1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Lina20 [59]
2 years ago
14

Find the prime factorization of 420​

Mathematics
2 answers:
nexus9112 [7]2 years ago
7 0

Answer:

420 = 2² × 3 × 5 × 7

Step-by-step explanation:

The first few prime numbers are:  2, 3, 5, 7, 11, 13, 17, ...

To find which prime numbers multiply together to make 420, start by dividing 420 by the first prime number, 2:

⇒ 420 ÷ 2 = 210

As 210 is not a prime number, we need to divide again.  Let's try dividing by 2 again:

⇒ 210 ÷ 2 = 105

As 105 is not a prime number, we need to divide again.  105 is not divisible by 2, so let's try dividing it by the next prime number, 3:

⇒ 105 ÷ 3 = 35

As 35 is not a prime number, we need to divide again.  35 is not divisible by 2 or 3, so let's try dividing it by the next prime number, 5:

⇒ 35 ÷ 5 = 7

As 7 is a prime number, we can stop.

Therefore, 420 is the product of all the prime numbers we found together with the final one:

⇒ 420 = 2 × 2 × 3 × 5 × 7

As 2 appears twice, we can write this using exponents:

⇒ 420 = 2² × 3 × 5 × 7

sineoko [7]2 years ago
5 0

Answer:

2,3,7,2,5

Step-by-step explanation:

When you factorize a number you divide them until the outcome numbers are prime. 420 is equal to 42 and 10.

42 is equal to 6 and 7 and 6 is 2 times 3

2,3,7 is prime

10 is 2 times 5

2 and 5 is prime

You might be interested in
If 4 video games costs $125, how much does 1 video game cost?
scoray [572]

Answer:

$31.25

Step-by-step explanation:

divide 125 by 4

hope this helps you!!! also good luck!!!!

8 0
3 years ago
Read 2 more answers
Michael has a substantial student debt, but he recently got a new job, which came with a signing bonus. He calculates that with
kykrilka [37]

Answer:

5000

Step-by-step explanation:

Given the question :

The size of debt after m months is respresented by the expression :

36,700 - (5000 + 500m)

Since Michael has decided to dedicate the entirety of his signing bonus towards paying his debt, then that is a constant and one-off payment.

Also, a fixed portion of his salary each month has also been assigned towards paying off his debt,

Then the amount paid from his salary after a certain number of months will be:

Fixed amount × number of months = 500 × m

Amount paid using signing bonus will be a constant = 5000

Total debt amount = 36,700

Size of debt left after m months :

Total debt - ( signing bonus - fixed amount × m)

Hence signing bonus = 5000

7 0
3 years ago
Which graph represents exponential decay?
faust18 [17]

Answer:

d

Step-by-step explanation:

6 0
2 years ago
A vendor sells hot dogs, bags of potato chips, and soft drinks. A customer buys 4 hot dogs, 3 bags of potato chips, and 4 soft d
GuDViN [60]

The price of chips is $ 0.75, the price of a hot dog is $ 2 and the price of a soft drink is $ 1.25.

Step-by-step explanation:

Given,

A customer buys 4 hot dogs, 3 bags of potato chips, and 4 soft drinks for $15.25.

The price of a hot dog is $1.25 more than the price of a bag of potato chips.

The cost of a soft drink is $2.75 less than the price of two hot dogs.

To find the cost of each item.

Let,

The price of chips = x

The price of a hot dog = x+1.25

Price of two hot dog = 2(x+1.25) = 2x+2.5

The price of a soft drink = 2x+2.5-2.75 = 2x-0.25

Now,

According to the problem,

4(x+1.25)+3x+4(2x-0.25) = 15.25

or, 15x+5-1 = 15.25

or, 15x = 11.25

or, x = 0.75

Hence,

The price of chips = $ 0.75

The price of a hot dog = $ 0.75+1.25 = $ 2

The price of a soft drink = $ 2×0.75-0.25 = $ 1.25

5 0
3 years ago
1) A cyclist travels a distance of 90 miles in 5 hours. What
Nostrana [21]

Answer:

Step-by-step explanation: <u>Speed</u> is distance an object travelled per unit time.

It is represented by letter v and can assume various units.

1) v=\frac{distance}{time}=\frac{d}{t}

v=\frac{90}{5}

v = 18 miles per hour

Her average speed is 18 mph.

2) Rearraging formula for distance:

d = v.t

d = 70 * 4

d = 280 miles

You would travel 280 miles.

3)  v=\frac{d}{t}

v=\frac{315}{6}

v = 52.5 mph

My average speed is 52.5 mph.

4) Rearranging formula to determine time:

t=\frac{d}{v}

t=\frac{210}{90}

t = 2.34 hours

It will take 2 hours and half to arrive in Leeds. So, we will be expected to arrive at 12:04.

5) The unit change but the way of calculating time is the same.

t=\frac{2000}{4}

t = 500 s

or t = 8.34 minutes

It will take, for an athlete to run 2000m, 8.34 minutes.

6) a) All units must match, so for a speed in mph:

45 minutes is 0.75 hours. Total time is 8.75 hours.

v=\frac{420}{8.75}

v = 560 mph

The average speed is 560 mph.

b) t=\frac{d}{v}

t=\frac{420}{63}

t = 6.67 hours

Sam will take 6.67 hours to covered the distance.

4 0
2 years ago
Other questions:
  • Which of the following is NOT a true statement?
    7·1 answer
  • Use the rules of multiplication by powers of 10 to calculate 20 times 100.
    11·2 answers
  • Century is to decade as dollar is to penny,nickel,dime,quarter
    11·1 answer
  • The chart shows how many people have signed up to go on a field trip each day. 62 students are allowed to go on the field trip.
    8·2 answers
  • On average, Johanna drinks 2/3 of a 12 ounce can of soda in one hour.
    9·1 answer
  • A 12 ft ladder leaning againist a house make a 64 degree angle with the ground will the ladder reach a window till that is 10.5
    15·1 answer
  • Find the sum of 4x^2<br> -4x + 10 and 2x^2+ 5x – 8.
    8·1 answer
  • Please help me with this problem, 35 points!
    15·2 answers
  • !pls help!<br> Use a net to find the surface area
    5·1 answer
  • a phone signals from a transmitter that is 19km west and 36km south of it. what is the bearing from the phone to the transmitter
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!