simple interest = P × r × t

Joe borrowed $900 from Sam for six months. How much will Sam earn if he charges Joe a simple interest rate of 4 percent?

Solution:

we have been asked to find the Least Common multiple of the given polynomial x² + x – 12 and x² + 2x – 15.

To find the least common multiple. Lets first find the factors.

[tex] x^2+x-12=x^2+4x-3x-12\\
\\
x^2+x-12=x(x+4)-3(x+4)\\
\\
x^2+x-12=(x+4)(x-3)\\ [/tex]

[tex] x^2+2x-15=x^2+5x-3x-15\\
\\
x^2+2x-15=x(x+5)-3(x+5)\\
\\
x^2+2x-15=(x+5)(x-3)\\ [/tex]

Hence the LCM of the given set of Polynomials is (x+4)(x-3)(x+5).

The LCM is (x+4)*(x-3)*(x+5)

Final answer:

In parallelogram DEFG, DH = x + 3, HF = 3y, GH = 3x – 3, and HE = 5y + 4. Solving the equations yields x = 9, y = 4.

Explanation:

To find the values of x and y in parallelogram DEFG, we'll use the properties of parallelograms. In a parallelogram, opposite sides are equal in length.

Given that DH = x + 3 and HF = 3y, and that DH is opposite to HF, we have:

x + 3 = 3y   ...(1)

Similarly, given GH = 3x - 3 and HE = 5y + 4, and that GH is opposite to HE, we have:

3x - 3 = 5y + 4   ...(2)

Now, we have a system of two equations (1) and (2) to solve for x and y.

From equation (1):

x = 3y - 3   ...(3)

Substitute equation (3) into equation (2):

3(3y - 3) - 3 = 5y + 4

9y - 9 - 3 = 5y + 4

9y - 12 = 5y + 4

4y = 16

y = 4

Now, substitute the value of y into equation (3):

x = 3(4) - 3

x = 12 - 3

x = 9

So, the values of x and y are x = 9 and y = 4. Thus, the correct answer is x = 9, y = 4.

Answer:

function f(x) first reflect across x axis and then shifted 4 unit up and then 2 unit down.

Step-by-step explanation:

Given  : Transformations of g(x)=-(2)x+4-2 from the parent function f(x)=2x.

To find : Which of the following describes the transformations.

Solution : We have given

Parent function f(x) = 2x.

Transformed function  g(x) = -(2)x+4-2.

By the transformation rule : (1) reflection across x - axis f(x) →→ -f(x) .

(2) f(x)  →→ f(x) + k  it mean function shifted up by k unit.

(3) f(x)  →→ f(x) - k  it mean function shifted down by k unit.

Then

f(x) = 2x →→→→-(2)x+4-2.

It mean function f(x) first reflect across x axis and then shifted 4 unit up and then 2 unit down.

Therefore,  function f(x) first reflect across x axis and then shifted 4 unit up and then 2 unit down.

Answer:

A. [tex]20\text{ in}^3[/tex]

Step-by-step explanation:

We have been given that a 300-page book is 10 inches long, 8 inches wide, and 3/4 inches tall. We are asked to find the volume of 100 pages of the book.

First of all, we will find the volume of whole book using volume of cuboid formula.

[tex]\text{Volume of cuboid}=l\cdot w\cdot h[/tex], where,

l = Length of cuboid,

w = Width of cuboid,

h = Height of cuboid.

Upon substituting our given values in volume formula we will get,

[tex]\text{Volume of entire book}=10\text{ in}\times 8\text{ in}\times \frac{3}{4}\text{ in}[/tex]

[tex]\text{Volume of entire book}=10\text{ in}\times 2\text{ in}\times 3\text{ in}[/tex]

[tex]\text{Volume of entire book}=60\text{ in}^3[/tex]

Since there are 300 pages in entire book and 100 is 1/3 of 300, so the volume of 100 pages will be the 1/3 of the volume of entire book.

[tex]\text{Volume of 100 pages}=\frac{60\text{ in}^3}{3}[/tex]

[tex]\text{Volume of 100 pages}=20\text{ in}^3[/tex]

Therefore, the volume of 100 pages will be 20 cubic inches and option A is the correct choice.

Answer:

the length of the actual wall= 80 feet

Step-by-step explanation:

A blueprint for a house has a scale of 1:10. A wall in the blueprint is 8in.

Blueprint has a scale ratio of [tex]\frac{1}{10}[/tex]

As per the scale, the wall in the blue print is 1 in then the length of the actual wall is 10 feet

A wall in the blueprint is 8 inches, the length of the actual wall is [tex]10*8= 80[/tex] feet

the length of the actual wall= 80 feet

Answer:

B.15,200

Step-by-step explanation:

The quantity of gas in a car's tank during a journey is continuous, whereas the number of students enrolled in a class is discontinuous due to discrete changes.

Continuous functions of time imply that values can change smoothly without jumps or breaks. For the quantity of gas in the tank of a car on a journey between New York and Boston, this would be a continuous function because the gas level decreases gradually as the car is driven. However, for the number of students enrolled in a class during a semester, this is a discontinuous function, because the enrollment can only change through discrete additions or subtractions when students enroll or drop out of the class.

To feed 100 guests with boneless chicken, divide the number of guests by 3.5 to get 28.57 pounds, and round up to the closest whole number or choose the closest option given. Therefore, you would need 30 pounds of chicken.

The question involves a calculation related to catering and food preparation. To find out how many pounds of boneless chicken are needed to serve 100 guests, use the provided guideline: 'for meat with little or no bone, divide the number to be served by 3.5.' Therefore, we perform the calculation:

Number of guests ÷ Serving ratio = Required meat in pounds

100 ÷ 3.5 = 28.57 pounds

Since you cannot have a fraction of a pound of chicken when buying, you would need to round up to the closest whole number. Therefore, you would need 29 pounds of boneless chicken to serve 100 guests. However, to answer the multiple choice question provided, the closest option given is 30 pounds, which should be sufficient to feed 100 guests with slight leftovers.

To compute for the total number of students in the class, you have to divide the fraction of the students who said they like word problems with the number of students who said they like word problems.

30 students / ¾ of the students said they like word problems = 40 students are there in the class

Answer:

1)

A single page of a Web site that consists of an HTML document.

2)

The entry page of the Web site.

3)

The object of storyboarding is to help you visualize your Web site before writing any pages in HTML.

Step-by-step explanation:

Web page:

A web page or webpage is a document commonly written in HTML (Hypertext Markup Language) that is accessible through the Internet or other networks using an Internet browser.

Hence, option: A is true.

Home page:

A home page also refers to the first page that appears upon opening a web browser, sometimes called the start page.

Hence, option: B is correct.

( The entry page of the Web site )

object of storyboarding:

The object of storyboarding is to help you visualize your Web site before writing any pages in HTML

Answer:

The determinant of matrix is -203            

Step-by-step explanation:

Given the matrix of order 3 i.e

[tex]A=\begin{bmatrix}-4&-4&-3\\ 3&3&-5\\ -5&2&-5 \end{bmatrix}[/tex]

we have to find the determinant of matrix A

[tex]|A|=-4(-5(3)-(-5)(2))-3((-4)(-5)-(-3)(2))+(-5)((-5)(-4)-(-3)(3))\\\\|A|=-4(-15+10)-3(20+6)-5(20+9)\\\\|A|=-4(-5)-3(26)-5(29)\\\\|A|=20-78-145\\\\|A|=-203[/tex]

Hence, the determinant of matrix is -203

Option A is correct.