option in the menu bar of the program or application you are using.

To take a  of the tools menu in step 20, you can follow these steps:Open the tools menu in the desired application or software.Press the "Print Screen" (PrtSc) button on your keyboard. This will capture a screenshot of your entire screen.

Open an image editing software or any program that allows you to paste imagesPaste the screenshot by pressing "Ctrl" + "V" on your keyboard.Save the image in your desired format.

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Answer:

Profit =\( \frac{80p + 170}{p} \)

Step-by-step explanation:

Cost of the Yield = \( \frac{100p + 200}{p} \)

Cost of the labour = \( \frac{10p + 50}{p} \)

Cost of the fertilisers = \( \frac{10p - 20}{p} \)

Total expenses = \( \frac{10p + 50}{p} + \frac{10p - 20}{p} = \frac{20p + 30}{p} \)

Profit = Total expenses - Cost of yield

\( = > \frac{100p + 200}{p} - \frac{20p + 30}{p} \)

\( = > \frac{80p + 170}{p} \)

Answer:

8/27

Step-by-step explanation:

\((\frac{2}{3})^3 = \frac{2}{3} * \frac{2}{3} * \frac{2}{3} = \frac{8}{27}\)

The correct answer is option C. At the point (2,1) on the curve x² - xy + y²= 3, the derivative dy/dx exists, and the tangent line at that point is neither horizontal nor vertical.

To determine the correct option, we need to analyze the properties of the curve x² - xy + y² = 3 at the point (2,1). First, let's find the derivative dy/dx. Taking the derivative of the given equation implicitly with respect to x, we get:

2x - y - x(dy/dx) + 2y(dy/dx) = 0

Rearranging the terms, we have:

dy/dx = (2x - y) / (x - 2y)

Now, substituting the values x = 2 and y = 1 into the expression for dy/dx, we can determine its value at the point (2,1):

dy/dx = (2(2) - 1) / (2 - 2(1)) = 3 / 0

Since the denominator is zero, dy/dx is undefined at (2,1). Therefore, option D, stating that dy/dx does not exist at (2,1) and the tangent line at that point is vertical, is incorrect.

However, we can still determine the nature of the tangent line at (2,1). Although the derivative is undefined, it is still possible for the tangent line to exist and have a defined slope. In this case, the tangent line would be neither horizontal nor vertical. Therefore, option C, which states that dy/dx exists at (2,1) and the tangent line at that point is neither horizontal nor vertical, is the correct answer.

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While a data set consisting only of anomalous objects is possible, it would be an abuse of the terminology since it would not reflect the expected or normal behavior of the system.

It's possible for a dataset to consist only of anomalous objects if the dataset has been specifically curated to include dissimilar documents, as you've described. In this context, the term "anomalous" refers to documents that are not highly related, connected, or similar to one another.

However, it's important to note that this might be an unusual case or an atypical use of the term "anomalous," as anomalies generally refer to rare or unexpected occurrences within a larger, more homogeneous dataset.

In your described scenario, the selected documents might be more accurately referred to as "diverse" or "dissimilar" rather than strictly "anomalous."

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The sum to infinity of the function is -3/2

from the question, we have the following parameters that can be used in our computation:

\(\sum\limits^{\infty}_{1} {3^n} \,\)

From the above sequence, we have

First term, a = 3

Common ratio, r = 3

The sum to infinity of the function is calculated as

Sum = a/(1 - r)

So, we have

Sum = 3/(1 - 3)

Evaluate

Sum = -3/2

Hence, the sum is -3/2

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Question

Calculate the sum to infinity of the function for

\(\sum\limits^{\infty}_{1} {3^n} \,\)

Answer:

The 3 consecutive odd numbers are -67, -65 and -63 and the least of them is -67.

Explanation:

Consecutive odd numbers means that the next number will be two more than the previous one.

Let the 1st number be y, the other 2 consecutive odd numbers will be y + 2 and y + 4.

We're also told that the sum of the 3 numbers is -195, so our equation can be written thus;

Let's collect like terms and solve for y;

So our 1st number is -67.

Let's go ahead and find the other 2 numbers;

2nd number: y + 2 = -67 + 2 = -65

3rd number: y + 4 = -67 + 4 = -63

Therefore, the 3 consecutive odd numbers are -67, -65 and -63 and the least of them is -67.

The probability that a randomly chosen item from this assembly line is defective is 0.125.

Probability simply means the likelihood of the occurence of an event.

From the information, the review of her record reveals that she accepts only 8% of all defective items and it was also found that 1% of all items from the assembly line are both defective and accepted by the inspector.

Therefore, the probability will be:

= Percentage of detectives / Percentage of defective accepted

= 1% / 8%

= 0.01 / 0.08

= 0.125

The probability is 0.125.

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The estimated area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints is approximately 0.8916.

To estimate the area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints, we can use the right Riemann sum method.

The width of each rectangle, Δx, is given by the interval width divided by the number of rectangles.

In this case, Δx = (π/2 - 0)/4 = π/8.

To calculate the right endpoint values, we evaluate f(x) at the right endpoint of each rectangle.

For the first rectangle, the right endpoint is x = π/8.

For the second rectangle, the right endpoint is x = π/4.

For the third rectangle, the right endpoint is x = 3π/8.

And for the fourth rectangle, the right endpoint is x = π/2.

Now, let's calculate the area for each rectangle by multiplying the width (Δx) by the corresponding height (f(x)):

Rectangle 1: Area = f(π/8) * Δx = 5cos(π/8) * π/8

Rectangle 2: Area = f(π/4) * Δx = 5cos(π/4) * π/8

Rectangle 3: Area = f(3π/8) * Δx = 5cos(3π/8) * π/8

Rectangle 4: Area = f(π/2) * Δx = 5cos(π/2) * π/8

Now, let's calculate the values:

Rectangle 1: Area = 5cos(π/8) * π/8 ≈ 0.2887

Rectangle 2: Area = 5cos(π/4) * π/8 ≈ 0.3142

Rectangle 3: Area = 5cos(3π/8) * π/8 ≈ 0.2887

Rectangle 4: Area = 5cos(π/2) * π/8 ≈ 0

Finally, to estimate the total area, we sum up the areas of all four rectangles:

Total Area ≈ 0.2887 + 0.3142 + 0.2887 + 0 ≈ 0.8916

Therefore, the estimated area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints is approximately 0.8916.

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The  confidence level were reduced from 99% to 90%, the margin of error would be smaller. This is because a lower confidence level requires a smaller margin of error.

If  the confidence level were reduced from 99% to 90%, the margin of error would be smaller. This is because a lower confidence level requires a smaller margin of error. When the confidence level is reduced, the z-score used in the calculation of the margin of error decreases, resulting in a smaller margin of error.

The formula for the margin of error (ME) is given by:

ME = z* (σ/√n)

Where z is the z-score, σ is the standard deviation, and n is the sample size. As the confidence level decreases, the value of z decreases, which reduces the margin of error. Therefore, if the confidence level were reduced from 99% to 90%, the margin of error would be smaller.

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Answer:

Step-by-step explanation: 5x-5=3x+13--->   5x-3x=13+5---> 2x=13+5---- 2x=18----> x=9 hope it helps

Answer:

Step-by-step explanation: 40

Answer:

Our X and Y make (2,-1)

Step-by-step explanation:

To find the point that is the solution for the system of equation, we must use the SUBSTUITION property,

\(2x+x-3=3\\\)

Now let's solve this, by adding common terms

\(2x+x=3x\\3x-3=3\)

Now we have to isolate the variable,

3x-3=3

Add 3 to both sides (opposite of the current)

3x=6 (DIVIDE three to both sides, to isolate the variable)

x=2 ( We know our x value is 2)

Now let's substitute this value into the Y.

y = 2-3 ( now subtract)

y= -1

Our X and Y make (2,-1)

Answer: Read below

Step-by-step explanation: Substituting 0 into x and y, you get the intercepts (0, -3.5) and (5, 0). Using these two points, you can connect them and get the line :>

\((2^{2} )^{3x} =(2^{2} )^{2} \\2^{2*3x} =2^{2*2} \\2^{6x} =2^{4} \\6x=4\\\frac{6x}{6} =\frac{4}{6} \\x=\frac{2*2}{2*3}\)

\(x=\frac{2}{3}\)

The toddler is at rest at t = 2 seconds. The toddler is at rest when the velocity, which is the derivative of the position function with respect to time, is equal to 0.

We need to find the time t for which s'(t) = 0.

Taking the derivative of s(t), we get:

s'(t) = 12t^3 - 24t^2 - 12t + 24

Setting s'(t) = 0, we can factor out a 12:

12(t^3 - 2t^2 - t + 2) = 0

We can see that t = 2 is a solution to the cubic equation in parentheses by plugging it in and verifying that the value of the expression is 0. We can then factor the cubic equation as:

(t - 2)(t^2 - t - 1) = 0

Using the quadratic formula or factoring further, we can find that the other two solutions are:

t = (1 ± sqrt(5))/2

However, we need to check that these solutions are valid by plugging them back into the original position function and making sure they correspond to a point where the toddler is at rest. We find that only t = 2 satisfies this condition, so the toddler is at rest at t = 2 seconds.

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List the following words in order from smallest to

largest

C. DNA, Gene, Chromosome, Nucleus

Answer:

A. Gene, DNA, Chromosome, Nucleus

Step-by-step explanation:

Hope this helps. Please give Brainest if it did. Good luck

Answer:

The answer to your question is given below

Step-by-step explanation:

8x – 3y = –21 ..... (1)

3x + y = –10 ...... (2)

To prove that x = – 3

Do the following:

8x – 3y = –21 ..... (1)

3x + y = –10 ...... (2)

Make y the subject in equation 2

3x + y = –10

Rearrange

y = –10 – 3x

Substitute the value of y into equation 1

To get the value of x.

8x – 3y = –21

y = –10 – 3x

8x – 3(–10 – 3x) = –21

Clear bracket

8x + 30 + 9x= –21

Collect like terms

8x + 9x = –21 – 30

17x = –51

Divide both side by 17

x = –51 / 17

x = – 3

Since, Marie is sailing in the direction s11 degrees west. after 10 hours, Marie was 4 miles due west of Frank. Therefore, Marie had sallied in the 38.6 miles

Given that

Frank is sailing in the direction s3 degrees east

Marie is sailing in the direction s11 degrees west

after 10 hours, Marie was 4 miles due west of frank.

Direction is the information contained in the relative position of one point with respect to another point without the distance information. Directions may be either relative to some indicated reference or absolute according to some previously agreed upon frame of reference.

Cardinal directions

The four cardinal directions or cardinal points are:

1.North

2.East

3.South

4.West

Draw 2 right triangles representing bearings. Triangles share the same south leg, y. Horizontal sides sum to 10 miles. X f +X m=10

Y tan(2)+Y tan(13)=10

Y=10/(tan(2)+tan(13))=37.62

Lm = distance traveled by Marie

cos(13)=Y/Lm

Lm=Y/cos(13) = 37.62/cos(13) = 38.6 miles.

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Answer:

45

Step-by-step explanation:

Let the length of the shorter leg be represented as x.

Let the length of the longer let let be represented as x+15

While the length of the hypotenuse be 2x-15.

From the knowledge of phythagoras theorem:

x^2+(x+15)^2 = (2x-15)^2

x^2+x^2+15x+15x+225 = 4x^2-30x-30x+225

2x^2+30x+225 = 4x^2-60x+225

2x^2-4x^2+30x+60x+225-225=0

-2x^2+90x+0= 0

2x^2-90x = 0

Divide through by 2

x^2-45x=0

x(x-45)=0

x = 0 or x-45=0

Considering x-45=0

x-45=0

x = 45

If x is for the shorter leg,

The length for the longer leg is: x+15

= 45+15

= 60

For the hypotenuse = 2x-15

= 2×45-15

= 90-15

= 75

The real values of $c$ for which $x^2 + 16x + c$ is the square of a binomial are $64$ and $0$.

To find these values, we can use the concept of completing the square. For a quadratic expression to be the square of a binomial, the coefficient of the linear term ($16x$) must be twice the product of the square root of the constant term ($c$) and the square root of the coefficient of the quadratic term ($1$). In this case, the coefficient of the linear term is $16$ and the coefficient of the quadratic term is $1$. So, we have $16 = 2\sqrt{c}\sqrt{1}$.

Simplifying this equation gives $16 = 2\sqrt{c}$. Dividing both sides by $2$ yields $\sqrt{c} = 8$. Squaring both sides gives $c = 64$. Thus, $c = 64$ is one possible value.

Additionally, if we consider the case when $c = 0$, the quadratic expression becomes $x^2 + 16x + 0 = (x + 8)^2$. Therefore, $c = 0$ is another possible value.

In summary, the real values of $c$ for which $x^2 + 16x + c$ is the square of a binomial are $64$ and $0$.

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The turntable turns through a 45.0 degree angle, the radial line also rotates by 45.0 degrees. Therefore, the direction of the ladybug's displacement vector is 45.0 degrees counterclockwise from the positive x-axis.

Part A:
The radius of the turntable is half of the diameter, which is 6.0 in. The ladybug crawls in a straight radial line to the edge, which means its displacement vector is equal to the radius of the turntable. Therefore, the magnitude of the ladybug's displacement vector is 6.0 in.

Part B:
The direction of the ladybug's displacement vector is the same as the direction of the radial line from the center of the turntable to the edge. This direction can be described by the angle between the positive x-axis and the radial line.

Since the turntable turns through a 45.0 degree angle, the radial line also rotates by 45.0 degrees. Therefore, the direction of the ladybug's displacement vector is 45.0 degrees counterclockwise from the positive x-axis.

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Step-by-step explanation:

A parenthesis is used when the number next to it is NOT part of the solution set

   like :   all numbers up to but not including 3 .    

  Parens are always next to  infinity  when it is part of the solution set .

  A bracket is used when the number next to it is included in the solution set.

Answer:

D. A reflection, a rotation, and a translation will prove that shape 2 is congruent to shape 1.

Step-by-step explanation:

A reflection over the x-axis, 90° clockwise rotation around the origin, and a translation down 1 unit would map shape 1 onto shape 2.

Answer:

1

Key:

Step-by-step explanation:

\(2^0=1\)