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
Bas_tet [7]
3 years ago
7

the sum of 2 consecutive integers is at most the difference between nine times the smaller and 5 times the larger

Mathematics
1 answer:
Reil [10]3 years ago
6 0
<h2>Answer:</h2>

x\geq 3 \ and \ x+1 \geq 4

<h2>Step-by-step explanation:</h2>

The question in this problem is:

<em>The sum of 2 consecutive integers is at most the difference between nine times the smaller and 5 times the larger. What are the numbers?</em>

<em />

First of all, let's name the first variable x which is the smaller number. Accordingly, the lager number will be x+1 given that those numbers are consecutive. On the other hand<em> at most </em>conveys the idea of an inequality, which is:

\leq \\ which \ means \ less \ than

So:

1. The sum of 2 consecutive integers can be written as:

v+(v+1)

2. Nine times the smaller and 5 times the larger can be written as:

9v-5(v+1)

Finally, the whole statement:

The sum of 2 consecutive integers is at most the difference between nine times the smaller and 5 times the larger:

x+(x+1) \leq 9x-5(x+1) \\ \\ x+x+1\leq 9x-5x-5 \\ \\ 2x+1 \leq 4x-5 \\ \\ 6 \leq 2x \\ \\

x+(x+1) \leq 9x-5(x+1) \\ \\ x+x+1\leq 9x-5x-5 \\ \\ 2x+1 \leq 4x-5 \\ \\ 6 \leq 2x \\ \\ \frac{6}{2} \leq \frac{2x}{2} \\ \\ 3 \leq x \\ \\ x\geq 3 \\ \\ and \\ \\ x+1 \geq 4

The two numbers are:

x\geq 3 \ and \ x+1 \geq 4

You might be interested in
What is the solution to the following equation?
lions [1.4K]

Answer:

D. x = 7

Step-by-step explanation:

NOTE : <u><em>there should be an equal sign somewhere in the given expression.</em></u>

suppose the equation is the following:

3(x-4)-5 = x-3

………………………………………………………

3(x - 4) - 5 = x - 3

⇔ 3x - 12 - 5 = x - 3

⇔ 3x - 17 = x - 3

⇔ 3x - 17 + 17= x - 3 + 17

⇔ 3x = x + 14

⇔ 2x = 14

⇔ x = 14/2

⇔ x = 7

8 0
2 years ago
Julio bought a total of 20 medium and large pumpkins. If he spent $53 and bought 6 more large pumpkins as medium pumpkins, how m
Tatiana [17]
20 medium and large pumpkins

m ... number of medium pumpkins
l ... number of large pumpkins

20 = m + l
20 = m + (m + 6)
20 = 2 * m + 6
2 * m = 20 - 6
2 * m = 14
m = 7 medium pumpkins

l = 20 - 7 = 13 large pumpkins

Result: Julio bought 13 large pumpkins.
5 0
3 years ago
Use pascal's triangle to expand the binomial (x+3)^4
ratelena [41]

Answer: the answer is in the photo pls check this out and hope this helps can u give me brainliest

Step-by-step explanation:

6 0
3 years ago
What is the product of the following equation??
Whitepunk [10]

Answer:

B

Step-by-step explanation:

1.(5x^3)(xy^4 -2x^3y)

2.5x^4y^4 -10x^6y

7 0
2 years ago
Justine has 4 1/2 pounds of red apples, 3 1/4 pounds of green apples, and 2 1/4 pounds of yellow apples. How many kilograms of a
Darina [25.2K]
4 1/2 + 3 1/4 + 2 1/4 = 10 pounds of apples.

10 pounds is approximately 4.5 kilograms.
7 0
2 years ago
Other questions:
  • Help me with the question in the picture?
    13·1 answer
  • A farmer has an orchard that covers an area of 40 acres. He grows apples on 25 acres, peaches on 7 acres
    11·1 answer
  • What is the value of Tan θ?
    10·1 answer
  • An Aluminum bar is 2 m long at a temperature of 20 degrees Celsius. What will it be at 100 degrees Celsius?
    8·2 answers
  • Use the distance formula to find the distance to the nearest 10th from R(7,-2) to w(-2,3).
    9·1 answer
  • In Texas, 30% of parolees from prison return to prison within 3 years. Suppose 15 prisoners are released from a Texas prison on
    10·1 answer
  • At 11:00 AM a bus left San Jose travelling to Los Angeles at 48 mph. Four hours later a motorcyclist started moving in the same
    15·1 answer
  • Can you please help me please with my work
    15·1 answer
  • Mr. Ealy works at a shoe store. Mr. Ealy's hourly pay is $14, and he also gets 8% commission on sales. He worked 80 hours over t
    7·1 answer
  • The following graph shows a proportional relationship.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!