Prove that if m + n and n + p are even integers, where m, n, and p are integers, then m + p is even. what kind of proof did you use?

Answers

Answer 1

Prove that if m + n and n + p are even integers, where m, n, and p are integers, then m + p is even.
m=2k-n, p=2l-n

Let m+n and n+p be even integers, thus m+n=2k and n+p=2l by definition of even
m+p= 2k-n + 2l-n substitution
= 2k+2l-2n
=2 (k+l-n)
=2x, where x=k+l-n ∈Z (integers)
Hence, m+p is even by direct proof.

Answer 2

This is about usage of direct proof.

m + p was proved to be even using direct proof.

We are given;

m, n and p are integers

m + n and n + p are even integers.

From direct proof in Maths;

If a is an even integer, then there will exist an integer b such that;

a = 2b

Applying that to our question, we can say that;

m + n = 2b

n + p = 2c

Adding both equations together gives;

m + 2n + p = 2b + 2c

We want to find if m + p is even. Thus, let's rearrange to get them on one side;

m + p = 2b + 2c - 2n

Factorizing, we have;

m + p = 2(b + c - n)

From earlier, b, c and n are integers. Therefore, from earlier formula about direct proof of even integers, we can equally say that m + p is also even.

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Related Questions

Should the quotient of an integer divided by a nonzero integer always be a rational number? Why or Why not?

Answers

YES , it is a rational number

a rational number is defined as

a/b , where a and b are integers, with bâ‰ 0

when you divide two integers you get exactly that form

Which product is negative

Answers

One thing for sure it is not b,d,c its a

1st one -*- =+,+*- = -,-*- = +

2nd one = 0

3rd one-*-=+,+*+=+,+*+=+

4th one +*-=-,-*-=+,+*- = -

4th one is negative

f(t)=10t2+5t+1 . Find the value of t for which the tangent line to the graph of f(t) has slope 1.

Answers

[tex]\bf f(t)=10t^2+5t+1\implies \stackrel{\textit{slope of tangent}}{\cfrac{df}{dt}}=20t+5\implies 1=20t+5 \\\\\\ -4=20t\implies -\cfrac{4}{20}=t\implies -\cfrac{1}{5}=t[/tex]

The value of t for which the tangent line to the graph of f(t) has slope 1 is -1/5.

The given function is f(t)=10t²+5t+1.

We need to find the value of t for which the tangent line to the graph of f(t) has slope 1.

What is the tangent line to the graph?

In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve.

Now, f'(t) = slope of the tangent line to the curve at the point (t, f(t)).

Given, f'(t) = 1

f(t)=10t²+5t+1

⇒f'(t)=20t+5

⇒1=20t+5

⇒20t=-4

⇒t=-4/20

⇒t=-1/5

Therefore, the value of t for which the tangent line to the graph of f(t) has slope 1 is -1/5.

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You are a contractor and charge $45 for a site visit plus an additional $24 per hour for each hour you spend working at the site.Write and solve an equation to determine how many total hours you have to work

Answers

so lemme ...
45+(24x)=h

I feel this is the best I can do with the given information ... hope this helps

Which number is 1/10 as great as 0.7?

Answers

Answer:

Step-by-step explanation:

It’s actually 7.

Michael plays 1/5 of a song in 1/15 pf a minute. How many minutes will it take to play whole song

Answers

well, a whole will be five fifths or 5/5.

now, he only plays 1/5 in 1/15, how many minutes will it take to play the whole 5/5 of the song?

[tex]\bf \begin{array}{ccll} \stackrel{part}{song}&\stackrel{part}{minutes}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \frac{1}{5}&\frac{1}{15}\\\\ \frac{5}{5}&m \end{array}\implies \cfrac{\frac{1}{5}}{\frac{5}{5}}=\cfrac{\frac{1}{15}}{m}\implies \cfrac{\frac{1}{5}}{\frac{5}{5}}=\cfrac{\frac{1}{15}}{\frac{m}{1}}\implies \cfrac{1}{5}\cdot \cfrac{5}{5}=\cfrac{1}{15}\cdot \cfrac{1}{m}[/tex]

[tex]\bf \cfrac{1}{5}=\cfrac{1}{15m}\implies 15m=5\implies m=\cfrac{5}{15}\implies m=\stackrel{\textit{minutes}}{\cfrac{1}{3}}[/tex]

A store is giving away a $10 to every 7th person to enter the store and a $25 coupon to every 18th person to enter the store . which person will be the first to get both coupons?

Answers

To do this we need to find the LCM of 7 and 18. This is 126.

So, it's the 126th customer

You need to find the Lcm of it which is the 126th person

4/9 divided by what equals 12

Answers

(4/9)/x= 12

Multiply both sides by x
4/9=12x

Divide both sides by 12
(4/9)*(1/12)= 4/108
4/108= 1/27

Final answer: 1/27

Housing expenses are commonly referred to as PITI. What does PITI stand for?

Answers

PITI: principal, interest, taxes, and insurance

Answer:

Step-by-step explanation:

PITI: principal, interest, taxes, and insurance

Nine coins are placed in a 3x3 matrix with some face up and some face down. you can represent the state of the coins using a 3x3 matrix with values 0 (heads) and 1 (tails). here are some examples: 0 0 0 1 0 1 1 1 0 0 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 1 each state can also be represented using a binary number. for example, the preceding matrices correspond to the numbers: 000010000 101001100 110100001 there are a total of 512 possibilities, so you can use decimal numbers 0, 1, 2, 3,...,511 to represent all the states of the matrix. write a program that prompts the user to enter a number between 0 and 511 and displays the corresponding matrix with the characters h and t.

Answers

Hello,

Here is the program in QB64

CONST Ordre = 3
DIM SHARED mat(1 TO Ordre, 1 TO Ordre) AS INTEGER, n AS INTEGER
CALL ReadN
CALL MakeMat
CALL SeeMat
END

SUB ReadN
SHARED n AS INTEGER
DIM k AS INTEGER
INPUT "0<=n<=511"; k
IF k < 0 OR k > (2 ^ (Ordre * Ordre)) - 1 THEN PRINT "erreur de valeur de n"; n: END
n = k
END SUB

SUB MakeMat
SHARED mat() AS INTEGER, n AS INTEGER
DIM i AS INTEGER, j AS INTEGER, x AS INTEGER
x = n
FOR i = 1 TO Ordre
    FOR j = 1 TO Ordre
        mat(i, j) = x MOD 2
        x = INT(x / 2)
    NEXT j
NEXT i
END SUB

SUB SeeMat
SHARED mat() AS INTEGER
DIM i AS INTEGER, j AS INTEGER
FOR i = 1 TO Ordre
    FOR j = 1 TO Ordre
        IF mat(i, j) = 0 THEN
            PRINT "h|";
        ELSE
            PRINT "t|";
        END IF
    NEXT j
    PRINT " "
NEXT i
END SUB

Explain why the function is differentiable at the given point then find the linearization of x/(x+y)

Answers

The differentiable functions are one for which there is a departure line at each position on the graph. The digression line to the graph y = f (x) at the point (a, f (a)) is given by the equation. Moreover the other line (at least near (a, f (a))), the function La is the best linear and find the best linear guess to the function f (x) = sqrt (x) near 100.

a number is double and than increased by nine. the result is ninety-one. what is the original number?

Answers

the original number is 41

What is the factored form of x2 − 4x − 5?

(x + 5)(x − 1)
(x + 5)(x + 1)
(x − 5)(x − 1)
(x − 5)(x + 1)

Answers

[tex] x^{2} -4x-5=(x-5)(x+1)[/tex]

If you used the foil method for (x-5)(x+1) and combined like terms you would get the same as

The factored form of the equation x² − 4x − 5 is ( x - 5 )( x + 1 ). The correct option is D.

What is a quadratic equation?

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that the quadratic equation is x² − 4x − 5. The value of x will be calculated as:-

x² − 4x − 5 = 0

x² - 5x + x - 5 = 0

x( x - 5 ) + 1 ( x - 5 ) = 0

( x - 5 ) ( x + 1 ) = 0

Hence, the factored form of the equation x² − 4x − 5 is ( x - 5 )( x + 1 ).

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What is the volume of the frustum?

Answers

depending on the value used for PI the answers vary

but attached picture is solution

Answer is A.503.77

503.77 thats the right answer

What number can be written as 40 plus 5

Answers

I am pretty sure it's 45, but it might be more complex and I just don't understand.

add them together: 40+5 = 45

the number is 45

I am not sure how to solve this

Answers

2x + 1 - 4 = -2x - 3

We're simply just trying to get "x" by itself :)

So, we have to add 2x to both sides.

2x + 2x + 1 - 4 = -3

Add like terms.

(2x + 2x) + (1 - 4) = -3

Simplify.

4x - 3 = -3

Then, we must add 3 to both sides.

4x = -3 + 3

Simplify.

4x = 0

Divide both sides by 4.

x = 0 ÷ 4

Simplify.

x = 0

~Hope I helped!~

a movie club charges a one time fee of $25 it allows members to purchase movies for $7 each another club does not charge a membership fee and sells movies $12 how many movies must a member purchase for the total cost of the two clubs to be equal

Answers

Club Members = $25 + $7 per movie(x)
No membership club = $12 per movie(x)
We need to know how many movies must each purchase to equal in costs.
Set up both equations to equal each other and solve for x=movies.
25 + 7x= 12x
25 + 7x -7x = 12x - 7x
25= 5x
25/5=5x/5
5=x it will take them both 5 movies each to have equal costs.

The number of movies in which the total cost of the two clubs should be equal is 5.

Given that,

The one-time fee is $25.The other club should be $7.The selling price of the movies should be $12.Let us assume the number of movies be x.

25 + 7x= 12x

Now put -7x in both sides

So,

25 + 7x -7x = 12x - 7x

25= 5x

x = 5

Therefore we can conclude that the number of movies in which the total cost of the two clubs should be equal is 5.

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or parallelogram ABCD, A(0, 0), B(a, b), and D(c, 0) are three of its vertices. Find the coordinates of C in terms of a, b, c.

Answers

Refer to the diagram below.

Because ABCD is a parallelogram, therefore
(i) AD = BC, so that
x - a = c - 0
x = a + c

(ii) AB = DC, so that
y - 0 = b - 0
y = b

he coordinates of C are (a+c, b).

Answer: (a+c, b)

Answer:

(a + b, c)

Step-by-step explanation:

I did this is school and this was the correct answer!

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DVD cases are sold in packages of 20 padded mailing envelopes or so in packets of 12 what is the least number of cases and envelopes you could buy so that there is one case for each envelope with none left over

Answers

The least number of cases and envelopes so that there would be no remainder can be determined by finding their least common multiple. The solution is as follows

4 | 20 12
---------------
| 5 3
-------------------

Multiplying 4*5*3 = 60. The least common multiple is 60. Thus, there should be at least 60 each of the envelopes and the packets.

Number of mailing envelopes = 20x = 60
x = 3
Number of packets = 12y = 60
y = 5

That would be 3 packs of the envelopes, and 5 packs of the packets.

Which number sentence correctly solves this problem?

Jill's dad spent $783 for home repairs and $390 for car repairs. How much did Jill's dad spend on the repairs?

A.

783 – 390 = 393

B.
783 + 390 = 1,073

C.
783 + 390 = 1,173

D.

783 – 390 = 493

Answers

How much means total. We have to prices 783 and 390 so we add.
783+390=1173.

The box office manager said about 5,000 people attended the show. Write a number that could be the actual attendance if he correctly rounded to the nearest hundred

Answers

it can be from 4,500 - 5,499

hope this helps

The entrance fee for an exhibition is $6 for an adult and $4 for a child. $700 was collected from the sale of tickets. There were 5 more adults than children. How many adults were there?

Answers

The answer should be 55 adults.

sin α = 21/29, α lies in quadrant II, and cos β = 15/17, β lies in quadrant I Find sin (α - β).

Answers

[tex]\sin(\alpha-\beta)=\sin\alpha\cos\beta-\cos\alpha\sin\beta[/tex]

[tex]\sin\alpha=\dfrac{21}{29}\implies \cos^2\alpha=1-\sin^2\alpha=\dfrac{400}{841}[/tex]

Since [tex]\alpha[/tex] lies in quadrant II, we have [tex]\cos\alpha<0[/tex], so

[tex]\cos\alpha=-\sqrt{\dfrac{400}{841}}=-\dfrac{20}{29}[/tex]

[tex]\cos\beta=\dfrac{15}{17}\implies\sin^2\beta=1-\cos^2\beta=\dfrac{64}{289}[/tex]

[tex]\beta[/tex] lies in quadrant I, so [tex]\sin\beta>0[/tex] and

[tex]\sin\beta=\sqrt{\dfrac{64}{289}}=\dfrac8{17}[/tex]

So

[tex]\sin(\alpha-\beta)=\dfrac{21}{29}\dfrac{15}{17}-\left(-\dfrac{20}{29}\right)\dfrac8{17}=\dfrac{475}{493}[/tex]

Final answer:

The value of sin (α - β), where sin α = 21/29 and α is in the 2nd quadrant, and cos β = 15/17 and β is in the 1st quadrant, is calculated to be 379/493.

Explanation:

In trigonometry, the formula for sin (α - β) is defined as sin α cos β - cos α sin β. Given the problem, we know sin α is 21/29 and cos β is 15/17.

However, we need to determine cos α and sin β. In these cases, we use the identity sin² α + cos² α = 1, and its counterpart for β. For α being in the second quadrant, cos α would be negative. Therefore, cos α = -√(1 - (21/29)²), which simplifies to -8/29. Similarly, for β in the first quadrant (where sin β is positive), sin β = √(1 - (15/17)²), which simplifies to 8/17.

Substitute these values into the formula for sin (α - β), we have sin (α - β) = (21/29 * 15/17) - (-8/29 * 8/17) = 315/493 + 64/493 = 379/493.

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Matt plans to put concrete on a rectangular portion of his driveway. The portion is 8 feet long and 4 inches high. The price of concrete is $98 per cubic yard. The total cost of the concrete Matt needs is $58.07. Which of the following is closest to the width of the portion of the driveway on which Matt plans to put concrete?

[1 foot = 12 inches; 1 yard = 3 feet]

0.5 feet
1.5 feet
3 feet
6 feet

any help is appreciated offering 15 points ;)

Answers

Hey! Hope that I can help.

Can someone help me understand why the mean travel for women is greater than the mean travel for men?

Problem Words:

"In San Jose, the amount of time it took each person to get to work was recorded and rounded up to the nearest 555 minutes. The data collected for men and women are shown in the bar graph to the left"

Answers

Final answer:

To ascertain why mean travel time for women could be greater than for men, one would analyze commuting data for both genders and possibly use hypothesis testing to determine if any observed difference is statistically significant.

Explanation:

Understanding the differences in mean travel time between men and women requires analysis of provided data and consideration of statistical methods. For instance, if in San Jose, the recorded commuting times were higher for women, this could be a result of many factors including job location, availability of transportation, or societal roles affecting women's work commute. In the hypothetical scenario provided, it appears there were no actual data points or a graph to refer to, but typically, one would calculate the average commute time for each gender groups and then compare the two means.

For example, if you have a dataset and you're trying to establish whether the mean travel time for women is greater than that for men, you could perform a hypothesis test. The null hypothesis would state there is no difference in the commuting times between men and women, while the alternative hypothesis would state that There is a significant difference in mean commute times. You would then use the data findings, such as sample means and standard deviations, to perform an appropriate statistical test, like a t-test, to determine if there is a statistically significant difference between the mean commute times of the two groups.

Concluding if this difference is significant would involve looking at a predefined significance level (like 5% or 10%) and comparing the p-value from the test to this level. If the p-value is less than the significance level, we reject the null hypothesis and can claim there is a significant difference in the mean travel times between men and women.

Three fourths of college students use the Internet more than the library. Nine hundredths use the library more. How many times more students use the internet?

Answers

Division
4/3X 100/9 = 8 1/3

99 Point question - Consider the graph of f(x) below. (See attachment)

Write the equation of f(x), and classify the function as linear, quadratic, cubic, exponential, or logarithmic.

Answers

A linear function is a straight line, so that's clearly not it

A quadratic function has one point where is switches from going up to going down (or down to up), but this has two, so that's not it.

A cubic function has 2 points where it goes from down to up or up to down, so this may just work.

An exponential function has a constant to the power of something, so it's either staying constantly up or down after 0 or jumping up and down with every x value, which it isn't doing.

Logarithmic functions are similar to exponential functions in that it usually stays either going up or down the whole time.

Using our definitions, a cubic function is the only one that fits

8.51 is what percent of 18.5

Answers

dive the two numbers:

8.51 / 18.5 = 0.46

0.46 = 46%

in a sale there is 25% off all prices a bed costs £33 in the sale what was the original price

Answers

If everything is 25% off, the sale price is equal to 75% of the original price.

Set up a proportion.
33/x= 75/100

Cross multiply
33*100=3300
3300/75=44=x

Final answer: $44

What is the area of a circle with a diameter of 8 meters (use 3.14 for O
)

Answers

the answer is A~50.27

The answer si A~50.27

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