Is the discriminant of f positive, zero, or negative?

The sum of the digits of a two-digit number is 12. The number formed by reversing the digits is 54 more than the original number

andreyandreev [35.5K]

Answer:

39

Step-by-step explanation:

let the 2 digit number be ab = 10a + b ( considering place value )

The reversed 2 digit number is ba = 10b + a

The sum of the 2 digit number is

a + b = 12 ( subtract b from both sides )

a = 12 - b → (1)

Expressing as an equation

ba = ab + 54 , that is

10b + a = 10a + b + 54

Substitute a = 12 - b into the equation

10b + 12 - b = 10(12 - b) + b + 54 , simplify both sides

9b + 12 = 120 - 10b + b + 54

9b + 12 = - 9b + 174 ( add 9b to both sides )

18b + 12 = 174 ( subtract 12 from both sides )

18b = 162 ( divide both sides by 18 )

b = 9

Substitute b = 9 into (1)

a = 12 - 9 = 3

Thus

the original 2 digit number = ab = 39

The reversed 2 digit number = ba = 93

which is 54 more than the original number

7 0

3 years ago

Norman makes $15 commission for selling $200 in merchandise. he makes $37.50 commission for selling $500 in merchandise. assumin

vladimir2022 [97]

So he needs to sell $2,000 in merchandise.

<h3>what is the total value of merchandise he needs to sell?</h3>

We can assume that we have a proportional relation:

y = k*x

Where y is the commission and x is what Norman sells, then:

$15 = k*$200

k = $200/$15 = 0.075

$37.50 = k*$500

k = $500/$37.50 = 0.075

Then the relation is:

y = 0.075*x

If he wants a commission of $150, then:

$150 = 0.075*x

$150/0.075 = x = $2,000

So he needs to sell $2,000 in merchandise.

If you want to learn more about proportional relationships:

brainly.com/question/12242745

#SPJ1

3 0

2 years ago

Help me please i’m really confused on it :) thankyou

Nata [24]

A is 6:55

B is 37 Minutes

C is 15:12

Step-by-step explanation:

so basically its just adding minutes to a clock, like if its 1:00 o clock and 40 minutes pass it will be 1:40 or if its 12:00 and 25 minutes pass it will be 12:55. There's 60 minutes in an hour so if the time is, let's say, 12:45 and 30 minutes go by itd be 1:15.

C is a little more tricky but thats just because its military time.:) basically instead of going to 12 am to 1 pm it would go from 12:00 AM to 13:00 PM

5 0

3 years ago

Can someone please help me with numbers 1, a, b, c, 2, a, b, c

algol [13]

Thank you thank you very much

7 0

3 years ago

A bowling leagues mean score is 197 with a standard deviation of 12. The scores are normally distributed. What is the probabilit

Bond [772]

Answer:

0.281 = 28.1% probability a given player averaged less than 190.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

A bowling leagues mean score is 197 with a standard deviation of 12.

This means that $\mu = 197, \sigma = 12$

What is the probability a given player averaged less than 190?

This is the p-value of Z when X = 190.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{190 - 197}{12}$

$Z = -0.58$

$Z = -0.58$ has a p-value of 0.281.

0.281 = 28.1% probability a given player averaged less than 190.

8 0

3 years ago