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
Troyanec [42]
3 years ago
9

find two positive even consecutive integers such that a square of the smaller integer is 10 more than the larger integer

Mathematics
1 answer:
nalin [4]3 years ago
6 0

Answer:

the two positive consecutive integers are 4 and 6.

Step-by-step explanation:

Let the smaller integer be s; then s^2 = (s + 2) + 10.

Simplifying, s^2 - s - 2 - 10 = 0, or

s^2 - s - 12 = 0.

Solve this by factoring:  (s - 4)(s + 3) = 0.

Then s = 4 and s = -3.

If the first even integer is 4, the next is 6.  We omit s = -3 because it's not even.

The smaller integer is 4.  Does this satisfy the equation s^2 = (s + 2) + 10?

4^2 = (4 + 2) + 10  True or False?

16 = 6 + 10 = 16.

True.

So the two positive consecutive integers are 4 and 6.

You might be interested in
0.7 is 10 times as much as
Neko [114]
0.7 is 10 times as much as 0.70
3 0
3 years ago
URGENT!! HELP! 25 POINTS FOR THESE QUESTIONS!
avanturin [10]

Answer:

The correct options are;

A. 120

B. 34

Step-by-step explanation:

The given parameters are;

Required to find how many of the permutations of 1, 2, 3, 4, 5, 6, have 1, 2, 3 arranged one after the other in the given order

Requirement to arrange 6 digits, 1, 2, 3, 4, 5, 6 in the order such that 1, 2, and 3 always appear in turn, they are as follows

When the first digit is 1, and the 2nd digit is 2 the number of ways of selecting the other  digits is 24

Arrangement,                                              Number of ways

1, 2, 3, 4, 5, 6,                                               24

1, 4, 2,                                                            18

1, 4, 5, 2,                                                        12

1, 4, 5, 6, 2,                                                     6

4, 1, 2,                                                             18

4, 1, 5, 2,                                                         12

4, 1, 5, 6,                                                         6

4, 5, 1, 2,                                                         12

4, 5, 1, 4, 2                                                      6

4, 6, 5,                                                            6

Total = 24 + 18 + 12 + 6 + 18 + 12 + 6 + 12 + 6 + 6 = 120 ways

The correct option is A. 120

2. The dimensions of the original rectangle = L by W

The dimensions of the lager rectangle = 1.5·L by 2·W

1.5·L × 2·W = 30

Given that L > W

∴ L×W = 30/(1.5 × 2) = 30/3 = 10

The possible integers that have a product of 10 are;

1 × 10 and 5 × 2

Therefore, since L > W, The dimensions of the larger rectangle are either 15 by 2 or 7.5 by 4

Which gives the perimeters as 2*(15 + 2) = 34 or 2*(7.5 + 4) = 23

Therefore, the largest possible rectangle is 34

The correct option is B. 34.

7 0
3 years ago
Factor 24a^2-6a-9............
777dan777 [17]
24a ^ 2-6a-9.
 you should do in this case is to see the terms that are repeated in the expression.
 WE have then that the terms are a and the multiples of 3.
 Making a common factor we have:
 24a ^ 2-6a-9.
 3 (8a ^ 2-2a-3).
 3 (a (8a-2) -3)
 Answer:
 The equivalent expression is:3 (a (8a-2) -3)
7 0
3 years ago
Jaxon is deciding between two landscaping companies for his place of business. Company A charges $45 per hour and a $150 equipme
FinnZ [79.3K]

Answer:

A

Step-by-step explanation:

It charges cheapeer

5 0
2 years ago
Amaya is graphing the inequality x greater-than 11 on a number line. Which statements below describe steps she may take to graph
loris [4]

Answer:

Draw open circle AT 11

Shade all numbers to the right of 11

Step-by-step explanation:

Have a great day!

3 0
3 years ago
Read 2 more answers
Other questions:
  • Please do it for me! I need both of this questions ans....
    13·1 answer
  • Find the exact circumference of a circle with the given radius. 3½ cm
    14·2 answers
  • A small engine can do 1000 joules of work in 45 seconds. Calculate its power in watts. Round
    15·1 answer
  • Rewrite the equation by completing the square.<br> x^2 - 4x + 3 = 0
    8·2 answers
  • K is between P and Q. Suppose PQ- 10x - 16, PK - 6x + 8, and KQ-8. What is PQ?
    5·1 answer
  • HELPPP FOR BRIANLEST!!!!
    13·1 answer
  • The mode of the data<br> set is 21. What number<br> is missing?<br> 21, 17, _25, 23, 13
    6·2 answers
  • Which Of The Following is Graphed Below
    7·1 answer
  • While walking between gates at an airport, you notice a child running along a moving walkway. Estimating that the child runs at
    15·1 answer
  • Based on the scatterplot, which equation BEST represents the relationship between velocity and time?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!