8,282 in verbal form

Answer:

(f - g)(x) = 2x² - 3x - 8

Step-by-step explanation:

Since , (f - g)(x) = f(x) - g(x)

Then

(f - g)(x) = (2x² - 5) - (3x + 3)

            = 2x² - 5 - 3x - 3

            = 2x² - 3x - 5 - 3

            = 2x² - 3x - 8

Answer:

Step-by-step explanation:

wheres the diagram?

Answer:B

Step-by-step explanation:

The 9th term of the given sequence is 78732.

The given sequence is 12, 36, 108... is a geometric sequence with a common ratio of 3.To find the 9th term of the given sequence, we will use the formula for the nth term of a geometric sequence, which is given by:

aₙ = a₁rⁿ⁻¹

Here, a₁ = 12 and r = 3.

Therefore, the formula for the nth term becomes:

aₙ = 12(3)ⁿ⁻¹

Now, we need to find the 9th term of the sequence. Hence, n = 9. Substituting the values of a₁ and r, and n in the formula, we get:

a₉ = 12(3)⁹⁻¹= 12(3)⁸= 12(6561)= 78732

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Answer:

\(v=\frac{80}{3}\pi \frac{m}{min}\)

Step-by-step explanation:

In order to start solving this problem, we can begin by drawing a diagram of what the problem looks like (see attached picture).

From that diagram, we can see that we have a triangle we can analyze. We'll call the angle between the vertical line and the slant line \(\theta\). And we'll call the distance between W and the point we are interested in l.

Now, there are different things we need to calculate before working on the triangle. For example, we can start by calculating the angle \(\theta\).

From the diagram, we can see that:

\(tan \theta = \frac{l}{3}\)

when solving for \(\theta\) we will get:

\(\theta = tan^{-1} (\frac{l}{3})\)

we could use our calculator to figure this out, but for us to get an exact answer in the end, we will leave it like that.

Next, we can calculate the angular velocity of the beam. (This is how fast the beam is rotating).

We can use the following formula:

\(\omega = \frac{2\pi}{T}\)

where T is the period of the rotation. This is how long it takes the beam to rotate once. So the angular velocity will be:

\(\omega = \frac{2\pi}{3} \frac{rad}{s}\)

Next, we can take the relation we previously got and solve for l, so we get:

\(tan \theta = \frac{l}{3}\)

\(l = 3 tan \theta\)

Now we can take its derivative, so we get:

\(dl = 3 sec^{2} \theta d\theta\)

and we can divide both sides of the equation into dt so we get:

\(\frac{dl}{dt} = 3 sec^{2} \theta \frac{d\theta}{dt}\)

in this case \(\frac{dl}{dt}\) represents the velocity of the beam on the wall and \(\frac{d\theta}{dt}\) represents the angular velocity of the beam, so we get:

\(\frac{dl}{dt} = 3 sec^{2} (tan^{-1} (\frac{l}{3})) (\frac{2\pi}{15})\)

we can simplify this so we get:

\(\frac{dl}{dt} = (\frac{2\pi}{5})sec^{2} (tan^{-1} (\frac{l}{3}))\)

we can use the Pythagorean identities to rewrite the problem like this:

\(\frac{dl}{dt} = (\frac{2\pi}{5})(1+tan^{2} (tan^{-1} (\frac{l}{3})))\)

and simplify the tan with the \(tan^{-1}\) so we get:

\(\frac{dl}{dt} = (\frac{2\pi}{5})(1+(\frac{l}{3})^{2})\)

which simplifies to:

\(\frac{dl}{dt} = (\frac{2\pi}{5})(1+(\frac{l^{2}}{9}))\)

In this case, since l=1, we can substitute it so we get:

\(\frac{dl}{dt} = (\frac{2\pi}{5})(1+(\frac{1}{9}))\)

and solve the expression:

\(\frac{dl}{dt} = (\frac{2\pi}{5})(\frac{10}{9})\)

\(\frac{dl}{dt} = \frac{20}{45}\pi\)

\(\frac{dl}{dt} = \frac{4}{9}\pi \frac{m}{s}\)

now, the problem wants us to write our answer in meters per minute, so we need to do the conversion:

\( \frac{dl}{dt} = \frac{4}{9}\pi \frac{m}{s} * \frac{60s}{1min} \)

\(velocity = \frac{80}{3} \pi \frac{m}{min}\)

Answer:

C. 8x²+x+3.

Step-by-step explanation:

A and B are not polynomials as they contain a division (A) and a square root (B).

D is a monomial ( just one term).

oc.8x²+x+3

Step-by-step explanation:

Which of the following is a polynomial?

OA. 5+x2²/X

OB. √x+2x-1

OC. 8x²+x+3

OD. 7x

Answer:

\(\huge\boxed{\sf \frac{2\sqrt{7}-4 }{3}}\)

Step-by-step explanation:

This is a rationalizing denominator question.

\(= \displaystyle \frac{2}{2+\sqrt{7} } \\\\Multiply \ and \ divide \ by \ conjugate \ 2 - \sqrt{7} \\\\= \frac{2}{2+\sqrt{7} } \times \frac{2-\sqrt{7} }{2-\sqrt{7} } \\\\\underline{\sf Using \ formula:}(a+b)(a-b)=a^2-b^2\\\\= \frac{2(2-\sqrt{7}) }{(2)^2-(\sqrt{7})^2 } \\\\= \frac{4-2\sqrt{7} }{4-7} \\\\= \frac{4-2\sqrt{7} }{-3} \\\\= \frac{-(4-2\sqrt{7}) }{3} \\\\= \frac{2\sqrt{7}-4 }{3} \\\\\rule[225]{225}{2}\)

According to the information, the percentage of students who answered Country and belong to ninth grade is 38.7%

To find the percentage of students who chose country as their favorite genre we have two options. We can establish what is the total percentage, what is the percentage in the student group of all the courses that answered country, and the percentage of all ninth grade students. The three procedures are shown below:

In the first case, we must add all the students and find the percentage that is equivalent to 24 students who belong to the ninth grade and who answered country.

Note: This question is incomplete. Here is the complete information:

Favorite type of Music

Grade Country Rap Rock Pop

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The quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

A division is a process of splitting a specific amount into equal parts.

We have to find 3x³-2x²+7x+9 divided by x²-3x

3x³-2x²+7x+9 is the dividend and x²-3x is the divisor.

The steps to solve this are given below.

Step 1: Take the first digit of the dividend from the left. Check if this digit is greater than or equal to the divisor.

Step 2: Then divide it by the divisor and write the answer on top as the quotient.

Step 3: Subtract the result from the digit and write the difference below.

Step 4: Bring down the next digit of the dividend (if present).

Step 5: Repeat the same process.

Hence, the quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

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Answer:

2g

Step-by-step explanation:

The range which at least 88.9% of the data will reside is 6.8 to 8.0.

Chebyshev's theorem states that for any data set, regardless of its distribution, at least 1 - (1/k²) of the data falls within k standard deviations of the mean, where k is any number greater than 1.

In this case, we want to find the range in which at least 88.9% of the data will reside. We can rewrite this as wanting to find the value of k such that 1 - (1/k²) = 0.889.

Solving for k:

1 - (1/k²) = 0.889

1/k² = 0.111

k² = 9

k = 3

So, at least 88.9% of the data will fall within 3 standard deviations of the mean. Using the formula for standard deviation, find the range as follows:

Range = mean +/- k × standard deviation

Range = 7.4 +/- 3 × 0.2

Range = [6.8, 8.0]

Therefore, we can conclude that at least 88.9% of the quiz scores will fall within the range of 6.8 to 8.0.

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The given equation above written in the form AX = b will be;

\(\left[\begin{array}{ccc}1&2\\2&3\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] =\left[\begin{array}{ccc}11\\18\\\end{array}\right]\)

Given the system of equation;

This equation can be represented in matrix form as \(AX = b\)

where:

The given equation above written in the form AX = b will be;

\(\left[\begin{array}{ccc}1&2\\2&3\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] =\left[\begin{array}{ccc}11\\18\\\end{array}\right]\)

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Answer:

20kg of rice in each bag

Step-by-step explanation:

we have 60kg of rice and 3 bags. we know that we need to have an eqal amount of rice in each bag so we can divide the 60kgs of rice by 3.

60÷3=20

Checking our Answer:

we can check our work by doing the opposite of division which is multiplication. to check our work we'd have to multiply the dividend (in our case 3) and our quotient (in our case 20) to see if we get the larger dividend (in our case 60) as our answer.

3×20=60

The total tax deduction for this person's weekly paycheck would be $85.00.

What is tax deduction?

To find the total tax deductions for each of the given weekly paychecks, we need to know the tax rate and any other applicable deductions for the person receiving the paychecks. Without this information, we cannot provide an exact answer. However, we can give an example of how tax deductions might be calculated for someone who earns a weekly paycheck of $340.00.

Let's assume that the person's gross pay is $340.00 per week and that their tax rate is 25%. This means that 25% of their gross pay will be withheld for taxes. The total tax deduction for this person's paycheck would be:

Total tax deduction = Gross pay x Tax rate

Total tax deduction = $340.00 x 0.25

Total tax deduction = $85.00

So the total tax deduction for this person's weekly paycheck would be $85.00.

It's important to note that this is just an example and the actual tax deductions for any given paycheck will depend on a variety of factors, including the person's income, tax rate, and any other applicable deductions or credits.

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Complete question is:  The total tax deductions would be $85.00 for weekly pay $199.00 $259.00 $340.00.

Answer: 0,06?

Step-by-step explanation:

The probability of having both lab work and a referral is 0.94

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

It is given that the probability of having neither lab work nor referral to a specialist is 0.21.

The probability of having lab work is 0.41 and the probability of having a referral is 0.53.

The probability of having both lab work and a referral;

0.41 + 0.53

= 0.94

Therefore, The probability of having both lab work and a referral is 0.94

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Answer:

$8 in 1 week mmmmmmmmmmmmnnnn

Answer:

$8

Step-by-step explanation:

If you save 32 dollars in 4 weeks, you want to divide it by 4 to get amount of dollars per week. 32 dollars/ 4 weeks = 8 dollars/ 1 week. If you have a question that asks how much will you save in, for example 9 weeks, just multiply 8 by 9, and get 72 dollars saved in 9 weeks.

The equation of the straight line joining A to B is y = (1/2)x + 3, the equation of the straight line joining B to C is y = (1/2)x + 3, and A, B, and C are collinear.

What are collinear points?

Collinear points are three or more points that lie on the same straight line. In other words, if three points A, B, and C are collinear, then there exists a straight line that passes through all three points. To determine if three or more points are collinear, we can find the slope of the line that passes through any two of the points. If the slope is the same for all possible pairs of points, then the points are collinear. Otherwise, they are not collinear.

a) To find the equation of the straight line joining A to B, we can use the slope-intercept form of the equation of a line:

y = mx + b

where m is the slope of the line, and b is the y-intercept.

The slope of the line passing through A and B is:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) = (-8, -1) and (x₂, y₂) = (-4, 1).

m = (1 - (-1)) / (-4 - (-8)) = 2/4 = 1/2

To find the y-intercept, we can use the point-slope form of the equation of a line:

y - y₁ = m(x - x₁)

where (x₁, y₁) = (-8, -1) and m = 1/2.

y - (-1) = (1/2)(x - (-8))

y + 1 = (1/2)(x + 8)

y = (1/2)x + 3

Therefore, the equation of the straight line joining A to B is y = (1/2)x + 3.

b) To find the equation of the straight line joining B to C, we can use the same method:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) = (-4, 1) and (x₂, y₂) = (12, 9).

m = (9 - 1) / (12 - (-4)) = 8/16 = 1/2

Using point-slope form with the point (x₁, y₁) = (-4, 1) and slope m = 1/2:

y - 1 = (1/2)(x - (-4))

y - 1 = (1/2)x + 2

y = (1/2)x + 3

Therefore, the equation of the straight line joining B to C is y = (1/2)x + 3.

c)  From the equations of the lines joining A to B and B to C, we can see that both lines have the same slope of 1/2. This implies that the three points A, B, and C are collinear, i.e., they lie on the same straight line.

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The expression for the original rational number is; x/(x + 10)

Let the numerator be x

Therefore, according to given condition, the denominator will be expressed as; (x + 10)

According to question If the numerator is increased by 1  and the denominator is decreased by 1, then new numerator is; x + 1

New denominator is (x + 10 - 1) = (x + 9)

Thus, the original rational number will be expressed as;

x/(x + 10)

The new rational number will be : (x + 1)/(x + 9)

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Answer:

Corresponding angles are congruent:

3x - 17 = 2x - 2, so x = 15.

Answer:

132

Step-by-step explanation:

60 + 60 + 12 = 132

Answer:

As = 256\(\pi\) or 804.25cm

Step-by-step explanation:

By formula As = \(4\pi r^{2}\)

As = 256\(\pi\) or 804.25cm

Answer:

Step-by-step explanation:

Answer:

2³ v66⁴ -5⁷. .....,...........

Answer:Therefore, the equation of the line with a slope of 9/7 and containing the midpoint of the line segment with endpoints (2, -3) and (-6, 5) is:

y = (9/7)x + 25/7.

Step-by-step explanation:Step 1: Find the midpoint of the line segment.

The midpoint formula is given by:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Given the endpoints of the line segment as (2, -3) and (-6, 5), we can find the midpoint as follows:

Midpoint = ((2 + (-6)) / 2, (-3 + 5) / 2)

Midpoint = (-4 / 2, 2 / 2)

Midpoint = (-2, 1)

So, the midpoint of the line segment is (-2, 1).

Step 2: Write the equation of the line using the slope-intercept form.

The slope-intercept form of a line is given by:

y = mx + b

where m is the slope and b is the y-intercept.

Given the slope as 9/7, we have:

y = (9/7)x + b

Step 3: Substitute the coordinates of the midpoint to find the value of b.

Using the coordinates of the midpoint (-2, 1), we can substitute these values into the equation:

1 = (9/7)(-2) + b

1 = -18/7 + b

To find the value of b, we can solve this equation:

1 + 18/7 = b

25/7 = b

Step 4: Write the final equation of the line.

Using the value of b, the equation becomes:

y = (9/7)x + 25/7

Answer:

The length of each side is 12cm.

Explanation:

The perimeter of a square is calculated by the formula:

P=4a, where P=perimeter, and a=length of any side, all sides being equal in a square.

From the given data we write:

48=4a

Divide both sides by 4.

12=a

The length of each side is 12cm.

We can complete the blanks with the following ratios:

(7.5 mi/1) * (1 mi/ 5280 ft) * (400ft/1 yd) * (3 ft/1 ft) =33 flags

Since we do not need a flag at the starting line, then 32 flags will be required in total.

To solve the problem, we would first convert 400 yds to feet and miles.

To convert to feet, we multiply by 3. This gives us: 400 yd * 3 = 1200 feet.

To convert to miles, we would have 0.227 miles.

Now, we divide the entire race distance by the number of miles divisions.

This gives us:

7.5 mi /0.227 mi

= 33 flags

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Answer:

Step-by-step explanation:

a