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3 years ago

What is GCF mean and Lcm ?

Mathematics

2 answers:

stich3 [128]3 years ago

6 0

GCF means greatest common factor and LCM means least common multiple. ;)

AleksAgata [21]3 years ago

3 0

GCF, is the Greatest Common Factor, meanwhile, LCM is Least Common Multiple. GCF is the greatest factor that divides two numbers. LCM is a number that is a multiple of two or more numbers.

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a scarf is originally priced at $30.00. it is then discounted by 25%. several days later, it is discounted 10% off the new price

jeka94

No.
a. take 35% off 30 =19.5
b. first take 25% off 30 = 22.5, then take 10% off 22.5 = 20.25

8 0

3 years ago

Use induction to prove: For every integer n > 1, the number n5 - n is a multiple of 5.

nignag [31]

Answer:

we need to prove : for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

1) check divisibility for n=1, $f(1)=(1)^{5}-1=0$ (divisible)

2) Assume that $f(k)$ is divisible by 5, $f(k)=(k)^{5}-k$

3) Induction,

$f(k+1)=(k+1)^{5}-(k+1)$

$=(k^{5}+5k^{4}+10k^{3}+10k^{2}+5k+1)-k-1$

$=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k$

Now, $f(k+1)-f(k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-(k^{5}-k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-k^{5}+k$

$f(k+1)-f(k)=5k^{4}+10k^{3}+10k^{2}+5k$

Take out the common factor,

$f(k+1)-f(k)=5(k^{4}+2k^{3}+2k^{2}+k)$ (divisible by 5)

add both the sides by f(k)

$f(k+1)=f(k)+5(k^{4}+2k^{3}+2k^{2}+k)$

We have proved that difference between $f(k+1)$ and $f(k)$ is divisible by 5.

so, our assumption in step 2 is correct.

Since $f(k)$ is divisible by 5, then $f(k+1)$ must be divisible by 5 since we are taking the sum of 2 terms that are divisible by 5.

Therefore, for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

3 0

2 years ago

Complete the square to re-write the quadratic function in vertex form: y=x2-x+3

Anna [14]

Answer:

Step-by-step explanation:

hello :

note : the vertex form is :

ax²+bx+c = a(x+(b)/(2a))²- delta/4a² and delta = b²- 4ac

in this exercice you have : a =1 b = -1 and c= 3

continu ..........

5 0

2 years ago

Which expression is equivalent to the number 144?

motikmotik

Answer:

Step-by-step explanation:

4 0

2 years ago

Someone please help me I only have until January 18th to turn this in. Question: Mr Lopez picks up 2 pallets of dog food to deli

miv72 [106K]

Answer:

Mr. Lopez delivers 1.5 tons of dog food to the animal shelter.

Step-by-step explanation:

Mr Lopez picks up 2 pallets of dog food to deliver to the animal shelter. Each pallet contains 40 bags of dog food, and the dog food weighs 37 1/2 pounds pet bag.

The weight of 1 bag of dog food = $37\frac{1}{2}\text{ pounds }$

The weight of 40 bags of dog food = $40 \times 37\frac{1}{2} =1500 \text{ pounds }$

Each pallet weighs = 1500 pounds

2 pallets weighs = 1500×2=3000 pounds.

We know that 2000 pounds = 1 ton

$\frac{3000}{2000} \text{ pounds}=1.5 \text{ tons}$

Hence, Mr. Lopez delivers 1.5 tons of dog food to the animal shelter.

6 0

3 years ago