Samuel paid $720 for a new music system. The list price for the music system was $800. What was his rate of discount?

Answers

Answer 1

the discount rate is 10%

Answer 2

Final answer:

Samuel received a 10% discount on the music system, calculated by finding the difference between the list price ($800) and the sale price ($720), then dividing that by the list price and multiplying by 100.

Explanation:

The question at hand is about calculating the rate of discount Samuel received on his new music system. Initially, the list price of the music system was $800, but Samuel paid $720 for it. To find the rate of discount, we first need to determine the discount amount which is the difference between the list price and the sale price.

List Price = $800Sale Price = $720Discount Amount = List Price - Sale Price = $800 - $720 = $80

Next, to find the rate of discount, we use the formula:

Rate of Discount = (Discount Amount / List Price) × 100

Substituting the values we have:

Rate of Discount = ($80 / $800) × 100 = 10%

Therefore, Samuel received a 10% discount on the music system.

Related Questions

Consider the function f(x)=−23x+5 . What is f(52) ? Enter your answer, as a simplified fraction, in the box.

Answers

Hey! the answer is -52.5
Hope this helps!

Answer: f(52) = -1191.

Step-by-step explanation:

Given function f(x)=−23x+5

We need to find f(52).

In order to find the value of f(52), we need to plug x= 52 in the given above linear function f(x) = -23x+5.

Plugging x= 52, we get

f(52) = -23(52) +5

On multiplying -23 and 52 we get -1196.

Therefore,

f(52) = -1196 +5

And

f(52) = -1191.

simplify the expression. write the answer using scientific notation 4(6.2x10^11)

Answers

Answer:
= 2.48 × 10¹²
(scientific notation)

= 2.48e12
(scientific e notation)

= 2.48 × 10¹²
(engineering notation)
(trillion; prefix tera- (T))

= 2480000000000
(real number)

The correct answer is 2.48*10^12.

Tom separated the rectangle shown below into 8 equal parts what fraction shows the area of one of the parts

Answers

the complete question in the attached figure

we know that
the total squares of the figure is------> 8*8-------> 64 squares
the area of one of the parts has-------> 4*2------> 8 squares
so
[the fraction ]=8/64-------> 1/8

the answer is 1/8

Tom divided the rectangle into 8 equal parts, and each part represents 1/8 of the total area. This fraction is derived from the fact that division of an area into equal parts means each part is one of those parts as a fraction of the whole.

Tom divided the rectangle into 8 equal parts. If we are to find the fraction that represents the area of one of these parts, we simply consider that each part should be an equal division of the whole. Hence, one part out of eight equal parts is represented by the fraction 1/8. This is because division by 8 is equivalent to multiplication by its reciprocal, which is 1/8. This is the same as dividing the rectangle into smaller, more manageable areas, such as rectangles, and determining the area of one such rectangular area.

It's important to understand that in a rectangle divided evenly into parts, any single part represents a fraction of the whole, with the denominator reflecting the total number of parts. In this case, since there are 8 parts, each individual part is 1/8 of the total area. This provides us with a simple way to address problems involving finding fractions of areas, particularly when the total area is partitioned into equally-sized segments.

Choose all equivalent expression(s).
HELP !!
answer choices in picture

Answers

The answer would be: B, C and D

The [tex] \frac{1}{4}[/tex] from [tex] \frac{1}{4} ^{3x^{2} }[/tex] can be converted into [tex] 4^{-1} [/tex] so it will be equal to [tex] 4^{-3x^{2} } [/tex]

The [tex] \frac{x}{4}[/tex] from [tex] \frac{x}{4} ^{3x }[/tex] can be converted into [tex] x^{1} [/tex] *[tex] 4^{-1} [/tex] so it will be equal to [tex] 4^{-3x^{2} } [/tex]

[tex] 4^{3x^{2} } [/tex] and [tex] 4^{-3x^{2} } [/tex] clearly not equivalent, so option A is out

PLZZ HELP AND PLZZ HURRY

What other information is needed to prove that △FGE ~ △IJH by the SAS similarity theorem?

A. ∠F ≅ ∠J
B. ∠I ≅ ∠F
C. ∠E ≅ ∠H
D. ∠G ≅ ∠I

Answers

Answer: The correct answer is Choice B.

In the diagram, we can see that we have two pairs of sides that are proportional.

10/15 = 20/30

One of the ways to prove triangles similar is with the SAS similarity theorem. Therefore, all we are missing is the included angle. Knowing that angle I is congruent to angle F would be enough to prove the triangles are similar.

Answer:

I think the answer is B. ∠I ≅ ∠F.

Step-by-step explanation:

Complete the following in 4 to 6 sentences: First, list two intellectual property rights. Then, describe why an intellectual property right provides incentives for people to produce creative work.

Answers

1. What is Intellectual Property
Intellectual property refers to creations of the mind: inventions; literary and artistic works; and symbols, names and images used in commerce.
1B. Intellectual property is divided into two categories:
Industrial Property includes patents for inventions, trademarks, industrial designs and geographical indications.

2. Copyright covers literary works (such as novels, poems and plays), films, music, artistic works (e.g., drawings, paintings, photographs and sculptures) and architectural design. Rights related to copyright include those of performing artists in their performances, producers of phonograms in their recordings, and broadcasters in their radio and television programs.

3. What are intellectual property rights?
Intellectual property rights are like any other property right. They allow creators, or owners, of patents, trademarks or copyrighted works to benefit from their own work or investment in a creation. These rights are outlined in Article 27 of the Universal Declaration of Human Rights, which provides for the right to benefit from the protection of moral and material interests resulting from authorship of scientific, literary or artistic productions.
The importance of intellectual property was first recognized in the Paris Convention for the Protection of Industrial Property (1883) and the Berne Convention for the Protection of Literary and Artistic Works (1886). Both treaties are administered by the World Intellectual Property Organization (WIPO).

Why promote and protect intellectual property?
There are several compelling reasons. First, the progress and well-being of humanity rest on its capacity to create and invent new works in the areas of technology and culture. Second, the legal protection of new creations encourages the commitment of additional resources for further innovation. Third, the promotion and protection of intellectual property spurs economic growth, creates new jobs and industries, and enhances the quality and enjoyment of life.

An efficient and equitable intellectual property system can help all countries to realize intellectual property’s potential as a catalyst for economic development and social and cultural well-being. The intellectual property system helps strike a balance between the interests of innovators and the public interest, providing an environment in which creativity and invention can flourish, for the benefit of all.

How does the average person benefit?
Intellectual property rights reward creativity and human endeavor, which fuel the progress of humankind. Some examples:
The multibillion dollar film, recording, publishing and software industries – which bring pleasure to millions of people worldwide – would not exist without

copyright protection.

Without the rewards provided by the patent system, researchers and inventors would have little incentive to continue producing better and more efficient products for consumers.

Consumers would have no means to confidently buy products or services without reliable, international trademark protection and enforcement mechanisms to discourage counterfeiting and piracy.

Final answer:

Intellectual property rights such as patents and copyrights incentivize creative work by providing creators a temporary monopoly, allowing them to recover development costs and potentially make a profit without immediate competition.

Explanation:

Two intellectual property rights are patents and copyrights. A patent gives the inventor the exclusive legal right to make, use, or sell an invention for a limited time, usually for 20 years, and a copyright provides the author exclusive legal rights over their creative works.

Intellectual property rights offer creators monopoly profits during this protected period, acting as significant incentives for the production of creative work.

This exclusive period allows researchers and companies to recover the costs associated with research and development. Without these protections, there would be little to no incentive to invest in creating new works if they could quickly be replicated without any benefit to the creator.

PLEASE CHECK THIS FOR ME

LET ME KNOW IF ITS CORRECT

Answers

1) W(n)=15 . b^n

Initial numbers of horse: W(0)=?
n=0→W(0) = 15 . b^0
W(0)= 15 . 1
W(0)= 15

Answer: Based on the model, the initial number of horses is 15.

2) If b=1.35, the annual percent growth rate of the number of horses: r=?
b=1+r
1+r=1.35
Solving for r:
1+r-1=1.35-1
r=0.35
r=0.35*100%
r=35%

Answer: If b=1.35, the annual percent growth rate of the number of horses would be 35 %.

Which graph is defined by f(x) = |x2 − x − 2|?

Answers

it should look like a parabola with the part below x-axis cut off. the left side starts from x=-1, opening upward & to the left, the right side starts from x=2, opening upward and to the right.

PLEASE HELP ASAP!
Volume of rectangular prism
Area of a parallelogram
Circumference of a circle
Area of a circle
Area of a triangle
Area of a trapezoid
Perimeter of a quadrilateral
-
Item bank:
2L + 2W
πd
πr2
bh
lwh
1/2(b1 + b2)h
1/2 bh

Answers

Area of a Parallelogram --- bh (base x height)
Circumference (Perimeter) --- πd
Area of a Circle --- πr2
Area of a Triangle --- 1/2 bh
Area of a Trapezoid --- 1/2(b1 + b2)h
Perimeter of a Quadrilateral/Rectangle --- 2L + 2W
Volume of a Parallelogram --- lwh

if it says i copied and pasted.. i didn't, i didn't have pi symbol so i copied and pasted that... hope this helped tho..

Final answer:

Clear geometry formulas for calculating volume, area, and perimeter include V = lwh for rectangular prisms, A = bh for parallelograms, and C = πd for the circumference of a circle, among others.

Explanation:

Understanding Geometry, Area, and Volume

To help with remembering formulas from geometry, it's essential to understand the relationships between shapes and their dimensions. Here are the correct formulas for each of the items listed:

Volume of a rectangular prism is given by the formula V = lwh (length × width × height).Area of a parallelogram is found using A = bh (base × height).Circumference of a circle requires the formula C = πd or C = 2πr where d is diameter and r is radius.Area of a circle is calculated by A = πr² (pi times radius squared).Area of a triangle can be computed using A = 1/2 bh (half the base times the height).Area of a trapezoid is found with A = 1/2(b1 + b2)h where b1 and b2 are the bases and h is the height.Perimeter of a quadrilateral is the sum of the lengths of all four sides, often expressed as P = 2L + 2W for rectangles, with L being length and W being width.

To solve problems in geometry effectively, it's helpful to visualize the shapes and understand how to derive their area and volume using standard formulas. This also applies when dealing with more complex objects, such as spheres and cylinders. In trigonometry, understanding the relationships within a right triangle can be crucial for solving spatial problems.

You have been really sick, so you went to the doctor. The culture taken shows you have 400,000 bacteria. Your doctor prescribes a strong antibiotic which makes the bacteria decrease by a half every 4 hours. How many bacteria will be left after a day?

Answers

Why did you delete my answer?

Graph the ordered pairs for y=4x+2 using x={-2,1,2}

Answers

The graph of the ordered pairs is a straight line graph with x,y values (-2, -6), (1, 6), and (2,10).

What are ordered pairs.

In geometry, Ordered pairs are the values of x and y on the coordinate plane. They are called ordered pairs because they are usually arrange in (x,y) axis.

For a linear equation, the graph is a straight line graph. From the information given:

y = 4x + 2

The slope of the line (m) = 4The y-intercept (b) = 2

The points x-axis {-2, 1, 2} are marked on the graph and the corresponding y-values are {-6, 6, 10} respectively.

In what ways do you think presidents today are more powerful than they were in the past?

Answers

The complex demands of the modern world has given present day presidents more power. It's better suited for the executive branch over the legislative since it's a more unified power. The modern media has given the president a decided advantage in building public support for his political objectives.

Final answer:

Modern presidents are more powerful than their predecessors due to access to advanced technologies, executive actions, and media influence.

Explanation:

Presidents today are more powerful than they were in the past due to various factors. Firstly, modern presidents have access to advanced technologies such as television, the internet, and social media, which allow them to shape public opinion and build support for their policies. Secondly, they have a greater ability to use executive action, including executive orders and signing statements, to bypass Congress and enact their own policies. Finally, modern presidents can use their popularity and media attention to increase pressure on Congress and influence policy change.

Learn more about Power of modern presidents here:

https://brainly.com/question/29360176

#SPJ3

Help. I need to explain if she’s right or not

Answers

The triangular pyramid is made of 4 congruent triangles. They all have the same shape and size, so they have the same area. The area of one triangle is

A = b*h/2
A = 5*4.3/2
A = 10.75

So four of them lead to a total surface area of 4*10.75 = 43 square meters

--------------------------

The rectangular prism has the dimensions
L = 5
W = 5
H = 4.3

The surface area is found through the formula below
SA = 2*(L*W+L*H+W*H)
SA = 2*(5*5+5*4.3+5*4.3)
SA = 136

--------------------------

So far we found that
surface area of pyramid = 43 square meters
surface area of prism = 136 square meters

Dividing the values, we get 136/43 = 3.16279 approximately. The result is not equal to 2, so Susan's statement is not correct. The prism has more than twice the surface area of the pyramid

The pyramid has 4 faces, each of which has an area that is 1/2*4.3*5 m^2.

The prism has 4 faces that have an area of 4.3*5 m^2 (double the area of the triangular faces) in addition to 2 faces that have an area of 5*5 m^2.

The prism must have an area more than double that of the pyramid, as it has additional faces beyond those that have double the area of the pyramid.

find the fraction
53*53−32*32/61*61−44*44

Answers

53 x 53 - 32 x 32 / 61 x 61 - 44 x 44
2809 - 1024 / 3721 - 1936
Then subtract
1785 / 1785 = 1
The answer is 1. So the fraction is a whole number
Hope this helps

The area of a regular octagon is 35 cm2. What is the area of a regular octagon with sides five times as long?

A. 625 cm2

B. 875 cm2

C. 175 cm2

D. 245 cm2

Answers

The answer is B. 875 cm2. This is calculated by taking 35 * 5 * 5. The relationships between areas and side lengths of similar shapes is a squared relationship. Since the answer wanted 5 times, we do 5 times 5 and multiply that by our current area.

Answer with Step-by-step explanation:

Area of octagon=2(1+√2)a²

Where a is the length of the side of the octagon

Area=35 cm²

Let a' be the length of side of new octagon

a'=5a

Area=2(1+√2)a'²

=25×2(1+√2)a²

=25×35 cm²

= 875 cm²

Hence, correct option is:

B. 875 cm²

PLEASE HELP!!!

Use a calculator to find the approximate value of arccos(0.63).
a) 39.05 degrees
b) 50.95 degrees
c) 78.1 degrees
d) 32.21 degrees

Please explain how you achieved this answer. Thanks!

Answers

The Answer is b: 50.95° see attachment for the explanation.

To find the approximate value of arccos(0.63), input 0.63 into the calculator and use the inverse cosine function to find the answer, which is approximately 50.95 degrees. So correct answer is option B.

The approximate value of arccos(0.63) can be found using a calculator.

To find arccos(0.63), you need to input 0.63 into the calculator and then find the inverse cosine or cos^-1 function. On most calculators, this is represented as cos^-1 or arccos.

When you calculate arccos(0.63), you will get approximately 50.95 degrees as the correct answer.

What is the quotient of -3/8 and -1/3

Answers

Lets get started :)

To find the quotient, we need to divide (÷)
[tex] -\frac{3}{8} [/tex] ÷ [tex]- \frac{1}{3} [/tex]

To divide 2 fractions, the best way is to change the ÷ to × and flip the second fraction (called as reciprocal)

[tex] -\frac{3}{8} [/tex] x [tex]- \frac{3}{1} [/tex] ([tex] -\frac{3}{1} [/tex] is simply -3)
[tex] -\frac{3(-3)}{8} [/tex] = [tex] \frac{9}{8} [/tex]

As a mixed fraction, it would be [tex] 1\frac{1}{8} [/tex]

Answer:

its actually a

Step-by-step explanation:

1.Which explanation justifies how the area of a sector of a circle is derived?

Determine how many triangles can fit into a circle. Divide 360° by the number of triangles. Multiply the quotient by the area of the circle .

Calculate the area of the circle. Then, determine the central angle of the sector and divide this angle by 360° to get a fraction. Multiply the area of the circle by this fraction.

Determine the degree of the sector. Divide by 180° and then multiply it by the area of the triangle the sector is in.

Partition the circle into unit squares. Determine the area of the sector and multiply the area by the degree of the circle.

Answers

the correct answer is
2) Calculate the area of the circle. Then, determine the central angle of the sector and divide this angle by 360° to get a fraction. Multiply the area of the circle by this fraction.
area of the circle is calculated by;
area = πr² , where r- radius of circle
the central angle of a circle is 360°. Area of the circle is calculated for central angle of 360°.
Sector is when 2 arms/ radii enclose a central angle between them.
area for 360° = πr²
area for 1 ° = area/ 360
area for central angle of sector = area * angle/ 360
the angle of sector is divided by 360 and taken as a fraction .this fraction of the total area of the circle is taken as the area of the sector.

rank from highest to lowest in order of decresing mass

1 Gg, 100 g, 1 kg, 50 cg, 1 cg, 1 dg, 50 million ng,

Answers

The best idea to solve this question is to convert all in same unit i.e. grams. 1 Gg = 10^9 g 100 g = 10^2 g 50 cg = 50*10^-2 g = 0.5 g 1 kg = 1000 g 1 cg = 0.01 g 1 dg = 0.1 g 50 mn ng = 50 * 10^6 * 10^-9 gram = 5* 10 ^-2 g = 0.5g So, the correct order is 1 Gg > 1 kg > 100 g > 50 cg = 50 mn ng > 1 dg > 1 cg

Randy drove 540 miles in three times the time it took Andy to travel 135 miles Andy’s speed was slower than Randy’s by 15 miles per hour what were the rate and time of each?

I really need help please!!!

Answers

Let's assume

Randy's speed =x mph

we have

Andy’s speed was slower than Randy’s by 15 miles per hour

so,

Andy's speed =x-15

Randy drove 540 miles

so, we can find time taken by Randy

time = distance / speed

so, we get

[tex]t_R=\frac{540}{x}[/tex]

we can find time taken by Andy

time = distance / speed

so, we get

[tex]t_A=\frac{135}{x-15}[/tex]

Randy drove 540 miles in three times the time it took Andy to travel 135 miles

so,

[tex]t_R=3t_A[/tex]

we can plug it

[tex]\frac{540}{x}=3*\frac{135}{x-15}[/tex]

now, we can solve for x

[tex]540\left(x-15\right)=405x[/tex]

[tex]135x=8100[/tex]

[tex]x=60[/tex]

so,

Calculation of rate:

Randy's speed is 60 mph

Andy's speed =x-15

Andy's speed =60-15=45mph

Calculation of time:

Randy's time is

[tex]t_R=\frac{540}{x}[/tex]

[tex]t_R=\frac{540}{60}[/tex]

[tex]t_R=9 hours[/tex]

Andy's time is

[tex]t_A=\frac{135}{x-15}[/tex]

[tex]t_A=\frac{135}{60-15}[/tex]

[tex]t_A=3 hours [/tex]

PLEASE HELP ASAP
EXTRA POINTS
Sheila places a 54 square inch photo behind a 12-inch-by-12-inch piece of matting.

The photograph is positioned so that the matting is twice as wide at the top and bottom as the sides.

Write an equation for the area of the photo in terms of x.

Answers

1. As you can see in the figure attached, the area of the photograph is:

A=LxW

A is the area of the photograph (A=54 in²).
L is the lenght of the photograph (L=12-4x).
W is the widht of the photograph (W=12-2x)

When you substitute these values into the formula A=LxW, you obtain:

A=LxW
54=(12-4x)(12-2x)

2. Now, you must apply the distributive property. Then:

54=144-24x-48x+8x²
8x²-72x+144-54=0

3. Therefore, you obtain a quadratic equation for the area of the photo:

8x²-72x+90=0

The answer is:

8x²-72x+90=0

Please help!!! Fast

Answers

2x + 5y = 4
5y = -2x + 4
y = -2/5 x + 4/5
parallel lines have same slope so slope = -2/5

equation
y +4 = -2/5 (x - 5)
y = -2/5 x + 2 - 4
y = -2/5 x - 2

answer is D
y = -2/5 x - 2

To solve 5(2^x+4)=15, first divide each side by

Answers

Divide both sides by 5

Answer:5

Step-by-step explanation:

(a - b)(a 2 + ab + b 2) HELP

Answers

Hey there :)

( a - b )( a² + ab + b² )
Let us distribute ( a - b ) into the other

a ( a² ) + a ( ab ) + a ( b² ) - b ( a² ) - b ( ab ) - b ( b² )
a³ + a²b + ab² - a²b - ab² - b³

We can further simplify
a²b - ab² = 0
ab² - ab² = 0

a³ - b³

You can see in the picture which I have attached. It is the 8th formula

Use FOIL.

(a - b)(a^2 + ab + b^2)
a^3 + a^2b + b^2a - a^2b - b^2a - b^3
a^3 - b^3 <----------Answer

There are 12 marbles in a bag, and the marbles are either yellow or green. Two marbles will be randomly picked from the bag, without replacing the first one picked. The probability that both marbles will be yellow is 5 33 . How many YELLOW marbles are in the bag?

Answers

7 green, 5 yellow. Just worked backwards. C(12,2) = 66, so probability given is also 10/66

If there are x yellow marbles, then C(x,2)•C(12-x,0)/C(12,2) = 10/66. Thus C(x, 2) = 10, so x = 5 = yellows. So greens = 12–5 = 7

Answer:

B) 5

Step-by-step explanation:

The probability of picking yellow first is

. The probability of picking yellow second is

x-1

. This will give a solution of

x (x-1)

132

is equivalent to

132

. 5 and 4 are the only two consecutive numbers that when multiplied together equal 20. Therefore there are 5 yellow marbles in the bag.

Raj writes a polynomial expression in standard form using one variable, a, that has 4 terms and is degree 5.

Nicole writes a polynomial expression in standard form using one variable, a, that has 3 terms and is degree 2.

Raj and Nicole’s polynomial expressions are added to create a sum, written in standard form.

What can you determine about the degree of the sum?

The sum will be degree
.

What can you determine about the number of terms of the sum?

The maximum number of terms of the sum is
, but it could be less.

Answers

Raj writes to polynomial expression in standard form using one variable, a, that has 4 terms and is degree 5
Could for example be the following polynomial:
Aa ^ 5 + Ba ^ 3 + Ca + D

Nicole writes a polynomial expression in standard form using one variable, a, that has 3 terms and is degree 2

The polynomial is:
Ea ^ 2 + Fa + G

Adding both polynomials we have:

(Aa ^ 5 + Ba ^ 3 + Ca + D) + (Ea ^ 2 + Fa + G)
Aa ^ 5 + Ba ^ 3 + Ea ^ 2 + (C + F) a + (D + G)

Answer:
The sum will be degree = 5
The maximum number of terms of the sum is 6, but it could be less. (5 in our example)

Answer:

the sum will be degree 5

the maximum number of terms of the sum is 6

Step-by-step explanation:

Ashley has 100 books that she wants to give away at the rate of n books per week. Write a recursive function that represents the number of books Ashley has at any time. The recursive function that gives the number of books Ashley has at any time is = , starting at

Answers

Final answer:

To describe Ashley's book giveaway scenario with a recursive function, define the base case as her starting with 100 books and the recursive step reflecting the weekly giveaway of n books, allowing the calculation of remaining books at any week.

Explanation:

Ashley's scenario of giving away books can be described using a recursive function. If she starts with 100 books and plans to give away n books per week, we can denote the total number of books she has after x weeks as f(x). The recursive function that represents this situation can be written as:

f(0) = 100 - This is our base case, where Ashley starts with 100 books before any are given away.

f(x) = f(x-1) - n - This is the recursive step, indicating that the total number of books Ashley has after x weeks is the number she had the week before, minus n, the number of books given away weekly.

This recursive formula allows you to calculate the number of books Ashley will have after any given number of weeks, as long as n is a known constant number of books she gives away each week.

What is the distance between point l (3,5) and point m (9,−7)?

Answers

√((-7-5)²+(9-3)²)=√(12²+6²)=√180=√(9*4*5)=6√5=13.42

◆ CO-ORDINATE GEOMETRY ◆

[tex]We \: are \: given \: the \: co - ordinates \: \: , \\ \\ l(3,5) \: \: \: \: \: \: and \: \: \: \: \: m(9, - 7) \\ \\ \\ By \: distance \: formula \: \: , \: \\ distance \: between \: two \: points \: \\ \\ (x1,y1) \: \: \: and \: \: \: (x2,y2) \: \: \: is \: given \: by \: , \\ \\ \sqrt{ {(x2 - x1)}^{2} + ( {y2 - y1)}^{2} } \\ \\ here \: , \: \: \\ (x1,y1) = (3,5) \: \: and \: \\ (x2,y2) =(9, - 7) \\ \\ Distance \: lm \: = \sqrt{ {(9 - 3)}^{2} + ( { - 7 - 5)}^{2} } \\ \\ lm = \sqrt{ {6}^{2} + ( { - 12)}^{2} } \\ \\ lm = \sqrt{36 + 144} \\ \\ lm \: = \sqrt{180} = 6 \sqrt{5} \: \: \: \: \: ans.[/tex]

The simple interest on a principal amount, P, borrowed for T years at R% annual interest is given by the following formula. Which of the following describes the relationship between the variables of the simple interest formula?

1.P depends on R and T
2.R depends on P and T
3.I depends on P, R, and T
4.R depends on I

Answers

3.

The formula for the question is

I = P R T
Interest = Principle x Rate x Time

Answer:

3. I depends on P, R, and T.

Step-by-step explanation:

We have been given the simple interest formula [tex]I=PRT[/tex], where,

I = Amount of simple interest,

P = Principal amount,

T = Time in years,

R= Interest rate.

The bigger principal amount and higher interest rate for a long period of time will result in big amount of interest, while small principal amount at a smaller interest rate and for a small period of time will result in small amount of interest.

Since amount of interest depends on principal amount, rate and time, therefore, 3rd option is the correct choice.

what is the inverse of the function f(x) = 4x + 8 a. h(x) 1/4 x - 2

Answers

Hello,

The function is y=4x+8.
We exchange x and y ==>x=4y+8
and we seach y:
4y=x-8 ==>y=(x-8)/4 ==> y=x/4-2
Answer A

The inverse of the function will be, ⁣[tex]\rm y=\frac{1}{4} x-2[/tex]. Option A is correct. The function is obtained by rearranging the equation.

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The given function is;

[tex]\rm f(x) = 4x + 8 \\\\ y=4x+8 \\\\[/tex]

After rearranging the equation, we get;

[tex]\rm x=4y+8 \\\\ y= \frac{1}{4} (x-8)\\\\ y=\frac{x}{4} -2\\\\ y=\frac{1}{4} x-2[/tex]

The inverse of the function will be, ⁣[tex]\rm y=\frac{1}{4} x-2[/tex].

Hence, option A is correct.

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