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
Eddi Din [679]
3 years ago
12

One positive number is 5 less than twice a second number, and their product is 117. Find the two numbers.

Mathematics
1 answer:
FrozenT [24]3 years ago
3 0

x,y - the numbers

one positive number is 5 less than twice a second number

(1)    x - 5 = 2y

their product is 117

(2)    xy = 117

(1)     x - 5 = 2y     <em>add 5 to both sides</em>

x = 2y + 5   <em>substitute it to (2)</em>

(2y + 5)y = 117     <em>use distributive property</em>

(2y)(y) + (5)(y) = 117

2y² + 5y = 117      <em>subtract 117 from both sides</em>

2y² + 5y - 117 = 0

2y² + 18y - 13y - 117 = 0

2y(y + 9) - 13(y + 9) = 0

(y + 9)(2y - 13) = 0 ↔ y + 9 = 0 ∨ 2y - 13 = 0

y + 9 = 0    <em>subtract 9 from both sides</em>

y = -9

2y - 13 = 0     <em>add 13 to both sides</em>

2y = 13     <em>divide both sides by 2</em>

y = 6.5

<em>substitute the values of y to (1)</em>

x = 2(-9) + 5 = -18 + 5 = -13 < 0

x = 2(6.5) + 5 = 13 + 5 = 18

<h3>Answer: x = 18 and y = 6.5</h3>
You might be interested in
Jack and Diane were saving money to go to a rock n roll concert. They need at least $750 in order to go if you count their gas,
nataly862011 [7]

Answer:

\left\{\begin{array}{l}y\le 4x\\ \\x\ge 10\\ \\50x+25y\ge 750\end{array}\right.

Step-by-step explanation:

Let x represents the number of nights Jack worked and y represents the number of nights Diane worked.

1. The number of nights Diane is scheduled to work is no more than four times the number of nights Jack is scheduled to play. Then

y\le 4x

2. Diane will work at least 10 times before the concert. Then

x\ge 10

3. Jack earns $50 per night that he plays, then he earned $50x in x nights. Diane earns $25 each night she works, then she earns $25y in y nigths. They need at least $750, so

50x+25y\ge 750

4. We get the following set of constraints to model the problem:

\left\{\begin{array}{l}y\le 4x\\ \\x\ge 10\\ \\50x+25y\ge 750\end{array}\right.

4 0
3 years ago
Agri-small business limited expenses on petrol for their fleet is r 4 850.00 at the end of september and they have a balance of
kotykmax [81]

The total income and expenditure of Agri-small business limited in September is R 299596 and expenditure is R 193236.

Given that the expenses on petrol be R4850.00 at the end of September, balance is R 106360.00, usage on income of salaries be 25%, on electricity,rates and taxes be 11%, 42% of the remaining on insurance and investments.

We are required to find the total income and expenditure in September.

Generally the equation for insurance is mathematically given as :

Insurance=42% of the balance

Insurance=0.42*0.64A

Insurance=0.2688A.

Generally the equation for the total after all the other expenditures is mathematically given as:

Total expenditure after all other expenditures=0.64A-0.2688A

Total expenditures after all other expenditures=0.3712A.

Total expenditures after all other expenditures is as 111210 (106360+4850)

Equating both the equation and value:

111210=3712A

A=299596

The total income is 299596.

Therefore the calculation of expense is given as:

Expense=0.25A+0.11A+0.2688A+4850

Expense=0.6288A+4850

=0.6288*299596+4850

=193236

The expense is 193236.

Hence the total income and expenditure in September are "Income is R 299596 and expenditure is R 193236.

Learn more about income at brainly.com/question/25745683

#SPJ4

5 0
2 years ago
Read 2 more answers
What is the answer to [(x²+4x)-2]²
Rudik [331]

Answer:

x^{4} + 8x³ + 12x² - 16x + 4

Step-by-step explanation:

Given

[(x² + 4x) - 2 ]² ← simplify contents of bracket

= (x² + 4x - 2)² = (x² + 4x - 2)(x² + 4x - 2)

Each term in the second factor is multiplied by each term in the first factor, that is

x²(x² + 4x - 2) + 4x(x² + 4x - 2) - 2(x² + 4x - 2) ← distribute parenthesis

= x^{4} + 4x³ - 2x² + 4x³ + 16x² - 8x - 2x² - 8x + 4 ← collect like terms

= x^{4} + 8x³ + 12x² - 16x + 4

6 0
3 years ago
4. You draw a single card from a standard deck of cards. What is the probability
zhenek [66]

OHHHHHHH..........OK

3 0
3 years ago
Heron's Formula:
zlopas [31]

Answer:

√s(s-a) (s-b) (s-c)

Step-by-step explanation:

123456

herons formula

6 0
2 years ago
Other questions:
  • Consider a picnic. If you want to buy enough hot dogs and buns without having any left over, you need to balance the number of p
    12·1 answer
  • Write two fractions that are equivalent to each fraction.
    8·1 answer
  • If an animal is a giraffe, then it has four legs. Counterexample
    12·1 answer
  • 8x + 4y= 12 <br> 2x+ y= 3
    11·1 answer
  • Compute the standard error for sample proportions from a population with proportion p= 0.55 for sample sizes of n=30, n=100 and
    10·1 answer
  • Diesel Inc. is making frames for a new product being launched at the end of the year. To keep the weight down, the area of the f
    10·1 answer
  • PLEASE HELP:(
    12·1 answer
  • Alex has one whole orange and one-fourth of a second orange. Write a mixed number that represents the amount of oranges he has
    9·1 answer
  • -3x+2y=11<br> 3x-4y=-19
    15·1 answer
  • What is the quotient of (x3 + 3x2 + 5x + 3) ÷ (x + 1)?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!