Prove: The square of the sum of
two consecutive integers is odd.

Prove: The Square Of The Sum Oftwo Consecutive Integers Is Odd.

Answers

Answer 1

[tex](2n+1)^2=4n^2+4n+1[/tex] therefore, the first blank is 1.

[tex]4n^2+4n+1=2(2n^2+2n)+1[/tex] therefore, the two other blanks are both 2.

Answer 2

The number in the proof ''The square of the sum of two consecutive integers is odd'' is 2 and 2.

To prove that, The square of the sum of two consecutive integers is odd.

The expression to prove is,

Let us assume that two consecutive integers are n and (n + 1).

Hence, the expression is written as,

[n + (n + 1)]² = (2n + 1)²

= (2n)² + 2 × 2n × 1 + 1²

= 4n² + 4n + 1

= 2 (2n² + 2n) + 1

= odd

Therefore, the number in the blanks are 2 and 2.

To learn more about the Number system visit:

https://brainly.com/question/17200227

#SPJ4


Related Questions

How to do this question plz answer my question step by step plzz plz plz plz plz ​

Answers

I hope this helps you!

Please answer quickly! A radio telescope has a parabolic surface, as shown below. A parabola opening up with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 1 meter and its width from left to right is 20 meters. If the telescope is 1 m deep and 20 m wide, how far is the focus from the vertex?

Answers

Answer:

Basing on the description, a parabola checking with vertex at origin, the formula with vertex at origin can be used, x^2 = 4py. p is the focus therefore with the dimensions given, we get yourself a 0.25 and this is the distance of the focus to the vertex.

Identify whether each phrase is an expression, equation, or inequality.
Term
Phrase
Expression
3 - 53 =y
Inequality
7-5 <2.9
2 + 0
Equation
24"
t

Answers

Answer:

The identities of the terms are;

3 - 53 = y is an equation

7.5 < 2.9 is an inequality

2 + 0 is an expression

t is a term

24" is a term

Step-by-step explanation:

An equation is an expression with the equal to sign

3 - 53 = y is an equation

An inequality is a mathematical expression that contains an inequality sign

7.5 < 2.9 is an inequality

A term is a sole number or variable or the product of variables and numbers that come before and after mathematical operators such as +, ×, -, or ÷

t and 24" are terms.

Please help!!! ***This is multiple choice!

Answers

Answer:

0.6

Step-by-step explanation:

A probability is the likelihood of an event occurring. A probability function is a function in which at any point, its probability value can be estimated. The integral of the probability function is always ≤ 1

To find the probability that x = 2 or 3, we simply add their respective individual probabilities, therefore:

P(X = 2 or 3) = P(X = 2) + P(X = 3) = P(2) + P(3) = 0.5 + 0.1 = 0.6.

P(X = 2 or 3) = 6

Which expressions are equivalent to 2(4f+2g)2(4f+2g)2, left parenthesis, 4, f, plus, 2, g, right parenthesis ? Choose 3 answers: Choose 3 answers: (Choice A, Checked) A 8f+2g8f+2g8, f, plus, 2, g (Choice B) B 2f(4 + 2g)2f(4+2g)2, f, left parenthesis, 4, plus, 2, g, right parenthesis (Choice C) C 8f+4g8f+4g8, f, plus, 4, g (Choice D, Checked) D 4(2f+g)4(2f+g)4, left parenthesis, 2, f, plus, g, right parenthesis (Choice E) E 4f+4f+4g4f+4f+4g

Answers

Answer:

8f + 4g

Step-by-step explanation:

Given

2(4f + 2g)

Required

Determine the equivalent expression

2(4f + 2g)

Open the bracket

2 * 4f + 2 * 2g

Perform right operations on the above

8f + 4g

The expression cannot be further simplified; Hence the result of  2(4f + 2g) when simplified is 8f + 4g

Answer: 8f + 4g also 4(2f + g) and 4f + 4f+ 4g

Step-by-step explanation:

Help? It hard I try my best on a Separate picese

Answers

Answer: 508.81

============================================

Work Shown:

3 & 1/2 = 3 + 1/2 = 3 + 0.5 = 3.5

3.5% = 3.5/100 = 0.035

r = 0.035 is the decimal form of [tex]3\frac{1}{2}\%[/tex] which is used along with

P = 500 (principal deposit)n = 12 (compounding 12 times a year)t = 0.5 (6 months is half a year)

to get the following

A = P*(1+r/n)^(nt)

A = 500*(1+0.035/12)^(12*0.5)

A = 508.81405074594

A = 508.81

Extra info: Gabe earned A-P = 508.81 - 500 = 8.81 dollars in interest.

Can you help me please.

Answers

Answer:

option 2.

Step-by-step explanation:

You use the y-intercept form: y=mx+b

mx=slope, and b=y-intercept.

Looking at this graph, you can see that the slope is -2/3 (rise over run), and the line is negative, so the slope becomes negative.

So now, we can see the only option having the slop -2/3x is option 2.

-4-(3+6²)÷13-1²•(-12)=

Answers

Answer:

5

Step-by-step explanation:

-4-(3+6²)÷13-1²•(-12)=

PEMDAS

parrenthesis:

-4-81÷13-1² x (-12)

exponent:

-4-81÷12 x (-12)

multiplication:

-4-81÷ (-144)

divison:

- 4 - (- 9)

subtraction (Actaully addition +):

= 5

-(- makes plus so -4 + 9 makes 5

Hope this helps, have a good day!! :)

Please answer the question in the image below ASAP

Answers

Answer:

Option A Center: 2,-3 radius =5

Step-by-step explanation:

[tex](x-h) ^2+(y-k) ^2 =r^2[/tex]

The above equation is the general standard equation for the circle centered at (h,k) with radius r

Given that the equation of the circle is

[tex](x-2) ^2+(y+3) ^2 =25[/tex]

Comparing this with the general equation we can get the center and the radius as

[tex](x-h) ^2+(y-k) ^2 =r^2\\(x-(2)) ^2+(y-(-3)) ^2 =5^2[/tex]

We can now see that

h= 2

k= -3 and

r= 5

2√63 what is the radical

Answers

Answer:

7.94

Step-by-step explanation:

Answer:

[tex]\Large \boxed{\sqrt{63}}[/tex]

Step-by-step explanation:

A radical is the root of a number.

[tex]2\sqrt{63}[/tex]

The radical in this expression is [tex]\sqrt{63}[/tex].

I NEED HELP I GIVE 5 STARS PLEASE ;(

Answers

the answer is 2 3/7

What is the measure of angle X?

Answers

Answer: 71 degrees

====================================================

Explanation:

Focus on triangle BDH

Interior angles B and D are given to be 40 and 31 respectively. Interior angle H is unknown

For any triangle, the interior angles always add to 180

B+D+H = 180

40+31+H = 180

H+71 = 180

H = 180-71

H = 109

Interior angle H is 109 degrees for triangle BDH

The exterior angle is 180 minus this measure

exterior angle = 180 - (interior angle)

exterior angle = 180 - 109

exterior angle = 71

Note how this is the sum of interior angles B and D, so you could use the remote interior angle theorem here.

Ikyume is 62m away from Amadi, on a bearing of 012°. Becky is 42m away from Ikyume and on bearing of 082°. How far is Amadi from Becky, and on what bearing?

Answers

Answer:

Amadi is 86m far from Becky

Amadi is on the bearing of 78° .

Step-by-step explanation:

From the information given ,

let I represent Ikyume

A represent Amadi  and B represent Becky

From the information in the diagrammatic expression shown below:

Using cosine rule;

i² = a² + b² - 2ab cos (I)

i² = 42² + 62² - 2(42×62) cos (110°)

i² =  1764 + 3844 - 5208 (- 0.342)

i² =  1764 + 3844 -  ( - 1781.136)

i² = 1764 + 3844 + 1781.136

i² = 7389.136

i = [tex]\mathtt{\sqrt{7389.136}}[/tex]

i = 85.96

i [tex]\simeq[/tex] 86 m

Amadi is 86m far from Becky

From  point I , 12° = 12° at point A (alternate  angles)

In that quadrant = 90 - 12° = 78°

Therefore, Amadi is on the bearing of 78° .

In ΔABC, and m∠ABC = 90°. D and E are the midpoints of and , respectively. If the length of is 9 units, the length of is units and m∠CAB is °.

Answers

Applying the midsegment theorem and the definition of isosceles triangle:

DE = 4.5 units

m∠CAB = 45°

The image that shows ΔABC is attached below.

Since AB = BC, therefore, ΔABC is an isosceles triangle.

This implies that, the base angles will be equal.

Thus:

If m∠ABC = 90°, therefore,

m∠CAB = ½(180 - 90)

m∠CAB = 45°.

DE is the midsegment of the triangle, and is parallel to the third side, CA = 9 units.

Based on the midsegment theorem, we have the following equation:

DE = ½(9)

DE = 4.5 units.

Therefore, applying the midsegment theorem and the definition of isosceles triangle:

DE = 4.5 units

m∠CAB = 45°

Learn more about midsegment theorem on:

https://brainly.com/question/7423948

Answer:

4.5
45

Step-by-step explanation:

I need help on this :(

Answers

Answer:

26⁹

Step-by-step explanation:

26 * 26⁸

= 26¹ * 26⁸

= 26¹⁺⁸

= 26⁹

Factor completely 3x^2 - x - 4

A.(3x - 4)(x + 1)

B.(3x + 4)(x - 1)

C.(3x - 2)(x + 2)

D.(3x - 1)(x + 4)

Answers

Answer:

B. [tex](3x-4)(x+1)[/tex]

Step-by-step explanation:

can someone plzz answer dis ma braincells dont seem to work ​

Answers

Answer:

Good luck undersatnding.

Step-by-step explanation:

1.

A) 27 (over) 4

B)  97 (over) 117

2.

C) 8

D) -243 (over) 32

3.

Square root of 25 is 5

Square root of 16 is 4

Square root of 9 is 3

Square root of 1 is 1

4.

E)  553 (over) 72

F) 11 (over) 56

G) 65 (over) 18

H) 28 (over) 9

5.

E) 35941

F) 81130

G) 79567.75

H) 20525.857

I dont know 7-8

9.

E) Negative

F) Positive

G) Positive

H) Negative

10.

Square root of 25 is 5

Square root of 64 is 8

Square root of 121 is 11

Square root of 225 is 15

I couldn't post images for 6, it wont let me.

I need help and I will give five stars and a big thank you comrades

Answers

Answer:

A.

Step-by-step explanation:

A way to find the equation of the graph is to find the solutions.

On the graph, the solutions are where the function intersects the x-axis. That would be where x = -2, x = 1, and x = 3.

In the equations, you will need to find factors when the x is inputted, the factor equals 0. For example, one of the factors is (x + 2). This is because x + 2 = 0, so x = 0 - 2, so x = -2. So, the three factors are (x + 2), (x - 1), and (x - 3).

The correct equation is A.

Hope this helps!

One hundred people, ages 11-15, were randomly surveyed to find their opinion of their favorite leisure time activity. Sixty-four percent of them said they liked to spend time watching TV. If there are 1500 students in your school, about how many of them would you predict would enjoy watching t.v. A.2343 B.960 C.640 D.500

Answers

Answer:

If there are 1500 students in your school then 960 students would enjoy watching TV

Step-by-step explanation:

Step 1: We know that 64% of kids aged from 11 to 15 enjoy watching TV and there is 1500 students in your school

Step 2: We now want to find 64% of 1500, we can rewrite 64% as 0.64. We multiple 1500 by 0.64 to find out how many students enjoy watching TV

0.64 x 1500 = # of students who like watching TV

960 = # of students who like watching TV

Therefore out of 1500 students, 960 would enjoy watching TV

Can someone pls help me &THANK YOU



SLATTTT!!!

Answers

BABYYYY SOSAAAAA CASH CARTIIII

Shea made 11 of her first 17 free-throw attempts. What is the minimum number of her next 20 free-throw attempts that she must make for her overall success rate to be at least $80\%$? Express your answer to the nearest whole number.

Answers

Answer:

19 throws.

Step-by-step explanation:

For her success rate to be 80% in 37 throws she must make  0.8 * 37

= 29.6 throw - that is 30 to nearest throw.

So for the next 20 throws she must make  30 - 11 = 19 throws.

Kyle rides his bicycle 15 mph for 2 hours how far does he travel

Answers

━━━━━━━☆☆━━━━━━━

▹ Answer

30 miles

▹ Step-by-Step Explanation

Multiply mph by hours:

15 mph * 2 hrs = 30 miles

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Y=-5x+30 x=10 what is the solution to the system of equations 1)(-20,10) 2)(10,-20) 3)(10,4) 4)(4,10)

Answers

Answer:

            2) (10, -20)

Step-by-step explanation:

y = - 5x + 30  and  x = 10  ⇒  y = -5•10 + 30 = -50 + 30 = -20

x = 10  and y = -20   ⇒  (10, -20)

Answer:

Its B. (10, –20)

Step-by-step explanation:

I just took the quiz on edge

hello :) why is the first one wrong?

Answers

Answer:

The cube only belongs to the x and not 2x.

The statement will only be true if there is a bracket around the 2x.

log₃(2x)³= 3log₃2x

logarithm power rule:

logₐ(x)^y = y ∙ logₐ(x)

Answer:

see explanation

Step-by-step explanation:

Given

[tex]log_{5}[/tex] 2x³

= [tex]log_{5}[/tex] 2 + [tex]log_{5}[/tex] x³

= [tex]log_{5}[/tex] 2 + 3[tex]log_{5}[/tex] x

Thirteen people on a sports team show up for a game. a. How many ways are there to choose 10 players to play the game? b. How many ways are there to assign the 10 different positions by selecting players from the 13 who show up?

Answers

Answer:

a)286 ways

b)1,037,836,800 ways

Step-by-step explanation:

a. How many ways are there to choose 10 players to play the game?

We have to take note of a key word here which is CHOOSE. For question a, order does not matter.

Hence, we use the combination formula. This is given as:

C(n, r) = nCr = n!/r! (n - r)!

n = 13, r = 10

13C10 = 13!/10! (13 - 10)!

= 13!/ 10! × (3!)

= 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 / (10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) × (3 × 2 × 1)

= 1716/6

= 286 ways.

b. How many ways are there to assign the 10 different positions by selecting players from the 13 who show up?

For question b as well, we take note of a key word which is ASSIGN. For question b, order is very important.

Therefore, the formula we use is the permutation formula.

P(n, r) = nPr = n!/(n - r)!

n = 13, r = 10

13P10 = 13!/ (13 - 10)!

= 13!/ 3!

= 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 / (3 × 2 × 1)

= 1,037,836,800 ways

Negative solution for Multi-step equations

Answers

Answer:

[tex]\frac{1}{2}(4x+6)+3x=7x+9[/tex]

[tex]\frac{1}{2}(4x+8)+3x=7x+9[/tex]

Step-by-step explanation:

By putting the numbers in the given equation,

[tex]\frac{1}{2}(4x+6)+3x=7x+9[/tex]

2x + 3 + 3x = 7x + 9

5x + 3 = 7x + 9

(5x + 3) - 7x = (7x + 9) - 7x

(5x - 7x) + 3 = 9

-2x + 3 = 9

(-2x + 3) - 3 = 9 - 3

-2x = 6

[tex]-\frac{2x}{2}=\frac{6}{2}[/tex]

-x = 3

x = -3

Therefore, our equation is correct which has a negative result.

In place of 6 if we use 8, value of x will be negative again.

Here is a rule to make a list of numbers: Each number is 4 less than 3 times the previous number. Start with 10, build a sequence of 5 numbers.

Answers

Answer:

10,26,74,218,650

Explanation:

Each number is 4 less then 3 times than previous number.

The list of number is bounded by a set of rules that guide the creation of the set of numbers. The first 5 terms are: 10, 26, 74, 218, 650

Represent the number of terms with n.

So, the nth term is: [tex]T_n[/tex]

The start of the build is 10 means:

[tex]T_1 = 10[/tex]

The rule to generate the next terms is:

[tex]T_{n+1} = 3 \times T_n - 4[/tex] ---- i.e. 4 less than 3 times the previous term

So, the next terms till the 5th are:

[tex]T_{2} = 3 \times 10 - 4 = 26[/tex]

[tex]T_{3} = 3 \times 26- 4 = 74[/tex]

[tex]T_{4} = 3 \times 74- 4 = 218[/tex]

[tex]T_{5} = 3 \times 218- 4 = 650[/tex]

So, the first 5 terms are: 10, 26, 74, 218, 650

Read more about patterns at:

https://brainly.com/question/13382968

A boom seller sold 50 books for $ 890.00 and earned a profit of $ 90.00. Find the cost price of 50 books.​

Answers

Answer:

$ 800

Step-by-step explanation:

number of books sold = 50

money earned = $ 890.00

profit = $ 90.00

Then the price of 50 books will be (money earned) - (profit)

= 890 - 90

= 800

So, the cost of 50 books is $ 800

HOPE IT HELPS :)

PLEASE MARK IT THE BRAINLIEST!

The quotient of x^2+x-6/x^2-6x+5*x^2+2x-3/x^2-7x+10 has ___ in the numerator and ______ in the denominator.

Answers

Answer:

So the quotient of [tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex] has (x + 3)² in the numerator and (x + 5)² in the denominator.

Step-by-step explanation:

[tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex]

Factorizing the expressions we have

[tex]\frac{x^{2} + 3x -2x - 6}{x^{2} -x - 5x + 5} X \frac{x^{2} + 3x - x - 3}{x^{2} -2x -5x + 10}[/tex]

[tex]\frac{x(x + 3)- 2(x + 3)}{x(x -1) - 5(x - 1)} X \frac{x(x + 3) - 1(x + 3)}{x(x - 2) - 5(x - 2)}[/tex]

[tex]\frac{(x + 3)(x - 2)}{(x - 5)(x - 1)}X\frac{(x + 3)(x - 1)}{(x - 2)(x - 5)}[/tex]

Cancelling out the like factors, (x -1) and (x - 2), we have

[tex]\frac{(x + 3)(x + 3)}{(x - 5)(x - 5)}[/tex]

= [tex]\frac{(x + 3)^{2} }{(x + 5)^{2} }[/tex]

So the quotient of [tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex] has (x + 3)² in the numerator and (x + 5)² in the denominator.

I need help and fast!!!!

Answers

Answer:

H. b/a

Step-by-step explanation:

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Step 1: Label our variables

y₂ = 2b

y₁ = b

x₂ = 2a

x₁ = a

Step 2: Plug into formula

m = (2b - b)/(2a - a)

Step 3: Evaluate

m = b/a

Answer:

b/a

Step-by-step explanation:

We have two points so we can use the slope formula

m = (y2-y1)/(x2-x1)

    = ( 2b - b)/ ( 2a -a)

   = b/a

Other Questions
A cylindrical grain silo, with a flat top, is 30 feet tall and has a radius of 12 feet. It is full to the top with shelled corn. If the density of shelled corn averages 45 pounds/cubic foot, what does the corn in the silo weigh to the nearest pound Think about your favorite superhero. Write a four sentence paragraph about yourfavorite superhero. Why do you like this superhero? Why qualities do they possess thatyou wish you had as well. How does your favorite superhero inspire you? plz help Can you help Jorge organize the results into a two-way frequency table? Please answer this ASAP Bias can _____ be completely eliminated. a) always b)sometimes c) never John used 1 3/4 kg os salt to melt the ice on the sidewalk. He then used another 3 4/5 kg on the driveway. How much salt did he use in all? PLEASE SHOW YOUR WORK I WILL MARK YOU BRAINIEST AND PLEASE EXPLAIN HOW YOU GOT YOUR WORK. What type of policy lowers interest rates to allow individuals access to more money for large purchases simplify (-x) 2-2x .... i repost bec brainly would not allow me to make it lager that is all i can do Greyson completes a dive from acliff 75-feet above a river. It takeshim only 1.5 seconds to hit thewater and then another 0.5second to descend 10 feet into the riverwhats the x axis and y axis? PLEASE ANSWER QUICKLY ASAP please read question carefully kinda stuck and would like help . A particular parcel of real estate (land) is sold for $20,000,000 and was originally purchased for $10,000,000. On a taxable sale, explain a circumstance (type of investor, intent, entity, etc.) that would pay the following U.S. federal income tax results on the $10,000,000 gain (exclude the 3.8% net investment income tax and any state taxes in the calculation): Four witches are making a brew.Patricia puts in x frogs legs.sheila puts in five more than patricia.Anne puts double the amount that Sheila adds,and Winifred adds three times the number Sheila adds.write down an algebraic expression for:Sheila. Anne. Winifred Describe a current situation in America that shares some similarities with the treatment of Japanese Americans during World War II. What good light novels or manga are recommended. A list of 20 at least plz. Telling me if theres anime adaptation is helpful too :) If there is a 1-degree change, coral reefs will become______? Which statements describe OneDrive?1. OneDrive is available to subscribers of Office 365.2. The OneDrive browser allows access to Excel online.3. OneDrive is a storage location on your personal computer.4. New documents can be created and uploaded on OneDrive5. OneDrive ensures that changes in files are updated in the computer and the cloud. Suppose you bought a bond with an annual coupon rate of 4.2 percent one year ago for $900. The bond sells for $950 today. a. Assuming a $1,000 face value, what was your total dollar return on this investment over the past year? b. What was your total nominal rate of return on this investment over the past year? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) c. If the inflation rate last year was 2.5 percent, what was your total real rate of return on this investment? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) A wire carries current in the plane of this paper toward the top of the page. The wire experiences a ma netic force toward the right edge of the page. The direction of the magnetic field causing this force is: A. in the plane of the page and toward the left edge B. in the plane of the page and toward the bottom edge C. upward out of the page D. downward into the page Haz parejas con los siguientes lugares y lo que se encuentra en ellos.