this is due in 30 min please please help me

(fg)(x)= x³ - 7x² - 9x + 8

domain is (-∞,∞)

Given: f(x)= x-8, g(x)= x² +1x - 1

To find (fg)(x) we multiply f(x) and g(x)

(fg)(x) = f(x) * g(x)

(fg)(x)= (x-8) (x²+x-1)

(fg)(x)= x³ + x² - x - 8x² - 8x +8

(fg)(x)= x³  - 7x²  - 9x + 8

we know, domain for all cubic function is set of all real numbers

domain is (-∞,∞)

Know more about "functions" here: https://brainly.com/question/12431044

#SPJ4

Answer:

-3

Step-by-step explanation:

The 100th term of the arithmetic sequence is 203.

Let the first term of the arithmetic sequence be a and the common difference be d.

The general term of the sequence is given by

\(T_{n} = a + (n-1)d\)

It is given that the 6th term is 15, we have :
\(T_{6} = a +5d\)  

a + 5d = 15......equation(1)

It is given that the 9th term is three times the 2nd term, we have :

\(T_{9} = 3*T_{2} \\a + 8d = 3(a +d)\\a + 8d = 3a +3d\\a -3a = 3d -8d = -5d\\-2a = -5d\\2a = 5d\\a = \frac{5d}{2}\)

Putting this value in equation(1)

\(\frac{5d}{2} + 5d = 15 \\\\5d + 10d = 30\\15d= 30\\d = \frac{30}{15} = 2\)

a = 5*2/2 = 5

Hence, the first term is 5 and the common difference is 2.

Now, evaluating the 100th term of the sequence, we have :

\(T_{n} = a +(n-1)d\\T_{100} = a +99d\\T_{100} = 5 +99*2 = 5 +198 = 203\)

Hence, the 100th term of the arithmetic sequence is 203.

To read more about the arithmetic sequences, visit https://brainly.com/question/6911789

#SPJ9

The fish's position with respect to the water's surface at 4:00 p.m. is 3/4.

What is a fraction?

Any number of equal parts is represented by a fraction, which also means a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

Here, we have

Based on the given conditions, formulate: 3 1/4 - 2 1/2

Remove the parentheses: 3 + 1/4 - 2 - 1/2

Reorder and combine like terms: (3-2)+1/4 - 1/2

Calculate the sum or difference: 1+ 1/4 - 1/2

Expand the fraction to get the least common denominator: 4/(1×4) + 1/4 - 2/(2×2)

Calculate the product or quotient: 4+1/4 - 2/(2×2)

Calculate the product or quotient: 4 + 1/4 - 2/4

Write the numerators over the common denominator: 4 + 1 -2/4

Calculate the sum or difference: 5 - 2/4

Calculate the sum or difference: 3/4

Hence, the fish's position with respect to the water's surface at 4:00 p.m. is 3/4.

To learn more about the fraction from the given link

https://brainly.com/question/17220365

#SPJ1

The American Heart Association provides a variety of delicious and easy-to-make recipes that are not only tasty but also heart-healthy.

These recipes are designed to be lower in sodium and lower in fat, making them a great choice for maintaining a healthy heart.

To find and save these recipes, you can visit the American Heart Association's official website or use their mobile application. They offer a wide range of recipes in various categories, including breakfast, lunch, dinner, snacks, and desserts. You can search for recipes based on your dietary preferences, ingredients, and cooking time.

By incorporating heart-healthy recipes into your meal planning, you can enjoy flavorful and nutritious meals while taking care of your cardiovascular health.

Learn more about range here:

https://brainly.com/question/29204101

#SPJ11

Answer:

  z = 12

Step-by-step explanation:

The two marked inscribed angles intercept the same arc, so have the same measure.

__

  ∠ADB = ∠ACB

  7z -4 = 5z +20 . . . . . . substitute degree measures

  2z = 24 . . . . . . . . add 4-5z

  z = 12 . . . . . . . divide by 2

Answer:

\(\frac{1}{2}\) (a + 2b)(a - b)

Step-by-step explanation:

Assuming you require the expression to be factored

Given

\(\frac{1}{2}\) a² + \(\frac{1}{2}\) ab - b² ← factor out \(\frac{1}{2}\) from each term

= \(\frac{1}{2}\) (a² + ab - 2b²) ← factor the quadratic

Consider the factors of the coefficient of the b² term(- 2) which sum to give the coefficient of the ab- term (+ 1)

The factors are + 2 and - 1, since

2 × - 1 = - 2 and 2 - 1 = + 1, thus

a² + ab - 2b² = (a + 2b)(a - b) and

\(\frac{1}{2}\) a² + \(\frac{1}{2}\) ab - b² = \(\frac{1}{2}\)(a + 2b)(a - b)

Answer:

100 g

Step-by-step explanation:

You would multiply the butter by 2.

Answer:

5.024 × 10^8 tons /day

Step-by-step explanation:

This question has to deal with conversion

We are told in the question that:

On average, water flows over a particular water fall at a rate of 2.05 x 10^5 cubic feet per second.

Water flow rate = 2.05 × 10^5 ft³/s

From the question,

One cubic foot of water weighs 62.4 lb.

1 ft³ = 62.4 lb

1 ton = 2200 lb

We are to calculate the flow rate in tons per day

Hence,

1 ft³ = 62.4 lb

2.05 × 10^5 ft³ =

Cross Multiply

2.05 × 10^5 × 62.4

= 12792000lb

Hence the water flow rate = 12792000lb/s

From the question,

2200 lb = 1 ton

12792000 Ib =

Cross Multiply

12792000lb × 1 ton/2200 lb

= 5814.5454545 tons

Hence the water flow rate = 5814.5454545 tons/second

We want the flow rate to be in tons/day

1 ton / second = 86400 tons / day

5814.5454545 tons/second = x tons/ day

Cross Multiply

x = 5814.5454545 tons/second × 86400 tons /day/ 1 ton / second

= 502376727.27 tons/day

= 5.0237672727 × 10^8 tons/day

Approximately ≈ 5.024 × 10^8 tons /day

Therefore, the rate of water flow in tons of water per day is 5.024 × 10^8 tons of water /day

The correct answer is 82% of 50 (41) / 170% of 30 (51) /65% of 80 (52)

Explanation:

The first step to know whether a value is greater than another is to find the value each percentage represents depending on the total. This process is shown below.

1. 65% of 80- This implies 80 is 100% and 85% needs to be found. Use the following formula:

80 / 100 = 0.8 x 65 = 52 or the total number divided by 100 and multiplied by the percentage you want to know

2. 82% of 50 - Repeat the same process

50 / 100 = 0.5 x 82 = 41

3. 170% of 30

30 / 100 = 0.3 x 170 = 51

4. Finally organize the values

82% of 50 (41)

170% of 30 (51)

65% of 80 (52)

Based on the information given about the percentages ,the ordering will be 82% of 50, 170% of 30, and 65% of 80.

It should be noted that 82% of 50 will be:

= 82% × 50

= 41

170% of 30 will be:

= 1.7 × 30

= 51

65% of 80 will be:

= 65% × 80

= 0.65 × 80

= 52

Learn more about percentages on:

https://brainly.com/question/24304697

The new area of the rectangular fence is w^2 + 15w + 54. Option C

The formula for area of a rectangle is given as;

Area = length × width

From the information given, we have that;

width = w + 6

length = 3 + w + 6 = 9 + w

Substitute into the formula for area

Area = (w + 6) ( 9 + w)

expand the bracket

Area = 9w + w^2 + 54 + 6w

collect like terms

Area = w^2 + 9w + 6w + 54

Area = w^2 + 15w + 54

Thus, the new area of the rectangular fence is w^2 + 15w + 54. Option C

Learn more about a rectangle here:

https://brainly.com/question/25292087

#SPJ1

Mode is the number that occurs the most so here the mode is 56

Join QuestionCove!! We have helpers willing to help!!

Answer:

pretty sure its D. 1.6 x 10^9

Answer:

30.01

Step-by-step explanation:

2.1^2 + 25.6

= 4.41 + 25.6

= 30.01

Answer:

12

Step-by-step explanation:

We know that 8x3=24, so we have to find what would equal 3 in the parenthesis.

12-9=3

The correct equation would be 8 (12-9) =24, or to be very simple, 8x3=24.

So y=12.

Answer:

Try D for an answer..good luck

Triangle ABC is indeed similar to Triangle CDE by the SAS (Side-Angle-Side) Congruence Postulate.

Assume that we have the following to prove congruence:

AB/DC = AC/CE (proportional sides)

AB || CD (parallel lines)

This means that angle ABC is congruent to angle CDE.

Looking at this, we can infer that Side AB is proportional to side DC. We also see that Angle ABC is the same as Angle CDE.

Going by the SAS Congruence theorem, Triangle ABC is indeed similar to Triangle CDE because two sides of the triangle are similar and one angle is congruent.

Find out more on congruence at https://brainly.com/question/18922904

#SPJ1

You will be able to withdraw approximately $3,076.32 at the end of 5 years.

To calculate the amount you will be able to withdraw at the end of 5 years, we can use the future value formula for compound interest.

The formula for calculating the future value (FV) of a present value (PV) invested at an annual interest rate (r) for a certain number of years (t) is:

\(FV = PV * (1 + r)^t\)

Given:

PV = $2,300

r = 6% = 0.06 (decimal representation)

t = 5 years

Substituting these values into the formula, we get:

FV = $2,300 * \((1 + 0.06)^5\)

Calculating the expression inside the parentheses:

\((1 + 0.06)^5 = 1.338225\)

Multiplying the present value by this factor:

FV = $2,300 * 1.338225

FV ≈ $3,076.32

Therefore, you will be able to withdraw approximately $3,076.32 at the end of 5 years.

Learn more about compound interest here:

https://brainly.com/question/14295570

#SPJ11

You deposit $2,300 into an account that pays 6% per year. Your plan is to withdraw this amount at the end of 5 years to use for a down payment on a new car. How much will you be able to withdraw at the end of 5 years? Do not round intermediate calculations. Round your answer to the nearest cent

a) The angle A is approximately 0.17 radians.

b)  Ashton has run approximately 0.595 km before stopping.

To determine the angle A and the distance Ashton has run before stopping, we can use the properties of right triangles and the relationship between angles and arc lengths on a circle.

a. To find the angle A in radians, we can use the relationship between the arc length and the radius of the circle. The arc length Ashton has traveled is given by the difference in x-coordinates of her starting and stopping positions, which is |-2.905 - (-3.5)| = 0.595 km. Since the radius of the circle is 3.5 km, we have:

Arc length = radius * angle

0.595 km = 3.5 km * angle

Dividing both sides of the equation by 3.5 km, we find:

angle = 0.595 km / 3.5 km ≈ 0.17 radians

The angle A is approximately 0.17 radians.

b. To find the distance Ashton has run before stopping, we can use the relationship between the circumference of the circle and the total angle around the circle, which is 2π radians. The distance Ashton has run is given by the ratio of the angle A to the total angle around the circle multiplied by the circumference of the circle. Since the radius is 3.5 km, the circumference is 2π * 3.5 km. We have:

Distance Ashton has run = (angle / (2π)) * (2π * radius)

Distance Ashton has run = angle * radius

Substituting the values, we find:

Distance Ashton has run = 0.17 radians * 3.5 km ≈ 0.595 km

Ashton has run approximately 0.595 km before stopping.

Learn more about angle here:

https://brainly.com/question/30147425

#SPJ11

Increasing marginal productivity infers that extra units of capital and labor contribute more to yield, driving productive asset allotment. ∝ and ß < 1 expect reducing returns, adjusting with reality.

To appear that the generation work has to expand the marginal productivity of capital (in case ∝ > 1) and labor (on the off chance that ß > 1), we ought to take fractional subsidiaries with regard to each input calculation. For capital (K), the fractional subsidiary of the generation work is:

\(\dfrac{dy}{dK }= \alpha AK^{(\alpha-1)}L^\beta\)

Since ∝ > 1, (∝ - 1) is positive, which implies that the fractional subordinate \(\dfrac{dy}{dK}\) is positive. This shows that an increment in capital input (K) leads to an increment in yield (y), appearing to expand the marginal efficiency of capital.

Additionally, for labor (L), the fractional subordinate of the generation work is:

\(\dfrac{dy}{dL} = \beta AK^{\alpha}L^{(\beta-1)}\)

Since \(\mathbf{\beta > 1, (\beta-1)}\) it is positive, which implies that the halfway subordinate \(\dfrac{dy}{dL}\) is positive. This demonstrates that an increment in labor input (L) leads to an increment in yield (y), appearing to increase the marginal productivity

The economic importance of increasing marginal productivity is that extra units of capital and labor contribute more to yield as their amounts increment.  This suggests that the more capital and labor a firm employments, the higher the rate of increment in yield. This relationship is vital for deciding the ideal assignment of assets and maximizing generation effectiveness.

In most generation capacities, it is accepted that ∝ and ß are less than 1. This presumption adjusts with experimental perceptions and financial hypotheses.

In case ∝ or ß were more prominent than 1, it would suggest that the marginal efficiency of the respective factor increments without bound as the calculated input increments.

In any case, there are decreasing returns to scale, which suggests that as calculated inputs increment, the Marginal efficiency tends to diminish. Therefore, accepting ∝ and ß are less than 1 permits for more reasonable modeling of generation forms and adjusts with the concept of diminishing marginal returns.

Learn more about the Marginal productivity of capital here:

https://brainly.com/question/18492635

#SPJ4

Answer:

251$

Step-by-step explanation:

Let's say x represents Joes's account.

And y represents Chandra.

Since Joses account was 1 more than one half of chandra, the amount for Joes would be x = 1/2*y + 1

Now we can just say y = Chandra's amount.

So x + y = 751

And x = 1/2*y + 1

We have a systems of equation, and just plug in 1/2*y + 1 for x.

1/2*y + 1 + y = 751

1/2*y + y = 750 (subtract both sides by 1)

distribute y so...

y(1/2 + 1) = 750

y = 750/1.5

y = 500

Remember, y is Chandra. So plug in 500 for y in Joses equation, so 1/2(500) +

is 250 +1 so 251.

Answer:

above sea level

Step-by-step explanation:

The position vector from (3, − 8,0) to ( − 9, − 7, − 6) is  (-12, 1, -6).

To find the position vector, we need to add this vector to the initial point (3, -8, 0). This gives us:
(3, -8, 0) + (-12, 1, -6) = (-9, -7, -6)
In mathematics, position vector refers to a vector that describes the position of a point relative to an origin point. In this question, we are asked to find the position vector that is equal to the vector from (3, -8, 0) to (-9, -7, -6).

To find the position vector, we need to add the vector from the initial point to the final point to the initial point itself. This gives us the endpoint of the vector, relative to the origin. The position vector is important in many applications, such as physics, engineering, and computer graphics, where it is used to describe the position of an object or point in space.

To know more about position vectors visit:

https://brainly.com/question/31289161

#SPJ11

It is to be noted that the graph comprises two inherent traits:
The domain and the range. Each of these qualities helps the user interpret and analyze data.

The domain of a graph consists of all the input values represented on the x-axis since the domain refers to the set of potential input values. The range represents the set of potential output values, which are shown on the y-axis.

In mathematics, domain and range are significant because they allow us to determine the set of all possible values for a function. Understanding a function's domain and range allows us to identify its inverse, graph it, and solve issues involving the function.

To acquire the domain and range, just solve the equation y = f(x) to discover the values of the independent variable x. To compute the function's range, just define x as x=g(y) and then discover the domain of g. (y).

It is to be noted that the question contains very limited information hence the general answer.

Learn more about Domain:
https://brainly.com/question/26098895
#SPJ1

Answer:

Please check the explanation.

Step-by-step explanation:

If the lines are identical, there must be an infinite number of solutions. In other words, they are the coordinate of all the points on that line.

It means the lines will be overlapping. Since lines will be overlapping, it means they are the same exact line.

Given the line

3y = 2x-9

As the system of equations has an infinite number of solutions, it means the lines must be identical.

So, the other line can be obtained by multiplying the line 3y = 2x-9 by any scalar number, let say by 2.

so

6y = 4x-18 will be another line.

Thus, the system of equations become:

3y = 2x-9

6y = 4x-18

The graph is attached below.

The graph indicates that both lines are overlapping with each other. Hence, the lines will be identical and the system of the equations will have an infinite number of solutions.

Answer:

y = 2x -4

Step-by-step explanation:

y2 - y1 / x2 - x1

-4 - (-6)/ 0 - (-1)

= 2

y = mx + b

y = -2x + b

-4 = -2(0) + b

-4 = 0 + b

-4 = b

So the equation is y = 2x -4

Sure!

The hundredths place is the second in a decimal.

with rounding, if the number is greater than or equal to 5, you round up, if not, you round down.

In this case we round up because 9 is bigger than 5.

So, it becomes 6.79

Therefore your answer is B

Answer:

50/77

Step-by-step explanation:

(1÷2 3/4)+(1÷3 1/2)

2 3/4 is same as 11/44

1/2 is same as 7/2

so to divide fraction you have to flip the second number and multiply

so 1 times 4/11=4/11

and 1 times 2/7=2/7

4/11 +2/7=28/77+22/77=50/77