Half of the smaller of two consecutive even integers is equal to two more than the larger integer find the smaller even integer

Answers

Answer 1

SOLUTION

Let the first even integer be 'a'.

Let the second integer be (a + 2) since the second is a consecutive even integer.

Half of the smaller (i.e. a) is equal to two more than the larger (i.e. a + 2). In other words:

[tex]\frac{a}{2}=(a+2)+2[/tex]

Evaluate for a

Simplify

[tex]\begin{gathered} \frac{a}{2}=a+2+2 \\ \frac{a}{2}=a+4 \end{gathered}[/tex]

Multiply all through by 2

[tex]\begin{gathered} 2\times\frac{a}{2}=2\times a+2\times4 \\ a=2a+8 \end{gathered}[/tex]

Collect like terms

[tex]\begin{gathered} -8=2a-a \\ -8=a \\ \therefore a=-8 \end{gathered}[/tex]

Hence, the smaller even integer is

[tex]-8[/tex]


Related Questions

ASAP please Hurry

The number of issues of books from a library are given for the years 2001–2011. The numbers are in hundreds of thousands.

Answers

Answer:

See attached graph.

Step-by-step explanation:

Use DESMOS graphing software.  Free.

What is -2=-1+n/8? I’ve been stuck on it for a while

Answers

Answer: n= -8

Step-by-step explanation:

1. -2 = -1 + [tex]\frac{n}{8}[/tex]

2. -1 =      [tex]\frac{n}{8}[/tex]

3. -8 = n

On what day does frank first get charged an overdraft fee? a. wednesday b. thursday c. friday d. saturday

Answers

Frank first get charged an overdraft fee on Wednesday

Frank has $66.50 in his account as of Sunday.

He made a debit of $60.33 on Monday (66.50 - 60.33), leaving him with a balance of $6.17. He added $80.75 to the account on that same Monday (6.17 plus 80.75). He has $86.92 left over as of Monday.

Frank had a balance of $86.92 on Tuesday when he made a $54.45 debit (86.92 - 54.45). The remaining balance is $32.47.

Frank had a balance of $32.47 at the beginning of the day on Wednesday. He subsequently made withdraw of $49.20. debit(32.47 - 49.20). Frank has overdrawn and will be assessed an overdraft fee following the debit because his balance is -$16.73. Frank still has a negative balance even after making a deposit of $15.

Therefore, Frank was therefore assessed an overdraft fee on Wednesday.

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what is Vivian's new account balance?

Answers

Answer: 218.65 US$

Step-by-step explanation: $187.56+$49.73= $237.29
237.29 US$- $18.64

Answer:

$218.65

Step-by-step explanation:

She starts with a balance of $187.56. When she deposits money she is adding to the account.

$187.56 + $49.73 = $237.29

When she spends money money is being subtracted from her account.

$237.29 - $18.64 = $218.65

Determine the intercepts of the line:
y = 10x - 32

Answers

Answer:

The x intercept is 3.2, and the y intercept is -32.

Step-by-step explanation:

give brainiest

y-intercept is -32, x intercept is 3.2

Step-by-step explanation:

y-int is whatever b is in y=mx+b

x-int is whatever makes the equation equal to zero

Can someone help me with this?

Answers

Answer:

y = 77

Step-by-step explanation:

[tex]\frac{7}{3}[/tex] = [tex]\frac{y}{33}[/tex] ( cross- multiply )

3y = 7 × 33 = 231 ( divide both sides by 3 )

y = 77

The answer to this math question is 77

2. What is the equation of a line that passes through the points (-0.92, 2.49) and (-5.62, 9.76)? Write your answer in point-slope form.​

Answers

Answer:

Step-by-step explanation:

-0.92 2.49

-5.62 9.76

Rise = 9.76 - 2,49 = 7.27

Run: -5.62 - (-0.92) = -4.7

Slope (Rise/Run) = (7.27.`-0.92) = -1.55

The line has the form:

y = 1.55x + b

We need to find a value of b that forces the line through both point, Use one of the points and solve for b. I'll use (-0.92, 2.49).

y = 1.55x + b

2.49 = 1.55(-0.92) + b

b = 2.49 - 1.426 = 1.064

The equation is y = 1.55x + 1.0

what is the size of the angle between south and south east

Answers

Answer:45°Step-by-step explanation:

The angle between north and south = 180°. The angle between East and South = 90°. The angle between South and West is 90° and between South and East is also 90°. So the sum of these two angles is equal to 180°. Since these two angles are adjacent to each other so they form a linear pair.

Door prizes for entrants in a young inventors competition are $100, $50, $25 and $10. In how many ways can the door prizes be awarded if there are 23 entrants?.

Answers

There are 212 520 ways that the door prizes can be awarded if there are 23 entrants

To solve this problem the formula and the permutation procedure we must use is:

nPr = n! / (n-r)!

Where:

nPr = permutationn = total number of objectsr = number of selected objects! = factorial of the number

Information about the problem:

n = 23 (entrants)r = 4 (prizes )23P4 =?

Applying the permutation formula we have:

nPr = n! / (n-r)!

23P4 = 23! / (23-4)!

23P4= 23! / 19!

23P4 = 23*22*21*20*19! / 19!

23P4 = 23*22*21*20

23P4 = 212520

What is permutation?

It is the ordered arrangement of members belonging to a set with no repeats.

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The impact of new entrants, new products, channel conflicts, and regulation would all be associated with the external opportunities and threats dimension of a SWOT website design analysis.

In summary, the impact of new entrants, new products, channel conflicts, and regulation are all factors that fall under the external opportunities and threats dimension of a SWOT website design analysis. 1. New entrants: When new companies enter the market offering similar website design services, it can increase competition and potentially affect the market share of existing website design businesses. This is an external threat as it poses challenges and risks to the current players in the industry. 2. New products: The introduction of new and innovative website design products can create opportunities for businesses to attract more customers and gain a competitive edge. This is an external opportunity that can be leveraged to improve market position.

3. Channel conflicts: Channel conflicts refer to conflicts or disputes that arise between different distribution channels. In the context of a SWOT analysis for website design, channel conflicts can impact how products and services are delivered to customers. For example, if a website design company relies heavily on a specific distribution channel and that channel experiences conflicts or disruptions, it can affect the company's ability to reach its target market. This is an external threat that needs to be considered.

4. Regulation: Regulations imposed by governing bodies can have a significant impact on website design businesses. For example, regulations related to data privacy, accessibility, or internet governance can affect how websites are designed and operated. Compliance with regulations is crucial to avoid penalties or legal issues. This is an external threat that businesses need to navigate.

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The lateral surface area of cone A is equal to the lateral surface area of
cylinder B.
A
2h
A. True
B. False

Answers

The lateral surface area of cone A is equal to the lateral surface area of

cylinder B. This is true.

How to illustrate the information?

Lateral area of cone is given by: πrl

where r is the radius and l is the slant height

Here r=r and l=2h

Hence, lateral area of cone A= π×r×2h =  2πrh

Lateral area of cylinder is given by: 2πrh

where r is the radius and h is the height

Lateral area of cylinder B=2πrh

Clearly, both the lateral areas are equal. Therefore, it's true.

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According to the rules of significant figures 7.898 + 5.23 = 13.13. This is because the least precise value in the problem is 5.23, which is precise only to the hundredths digit, so the answer must also be rounded to the nearest hundredths.True or False

Answers

The given expression is

[tex]7.898+5.23=13.13[/tex]

It's important to know that the rules of significant figures state that the resulting number of a sum of decimal numbers may have no more significant numbers than the least number of significant figures.

In other words, the answers can't be more precise than the least precise number in the sum.

Therefore, the given statement is true.

The sum of 4 consecutive integers is 170. What is the largest number in the group?

Answers

The largest number when the sum of 4 consecutive integers is 170 will be 44.

According to the question,

We have the following information:

Sum of four consecutive integers = 170

Now, let's take the first integer to be x.

So, the next 3 integers will be (x+1), (x+2) and (x+3) respectively.

Now, the largest number will be (x+3).

Adding 4 consecutive integers:

x+ (x+1) + (x+2) + (x+3) = 170

4x+6 = 170

4x = 170-6 (Moving 6 from the left hand side to the right hand will result in  the change of the sign from plus to minus.)

4x = 164

x = 164/4

x = 41

So, the next three consecutive integers will be 42, 43 and 44.

Hence, the largest of the four consecutive integers is 44.

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Greg is at his house he gets in his car drives north 8. 9 miles and stops at a store then he turns around and drives south 7. 7 miles to his friends house how far is the friends house from Greg’s houses?

Answers

His friend's house is 1.2 miles away from his house.

How do you know his friend's house is 1.2 miles away from his house?

Well, the solution to this math problem is very simple. We just need to remove a number away from another. In other words, we only need to do some subtraction.

Subtraction is one of four main arithmetic operations in which we use to take away a number or an amount from another number or amount. Remember that the commutative law doesn't apply to subtraction, so we really need to be careful to pick what number is subtracted by the other number.

The distance from Greg's house to the store is 8.9 miles away. That's the number that is going to be subtracted. His friend's house is 7.7 miles away from the store. This is the number that we're going to subtract from the previous number. Mathematically, we can express this as:

8.9 - 7.7 = 1.2

We're left with 1.2, which is the distance in miles from Greg's house to his friend's house.

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A normal distribution has = 32 and = 5.
(a) Find the z score corresponding to
x = 27.



(b) Find the z score corresponding to
x = 43.



(c) Find the raw score corresponding to
z = −3.



(d) Find the raw score corresponding to
z = 1.1.

Answers

a) z score corresponding to x = 27 is -1

b) z score corresponding to x = 43 is 2.2

c)  Raw score corresponding to z = -3 is 17.

d) Raw score corresponding to z = 1.1 is 37.5

Given,

Normal distribution with μ = 32 and σ = 5

a) z score corresponding to x = 27

z = (x - μ) / σ

Then,

z = (27 - 32) / 5 = -5/5 = -1

That is, z score corresponding to x = 27 is -1.

b) z score corresponding to x = 43

z = (x - μ) / σ

Then,

z = (43 - 32) / 5 = 11/5 = 2.2

That is, z score corresponding to x = 43 is 2.2

c) Raw score corresponding to z = -3

z = (x - μ) / σ

Then,

-3 = (x - 32) / 5

-3 × 5 = x - 32

-15 = x - 32

x = 32 - 15 = 17

That is, raw score corresponding to z = -3 is 17.

d) Raw score corresponding to z = 1.1

z = (x - μ) / σ

1.1 = (x - 32) / 5

1.1 × 5 = x - 32

x = 32 + 5.5 = 37.5

That is, raw score corresponding to z = 1.1 is 37.5

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13+14=3×f;f=9 helppp

Answers

Answer: 3x=13+14

3x=27

x=27/3

x=9

Step-by-step explanation: Maybe.


[tex]10 \sqrt{3} - 4 \sqrt{48} - \sqrt{75} [/tex]
10v3-4v48-v75 help pld​

Answers

The most appropriate choice for surds will be given by-

[tex]-11\sqrt{3}[/tex] is the correct answer.

What are surds?

There are some natural numbers which are not perfect squares. Their square root are not natural numbers. Those numbers are called surds. The most important method for simplification of surds is prime factorization.

[tex]10\sqrt{3} - 4 \sqrt{48}-\sqrt{75}\\10\sqrt{3} - 4\sqrt{2\times2\times 2\times 2\times3}-\sqrt{3\times 5\times5}\\10\sqrt{3} - 4\times 2\times 2\sqrt{3} - 5\sqrt{3}\\10\sqrt{3} - 16\sqrt{3}-5\sqrt{3}\\-6\sqrt{3} - 5\sqrt{3}\\-11\sqrt{3}[/tex]

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18. An 80-pound grass seed mixture is 30% bluegrass seed. How many pounds of seed
containing no bluegrass seed (0%) should be added to the seed mixture for a resulting
blend that is 20% bluegrass seed? Construct a table, then solve.

Answers

Step-by-step explanation:

what table is your teacher taking about ?

in any case this is resistive easy to solve

80 pounds of 30% with x pounds of 0% result in 80+x pounds of 20% :

80×0.3 + x×0 = (80 + x)×0.2 = 80×0.2 + x×0.2

80×0.1 = x×0.2

x = 80×0.1/0.2 = 80/2 = 40 pounds

so, 40 pounds of 0% have to be added to the 80 pounds of 30% to get a mixture of 20% (80+40 = 120 pounds).

due in an hour pls help!!


just tell me where to put the points

Answers

   Translation is defined as an interpretation into another language or context. The Spanish word "bueno," which translates to "good," serves as an illustration. A translation can involve explaining to a parent the significance of their teen's expression.

What is the translational equation?  

The translation equation or formula is written as g(x) = f(x+k) + C.

Example

(x -3, y - 2)

x - 3 y - 2 ;

x-3 y-2

x-3y - 2

x² -  x - 6 =0

-x + 3 > 2x + 1

line(1, 2),(3 ,1)

f(x) = x³

prove tan²(x) - sin ²(x) = tan²(x) sin²(x)

d /dx(3x + 9/2 -x)

(sin²(0))

sin (120)

lim(x -> 0 (xln(x))

= 0 3/2n.

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PLSSSSSS ANSWER SOON!!!!!!!
There is a pic
solve for P

Answers

Answer:

48x

Step-by-step explanation:

15+2+7+15+2+7=48 + x = 48x

Hope this helps!

the masses of 4 different animals from the zoo are shown in the table below. convert each measure to pounds. then sort the animals from least to greatest weight.
Animals: (mass kg)
brown bear: 272.16 kg
giraffe: 1,124.0 kg
lion: 226.8 kg
rhinoceros: 1,587.6 kg

Answers

1. When we convert each measurement to pounds, we have

Brown bear: 600 poundsGiraffe: 2478 poundsLion: 500 poundsRhinoceros: 3500.1 pounds

2. When we arrange from least to greatest, we have

Lion, brown bear, giraffe, rhinoceros

1. How to convert kilogram to pound

Coversion scale

1 kg = 2.20462

With the above scale, we can convert each measurement to pound as follow:

I. Brown bear

1 kg = 2.20462

Therefore,

272.16 Kg = 272.16 × 2.20462

272.16 Kg = 600 pounds

II. Giraffe

1 kg = 2.20462

Therefore,

1124.0 Kg = 1124.0 × 2.20462

1124.0 Kg = 2478 pounds

III. Lion

1 kg = 2.20462

Therefore,

226.8 Kg = 226.8 × 2.20462

226.8 Kg = 500 pounds

IV. Rhinoceros

1 kg = 2.20462

Therefore,

1587.6 Kg = 1587.6 × 2.20462

1587.6 Kg = 3500.1 pounds

2. How to arrange for least to greatest

Brown bear: 600 poundsGiraffe: 2478 poundsLion: 500 poundsRhinoceros: 3500.1 pounds

Thus, arranging from least to greatest, we have

Lion, brown bear, giraffe, rhinoceros

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For Point A (m,n) to fall in the correct quadrant, if the value of m is 6, the 6 would be
, and if the value of n is 3, the 3 would be

6 positive or negative
3 positive or negative

Here's the picture if you are confused I guess

Answers

6 must be negative and 3 is also negative

Provide an example and explain the steps to convert a fraction into a percent.

Answers

Fractions can be converted to percentages by multiplying by 100. ...
A fraction is one way of writing a division. ...
Convert 2⁄5 to a percentage. ...
Divide the numerator (2) by the denominator (5). ...
To convert 2⁄5 to a percentage, divide 2 by 5 and then multiply the result by 100.

Photo plus charges $2 for each print plus a $6 processing fee. Picture time charges $3 for each print plus a $4 processing fee. for what number of prints is the price the same at both stores

Answers

I think the answer is 15 or 16.
I think the answer is 15 or 16.

what is 4.5=m + 2.75

Answers

4.5 = m + 2.75

Solving for m:

Subtract 2.75 from both sides:

4.5 - 2.75 = m + 2.75 - 2.75

1.75 = m

m = 1.75

10) Find DF if LF = 2X - 8 and LD = X - 3 ​

Answers

Answer:

  DF = 4

Step-by-step explanation:

You want DF when L is the midpoint, LD = x-3 and LF = 2x-8.

Congruent segments

Segments DL and LF are marked the same, so are congruent. Using the given expressions, we have ...

  LF = LD

  2x -8 = x -3

  x = 5 . . . . . . . . add 8-x to both sides

Then the measures of the segments are ...

  LF = 2(5) -8 = 2

  LD = 5 -3 = 2

  DF = DL +LF = 2 +2 = 4

The length of DF is 4 units.

Please Help Please ASAP

Answers

it is the bottom right graph

Please help CORRET ANWSERS ONLY!

Answers

Answer:uhh

Step-by-step explanation:

What number should be subtracted from both sides of the following equation to solve for x?x + 27 = 303027573

Answers

Step 1

Given;

[tex]x+27=30[/tex]

Required; To solve for x

Step 2

Add -27 to both sides

[tex]\begin{gathered} x+27-27=30-27 \\ x=3 \end{gathered}[/tex]

Answer; The number that should be subtracted from both sides of the equation is 27

You would minus 27 from both sides.

Look at the table below. Which of the following is the constant rate of change?

Answers

Given data:

The first value of x is a=-16.

The first value of y is b=20.

The second value of x is c=-12.

The second value of y is d=15.

The expression for the rate change is,

x=(d-b)/(c-a)

Substitute the given values in thhe above expression.

x=(15-20)/(-12+16)

=-5/4

Thus, he constant rate of change is -5/4.

Triangle ABC is shown below, with the angle measures as marked.
What is the measure of Angle A and B?

Answers

The measure of Angle A and Angle B are 54° and 122° respectively.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In triangle ABC,

The measure of angle A = (n + 20)°

The measure of angle B = (3n - 10)°

The measure of angle C = n°

Now,

The sum of all the angles of the triangle = 180°

So, we can formulate;

(n + 20)° + (3n - 10)° + n° = 180°

Solve for n as;

n + 20 + 3n - 10 + n = 180

5n + 10 = 180

5n = 180 - 10

5n = 170

Divide by 5, we get;

n = 170/5

n = 34

Thus, The measure of angle A = (n + 20)°

                                               = 34 + 20

                                               = 54°

And, The measure of angle B = (3n - 10)°

                                             = 3 x 34 + 20

                                             = 102 + 20

                                             = 122°

Therefore,

The measure of Angle A and Angle B are 54° and 122° respectively.

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Other Questions
Before answering the question, read the following excerpt.Whatever the reason, it is clear that the empires of Byzantium and Persia failed to keep in check the steppe peoples within and beyond their borders in the late sixth and early seventh centuries. The Turks, Avars, and Arabs are all able to make significant encroachments over the course of this period. The same can be said for China where the Wei dynasty collapsed in 534 and decades of infighting ensued, which was reduced somewhat by the Sui dynasty (589618) but only properly brought under control with the establishment of the Tang dynasty by Emperor Gaozu (61826). The Persian Empire suffered the most, since its capital, Seleucia-Ctesiphon, was dangerously close to the steppe lands, and the deserts and mountains within its realm favored regional autonomy and limited centralization.Ignominious [shameful] defeat at the hands of Emperor Heraclius and an ensuing civil war fatally weakened the regimes ability to respond when the Arabs overran their lands. The capitals of the Byzantine and Chinese empires, on the other hand, were far from the steppe and extremely well defended, and the empires themselves, organized around large bodies of water (the Mediterranean Sea and the Yellow and Yangtze Rivers, respectively), were reasonably well integrated. This meant that though they also suffered many defeats at the hands of steppe raiders, they were able to weather the storm. The Avars and Turks clearly had ambitions to penetrate further into the lands of Byzantium and Persia, but they were coming from the difficult northern and eastern sides of the two empires, where they faced substantial man-made and natural obstacles, whereas the Arabs were directly adjacent to the soft southern underbellies of these empires, and so it was they who ultimately triumphed in this seventh-century great game.From Robert Hoyland's In God's Path: The Arab ConquestFrom this excerpt, what argument can be made about imperial expansion and conflict?Choose 1 answer:Choose 1 answer:(Choice A)AEmpires grow weak when they overextend themselves militarily, opening themselves up to invasion from outside forces or infighting(Choice B)BBecause of their strategy of raiding, steppe peoples do not have stable enough economies to run an empire(Choice C)CThe best borders for an empire are natural borders: mountains, rivers, and oceans(Choice D)DRegional autonomy always leads to greater imperial stability Which of these equations is perpendicular to the midpoint of the line segment that contains the point (-4,4) and (2,-2)? I need help with this you own a pet store that sells fish tank you brought a fish tank for $35 and are going to mark it up 20% what is the selling price going to be on the fish tank Hi. Been out due to medical issues trying to catch-up and learn my work. Thank you in advance A single die is rolled twiceFind the probability of rolling a 6 the first time and a 1 the second time. An e-verify case must be created no later than the end of ___ business days after the employee begins work for pay. A recipe uses 6 cups of flour to 1 1/10 cups of milk. If you have 2 cups of flour, how much milk should you use? 9. Which of the following actions would NOT help identify your personalethics?a. Describe yourself.b. Conduct a genetic study of your extended family.c. Identify the influences of your work environment.d. Prepare a list of values that are most important to you. The simple interest charged on a 65 day loan of $1250 is $7.75. Find the annual simple interest rate in precent for this loan round to the nearest tenth of a percent. Use 360 days in 1 year what characterizes all ecdysozoans? ecdysozoans practice suspension feeding. ecdysozoans reproduce clonally (asexually). ecdysozoans are sessile (don't move) in the adult stage. ecdysozoans grow by molting. Writing a research based informative essay about language essay Poikilotetherms - how they use behavior to maintain body temperature A rectangle is bounded by the x-axis and the semicircle y = 49 x2 What length and width should the rectangle have so that its area is a maximum? The radius, R, of a sphere is 5.7 cm. Calculate the sphere's volume, V.Use the value 3.14 for r, and round your answer to the nearest tenth. (Do not round any intermediate computations.) If you were in Brian's shoes (alone, starving and lost) when he was at the raspberrybush, what would you have done? Which type(s) of genetic material can viruses have? Check all that * 5 points apply. [4 answers] Use the cross Products Property to solve the proportions.1. 3/4 = v/142. 5/n = 16/32 A circle has a diameter of 12 inches. Find its exact and approximate circumference and area. What is the magnitude of the x-component of force ?