For f(x) = 3x+1 and g(x)=x2-6, find (f- g)(x).

Answer: C

Step-by-step explanation: 5x5=25

pls mark as brainliest

Answer:

The correct option is

C. \(18x^2y^2\sqrt[3]{3xy^2}\\\)

Step-by-step explanation:

We have the expression,

\(3x\sqrt[3]{648x^4y^8}\)

Simplifying,

\(3x\sqrt[3]{648x^4y^8}\\3x\sqrt[3]{648x^3xy^6y^2}\\3x\sqrt[3]{648(x)^3x(y^2)^3y^2}\\\)

Taking out x and y^2,

\(3xxy^2\sqrt[3]{648xy^2}\\3x^2y^2\sqrt[3]{(2)(2)(2)(3)(3)(3)(3)xy^2}\\3x^2y^2\sqrt[3]{(2)^3(3)^3(3)xy^2}\\\\(3)(2)(3)x^2y^2\sqrt[3]{(3)xy^2}\\18x^2y^2\sqrt[3]{3xy^2}\\\)

Hence the correct option is C

Answer:

16

Step-by-step explanation:

it is not  728728827632788763728 that is wrong it is 100 divided by 10 =10

160 divided by 10 =16

If Christina does her due diligence and carefully weighs the costs and potential income, buying and renting out the holiday apartment could be a sound investment. However, she should carefully assess the market demand and legal requirements before making any final decisions.

Secondly, Christina needs to consider the costs involved in purchasing and maintaining the holiday apartment. She should factor in the purchase price, any renovation or repair costs, ongoing maintenance costs, and taxes and insurance. She also needs to consider any potential income from renting out the apartment and weigh that against the costs.
Thirdly, Christina should research the legal and regulatory requirements for renting out a holiday apartment in the area. She needs to ensure that she is complying with all relevant laws and regulations, such as obtaining any necessary permits or licenses and adhering to safety standards.

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If Christina is considering buying this holiday apartment for rental purposes, she should do thorough research before making a final decision. The apartment's location, amenities, and rental potential are important factors to consider.

She should also evaluate the cost of purchasing and maintaining the property versus the potential rental income it could generate. It's advisable to speak with a real estate agent or property management company to gain insights on the rental market in the area. Furthermore, Christina should ensure that the apartment meets all legal requirements for rentals in the location she plans to rent it out in. By taking these steps, Christina can make an informed decision on whether to invest in the holiday apartment and earn a steady income from renting it out to holiday guests.

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The composite function is f(t(p)) = 8e^(4p^2).

First, we need to substitute the expression for t in terms of p into the expression for f. We get:

f(t(p)) = 8e[t(p)]

Now, we can substitute the expression for t in terms of p:

f(t(p)) = 8e[4p^2]

Simplifying the expression, we get:

f(t(p)) = 8e^(4p^2)

Therefore, the composite function is f(t(p)) = 8e^(4p^2).

When working with functions, sometimes it is useful to combine them into a single composite function. To do this, we can substitute the expression for one function into the other and then simplify.

In this problem, we are given two functions, f(t) and t(p), and we are asked to write them as a single composite function using p as the independent variable.

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The length of the similar triangle are 45 unit and 36 unit.

A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.

Since right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse.

Consider triangle ABC is a right angled triangle with side AB = 24, AC = 32 and the hypotenuse BC = 40.  

Given that Triangle PQR is a right angled triangle similar to triangle ABC with side PQ = 27,  PR= b and the hypotenuse QR = a.

We know that Two triangles are said to be similar if they have proportional angles or proportional sides that is they have the same shape.

For similar triangles, the ratio of their corresponding side are the same so;

Given that triangle ABC is similar to triangle PQR, therefore:

\(\frac{AB}{AC}=\frac{PQ}{PR}\\ \\\frac{24}{32}=\frac{27}{b}\\\\b=\frac{27*32}{24}\\ b=36\)

a = 27  x10/24

a = 45

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Answer: 201

Step-by-step explanation: Ok this is very simple for those of you who are stuck on this. First you divide 12 by 268. You would get 22 with a remainder of 4. This in fractions would be 22 1/3. So he would be driving 22 1/3 miles with 1 galloon of gas. If you multiply this by 9 you would get 201 miles which is how much he can drive in 9 gallons of gas.

Hoped this helped!

Answer:

√32 = c

Step-by-step explanation:

a^2 + b^2 = c^2

4^2 + 4^2 = c^2

16 + 16 = c^2

32 = c^2

√32 =c

Answer:

4.4471336 * 10^2.

Step-by-step explanation:

(6.253•10^-2)(7.112x10^3)

= 6.253*7.112 * 10^-2*10^3

= 44.471336 * 10^1

= 4.4471336 * 10^2.

The solid of intersection of the two right circular cylinders of radius r whose axes meet at right angles is known as a Steiner's Reversed Cycloid. It has a volume of V=16πr³/9. The intersection volume between two identical cylinders whose axes meet at right angles is called a Steiner solid (sometimes also referred to as a Steinmetz solid).

To find the volume of a Steiner solid, you must first define the radii of the two cylinders. The radii of the cylinders in this question are r. You must now compute the volume of the solid formed by the intersection of the two cylinders, which is the Steiner solid.

A method for determining the volume of the Steiner solid formed by the intersection of two cylinders whose axes meet at right angles is shown below. You can use any unit of measure, but be sure to use the same unit of measure for each length measurement. V=16πr³/9 is the formula for finding the volume of the Steiner solid for two right circular cylinders of the same radius r and whose axes meet at right angles. You can do this by subtracting the volumes of the two half-cylinders that are formed when the two cylinders intersect. The height of each of these half-cylinders is equal to the diameter of the circle from which the cylinder was formed, which is 2r. Each of these half-cylinders is then sliced in half to produce two quarter-cylinders. These quarter-cylinders are then used to construct a sphere of radius r, which is then divided into 9 equal volume pyramids, three of which are removed to create the Steiner solid.

Volume of half-cylinder: V1 = 1/2πr² * 2r

= πr³

Volume of quarter-cylinder: V2 = 1/4πr² * 2r

= πr³/2

Volume of sphere: V3 = 4/3πr³

Volume of one-eighth of the sphere: V4 = 1/8 * 4/3πr³

= 1/6πr³

Volume of the Steiner solid = 4V4 - 3V2

= (4/6 - 3/2)πr³

= 16/6 - 9/6

= 7/3πr³

= 2.333πr³ ≈ 7.33r³ (in terms of r³)

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Answer:

I think the answer is A

1,2

Counting from point M (0 unit) on this number line, we can logically deduce that point H is located at -7.

A numerical data is also referred to as a quantitative data and it can be defined as a data set that is primarily expressed in numbers only. This ultimately implies that, a numerical data refers to a data set consisting of numbers rather than words.

In Mathematics, there are six (6) common types of numbers and these include the following:

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length. Also, the negative numerical values are positioned at the left from zero while the positive numerical values are positioned at the right from zero.

Note: Each of the tick represents 1 unit.

Therefore, counting from point M (0 unit) on this number line, we can logically deduce that point H is located at -7.

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In philosophy, objectivity is a central concept that generally denotes an objective and impartial approach to something. The opposite is subjectivity.

That something is objectively true, an objective truth, means that it is true regardless of subjectivity. Objectivity is usually an ideal in connection with research, as the result is expected to be as independent of the researcher's opinions or ideas as possible.

Objectivity is often also emphasized as a basic ideal in journalistic work. An important question in philosophy is whether it is possible to experience something objectively.

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The relation R on the set of all real numbers, where (x, y) = R if and only if x + y = 0, is reflexive and symmetric, but not antisymmetric or transitive.

A relation is reflexive if every element is related to itself. In this case, for any real number x, we have x + x = 2x, which is not equal to 0 unless x = 0. Therefore, the relation is not reflexive.

A relation is symmetric if whenever (x, y) is in R, then (y, x) is also in R. In this case, if x + y = 0, then y + x = 0 as well. Thus, the relation is symmetric.

A relation is antisymmetric if whenever (x, y) and (y, x) are in R and x ≠ y, then it implies that x and y must be the same. Since x + y = 0 and y + x = 0 imply that x = y, the relation is not antisymmetric.

A relation is transitive if whenever (x, y) and (y, z) are in R, then (x, z) is also in R. However, this is not true for the given relation since if x + y = 0 and y + z = 0, it does not guarantee that x + z = 0. Therefore, the relation is not transitive.

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since the powers are same, ignore 'em , and let's calculate the bases.

-16.(1/2)

-8.1 (upon cancellation)

ans = -8

hope it helps...!!!

This triangle is called a 45-45-90 triangle, and the side ratio for the sides opposite to the 45-45-90 degree angles respectively are 1-1-sqrt2

Now we know one side is 6 and its opposing the 45 degrees angle and BC is opposing the 90 degrees angle the ratio between the sides are 1:sqrt2

Therefore BC=6*sqrt2=6sqrt2

Thus B is the correct answer!

Hope this helped any questions just leave them in the comments of this answer.

The exact value of the given expression is:(sqrt(15) + 2)/8.We are given that sin(theta) = 1/4 and tan(theta) > 0, where 0 ≤ theta ≤ 2pi. We need to find the exact value of cos(theta/2).

From the given information, we can find the value of cos(theta) using the Pythagorean identity:

cos(theta) = sqrt(1 - sin^2(theta)) = sqrt(15)/4.

Now, we can use the half-angle formula for cosine:

cos(theta/2) = sqrt((1 + cos(theta))/2) = sqrt((1 + sqrt(15)/4)/2) = sqrt((2 + sqrt(15))/8).

Therefore, the exact value of cos(theta/2) is:

cos(theta/2) = sqrt((2 + sqrt(15))/8).

Alternatively, if we rationalize the denominator, we get:

cos(theta/2) = (1/2)*sqrt(2 + sqrt(15)).

Thus, the exact value of cos(theta/2) can be expressed in either form.In the second part of the problem, we are given an expression:

sqrt(10)/4 * sqrt(6)/4 + sqrt(8 + 2sqrt(15))/4 * sqrt(8 - 2sqrt(15))/4.

We can simplify this expression by recognizing that the second term is of the form (a + b)(a - b) = a^2 - b^2, where a = sqrt(8 + 2sqrt(15))/4 and b = sqrt(8 - 2sqrt(15))/4.

Using this identity, we get:

sqrt(10)/4 * sqrt(6)/4 + sqrt(8^2 - (2sqrt(15))^2)/16

= sqrt(10*6)/16 + sqrt(64 - 60)/16

= sqrt(15)/8 + sqrt(4)/8

= (sqrt(15) + 2)/8.

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Answer:

3,240

Step-by-step explanation:

Calculating this expression will give us the amount the farmer needs to save annually over the 8-year period.

Given:

Payment required at the end of each year: P50,000

Number of years until the daughter starts college: 8

Interest rate: 7% (compounded annually)

We can calculate the annual savings using the formula for the present value of an ordinary annuity:

P = \dfrac{PMT \times (1 - (1 + r)^{-n}{r}

Where:

P = Present value (amount to be saved annually)

PMT = Payment amount (P50,000)

r = Interest rate per period (7% or 0.07)

n = Number of periods (8)

Let's substitute the given values into the formula:

\[ P = \dfrac{50,000 \times (1 - (1 + 0.07)^{-8}{0.07} \]

Calculating this expression will give us the amount the farmer needs to save annually over the 8-year period.

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The individual counted a higher ratio of cars to trucks  at the second rest stop, since 17/22 was larger than 3/4.

At the first rest stop, the ratio of cars to trucks was 15:20 or 3:4. At the second rest stop, the ratio of cars to trucks was 17:22 or 17/22. Since 17/22 is larger than 3/4, the individual counted a higher ratio of cars to trucks at the second rest stop. To illustrate this using formulas, we can divide the number of cars by the number of trucks at each rest stop. This gives us 15/20 = 0.75 for the first rest stop and 17/22 = 0.77 for the second rest stop. Since 0.77 is greater than 0.75, the individual counted a higher ratio of cars to trucks at the second rest stop.

At the second rest stop, the individual counted a higher ratio of cars to trucks.The individual counted a higher ratio of cars to trucks  at the second rest stop, since 17/22 was larger than 3/4.

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Where h is the number of hours Melanie can rent the bike, and the solution is h < 5.5.

Let's first determine the cost of renting a bike for h hours:

Cost = 8h + 6

Since Melanie wants to rent a bike for less than $50, we can set up the following inequality:

8h + 6 < 50

Now we can solve for h:

8h < 44

h < 5.5

Since Melanie cannot rent a bike for a fraction of an hour, the maximum number of hours she can rent the bike is 5 hours.

Therefore, the inequality that will help Melanie find the maximum number of hours she can rent the bike is:

8h + 6 < 50

Where h is the number of hours Melanie can rent the bike, and the solution is h < 5.5.

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Answer:

The water falls a total length of 2,425 feet

Step-by-step explanation:

In order to calculate the total length of the waterfall, we will find the sum of the three parts of the waterfall.

Length of upper fall = 1430 feet

Length of middle cascade = 675 feet

Length of lowe fall = 320 feet

Total length of fall = (Length of upper fall) + (Length of middle cascade) + (Length of lowe fall)

= 1430 + 675 + 320 = 2,425 feet

Total length that the water falls = 2,425 feet

Answer:

Accounts receivable in January = $68,432.60

Accounts receivable in February = $55,929.20

Accounts receivable in March = $55,958.95

Step-by-step explanation:

65% of sales collected in the month of sales + 25% in the following month + 10% in second month after sales.

In January, total accounts receivable will be the amounts outstanding or unpaid by the end of January. By the end of January, a total of 10% of December sales & 35% of January sales remain outstanding.

Accounts receivable in January = 35% of January sales + 10% of December sales

Accounts receivable in January = (35% * $124298) + (10% * $249283)

Accounts receivable in January = $43504.3 + $24928.3

Accounts receivable in January = $68432.60

In February, total accounts receivable will be the amounts outstanding or unpaid by the end of February. By the end of February, a total of 10% of January sales & 35% of February sales remain outstanding.

Accounts receivable in February = 35% of February sales + 10% of January sales

Accounts receivable in February = (35% * $124284) + (10% * $124298)

Accounts receivable in February = $43,499.4 + $12,429.8

Accounts receivable in February = $55,929.20

In March, total accounts receivable will be the amounts outstanding or unpaid by the end of march. By the end of March, a total of 10% of February sales & 35% of March sales remain outstanding.

Accounts receivable in March = 35% of March sales + 10% of February sales

Accounts receivable in March = (35% * $124373) + (10% * $124284)

Accounts receivable in March = $43530.55 + $12428.4

Accounts receivable in March = $55,958.95

Answer:

\(\mathrm{a=-50,\ d=7,\ general\ formula=7(n-1)-50}\)

Step-by-step explanation:

\(\mathrm{Solution,}\\\mathrm{Given,}\\\mathrm{15^{th}\ term(t_{15})=48}\\\mathrm{or,\ a+14d=48.........(1)}\\\mathrm{And\ 40^{th}\ term(t_{40})=223}\\\mathrm{or,\ a+39d=223......(2)}\\\mathrm{n^{th}\ term(t_n)=\ ?}\\\mathrm{Subtracting\ equation(1)\ from\ (2),}\\\mathrm{25d=175}\\\mathrm{or,\ d=7}\\\mathrm{Now,\ a+14d=48\ or,\ a=48-14d=48-14(7)}\\\mathrm{\therefore a=-50}\)

\(\mathrm{t_n=a+(n-1)d}\\\mathrm{or,\ t_n=-50+(n-1)7}\\\mathrm{\therefore general\ formula=7(n-1)-50}\)

Answer:

Let the length parallel to the house be y

let each of the other two equal sides be x

2x + y = 120

y = 120 - 2x

Area = xy

= x(120 - 2x) or -2x^2 + 120x

b) you want the vertex.

x of the vertex is -120/(-4) = 30

when x = 30

y = 60

Maximum area = xy = 1800 ft^2

The quadratic function that represents the area of the rectangular enclosure is  -2x² + 120x and x = 30 and y = 60 will make the area maximize.

A rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

Area of rectangle = length × width.

Perimeter of rectangle = 2( length + width).

Let's suppose the length parallel to the house is y

And the remaining side is x then,

Perimeter = x + x + y

2x + y = 120

y = 120 - 2x

The area of the rectangle = xy

Area = x(120 - 2x)

⇒ -2x² + 120x

To find the maximum first derivate of the function area with respect to x compare with zero.

d/dx(-2x² + 120x) = 0 ⇒ -4x + 120 = 0

x = 30 so y = 120 - 2(30) = 60

Hence "The quadratic function that represents the area of the rectangular enclosure is  -2x² + 120x and x = 30 and y = 60 will make the area maximize".

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By using the given formula and solving we get, the original value of the vase is 5000 pounds.

A percentage is a way to express a number as a fraction of 100. It is often denoted by the symbol "%". For example, 25% means 25/100 or 0.25. Percentages are often used to express rates of change or proportions.

A rate is a ratio that compares two quantities of different units, such as distance and time, or weight and volume. It is often represented as a fraction or a decimal and can be converted to a percentage by multiplying by 100.

The given formula tells us how the value of the vase changes over time, with the value increasing by a factor of 1.28 (28% increase) every year.

To find the original value of the vase, we need to know the value of the vase when n = 0.

Substituting n = 0 into the formula, we get:

value in pounds = 5000*1.28^0

When n = 0, 1.28^0 = 1, so the original value of the vase is:

value in pounds = 5000*1 = 5000 pounds

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