1. Prove that the product of the second and third numbers out of four consecutive whole numbers is two greater than the product of the first and the fourth numbers.


2. Prove that the square of the second number out of three consecutive odd numbers is four greater than the product of the first and third numbers.

Answers

Answer 1

Answer:

1.

(x+1)(x+2)>x(x+3)

x^2+2x+x+2>x^2+3x

x^2+3x+2>x+3x

2>0

2.

(x+2)^2>x(x+4)

x^2+4x+4>x^2+4x

4>0

Step-by-step explanation:

1.

Suppose x is the lowest number in the set of 4 consecutive numbers, then x+1, x+2, and x+3 are then the next numbers in the sequence since they are the next whole numbers.

Then, to follow the conditions of the problem, we make the equation:

(x+1)(x+2)>x(x+3)

Using the formula of (a+b)(c+d)=ac+ad+bc+bd, we can expand both sides of the equation into this:

x^2+2x+x+2>x^2+3x

=x^2+3x+2>x^2+3x

We can then cancel x^2+2x from both sides and we are left with 2>0.

2.

Again, suppose x is the lowest value in the set of consecutive numbers. In this case, odd numbers increase by 2 each time so the series of numbers are:

x, x+2, x+4

Therefore, to follow the conditions of the problem, we make the equation:

(x+2)^2>x(x+4)=

(x+2)(x+2)>x(x+4)

Using the same formula of (a+b)(c+d)=ac+ad+bc+bd, we get:

x^2+4x+4>x^2+4x

Cancel x^2+4x from both sides and we are left with 4>0

Hope this helps!


Related Questions

What is the greatest common factor of the terms of 3y2−21y+36
?

Answers

Answer:3(−4)(−3) This the answr can u solve my question maybe?

Solve equation by using the quadratic formula.
25x^2 + 60x = -36

Answers


...........................

I WILL GIVE OUT BRAINELIST Quadratic functions g(x) and h(x) are graphed on the same coordinate grid. The vertex of the graph of h(x) is 12 units above the vertex of the graph of g(x) .

Which pair of functions could have been used to create the graphs of g(x) and h(x)?

h(x)=(x+12)2 and ​g(x)=x2​

h(x)=x2−12 and g(x)=x2

h(x)=x2+12 and ​g(x)=x2​

h(x)=(x−12)2 and ​g(x)=x2

Answers

Answer:

  h(x)=(x-12)2 and g(x)=2

please help me i really need to do well on this test! show your work :)

Answers

Step-by-step explanation:

a point is 0,-2. if you test all the others the equations are not true, so that's the only one that works and makes both equations true.

please help The perimeter of a rectangular shape electronic keyboard is 14 ft. Its width is 3 ft longer than its depth
!. How wide and deep is the keyboard

2. what is the area of the keyboard

Answers

Answer:

Width = 6ft Area = 54 sq ft

Step-by-step explanation:

First, re-read the problem until you understand it and can put it into your own words.  I re-wrote it like this:  "Find the area of a rectangle by first finding the length (L) and the width (W)."   [note that I added "find L and W," but that is how I'm going to solve the problem;  I could also have said that we will need the formulas, P=2L+2W and A=LW, but you knew that already, right?).

 

Translate the problem:

 "The length of a rectangle is 3 ft longer than its width"      means

         L                             =    3             +         W                 (eq1)

 "the perimeter of the rectangle is 30 ft"     means

            P                                = 30                      (eq2)

 

So, now the math is easy, just find L and W so we can compute the area:

     P = 30 = 2L + 2W                         (eq3; from eq2 and the formula for P)

          30 = 2(3+W)  +  2W              (use eq1 to substitute for L)

          30 = 6 + 2W   + 2W              (distribute)

           30 = 6 + 4W                       (collect terms)

            24 = 4W                        (subtract 6 from both sides)

            6 ft = W                         (divide both sides by 4)

 

Use the easiest equation (either eq1 or else eq3) to find L:

          L = 3 + W        (eq1)

          L = 3 + 6

          L = 9 ft

What is the area (A)?

          A = L*W

          A = (9 ft)*(6 ft)

          A = 54 sq ft

Seven hours were allotted for a trip. If Saul's average speed was 65 miles per hour
how far could he go in the allotted time

Answers

Answer:

455 mph (miles per hour)

Step-by-step explanation:

65 x 7 = 455

Sorry if it is short. I wanna get as much answers before Exam Mode starts.

60 is 150% of what number?

Answers

Answer:

40

Step-by-step explanation:

You write down the %/100 = is/of 1st

So what you want to do is remove the percentage first and the place 150% And then place 60 on the "is" Numerator. And as u can see you do 100 * 60, that'll give you 600 and then the 150% is left alone, so you divide 600 and 150 And the answer is going to be 40

Hope this helps! Mark one of us as brainliest

Answer:

40

Step-by-step explanation:

x = 60 ×  100 /150

x= 40

What multiplies to make 400 and adds to make -40 PLS HELP

Answers

Answer:

-20 and -20

Step-by-step explanation:

Mark brainliest please

HELP WHATS THE SCALE FACTOR FOR THIS

Answers

Answer:1.25

Step-by-step explanation:

Answer:

4:5 (with regards to small:big polygon)

Step-by-step explanation:

12:15 = 4:5

An investment of 4,000 earns 2% interest compounded annually. What will be value of the investment in 7 years

Answers

Start with your exponetial growth formula: y = a(1 + r)^t.

Now, a is going to be your initial amount, r is the rate, and t is the time.

So we have y = $4,000(1 + .02)^7.

Now simplify inside the parenthses first.

So we have y = $4,000(1.02)^7.

Simplifying further gives us y = $4,000(1.14868).

Now use a calculator to get y = $4,594.72

Evan spent $15.89 on 7 pounds of birdseed. how much did the bridseed cost per pound​

Answers

HERE YOU GOOOOOOOOOO

(ख) अर्धव्यास 'a' भएको वृत्तको परिधि निकाल्ने सूत्र लेख । Write
down the formula for finding the circumference of a
circle with radius 'a'.
( (Ans: 2tta)
ATT
10pmलालाटा
AT​

Answers

Answer:

i cant undersand!

Step-by-step explanation:

The radius of a circle is 5 cm. Find its circumference in terms of \piπ.

Answers

The formula is C=2(3.14)r

So we plug in the radius and multiply.

C=2(3.14)(5)

C=6.28x5

C=31.4

---

hope it helps

im supposed to solve this, but im first supposed to convert the bases to be the same and thats what im struggling with​

Answers

9514 1404 393

Answer:

  1

Step-by-step explanation:

From your knowledge of multiplication tables, you know that ...

  8 = 2×2×2 = 2³

  4 = 2×2 = 2²

so the problem can be rewritten as ...

  [tex]\dfrac{8^4}{4^6}=\dfrac{(2^3)^4}{(2^2)^6}=\dfrac{2^{3\cdot4}}{2^{2\cdot6}}=\dfrac{2^{12}}{2^{12}}=\boxed{1}[/tex]

__

The applicable rule of exponents is ...

  (a^b)^c = a^(bc)

______

Alternate solution

You could use 8^2 = 64 and 4^3 = 64. Then this is (8^2)^2/(4^3)^2 = 64^2/64^2, where the common base is 64, not 2.

PLEASE HELP ASAP!!! 15 POINTS.

Answers

Answer:

option 4

Step-by-step explanation:

Hey There!

A line that has a negative slope will be going from left to right downwards if that makes sense

Thus meaning that option 4 has a negative slope

Shop Rite ordered 336 cases of Oreos with 42 packages in each case. What is the total number of Oreo packages that Shop Rite ordered?

Answers

Answer:

14112

Step-by-step explanation:

USE A CALCULATOR

Answer: 14112

Step-by-step explanation:

42 x 336 = 14112

Help me with this question ​

Answers

try the app photomath
0.0625 ________________

Work out the percentage change when a price of £50 is increased to £80.

Answers

Answer:

50 to 80 = 60%

Step-by-step explanation:

(80 -50) / 50 x 100 = 60%

3.
Find the rate of change for the situation. A chef cooks 9 lbs of chicken for 36 people and 17 lbs of chicken for 68 people.


A. 4 lb per person

B. [tex]\frac{1}{4}[/tex] lb per person

C. [tex]\frac{9}{17}[/tex] lb per person

D. 36 people

Answers

Answer:    1/4

Answer:

Step-by-step explanation:

Here is the complete question: Find the rate of change for the situation:

A chef cooks 9 lbs of chicken for 36 people and 17 lbs of chicken for 68 people.

Given: 1st situation, A chef cook 9 lbs chicken for 36 people.

          2nd situation, chef cook 17 lbs chicken for 68 people.

∴ 1st situation, weight of chicken per person=  

 Weight of chicken per person=  

2nd situation, weight of chicken per person=  

Weight of chicken per person=  

In both the situation chef cook same amount of chicken per person, which is  

∴ Rate of change is

Step-by-step explanation:

There are several important information's already given in the question. Based on those information's the answer can be easily deduced.

In the first case,

The amount of chicken the chef cooks for 36 people = 9 pounds

Then

The amount of chicken the chef cooks for 1 person = 9/36

                                                                                 = 1/4 pounds

Now let us take the second case

The amount of chicken the chef cooks for 68 people = 17 pounds

Then

The amount of chicken the chef cooks for 1 person = 17/68

                                                                                 = 1/4 pounds

From the above deductions, it can be concluded that the correct option among all the options given in the question is the third option or option "B".

The tires on a mining truck are 14 ft tall is it a circumference,radius,diameter

Answers

Answer:nooooo

Step-by-step explanation:

fsdf

what is the explicit formula

Answers

Answer:

a(n) = 13 - 2n

Step-by-step explanation:

The explicit formula variables are a(n) = a(1) + d (n - 1). The a(1) is your number you started out with, and the d is the common difference. From the recursive formula example, you see that your first number is 11 and your difference is -2.

1. Plug the numbers into the equation : a(n) = 11 - 2 (n - 1)

2. Distribute: a(n) = 11 - 2n + 2

3. Add like terms: a(n) = 13 - 2n

If you want to double check, you can plug 1 into n and see if you get 11. I did this, and I did so it should be correct. Hope this made sense! Have a great day :)

Please help as soon as possible

Answers

Answer:

The answer is 17.5

Hope this helps

I’m pretty sure the answer is 17.5

(Hope this helps!!!)

Can I pls have a brainliest?

write the coordinates of a point whose Abcissa is -7 and ordinate is -2​

Answers

Answer:

Abcissa = X, and Ordinate = Y

(-7,-2)

Is the answer

The length of a rectangle is 5 inches less than twice its width. The perimeter of the rectangle is 60 inches. Which system of equations can
be used to determine the length, L, and the width, W, of the rectangle?

Answers

Answer:

Step-by-step explanation:

L=2W-5 and P=2(L+W) is the system

Substituting L=2W-5 into P=2(L+W) gives you

2(2W-5+W)=P=60

2(3W-5)=60

3W-5=30

3W=35

W=35/3, L=2W-5

L=55/3

Help me with this pls

Answers

Answer:

C

Step-by-step explanation:

Please answer this math problem soon! No need for an explanation

Answers

Answer:

32

Step-by-step explanation:

Did this before I got 32 and it was correct

the diagram shows triangle ABC

work out the sizes of angles x,y and z

Answers

Answer:

Step-by-step explanation:

x= 180-110(angles on a straight line)

x= 70

y=x=70 (alternate angles)

z= 110(alternate angles)

hey guys its my bday and i don't have time to do work rn but I need the answer for this. I will give brainly away

Answers

SAS, SSS, SSA all prove the congruency of the two triangles.

1- Jordana borrowed $72 from her sister. She paid her
sister back $72. How much does Jordana owe her
sister now?
A. $0
B. $36
C. $72
D. -$72

Answers

Answer:

it is - 72 are 0

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

jordan took 72 dollars and gave 72 dollars back

so -72+72=0

HEEELP MEEEE FIND THE CIRCUMFERENCE

Answers

Answer: 56.52

Step-by-step explanation:

Other Questions
There is sales of 40% off of the original price. If a mobile phone has a sale price of $180, what was the original price? Choose the correct answer.A) $200B) $280C) $300D) 320$ Help, please help!!!!!!!!!!!!!!!!! Open the Screenshot to see the problem a disgruntled customer will tell how many people Please help ASAP!! Im stuck!!Which statement is true based on the formula?6CO2 + 6H2O > C6H12O6+ 6O21. The mass of carbon dioxide plus water is equal to the mass of sugar plus oxygen 2. The mass of carbon dioxide plus water is less than the mass of sugar plus oxygen3. The mass of carbon dioxide plus water is greater than the mass of sugar plus oxygen Which of the following would be the most logical first step to solving thisquadratic equation?x2 - 4x + 16 = 2 What are humans and where do they live? Due today please help how much force is needed to accelerate a 66kg skier at 2m/second FIFTY POINTS IF YOU CAN HELP ME!!!!You have been looking for a part-time job and it looks like you have found a good fit. You researched the listings on a job board, emailed your rsum to the companys HR department, and got a phone call back. They gave you login information for a private system so you could take an online test, and now youve just had an online video interview. Which networking features have you used so far in your job search? Help im confused like alot HELP PLEASE!!Planes that fly at high speeds and low elevations have radar systems that can determine the range of an obstacle and the angle of elevation to the top of the obstacle. The radar of a plane flying at an altitude of 20,000 feet detects a tower that is 25,000 feet away, with an angle of elevation of 1.a. How many feet must the plane rise to pass over the tower?The plane must rise at least _____feet to pass over the tower.Question 2b. Planes cannot come closer than 1000 feet vertically to any object. At what altitude must the plane fly in order to pass over the tower?The plane must fly at an altitude of at least ____ feet to pass over the tower. Barak spent $20 at the mall. This represents 16% of the money he earned working at the pizza parlor last week. How much money did Barak earn at the pizza parlor last week? PLS HELP FAST ILL GIVE BRAINLIESTWhen y=48, x=4.2. If the value of y varies directly with x, what is the value of y when the value of x is 10.6? What determines the role of a municipal government? A. the United States Constitution B. a charter issued by the county C. a charter issued by the state D. a vote from the majority of citizens Notice the differences in the number of amino acids in cytochrome c between each organism and humans. How might these differences explain the relatedness for each organism to humans Read the passage below from The First Men in the Moon.He advanced staring. I dare say I looked a ferocious savage enoughdirty, unkempt, to an indescribable degree; but it did not occur to me at the time. He stopped at a distance of twenty yards. "Hul-lo, my man!" he said doubtfully.What can the reader infer about the strangers reaction to Mr. Bedford?He doesnt like outsiders.He doesnt trust Mr. Bedford.He is excited to help Mr. Bedford.He is curious about space travel. Which two words are the closest synonyms?Aimperialist and ingenuousBexpansion and extortionCpigment and figmentDsynthetic and fabricated I WILL GIVE BRAINLIEST :)The two lines graphed on the coordinate grid each represent an equationWhich ordered pair represents a solution to both equations?(1,5)(-5,1)(5,1)(-1,5) 2. Something an organism does in response to a change in its environment 2 pointo ensure its survival. *Structural adaptationFunctional apadtationBehavioral adaptationMutual adpatation