Prove that the difference of the squares of 2 consecutive numbers is always the sum of the 2 numbers

Answers

Answer 1

Answer:

see explanation

Step-by-step explanation:

let the 2 consecutive numbers be n and n + 1

sum = n + n + 1 = 2n + 1

and

(n + 1)² - n² ← difference of the squares

= n² + 2n + 1 - n²

= 2n + 1 = sum of 2 numbers


Related Questions

Find the circumference of the circle below. (Use 3.14 for Pi)

A. 78.5 cm
B. 15.7 cm
C. 31.4 cm
D. 314 cm

Answers

so the right answer is 31.4 cm(option C)

please see the attached picture for full solution

Hope it helps

Good luck on your website

Answer:

C. 31.4 cm

Step-by-step explanation:

→The formula for finding the circumference of a circle is:

C = 2πr

→However, it states that we use 3.14 for π:

C = 2(3.14)r

→The "r," is the radius, which is a straight line from the perimeter to the center. In this case, it is already given to us as 5 cm.

C = 2(3.14)(5)

C = 31.4

Solve for y.

–0.8y + 5.49 = –19.86 − 2.3y

y =

Answers

Answer:

y = -16.9

Step-by-step explanation:

→Add 0.8y to both sides:

-0.8y + 5.49 = -19.86 - 2.3y

5.49 = -19.86 - 1.5y

→Add 19.86 to both sides:

25.35 = -1.5y

→Divide both sides by -1.5:

-16.9 = y

Answer:

[tex] \boxed{y = - 16.9} [/tex]

Step-by-step explanation:

[tex] = > - 0.8y + 5.49 = - 19.86 - 2.3y \\ \\ = > - 0.8y + 2.3y + 5.49 = - 19.86 \\ \\ = > 1.5y + 5.49 = - 19.86 \\ \\ = > 1.5y = - 19.86 - 5.49 \\ \\ = > 1.5y = - 25.35 \\ \\ = > y = - \frac{25.35}{1.5} \\ \\ = > y = - 16.9[/tex]

f(x)
- 4x² + 4x-4
Find f(3)

Answers

F(3)=-4(3)^2+4(3)-4
= -4(9)+12-4
= -36+12-4
F(3)= -28

Scores of an IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 20. Use the empirical rule to determine the followinWhat percentage of people has an IQ score greater than 120?

Answers

Answer:

Percentage of people with IQ greater than 120 is 84.134%

Step-by-step explanation:

First thing we do here is to calculate the

z-score

Mathematically;

z-score = (x-mean)/SD

here, x = 120, mean = 100 while SD = standard deviation = 20

z-score = (120-100)/20 = 20/20 = 1

The probability we want to calculate is;

P(x > 120) or P(z >1)

we proceed to use the standard score table to get this;

From the standard score table ;

P(z >1) = 0.84134

which is in percentage = 84.134%

The dual bar chart shows the hair colour of boys and girls in a year group. What fraction of the red haired students are boys? Give your answer in its simplest form

Answers

Answer:

[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Total red haired students = 15+5 = 20

Boys = 15

Fraction:

=> [tex]\frac{15}{20}[/tex]

In simplest form:

=> [tex]\frac{3}{4}[/tex]

what is = to 95
if u do iwill give u brainliest

Answers

Answer:

19 x 5

Step-by-step explanation:

[tex]19 \times 5 = 95[/tex]

19 X 5 that’s is it

Which situation involves a change modeled by a positive number but an end result modeled by a negative number? A.Leo enters an elevator on the second floor and goes down four floors. B. A plane, flying at an altitude of 300 feet, descends 50 feet. C. Irene is scuba diving at –30 feet. She swims 10 feet toward the surface to watch a school of fish. D. April owes her brother $5. On Friday, she gets $10 for her allowance.

Answers

The positive number but a negative result would be :

C. Irene is scuba diving at –30 feet. She swims 10 feet toward the surface to watch a school of fish.

The positive value is she swam 10 feet up to the surface, but she is still below the surface, which would be a negative result.

The situation that would involve a change that is from a positive number but ended in a negative number is option C.

This option tells us that at the negative number she was 30 feet below the surface of the water, while at positive number she was 10 feet up the water surface.

What is a positive number?

This is a number that is greater than 0.

What is a negative number?

This is a number that is less than 0.

Read more on positive and negative numbers here:

https://brainly.com/question/13831313

Which polynomial is prime? A. x^4 + 3x^2 – x^2 – 3 B. x^4 – 3x^2 – x^2 + 3 C. 3x^2 + x – 6x – 2 D. 3x^2 + x – 6x + 3

Answers

Answer:

A and B

Step-by-step explanation:

A polynomial with integer coefficients that cannot be factored into polynomials of lower degree, also with integer coefficients, is called an irreducible or prime polynomial  

As  per above definition, A and B polynomials have coefficients 1 or 3, so are prime polynomials.

C and D polynomials have coefficient of 6 which can be further factored

A. x^4 + 3x^2 – x^2 – 3

yes

B. x^4 – 3x^2 – x^2 + 3

yes

C. 3x^2 + x – 6x – 2

no

D. 3x^2 + x – 6x + 3

no

True or false? The degree of a binomial is always equal to 2

Answers

Answer:

false

Step-by-step explanation:

the degree is found by looking at the term with the highest exponent of the variable..

Answer:

It's False..........

Complete the statements.
A triangular prism has__bases and___lateral faces
A triangular pyramid has____
bases and___lateral faces

Answers

Answer:

A triangular prism has two bases and three lateral faces.

A triangular pyramid has one  base and three lateral faces.

Step-by-step explanation:

A triangular prism is a solid geometrical shape. The base is triangular in shape. There are two bases that are triangular. Other lateral faces are rectangular in shape. They are three in number.

A triangular pyramid is also a solid geometrical shape. The base is a polygon. The lateral faces are triangular in shape and are three in number. The lateral faces are congruent.

Answer:

So im to lazy to right the answer so just look above me so hows it going?

Step-by-step explanation:

Alex is drawing rectangles with different areas on a centimetre grid he can draw 3 different rectangles with an area of 12cmsquared a) How many different rectangles could alex draw with an area of 11cmsquared? B)Give a reason for ur anwser

Answers

Answer:

Alex can only draw a rectangle with an area of 11 cm²

The reason for the answer is that 11 is a prime number

Step-by-step explanation:

We are told that Alex is drawing rectangles with different areas on a centimeter grid, and he can draw 3 different rectangles with an area of 12 cm²

We have the minimum grid length of centimeters = 1 cm, since we assume that only integers can be used.

That is to say:

12 = 1 x 12

12 = 2 x 6

12 = 3 x 4

These are the 3 different rectangles with an area of 12 cm²

Now we have to find how many rectangles Alex could draw with an area of 11 cm²

11 = 1 x 11

Therefore, only one factorization is possible. Which means that you can only draw a rectangle with an area of 11 cm²

The reason for the answer is that 11 is a prime number, which means only the common factor of 1 and the number itself, that is, 11.

PLEASE HELP ... how many students are in each van? And how many students are in each bus ?

Answers

Answer:

7 students in each van and 52 students in each bus.

Step-by-step explanation:

v = no of students in van, b = no of student in bus

High school A ⇒ 3v + 6b = 333 ---------- Equation (1)

High school B ⇒ 11v + 6b = 389 ------------ Equation (2)

Solve equation (1) & (2) simultaneously :

11v + 6b = 389

3v + 6b = 333

----------------------- MINUS

8v + 0 = 56

v = 56 / 8

v = 7

Put v = 7 into Equation (1) to get b:

3v + 6b = 333

3 (7) + 6b = 333

21 + 6b = 333

6b = 312

b = 312 / 6

b = 52

So there are 7 students in each van and 52 students in each bus.

Evaluate this expression for a = 3 and b = 4.
B
(a + 4)-
3(3 + 2)
+
3 - 2
OA. 6
OB.
9
O C.
11
OD.
8

Answers

Answer:

14

Step-by-step explanation:

a = 3

b = 4

[tex]b(a + 4)-3(3 + 2)+3 - 2\\a = 3,b=4\\4(3+4)-3(5)+3 - 2\\4(7)-15+3 - 2\\28-14\\\\14[/tex]

hey pls answer
WHAT IS THE PRODUCT OF 2 AND 3

i'm having trouble with this, pls help!

Answers

Answer:

6

Step-by-step explanation:

2(3)=6

Answer:6

Step-by-step explanation:

2x3 is 6

100*9-2+12/2=

Just need the answer

Answers

Answer:

904

Step-by-step explanation:

According to PEMDAS, we must multiply 100 and 9 first, which gets us 900. Then divide 12 by 2, which gets us six. 900 - 2 + 6 = 898 + 6 = 904.

Answer:

904

Step-by-step explanation:

100 * 9 = 900 -2 =898 +12/2 →898+6= 904

12/2 = 6

Have a good day and stay safe!

Write an equation of the line passing through the point (5,1) that is perpendicular to the line 5x+3y=15

Answers

Step-by-step explanation:

answer in photos

here m is intercept

Answer:

y  =  3÷5x−2

Step-by-step explanation:

the answer is y  =  3÷5x−2

The number of phone calls received by the complaint department of a
small company over a five day period is as follows:
28, 26, 33, 41,47
Find the mean deviation for this data.​

Answers

Answer:

62.8

Step-by-step explanation:

A bank is offering a simple interest rate of 5% — that is, the bank will pay a fixed 5% of an initial investment as interest each year. By contrast, a stockbroker is offering a 4% interest rate compounded annually: 4% of the total value of the investment at the end of the year. If $1000 is invested in the bank and $1000 is invested with the stockbroker, after 4 years, what will be the total value of the two investments combined? Round to the nearest dollar.

Answers

25 would be the nearest to your question and complete 100 with the 4

Cuanto son 2 mas 2?

Answers

Answer:

4

Step-by-step explanation: 2x2=4

Answer:

4

Step-by-step explanation:

The slope of the line is y-4= 1/2 (x-1)

Answers

Answer:

1/2

Step-by-step explanation:

in point slope form (y-h) = slope(x-k)

The equation in the slope-intercept form will be y = x/2 + 7/2. Then the slope of the equation is 1/2.

What is a linear equation?

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equation is given below.

y - 4 = 1/2 (x - 1)

Convert the equation into a slope-intercept form. Then we have

y - 4 = 1/2 (x - 1)

y - 4 = x/2 - 1/2

y = x/2 - 1/2 + 4

y = x/2 + 7/2

The equation in the slope-intercept form will be y = x/2 + 7/2. Then the slope of the equation is 1/2.

More about the linear equation link is given below.

https://brainly.com/question/11897796

#SPJ2

During the Hari Keusahawanan in a school, 800 booklets of coupons were sold. The price of each booklet of coupons was RM30 and RM50 respectively. The total amount collected was RM30 000. How many booklets of RM30 and RM50 coupons were sold?

(**please use the simultaneous linear equations in two variables to solve this question) ​

Answers

Answer:

hope this is correct

i don't even know what this is literally someone help me (khan)

Answers

Answer:

5√2

Step-by-step explanation:

√50=√25*2=√5^2*2=5√2

Answer:

5[tex]\sqrt{2}[/tex]

Step-by-step explanation:

[tex]\sqrt{50}[/tex] is equal to [tex]\sqrt{25}[/tex] · [tex]\sqrt{2}[/tex]

This can be simplified to 5[tex]\sqrt{2}[/tex]

Which of the following is the equation of a line in slope intercept from a line with the slope of 2/3 and Y intercept at 0,-2

Answers

Answer:

y= 2/3x - 2

Step-by-step explanation:

b is were the line crosses the y intercept so its -2

and the slope is 2/3x

hope this helps:)

How do you complete the square of h(x)= x^2 + 6x + 7

Answers

Answer:

[tex] (x + 3)^{2} - 2[/tex]

Step-by-step explanation:

[tex]h(x)= x^2 + 6x + 7 \\ = x^2 + 2.3.x + {3}^{2} - {3}^{2} + 7 \\ = (x + 3)^{2} - 9 + 7 \\ \purple { \bold{h(x)= (x + 3)^{2} - 2 }}[/tex]

pis possib
How many gallons of a 60% antifreeze solution must be mixed with 100 gallons of 15% antifreeze to get a mixture that is
50% antifreeze? Use the six-step method.
Gallons of
Antifreeze
Strength Gallons of
Solutions
60%
X
15%
100
50%
X + 100

Answers

Answer:

x = 350 gallons (amt of 60% solution that must be added)

Step-by-step explanation:

Amt of 60% solution = x gallons ; Amt of active ingredient = 0.6x gallons

Amt of 15% solution = 100 gallons ; Amt of active ingredient = 15 gallons

Amt of 50% solution = 100+x gallons ; Amt of active = 50 + 0.5x gallons

EQUATION:

Active ingredient: 0.60x + 15 = 50 + 0.50x

0.10x = 35

x = 350 gallons (amt of 60% solution that must be added)

FIND THE VALUE OF X FOR THIS MATH QUESTION

Answers

Answer:

x = 2

Step-by-step explanation:

Since the central angles are congruent, and all radii are congruent, the triangles are congruent. By CPCTC x = 2.

Choose which of these is the net of a cube.

Answers

Answer:

A

Step-by-step explanation:

PLS GIVE BRAINLIEST!

You flip two coins and roll a dice. What is the probability of flipping two tails and rolling an even number?

Answers

1/24 i think, not sure

Determine and prove which lines are parallel.: Need by Tuesday!! Thanks!

Answers

If the gradients are not the same, then there will be a point, which intersects. That contradicts the statement that theclines have no points in common.

Step-by-step explanation:

Parallel lines are lines that have the same gradient.

Because parallel lines have a fixed distance between each other,it means they will never meet, no matter how long they are extended.

Since parallel lines have the same slope by definition, they will never intersect. Parallel lines continue, literally, forever without touching.

Prove:

Suppose that there are two lines, line l and line m, which have no points in common. Both lines are in the same plane.

If the gradients are not exactly the same, then there will be a point, which intersects. That contradicts the first statement (which says l and m have no points in common), therefore the gradients must be the same in order for l and m to have no points in common.

what is the combined lenght of all buttons longer than 1 inch?

Answers

Answer:

2 12 1/2 inches

Step-by-step explanation:

1: 1 1/4 + 1 1/4

2: 1+1 = 2; 1/4 + 1/4 = 2/4

3:  2 2/4

Answer:  2 2/4

Hope this helps.

Answer:

2 12 1/2 inches

Step-by-step explanation:

Hope it helps <3

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