Rathan thinks all factors of even numbers are even. Which explains whether Rathan is correct?

2 answers:

7 0

In order to prove Rathan wrong, we only need one counterexample. Take the number 6. 6 is even, but it has the odd number 3 as a factor, so clearly, not all factors of even numbers are even.

Dominik [7]3 years ago

3 0

Answer: Rathan is incorrect.

Step-by-step explanation:

For a number X, the factors of the numer are other numbers that we multiplicate togheter to get the number X.

for example if X = 16, the factors of 16 can be:

2*8 = 16

4*4 = 16

etc.

Now, let's take some even numbers like 6 and 24.

Now, those two numbers have a factor in common.

3*2 = 6

3*8 = 24

both numbers have the same factor, 3, wich is an odd number. So we have found an example that says that Rathan is incorrect.

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David charges $4 to wash all the windows of a car, inside and out. The amount of money he earns washing the windows must end in

nordsb [41]

Answer:

The possible digits are : 0, 2, 6, 4, 8

Step-by-step explanation:

Money charged by David to wash the windows of a car = $4

Let total number of cars he washed be x

Now, Total money earned by washing windows of a car = Money charged for washing all windows of one car × Total number of cars washed

⇒ Total money earned = 4 × x

So, the amount will always end in the digits which comes at the end of multiples of 4 because the amount will be always in the multiples of 4

⇒ 4 × 1 = 4 , 4 × 2 = 8 , 4 × 3 = 12 , 4 × 4 = 16 , 4 × 5 = 20 ......

So, the possible digits are : 0, 2, 6, 4, 8

4 0

4 years ago

GOF

Daniel [21]

Answer:

(x-10)(x+10)

Step-by-step explanation:

x^2 – 100

This is the difference of squares

x^2 - 10^2

We know that (a^2 - b^2) = (a-b) (a+b)

(x-10)(x+10)

3 0

3 years ago

Khianna is trying to help her neighbor Mrs. Johnson design and estimate the cost of a new square patio to be made from 16 inch s

Gnoma [55]

Part I: Scale Drawing

Decide on a scale factor to represent the distance covered by the patio. Then, use the space below to design Mrs. Johnson’s patio to be a square that is at least 8 feet on each side.

a) Scale Factor: 1 in/ 2 ft

Use a straightedge and a ruler to draw to scale a design for Mrs. Johnson’s patio

b) see the picture attached

Mrs. Johnson’s patio to be a square that is 10 ft x 10 ft

c) What are the dimensions of Mrs. Johnson’s patio? 
the dimensions of Mrs. Johnson’s patio are 10 ft x 10 ft

d) Calculate the area of Mrs. Johnson’s patio. Show all work.
 
area of the square=b²
where b is the length side of the square
b=10 ft
so
Area=10²-----> area =100 ft²

e) How many pavers will be needed? Show all work. 

we know that
1 paver is 16 in x 16 in dimensions
convert to ft
1 ft----------->12 in
x ft-----------> 16 in
x=16/12-----> x=4/3 ft
so
1 paver is (4/3) ft x (4/3) ft dimensions

area of one paver=(4/3)²----> 16/9 ft²

if one paver has an area of----------------> 16/9 ft²
x pavers-----------------------> 100 ft²
x=100/(16/9)------> x=100*9/16-----> x=56.25 pavers

if one box --------------> 12 pavers
x box---------> 56.25 pavers
x=56.25/12-----> x=4.68 box-------> x=5 boxes
5 boxes of pavers will be needed

f) What will it cost to build the patio? Show all work.
 
the cost of one box is--------> $99.99
5 boxes-----------> x
x=5*$99.99------>x=$499.95

the cost to build the patio is $499.95

Part II: Bigger Design

There is a saying that bigger is better, so why not double the dimensions of Mrs. Johnson’s patio to make the side measurement twice as big? Mrs. Johnson and I think that it would better meet her needs. After seeing the original estimation, she thinks that she could afford to double the size. I explained that making the patio twice as big would mean twice the cost. Mrs. Johnson says, “Let’s do it!”

a) What would be the new dimensions of Mrs. Johnson’s patio?
the new dimensions of Mrs. Johnson’s patio are 20 ft x 20 ft

b) Calculate the new area of Mrs. Johnson’s patio. Show all work.
area of the square=b²
where b is the length side of the square
b=20 ft
so
Area=20²-----> area =400 ft²

c) How many pavers will be needed for the new design? Show all work.
 
1 paver is (4/3) ft x (4/3) ft dimensions

area of one paver=(4/3)²----> 16/9 ft²

if one paver has an area of----------------> 16/9 ft²
x pavers-----------------------> 400 ft²
x=400/(16/9)------> x=400*9/16-----> x=225 pavers

if one box --------------> 12 pavers
x box---------> 225 pavers
x=225/12-----> x=18.75 box-------> x=19 boxes
19 boxes of pavers will be needed

d) What will it cost to build the bigger patio? Show all work.
the cost of one box is--------> $99.99
19 boxes-----------> x
x=19*$99.99------>x=$1899.81
the cost to build the bigger patio is $1899.81

e) Is Khianna right? Will doubling the size of the patio, double the cost?

Khianna is wrong to double the dimensions the cost quadruples