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
algol13
2 years ago
15

The square of the sum of two consecutive positive even integers is greater than the sum of their squares by 48. Find the two int

egers.​
Mathematics
1 answer:
koban [17]2 years ago
3 0

Answer:

  • 4 and 6 or -6 and -4

Step-by-step explanation:

Let the numbers are 2x and 2x + 2.

<u>We have:</u>

  • (2x + 2x + 2)² = (2x)² + (2x + 2)² + 48
  • 4(2x + 1)² = 4x² + 4(x + 1)² + 48
  • (2x + 1)² = x² + (x + 1)² + 12
  • 4x² + 4x + 1 = x² + x² + 2x + 1 + 12
  • 2x² + 2x - 12 = 0
  • x² + x - 6 = 0
  • (x - 2)(x + 3) = 0
  • x = 2, x = -3

<u>The numbers are:</u>

  • 4 and 6 or - 6 and - 4

You might be interested in
Which of the following is the graph of (x + 1)2 + (y − 6)2 = 36?
Brrunno [24]

Answer:

Step-by-step explanation:

Slope:  

− 1

y-intercept:  

23

5 0
2 years ago
Read 2 more answers
The length of a rectangle is four times the width minus three. If the perimeter of the rectangle is 64 meters, what is the lengt
Nastasia [14]

Answer:

L = 25 m

Step-by-step explanation:

L = 4W - 3

perimeter = 2(L + W)

64 = 2(4W - 3 + W)

divide both sides by 2:

32 = 5W - 3

add 3 to each side:

5W = 35

divide both sides by 5:

W =7

L = 4(7) - 3 = 25

6 0
2 years ago
What is the perimeter of a polygon with verticals at (-1, 3) , (-1, 6) , (2, 10) , (5, 6) , and (5, 3)
Marat540 [252]

Answer:

22 units

Step-by-step explanation:

The perimeter of a polygon is said to be the sum of the length of it's sides.

From the question, we have 5 vertices. This means the polygon is a pentagon. It's given vertices are

A = (−1, 3)

B = (−1, 6) ​

C = (2, 10)

D = (5, 6) ​​

E = (5, 3) ​

To find the distance between two points, we use the formula

d = √[(y2 - y1)² + (x2 - x1)²]

Between A and B, we have

d(ab) = √[(6 - 3)² + (-1 --1)²]

d(ab) = √(3²) + 0

d(ab) = √9 = 3

Between B and C, we have

d(bc) = √[(10 - 6)² + (2 --1)²]

d(bc) = √[4² + 3²]

d(bc) = √(16 + 9) = √25 = 5

Between C and D, we have

d(cd) = √[(6 - 10)² + (5 - 2)²]

d(cd) = √[(-4)² + 3²]

d(cd) = √(16 + 9) = √25 = 5

Between D and E, we have

d(de) = √[(3 - 6)² + (5 - 5)²]

d(de) = √(-3)² + 0

d(de) = √9 = 3

Between E and A, we have

d(ea) = √[(3 - 3)² + (5 --1)²]

d(ea) = √[0 + (6)²]

d(ea) = √36 = 6

The perimeter is given as

d(ab) + d(bc) + d(cd) + d(de) + d(ea) =

3 + 5 + 5 + 3 + 6 = 22 units

7 0
2 years ago
A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and tes
DerKrebs [107]

Answer:

a) The probability that this whole shipment will be​ accepted is 30%.

b) Many of the shipments with this rate of defective aspirin tablets will be rejected.

Step-by-step explanation:

We have a shipment of 3000 aspirin tablets, with a 5% rate of defects.

We select a sample of size 48 and test for defectives.

If more than one aspirin is defective, the batch is rejected.

The amount of defective aspirin tablets X can be modeled as a binomial distribution random variable, with p=0.55 and n=48

We have to calculate the probabilities that X is equal or less than 1: P(X≤1).

P(X\leq1)=P(X=0)+P(X=1)\\\\\\P(0)=\binom{48}{0}(0.05)^0(0.95)^{48}=1*1*0.0853=0.0853\\\\\\P(1)=\binom{48}{1}(0.05)^1(0.95)^{47}=48*0.05*0.0897=0.2154\\\\\\P(X\eq1)=0.0853+0.2154=0.3007

8 0
3 years ago
Yao's Asian Market sells dragon fruit for $3 each. The store usually sells 20 dragon fruits a week. Dragon fruit is in season, a
exis [7]
The quantity demanded would increase due to the cheaper price people would want to take advantage and buy it when it was on sale. There is not enough information to determine whether the supply or demand would maintain so D is your answer.

4 0
3 years ago
Other questions:
  • Which of the following is a line perpendicular<br> to y = 3x-7?
    7·1 answer
  • Plot the axis of symmetry and the vertex for this function: h(x) = (x − 5)2 − 7.
    7·1 answer
  • Answer this question please than you now by tody
    7·1 answer
  • In 3434 pound of a spice mix, there is 5656 cup of cinnamon. How much cinnamon does the spice mix contain per pound? 5858 cup ​
    15·1 answer
  • Find the slope between points (4,-5) and (5,-1)
    9·1 answer
  • Help me out please it’s homework
    12·2 answers
  • Divide. Express your answer in simplest form.<br> 8 divided by 2 4/9
    9·2 answers
  • <img src="https://tex.z-dn.net/?f=%5Csf%20Solve%5C%3A%20for%5C%3A%20x%3A-" id="TexFormula1" title="\sf Solve\: for\: x:-" alt="\
    8·2 answers
  • 20men working 8hours a day took 18days to complete a work . How long will 24 men working 5 hours a day take to complete the some
    7·1 answer
  • Plz help!! 30 points!!
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!