Given that f(x)=x^2-3x-54and g(x)=x-9 find (x)(f⋅g)(x)

Answer:

Step-by-step explanation:

looking at all the stress you're in I knew I had to help so all your lists are bunched up, so I went of the picture C is correct because B 4 and 7 aren't even a part of the question itself and A has 16 and 49 but it doesn't have sqrt so it's not = to the question and D is not correct either because it doesn't have one sqrt it has two on top of each other. HOPE THIS HELPED!

The smallest integer greater than 800 that is relatively prime to 10! is 801

The term relatively prime refers to numbers who has a greatest common factor of 1. If two numbers have a greatest common factor of 1 the two numbers are said to be relatively prime

solving for 10!

10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

= 362880

prime factorization of 10!

= 2^7 * 3^4 * 5 * 7

prime factorization of 801

= 3^2 * 89

The greatest common factor of both numbers is 1, this is not included to the factors in the prime factorization but 1 is a known common factor already.

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Answer:

d.2180

Step-by-step explanation:

add the two sides and subtract that one number on top I believe

An airship propelled by some mechanical device travels five miles in ten minutes in the direction of the wind, but requires one hour to go back again to the starting point against the same wind. How long would it have taken to go the whole ten miles in a calm day without any wind? Hint: You don't have to use equations to solve this problem.

we have that

5 miles -------> 10 minutes (direction of the wind)

5 miles ------> 1 hour (against the same wind)

therefore

10 miles ------> ? (without any wind)

so

Let

x -----> speed of the wind

y -----> speed of the airship

direction of the wind

speed=d/t ------> 5/10=0.5 miles per min

against the same wind

speed=5/60=1/12 miles per min

so

x+y=0.5 ------> x=0.5-y -----> equation 1

y-x=1/12 -----> equation 2

solve the system

substitute equation 1 in equation 2

y-(0.5-y)=1/12

2y=(1/12)+1/2

2y=7/12

y=7/24=0.2917 miles per min

Find the value of x

x=(1/2)-7/24

x=5/24=0.2083 miles per min

therefore

10 miles without any wind

speed=d/t ------> t=d/speed

t=10/(7/24)

The constant of proportionality between x and y in the given graph above is determined as: 2.

The constant of proportionality of a proportional relationship between two variables, x and y, can be defined as the ratio of y to x, which is expressed as, k = y/x, where x and y are the coordinates of one point one the line that represents the proportional relationship.

Using the coordinates of a point on the graph, (2, 4), find the constant of proportionality, k:

Constant of proportionality (k) = y/x = 4/2

Constant of proportionality (k) = 2

Therefore, the constant of proportionality that represents the proportional relationship between the variables, x and y, is calculated as, 2.

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Answer:

Solve with the Quadratic Formula

Let's solve your equation step-by-step.

(3x)2+4x+1=0

Step 1: Simplify both sides of the equation.

9x2+4x+1=0

For this equation: a=9, b=4, c=1

9x2+4x+1=0

Step 2: Use quadratic formula with a=9, b=4, c=1.

x=

−b±√b2−4ac

2a

x=

−(4)±√(4)2−4(9)(1)

2(9)

x=

−4±√−20

18

Answer:

No real solutions.

Step-by-step explanation:

I did my best

The arithmetic says we should subtract find the difference between 86.89 and 56.389.

Notice we have to put a place holder of 0 at the ending of 86.89 to do the subtraction. Then we have to borrow 1 from the hundredth term(9) of 86.890 to make 0 ten . so ten minus 9 should be 1. Then the difference of the hundreth term(8 - 8) is 0. 8 minus 3 is 5. 6 minus 6 is zero and finally 8 minus 5 is 3.

The answers are B and D

Answer:  70

Step-by-step explanation:

easy addition

The lower cost will occur at the extreme point, that is if the number of videos rented daily is 8 pieces and the cost will be $550.

The cost function is given by:

C(x) = 2x² - 32x + 678

The lowest cost happens at the extreme point. In this point the derivative of C(x) is equal to zero.

Take the derivative:

C'(x) = 4x - 32 = 0

4x = 32

x = 32/4 = 8

Hence, the lowest cost will occur if the number of video rented daily is 8 pcs.

Substitute x = 8 into the cost function:

C(8) = 2(8)² - 32.(8) + 678 =  550

Complete question:

The owner of a video store has determined that the cost c, C(x) = 2x² - 32x + 678 in dollars, of operating the store is approximately given by where x is the number of videos rented daily. find the lowest cost to the nearest dollar

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Answer:

560 pounds

Step-by-step explanation:

175 pounds divided by 5 minutes.

= 35 pounds per minute

35 pounds per minute multiplied by 16 minutes

= 560 pounds

The table of values for the given equation is presented below:

x       y

-3    17

-2   2

-1    -7

0   -10

1    -7

2    2

3    17

The Standard form for a quadratic equation is  ax²+ bx + c=0, where: a, b and c are your respective coefficients. In the quadratic function, the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

To solve a quadratic function, you should find the discriminant: D=b²-4ac and then use this variable in the formula: [tex]x=\frac{-b \±\sqrt{\Delta} }{2a}[/tex].

The given equation is a quadratic function because have a degree equal to 2. Then, when you plot the graph, you obtain a parabola.

First, you should replace the given values for x in the equation y=3x²-10

x        y

-3   y=3*(-3)²-10= 3*9-10=27-10=17

-2   y=3*(-2)²-10= 3*4-10=12-10=2

-1    y=3*(-1)²-10= 3*1-10=3-10= -7

0    y=3*(0)²-10= 3*0-10=-10= -10

1     y=3*(1)²-10= 3*1-10=3-10= -7

2    y=3*(2)²-10= 3*4-10=12-10= 2

3    y=3*(3)²-10= 3*3-10=27-10= 17

Now, you have the points to draw the graph, show the attached image.

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The sub-atomic particles located in the nucleus of an He^4 atom are 2 protons and 2 neutrons.

Helium belongs to double-electronic species, unlike alpha-particles which are devoid of electrons. The two electrons of Helium are accommodated in the 1s orbital, outside the nucleus.

Nucleons are always present in the nucleus of various elements. Nucleons collectively refer to protons and neutrons. In this case, 2 protons and 2 neutrons reside in the nucleus.

The number of protons is always equal to the atomic number of the element. The number of neutrons is always equal to the difference between the mass number and the atomic number of the element.

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Answer:

see explanation

Step-by-step explanation:

(a)

given y is inversely proportional to x³ then the equation relating them is

y = [tex]\frac{k}{x^3}[/tex] ← k is the constant of proportion

to find k use any of the ordered pairs from the table

using (1, 8 ) , then

8 = [tex]\frac{k}{1^3}[/tex] = [tex]\frac{k}{1}[/tex] ⇒ k = 8

y = [tex]\frac{8}{x^3}[/tex] ← equation of proportion

(b)

when y = 64 , then

64 = [tex]\frac{8}{x^3}[/tex] ( multiply both sides by x³ )

64x³ = 8 ( divide both sides by 64 )

x³ = [tex]\frac{8}{64}[/tex] = [tex]\frac{1}{8}[/tex] ( take cube root of both sides )

x = [tex]\sqrt[3]{\frac{1}{8} }[/tex] = [tex]\frac{1}{2}[/tex]

Step 1: Let the remaining number of words be X.

The inequality equation becomes:

Hence, the number of words Petra has to write to have more than 1000 words should be greater than 316 words.

Answer: The answer is no solution because the x cancels out

The fraction, 13 / 20 when converted to percentage is 65%.

A fraction is a non-whole number that has a numerator and a denominator. An example of a fraction is 13 / 20. 13 is the numerator and 20 is the denominator.

A percentage is when a fraction is converted to a number out of 100. In order to convert a fraction to a percentage, multiply the fraction by 100. The sign that represents percentage is %. Percentage is used to measure the frequency of a dataset.

In order to rewrite the fraction as a percentage, multiply the fraction by 100.

Percentage of times he hit the target = ( number of times he hit the target / number of hits) x 100

(13 / 20) x 100 = 65%

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Answer:

7g + 3n - 2

Step-by-step explanation:

(7g - 6) - (-3n - 4)

7g - 6 + 3n + 4

7g + 3n - 2

I hope this helps!

The equation used to find the amount of time Emmet answers phone calls is t +25= 45

An equation is an expression that shows the relationship between two or more numbers and variables.

The amount of time Emmet answers phone calls = 20

She spends delivering flowers to patient's room= 25 minutes

She spends meetings volunteering at the hospital=  45

Let t be the amount of time Emmet answers phone calls in the hospital

Hence the equation used to calculate the amount of time spent on calls;

t + 25= 45

Now collect the like terms;

t= 45-25

t= 20

Hence, The equation used to find the amount of time Emmet answers phone calls is t +25= 45

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1. The scale is of 1:400,000.

2. The distance between A and B is of 36 km.

3. The diagram with city C is given at the end of the answer.

The scale of a drawing is how much each unit in the drawing represents in actual distance.

In the context of this problem, the scale is given as follows:

1 cm = 4 km

Meaning that each cm drawn represents 4 km of actual distance.

Using the same unit, we have that:

4 km = 4 x 100,000 cm = 400,000 cm.

Hence the scale is given by:

1:400,000.

Measuring on the drawing, the distance between A and B is of 9 cm, hence, applying the scale, the real distance is of:

9 x 4 km = 36 km.

In the diagram, considering the given scale, we want to position city C 3 cm from City A, to the west = to the left.

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The phrase of the expression x - 6 is 6 less than a number.

Expression:

The expression refer the sentence with a minimum of two  numbers/variables and at least one math operation in it.

Given,

Here we have the expression x -6.

And we need to convert this expression in order to get the phrase form.

In order to get the phrase form, we have to translate the given expression into word.

While we looking into the given expression we have identified the following three terms.

They are, x , (-) and 6.

Here x represents the unknown number.

(-) represents that we have to less the unknown number by the given number.

And 6 is the given number.

So, the phrase for this situation is 6 less than a number.

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Step 1: Represent a with an unknown

Let a number be x

Step 2: Represent the given information with an equation

From the first statement, the sum of a number and seven is tripled can be represented with the equation below:

The second statement reflects that the result of the first statement is eight times a number. Eight times a number is

The result of the first statement and the second statement is

Step 3: Solve for the unknown

The solution of the unknown is as shown below:

Hence, the number is 4 1/5

It will take 28.5 seconds to Makayla to be twice as deep as Jonah.

What is an equation?

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. For example, 3x + 5 = 15.

Given,

Jonah is at a depth of -20ft.

Makayla is at a depth of -12.5ft.

at the rate of descending is 0.5.

Given equation is

2(-20+0.25s) = -12.5-0.5s

-40 + 0.5 s = -12.5 -0.5s

0.5s + 0.5s = -12.5+40

1s = 28.5

Hence, the solution of the equation is 1s = 28.5.

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The sampling distribution of the sample mean approaches a Normal Distribution when the sample size becomes larger.

According to the central limit theorem for samples, if we keep drawing larger .And larger samples and calculating their means, then the sample forms its . Own normal distribution (the sampling distribution). The mean of normal distribution has the same the original distribution and a variance that is equal to the original variance divided by the sample size. The variable p is the number of values whose average is taken together ,and not the number of times we do the experiments.

Thus, for a large random sample, the sample does not resemble the regular curve but for a large random sample it will closely resemble the normal curve.

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Answer:

30%

Step-by-step explanation:

Omar went shopping for a new video game because of a sale. The price on the tag was $37, but Omar paid $25.90 before tax. Find the percent discount.

(37 - 25.9)/37 = 0.3 or 30% discount

check:

70% of $37 = $25.90

The speed is calculated as distance over time, so:

Replacing distance by 60 m and time by 3 seconds, we get:

The speed of the vehicle is 20 m/second

Answer:

B C and D

Step-by-step explanation:

Answer:

2π=6.2831853071795864769252867

The approximate net pay of Juanita is $500. Therefore, option B is the correct answer.

Given that, Juanita has a part-time job that pays $12/hour and works about 50 hours every month.

Net pay means take-home pay or the amount employees earn after all payroll deductions are subtracted from their gross pay.

Now, total money earned in a month

= 12 × 50 = 600

Now

6.2% of 600 = $37.2

= 600 - 37.2 = $562.8

1.45% of 562.8 = $8.1606

= 562.8 - 8.1606 = $554.6394

10% of 554.6394 = $55.46394

= 554.6394 - 55.46394 = $499.17546

Total deductions = $499.17546

So, net pay = grass pay - deductions

= 600 - 105.9

= $499.17546

The approximate net pay of Juanita is $500. Therefore, option B is the correct answer.

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The 90% confidence interval for the class is [73.49, 76.51].

Confidence interval is defined as the range of values where a parameter might fall at a given confidence level. It can be calculated using the formula below.

CI = μ ± z x SD/√n

where CI = confidence interval

μ = sample mean = 75

z = found by using a z-score table

SD = sample standard deviation = 5

n = sample size = 30

At 90% confidence level, the area in each tail of the standard normal curve is 5, and the cumulative area up to the second tail is 95.

(100 - 90) / 2 = 5

100 - 5 = 95

Find 0.95 in the z-table to get the value of z.

At p = 0.95, z = 1.65

Plug in the values to the formula for confidence interval, CI.

CI = μ ± z x SD/√n

CI = 75 ± 1.65 x 5/√30

CI = 75 ± 1.51

CI = [73.49, 76.51]

Hence, for every 100 samples, at 90% confidence level, the mean will be between 73.49 and 76.51.

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The statements about triangles FAD and DCE which are translations of triangle ABC include the following:

A. Points B, A, and F are collinear.

(B.) The measure of angle BCA is the same as the measure of angle CED.

C. Line AD is parallel to line BC.

(E.) The measure of angle DAC is the same as the measure of angle BCA.

Generally, there are four (4) main types of transformation and these include the following:

In Geometry, a translation can be defined as a type of transformation which moves every point of a geometric figure (object) in the same direction, as well as for the same distance.

Since triangles FAD and DCE both represent the translations of triangle ABC (see attachment), we can logically deduce the following information:

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