Mathematics High School

Mrs. simms told her class to find two consecutive even integers such that twice the lesser of two integers is 4 less than two times the greater integer.
a. write and solve an equation to find the integers.
b. does the equation have one solution, no solutions, or is it an identity? explain.

Answers

Answer 1

Final answer:

To find two consecutive even integers, we can set up and solve an equation. The equation in this case is an identity, meaning it is true for all values of x. Therefore, there are infinitely many solutions.

Explanation:

To find two consecutive even integers, let's represent the first integer as x and the second integer as x + 2. Now, according to the given information, twice the lesser of the two integers is 4 less than two times the greater integer. We can write this as:

2x = 2(x + 2) - 4

Simplifying the equation:

2x = 2x + 4 - 4

2x = 2x

This equation is an identity, meaning it is true for all values of x. Therefore, there are infinitely many solutions. In this case, there are infinitely many pairs of consecutive even integers that satisfy the given conditions.

Related Questions

An urn contains 3 green balls, 2 blue balls, and 4 red balls. in a random sample of 5 balls, find the probability that at least one blue balls is selected.

Answers

Well, it depends. If you take one, do you leave it out, or put it back?? If you leave the ball in, then the probability would be 0.05419228% or 32/59049 but if you put the ball out of the urn, then the probability would be 0.211640211% or 32/15120. YOU'RE WELCOME :)

Final answer:

To find the probability of at least one blue ball being selected from an urn with green, blue, and red balls in a sample of 5, calculate the probability of not selecting any blue balls and then subtract it from 1.

Explanation:

An urn contains 3 green balls, 2 blue balls, and 4 red balls. In a random sample of 5 balls, find the probability that at least one blue ball is selected.

Calculate the probability of not selecting any blue balls: P(no blue) = (7/9) * (6/8) * (5/7) * (4/6) * (3/5) = 0.167

Find the probability of at least one blue ball: P(at least one blue) = 1 - P(no blue) = 1 - 0.167 = 0.883

Which postulate or theorem can be used to prove that △ABC≅△ADC? ​ ASA Congruence Postulate ​ ​ SAS Congruence Postulate ​ ​ HL Congruence Theorem ​ ​ SSS Congruence Postulate ​

Answers

  Both the triangles ΔABC and ΔADC are congruent by SSS postulate of congruence.

From the picture attached,

In ΔABC and ΔADC,

AB ≅ AD (Given)

BC ≅ CD (Given)

AC ≅ AC (Reflexive property)

Since, corresponding sides of ΔABC are equal to ΔADC,

Therefore, ΔABC ≅ ΔADC (By S-S-S postulate of congruence)

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What's the intuition behind the equation 1+2+3+⋯=−1121+2+3+⋯=−112 ?

Answers

The sum clearly diverges. This is indisputable. The point of the claim above, that

[tex]1+2+3+\cdots=-\dfrac1{12}[/tex]

is to demonstrate that a sum of infinitely many terms can be manipulated in a variety of ways to end up with a contradictory result. It's an artifact of trying to do computations with an infinite number of terms.

The mathematician Srinivasa Ramanujan famously demonstrated the above as follows: Suppose the series converges to some constant, call it [tex]C[/tex]. Then

[tex]\begin{matrix}C&=&1&+2&+3&+4&+5&+6&+\cdots\\4C&=&&+4&&+8&&+12&+\cdots\\-3C&=&1&-2&+3&-4&+5&-6&+\cdots\end{matrix}[/tex]

Now, recall the geometric power series

[tex]\displaystyle\sum_{n\ge0}x^n=1+x+x^2+x^3+\cdots=\dfrac1{1-x}[/tex]

which holds for any [tex]|x|<1[/tex]. It has derivative

[tex]\displaystyle\sum_{n\ge1}nx^{n-1}=1+2x+3x^2+4x^3+\cdots=\dfrac1{(1-x)^2}[/tex]

Taking [tex]x=-1[/tex], we end up with

[tex]1+2(-1)+3(-1)^2+4(-1)^3+\cdots=1-2+3-4+\cdots=\dfrac14[/tex]

and so

[tex]-3C=\dfrac14\implies C=-\dfrac1{12}[/tex]

But as mentioned above, neither power series converges unless [tex]|x|<1[/tex]. What Ramanujan did was to consider the sum [tex]1-2+3-4+\cdots[/tex] as a limit of the power series evaluated at [tex]x=-1[/tex]:

[tex]\displaystyle-3C=\lim_{x\to-1^+}\sum_{n\ge1}nx^{n-1}=\lim_{x\to-1^+}\frac1{(1-x)^2}=\frac14[/tex]

then arrived at the conclusion that [tex]C=-\dfrac1{12}[/tex].

But again, let's emphasize that this result is patently wrong, and only serves to demonstrate that one can't manipulate a sum of infinitely many terms like one would a sum of a finite number of terms.

This figure shows the procedure for constructing a
A. Pair of parallel lines
B. Bisector of an angle
C. Perpendicular from a point on a line
D. Perpendicular bisector

Answers

B. is your answer hope this helps.

Answer:

B

Step-by-step explanation:

Perform the indicated computation. write the answer in scientific notation. 12x10^4

Answers

The answer is:  " 1.2 * 10⁵ " .
_____________________________________________________

Select the postulate that is illustrated for the real numbers. 5 + (-5) = 0

The commutative postulate for multiplication
Multiplication by one
The addition inverse postulate
Commutative postulate for addition
The distributive postulate
The addition of zero postulate
The multiplication inverse

Answers

the answer is F.The addition of zero postulate

The addition inverse postulate explains the relationship between numbers like 5 and -5 that add up to zero, crucial for understanding real number properties.

The addition inverse postulate is illustrated by the expression 5 + (-5) = 0 for real numbers. This postulate states that for every number, there exists an additive inverse that when added together results in zero.

For example, in the given expression, 5 and -5 are additive inverses of each other, and when added, they cancel out to give zero, satisfying the addition inverse postulate.

This concept plays a crucial role in understanding the properties and operations of real numbers.

To which place value is the number rounded 6.706 to 6.71

Answers

100th becuz it’s in that spot specifically and might as well look it up too

There are X giraffes at the zoo the number of elephants is 4 Less Than 3 times the number of giraffes and there are more than 23 elephants

Answers

 X   the number  of giraffes
the number of elephants is   3x -4 


3X - 4 > 23

3X > 23 + 4
3X > 27
X > 9
there are  more then 9 giraffes in the zoo.



Color in equations what to color in 1+2+3+4=10 What cubes to color in?

Answers

can you explain more

please explain what the question is more clearly please.

Evaluate. 3−1⋅(4⋅6)⋅2−3 Enter your answer in the box.

Answers

The answer to this question is 1

Brand A cereal contains 10 cups of cereal. How many more cups of cereal are in Brand B cereal? 30% more cereal

Answers

There are 13 cups of  more cereal in Brand B.

Answer:

there are 13 more cups

Step-by-step explanation:

i already did it

Select the classification of the polynomial using its degree and number of terms. 6x^3 The polynomial is classified as a

-cubic monomial
-quadratic monomial
-cubic trinomial

Answers

This expression has 1 term. Why? A term consists of a set of numbers with or without any basic operations. For example, Terms can be represented as 1x + 6. That is two terms because they are separated with an addition sign. So from that knowledge, let's see our options.

1.) Cubic Monomial. Cubic is any number raised to the third power. Since the x is raised to the third power, you can figure it out easily. This only has one term therefore, it is a Monomial. Monomial has a prefix of "Mono=One"

2.) Quadratic Monomial. There is no value raised to the 2nd power (Quadratic)

3.) This only has one term therefore cannot be a Trinomial (Three terms)


Number 1 is the best choice.

An employee contributes $75 each month to her 401(k). What will be the value of her 401(k) after the 240th deposit (20 years) if the per annum rate of return is assumed to be 12% compounded monthly?

Answers

The value of her 401(k) will be 2,160 compounded monthly.
Final answer:

To calculate the value of the 401(k) after 240 deposits (20 years), you can use the formula for compound interest. Using the formula A = P(1 + r/n)^(nt), where A is the future value, P is the principal investment, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years, you can plug in the values to find the answer.

Explanation:

To calculate the value of the 401(k) after the 240th deposit, we can use the formula for compound interest:

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

Where:

A is the future value of the investmentP is the principal investment ($75 per month)r is the annual interest rate (12%)n is the number of times the interest is compounded per year (12 times for monthly compounding)t is the number of years (20 years)

Using these values, the formula becomes:

A = 75(1 + 0.12/12)^(12*20)

Calculating this expression will give us the value of the 401(k) after 20 years.

I need help on this immediately. Please help me.

Answers

Short Answers (Explanation in next section below)

Reason A: Given

Reason B: Angle Addition Postulate

Reason C: Substitution Property

Reason D: Subtraction Property of Equality

----------------------------------------------------------

Further Explanation:

Reason A: At the very top of the problem, it states "given: ..." with the given angle property. All we do for the first line of any proof is repeat what is given to us. It seems silly and redundant, but it is important. Whenever you do a proof you always start with what you're given (some fact or theorem already proven earlier) and you somehow try to connect it to what you are trying to prove. 

Reason B: The angle addition postulate is essentially the idea where we break up an angle into smaller pieces. This is probably better shown in a visual style instead of using words. Have a look at the attached image. Notice how the green angle ABD and the red angle DBE combine to form the purple angle ABE. Hopefully the image is clear enough. If not, then feel free to ask any questions. 

Reason C: We're using the substitution property here. If x = a and x = b, then we can say that a = b. That's what is going on but on a more complicated level. 

Reason D: We subtract the quantity "measure of angle DBE" from both sides. It is like going from x+2 = y+2 to x = y (subtract 2 from both sides). This is the subtraction property of equality in action. In general the rule is if a = b, then a-c = b-c

A charity organization had a fundraiser where each ticket was sold for a fixed price. They had to sell a few tickets just to cover necessary production costs of $1200\$1200 $1200 dollar sign, 1200 . After selling 200200 200 200 tickets, they had a net profit of $12,000\$12{,}000 $12,000 dollar sign, 12, comma, 000 . Let P(n)P(n) P(n) P, left parenthesis, n, right parenthesis denote the net profit from the fundraiser PP P P (measured in dollars) as a function of the number of tickets sold nn n n . Write the function's formula

Answers

P(n)=66n-1200
12000+1200=13200,
13200/200+66,
it asks net profit, so you need to minus $1200 to find it.

Answer:

[tex]P(n)=66n-1200[/tex]

Step-by-step explanation:

Let x be the revenue collected from selling each ticket.

We have been given that a charity organisation had to sell a few tickets just to cover necessary production costs of $1200. After selling 200 tickets, they had a net profit of $12,000.

Since we know that net profit is the difference between total revenue and total cost.

[tex]\text{Net profit}=\text{Total revenue- Cost}[/tex]

We can represent our given information in an equation to find the revenue collected from each ticket:

[tex]12000=200x-1200[/tex]

Let us solve for x by adding 1200 to both sides of equation.

[tex]12000+1200=200x[/tex]

[tex]13200=200x[/tex]

[tex]x=\frac{13200}{200}[/tex]

[tex]x=66[/tex]

Therefore, the revenue collected from selling each ticket is $66.

Now let us write the net profit, P(n), from fundraiser as the function of number of tickets sold,n.

The revenue from selling n tickets will be 66n.

Production costs = 1200

[tex]P(n)=66n-1200[/tex]

Therefore, our desired function will be: [tex]P(n)=66n-1200[/tex].

One of the largest pumpkins ever grown weighed about 3/4 ton how many lb did the pumpkin weigh

Answers

one ton is 2000 pounds. 2000 divided by 0.75 (which is also 3/4) is 1500 pounds

Mandy divided a 12-pound bag of sand into 5 equal pilss What is the weight of each pile

Answers

Mandy divided a 12 - pound bag of sand into equal piles. Is the weight of each pile. - 6045197.

Two cab rides cost the same amount for the same number of miles, m. Which situation can be represented by the equation 2.50 + 0.50m = 1.00 + 0.75m?

Answers

One cab charges an initial fee of $2.50 and then $0.50 for every mile. The other cab company charges an initial fee of $1.00 and then $0.75 for every mile.

The value of m is 6 in the equation 2.50 + 0.50m = 1.00 + 0.75m.

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

Given that Two cab rides cost the same amount for the same number of miles, m.

The given equation is 2.50 + 0.50m = 1.00 + 0.75m.

Two point five zero plus zero point five zero times m equal to one point zero plus zero point seven five times m.

First cab charges an initial fee of $2.50 and then $0.50 for every mile. The other cab company charges an initial fee of $1.00 and then $0.75 for every mile.

2.50 + 0.50m = 1.00 + 0.75m

2.50-1.00=0.75m-0.50m

1.5=0.25m

Divide both sides by 0.25

m=6

Hence, the value of m is 6 in the equation 2.50 + 0.50m = 1.00 + 0.75m.

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harold serves himself 1 1/2 ounces serving of cereal each morning. How many servings does he get from a box of his favorite cereal?

Answers

He gets 5 1/2 servings from the box of his favorite cereal.


20 point to whoever answers first

What is the MEDIAN of may's temperatures

A. 72

B. 61

C. 71

D. 74

Answers

total the temperatures given

 total = 497

 divide by how many they gave (7)

497 / 7 = 71

 answer is C 71 degrees

Answer:

c

Step-by-step explanation:

497 / 7 = 71

Branliest offered

A. What is the circumference of the colony?
B. What is the radius of the colony?

Bacteria lives in groups called colonies colonies are usually circular the diameter of a particular bacterial colony is 12 mm their circumference of a circle is equal to Pi 3.14 times its diameter c= πd

Answers

The circumference can be obtained fairly easily by simply substituting the d in c = πd for the colony's given diameter of 12 mm. Performing that calculation using the approximation of π ≈ 3.14, we obtain a circumference of 12 x 3.14 = 37.68 mm.

To find the radius, remember how the diameter and radius of a circle are defined. The radius is a length extending from the center of a circle to a point on its circumference, and a diameter is a line extending from one point on the circle's circumference to an opposite point, passing through the circle's center along the way. The diameter can, in this way, be defined as twice the length of the radius, which means we can find the radius of a circle by taking half of its diameter. In this case, our diameter is 12 mm, so our radius would be 6 mm.

The measure of an angle is 8 greater than 3 times its supplement. Find he measurement of the angle.

Answers

x + 3x + 8 = 180
4x = 172
  x = 43

its supplement = 3x + 8 = 3(43) + 18 = 129 + 8 = 137

answer
angles are 43 and 137

What is 24 ten thousands in standard form

Answers

We have that the standard form of 24 ten thousands is

240,000

From the Question we are told that

24 ten thousands is given

Where

24 ten thousands=24*10000=240,000

Generally the standard form of 24 ten thousands is

240,000

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Which characteristic is used to group artworks into periods or styles?

A: Abstract
B: Similar

Answers

i believe it is A, forgive me if i am wrong ..
a is the answer to this problem

In 1997, there were 43.2 million people who used free weights. Assuming the use of free weights increases 6% annually, which equation can be used to predict the number of people using free weights t years from 1997?
p = 43.2(0.06)t
p = 43.2(1.06)t
p = 43.2(0.94)t
p = 43.2(1.005)t

Answers

P=43.2(1.06)^t, Would Be The Answer.

The correct equation to predict the number of free weight users is option B) p = 43.2(1.06)t. This equation accounts for a 6% annual increase in users.

Predicting the Number of Free Weight Users

In 1997, there were 43.2 million people using free weights. Given that the annual increase rate is 6%, we use the exponential growth formula to predict the number of people in future years. The correct equation to use is:

p = 43.2(1.06)t

This equation represents an exponential increase, where 'p' is the number of people using free weights and 't' is the number of years since 1997. This can be explained by the fact that a 6% annual increase multiplies the original number of users by 1.06 each year.

Four students wrote statements about cosecant, secant, and cotangent values as shown below.

Anik

The cosecant, secant, and cotangent of an acute angle may be greater than 1 or less than 1.


Isabella

The cosecant, secant, and cotangent of an acute angle are always greater than 1.


Kayla

The cosecant and secant of an acute angle are always greater than 1, but the cotangent can be greater than 1, less than 1 or equal to 1.


Morris

The cosecant and secant of an acute angle may be greater than or equal to 1, but the cotangent of an acute angle is always less than 1.

Which student is correct?

Answers

Answer:

c Kayla is answer

Step-by-step explanation:

Since sine lies between-1 and +1 we have cosecant, reciprocal of sin lying always outside -1 and 1.

i.e. |cosec x|>1

For acute angle sine, cos , tan are positive

So cosec x >1 and similarly since cos x <1, sec x >1 always

But tanx varies between 0 and infinity for acute angles

Hence cot can take values from 0 to infinity

Hence the correct answer is that of Kayla

The cosecant and secant of an acute angle are always greater than 1, but the cotangent can be greater than 1, less than 1 or equal to 1.

The statement about cosecant, secant, and cotangent values that is correct is Kayla's: The cosecant and secant of an acute angle are always greater than 1, but the cotangent can be greater than 1, less than 1 or equal to 1.

What is the sine of an angle?

In Trigonometry, the sine of an acute angle is a ratio of the length of an opposite side of a right-angled triangle to the length of its hypotenuse.  Also, the sine of an angle generally lies between -1 and 1.

What is the cosecant (cosec) of an angle?

In Trigonometry, the cosecant (cosec) of an acute angle is a ratio of the length of its hypotenuse to the length of an opposite side of a right-angled triangle. Thus, the cosecant of an angle is the reciprocal of the sine function and as such lies outside -1 and 1.

What is the cotangent of an angle?

The cotangent of an acute angle is a ratio of the length of its adjacent side to the length of an opposite side of a right-angled triangle.

In conclusion, Kayla's statement about the values of cosecant, secant, and cotangent is correct.

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The equation 9.95 + 0.30s=c gives the cost c in dollars that a website charges for downloading songs. The variable s stands for the number of songs downloaded. Find the cost of downloading 35 songs

Answers

9.95 + 0.30s=c

 replaces s with 35

9.95 +0.30(35) =c

9.95 + 10.50 = 20.45

 it will cost $20.45

PLEASE HELP!!!!!!!!!!
Whats the value of a?
a-2=3+6a/3
a=

Answers

Solve for a by simplifying both sides of the equation, then isolating the variable.

a = -5

Answer:

a–2=3 6a/3

So I was told The answer was -5 but all the people r wrong its -3

proof

I don’t understand 9) PLEASE HELP!!! The line y=2.5x-7

Answers

The residual of a line is the observed Y value (the numbers in the table) minus the actual value (the Y value you get when you plug in the X value into the equation)... This question is asking you to find the residuals of all the points, square them, and add them... 

For example, the observed Y value for -4 is -15. When you plug in -4 into the equation, you get this: 

2.5x-7
2.5(-4) -7
-10 -7
=-17

The observed Y val. is -15, while the actual (equation) one is -17. -15 -(-17) is 2. 2^2 = 4

Do this process for all of the points, the add up the squared residuals, and you'll be done! 

Hope this helped!

Suppose you invest $2000 at an annual interest rate of 4.5%. how long will it take for it to earn $495?

Answers

100%:2000$=4.5%:x$, x=90$. After 1st year I earned 90$, now I have 2090$.
100%:2090$=4.5%:x$, x=94.5$. After 2nd year I earned 94.5$ more, now I have 2184.05$.
100%:2184.05$=4.5%:x$, x=98.28$. After 3rd year I have 2282.33$.
100%:2282.33$=4.5%:x$, x=102.71$. After 4th year I have 2385.04$.
100%:2385.04$=4.5%:x$, x=107.33$. After 5th year I have 2492.37$.

So I need 6 years to earn 495$.
Final answer:

To calculate how long it takes for an investment to earn a certain amount in simple interest, use the formula T = I / (PR), where I is the interest, P is the principal, R is the rate of interest, and T is the time. For a $2000 investment at 4.5% interest to earn $495, it would take approximately 5.5 years.

Explanation:

The subject of this question is Simple Interest. The formula for calculating simple interest is I = PRT, where I is the interest, P is the principal (the initial amount of money), R is the rate of interest per time period, and T is the time. In this case, we know the interest ($495), the principal ($2000), and the rate (4.5% or 0.045 as a decimal). We're trying to find out the time, so we rearrange the formula to T = I / (PR).

Substituting our known values, we get T = 495 / (2000 * 0.045). Doing the math, the time it takes for the investment to earn $495 is approximately 5.5 years.

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