The difference of the squares of two positive consecutive even integers is 20 . find the integers. use the fact that, if x represents an even integer, then xplus 2 represents the next consecutive even integer.

Answers

Answer 1

If x is the first number, x+2 is the next consecutive even integer. The difference (subtraction) of their squares equals 20. Therefore:
(x+2)²-x²=20...expand this:
x²+4x+4-x²=20
x²+4x+4-x²=20
4x+4=20
4x=16
x=4. Therefore the next consecutive even integer is x+2=6.
To check: 6²-4² must equal 20
36-16=20 check!

Answer 2

The positive even numbers are 4 and 6.

Equation

State of quality between two expressions consisting of variable and/or number.

Given

The difference of the squares of two positive consecutive even integers is 20.

To find

The number will be

How do find the numbers?

The difference of the squares of two positive consecutive even integers is 20.

Let x be the even number and positive consecutive even is (x+2)

Then according to the condition

[tex]\begin{aligned} (x+2)^{2} -x^{2} &=20\\x^{2} +4x+4-x^{2} &= 20\\4x &= 20-4\\4x &= 16\\x &= \dfrac{16}{4}\\x &= 4\end{aligned}[/tex]

Then the positive even numbers are 4 and 6.

More about the equation link is given below.

https://brainly.com/question/2263981

Related Questions

Find the domain and range of the relation and determine whether it is a function. y=x2-3

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is that supposed to be x squared or 2x

A relation is a set of pairs, like {(2, 1), (5, 9), (3, 7)}

If the first coordinate is not repeated, like in this example, were we have only (2, 1) and not also (2, 8), for instance, then the relation is called a function.

A relation sometimes has too many pairs to be expressed by listing all of them. in such cases we use formulas which describe all the pairs.

We are given the relation is [tex]y=x^2-3[/tex]. This means that all pairs of this relation, are such that the second coordinate, is the first one squared, minus 3.

So each pair of this relation is : [tex](x, x^2-3)[/tex]

For any x, [tex]x^2-3[/tex] is only one value,

for example, if x=10, y can only be [tex]x^2-3=10^2-3=97[/tex]

We cannot possibly have both (10, 97) and (10, 16), for example, because the formula does not allow that.

this means 10 does not repeat as a first pair in this relation, and nor does any other value.

this makes the relation a function

The Domain is the set of all possible values x can be. Clearly, x can be any value, because no x makes [tex]x^2-3[/tex] undefined

Answer: The relation is a function, with Domain all real numbers

420,983 estimate it then estimate 39,932 then you have to add thoes then you have to add that and that and then you have to add 420,983 plus 39,932 and see if your answer is close to the estimate

Answers

Final answer:

By rounding numbers to the nearest large place value, we estimated the sum of 420,983 and 39,932 as 460,000. The exact sum is 460,915, demonstrating that our estimation was a close approximation to the actual value.

Explanation:

To estimate the sum of 420,983 and 39,932, we can round these numbers to the nearest ten thousand and thousand, respectively. Rounding 420,983 to the nearest ten thousand gives us 420,000, and rounding 39,932 to the nearest thousand gives us 40,000.

Now, we add the estimated numbers: 420,000 + 40,000 = 460,000.

To find the exact sum of 420,983 and 39,932, we add the two numbers together without estimating: 420,983 + 39,932 = 460,915.

Comparing our estimate of 460,000 with the exact answer of 460,915, we can see that our estimate is very close to the exact amount, showing that our estimation was a good approximation. To find the estimate for 420,983, we round it to the nearest 100,000, which is 400,000. For the estimate of 39,932, we round it to the nearest 10,000, which is 40,000. When we add these two estimates, we get 440,000. Next, we add the actual numbers 420,983 and 39,932, which gives us 460,915. Comparing this with our estimate, we can see that our answer is close to the estimate.

Final answer:

To estimate the sum of 420,983 and 39,932, round each number to the nearest thousand and add them together. Then compare the estimate with the actual sum.

Explanation:

To estimate the sum of 420,983 and 39,932, we can round each number to the nearest thousand. 420,983 rounded to the nearest thousand is 421,000, and 39,932 rounded to the nearest thousand is 40,000. Now, we can add these rounded numbers together: 421,000 + 40,000 = 461,000. This is our estimate for the sum.

Next, we add the actual numbers 420,983 and 39,932 together: 420,983 + 39,932 = 460,915. Finally, we compare our estimate (461,000) with the actual sum (460,915) to see if they are close. In this case, our estimate is slightly higher than the actual sum.

3x-2y=-39 and x+3y=31 solution using elimination

Answers

This is hard to write... I hope this makes sense to you...
3x-2y=-39
x+3y= 31
We want to use elimination therefor, we need to either get our x or our y to add together to get zero.
To do this, we will multiply -3 to (x=3y=31)
NEW EQUATION
3x-2y=-39 PLUS
-3x-9y= -93 Equals
Answer: -11y= -54
y= 4.9
Plug in to solve for x (put new y in)
3x-2(4.9)=-39
x= -9.73

Solving for x on 3x - 2y = -39:
First, we must add 2y to both sides.
3x - 2y + 2y = -39 + 2y
3x = 2y - 39
Next, we divide both sides by 3.
3x/3 = 2y - 39/3
Answer: 2/3y - 13

Solving for y on x+3y=31:
First, we must add -x to both of the sides.
x + 3y + -x = 31 + -x
3y = -x + 31
Next, we must divide both sides by 3. (Like last time.)
3y/3 = -x + 31/3
Answer: y = -1/3x + 31/3

I hope this helps! (And what you're looking for! :>)

Question #12 assessment progress 30 percent suppose that the functions r and s are defined for all real numbers x as follows. =rx4x2 =sx2x

Answers

uwixdybuyxbdsugvdcadugfcvsd djhcbk sduhkccbdsyiobfcdyifcbdsyicfds sdfchibsdcioydsbcfisdhfcbdsuyfcdsoufcs douhfcw dgc csduoh cdusdoycfvds cqgv yvchv dsh csdcdscbj k adc iyvdaoiyc vaduvc adsugkc ouysd c ozdyibc odsiydcbyadoidcdadcbeqdc

Solve the equation a+b-c=180 for c

Answers

We need to make sure c is on one side:

a + b - c = 180

So let’s subtract a and b from both sides:

-c = -a -b + 180

Now, multiply both sides by -1:

c = a + b - 180

Hope this helps!

Answer:

Step-by-step explanation:

we are given the equation a+b-c=180

Now to solve it for c we need to isolate the c

first step can be addition of c to both side

a+b-c+c=180+c

a+b=180+c

now in second step we subtract 180 from both sides to get

a+b-180=180+c-180

a+b-180 = c

c= a+b-180

Harvey collects rare marbles. He has 112 marbles in his collection. If he uses Seven Trees to hold all of the marbles, how many marbles will he display on three trays? Is tray hold an equal number of marbles answers at brainly.com

Answers

three trays will hold 48 marbles because each treat will be able too hold 16 marbles.

Final answer:

Harvey has 112 marbles distributed equally across seven trays. Each tray holds 16 marbles, therefore, on three trays, Harvey will display a total of 48 marbles.

Explanation:

Harvey has 112 marbles in his collection and uses seven trays to hold all of the marbles. To find out how many marbles Harvey will display on three trays, we need to divide the total number of marbles by the total number of trays to find out how many marbles each tray holds.

First, divide 112 marbles by 7 trays to find out how many marbles go on each tray. The calculation is as follows:

112 marbles ÷ 7 trays = 16 marbles per tray

Now that we know each tray holds 16 marbles, to find out how many marbles are displayed on three trays, we multiple the number of marbles per tray by the number of trays:

16 marbles per tray × 3 trays = 48 marbles

Therefore, Harvey will display 48 marbles on three trays.

which system of equations represents the matrix shown below? See picture

Answers

Answer to this question is B

B is the correct solution. A shows a negative 7 and c and d show a z when there is none on the 1st equatiom

If l and m are parallel, which pairs of angles are supplementary?

Answers

Pairs:

1 and 2

3 and 7

6 and 7

1 and 6

So therefore the answers would be:

1 and 2

3 and 7

6 and 7

Hope This Helps :)

Please mark as brainiest

Answer:

1 and 2

3 and 7

6 and 7

Step-by-step explanation:

What type of function has an inverse that is also a function?

Answers

inverse proportional function

Which grouping shows duple meter?
a. one two three four five, one two three four five
b. one two three four five six, one two three four five six
c. one two three, one two three
d. one two, one two, one two, one two?

Answers

Duple meter is a musical meter considered by a main division of 2 beats to the bar, typically specified by 2 and multiples (simple) or 6 and multiples (compound) in the upper figure of the time signature. It is ONE TWO, ONE TWO, ONE TWO, ONE TWO which is letter d.

Answer: D: ONE TWO, ONE TWO, ONE TWO, ONE TWO

Step-by-step explanation:

how would you solve 3x-4=9x-21

Answers

3x - 9x = -21 + 4
-6x = -17
x = -17/-6
x = 17/6

3x - 4 = 9x - 21

Subtract 9x from both sides.

3x - 9x - 4 = -21

Add 4 to both sides.

3x - 9x = -21 + 4

Simplify.

-6x = -17

Divide both sides by -6.

x = 17/6 AND 2 5/6

~Hope I helped!~

What constant would be added to the expression x2−7xx2−7x in order to make it a perfect square?

Answers

ok

assuming ya mean [tex]x^2-7x[/tex]
since the quadratic coefient is 1, take 1/2 of the liner coeficient and square it
the linear coefient is -7
half of that is -7/2
squared we get 49/4
add that to get
[tex]x^2-7x+\frac{49}{4}[/tex]
it factors to
[tex](x-\frac{7}{2})(x-\frac{7}{2})[/tex] or [tex](x-\frac{7}{2})^2[/tex]

you must add [tex]\frac{49}{4}[/tex] to make it a perfect square

The width of a rectangle is one half it's length. The perimeter is 54 cm. What are the width and the length of the rectangle?

Answers

If the width is w and the length is l, we have l/2=w and 2w+2l=54 (given the formula for the perimeter of a rectangle). Plugging l/2=w into the second equation, we have 2(l/2)+2l=54=l+2l=3l. Dividing both sides by 3, we get l=18. Since w=l/2, w=18/2=9

Can anyone help me with this, and maybe explain it?

Answers

A linear equation has the form y = mx + b where m and b are real numbers. The value of b (you may know this as the y-intercept) is the value of y when x = 0. The value of m (the slope) is the RATE of increase; it tells how much y changes when x increases by 1.

In this problem, x represents the number of years since 2000, so x = 0 represents the year 2000.

Midwest: the value of y begins with 64.4 and increases by 0.3 each year.
y = 64.4 + 0.3x

West: the value of y begins with 63.2 and increases by 1.0 each year.
y = 63.2 + 1.0x

Find the quotient of 5/31 divided by 15/23. Reduce your answer to the lowest fraction.

Answers

Since (5/31)/(15/23)=(5/31)*(23/15) (by finding the reciprocal and multiplying), we get 115/465. Since they are both divisible by 5, we learn that 5 goes into 115 23 times and into 465 93 times (since 465/5=93), resulting in 23/93. Since 23 is a prime number (their only factors are 23 and 1), we end there

what is 4 less than three sevenths of y written as an algebraic expression

Answers

IT means that u need to subtract 4 from 3/7 of y i.e
3/7 of y = 3Y/7
subtract 4 from it we get
{(3Y/7)- 4}

hope this helps, Gastondekota! :-)

Final answer:

The algebraic expression for 'four less than three sevenths of y' is (3/7)y - 4. This involves finding three sevenths of y and then subtracting four.

Explanation:

The phrase 'four less than three sevenths of y' is asking us to first find three sevenths of y, and then subtract four from that number. In algebra, this is represented as (3/7)y - 4. The expression (3/7)y means 'three sevenths of y', and the '- 4' indicates we are finding 'four less than' this quantity.

Learn more about Algebraic Expression here:

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matt ryan throws a ball 26 yards how many inches did he throw

Answers

936 inches. One yard alone is 36 inches so 26 yards is a very large number!

Use compatible numbers to solve the problem 326 divided by 44.
A 320 divided by 32 = 10
B 320 divided by 40 = 8
C 330 divided by 30 = 11
D 352 divided by 44 = 8

Answers

b. is the answer to this problem

Is the correct answer E)1 ?

Answers

It's either B C or D, the question asks which "values", meaning there are multiple values.

The correct answer is A

This is because its asking for which x-values would the y's be be constant. This would be the numbers greater than 2 because the line is constant.

Use the four-step procedure to solve the following problem. How much water must be added to a gallon of 10% saline solution to create a 2% solution?

Answers

We have 1 gallon of 10% saline.
How much water (x liters of 0% saline) must be added to make a 2% saline solution?
.10 * 1 + 0x = .02 * (1 +x)
.1 = .02 + .02x
.08 = .02x
x = 4 gallons of water must be added

Answer:

4 gallons of water should be added in 10% saline solution.

Step-by-step explanation:

Let x gallon of water is added in one gallon of 10% saline solution.

Therefore total volume of 10% saline solution will become (1 + x) gallons

Since concentration of water is 0% so equation will be

0.10(1) + 0(x) = .02(1 + x)

0.10 = 0.02(1 + x)

1 + x = [tex]\frac{0.10}{0.02}[/tex]

x + 1 = 5

x = 5 - 1

x = 4 gallons

Therefore, 4 gallons of water should be added to 10% saline solution to create 2% solution.

Convert 4 radians to degrees.

Answers

Hello!

To convert radians to degrees, we have to multiply them by [tex]180/ \pi [/tex].
Let's multiply.
[tex]4*180/ \pi [/tex]
≈ 229.18311805

Please note that since we are using [tex] \pi [/tex], we need to use the approximation sign.

4 radians ≈ 229.18311805°

You can feel free to let me know if you have any questions regarding this!
Thanks!

- TetraFish

Kara bought a DVD for $22 and a cd for less then the cost of the DVD. Let c represent the cost of the cd. Write an inequality to show the cost of the cd

Answers

c<d

The cd costs less than the dvd, therefore, the cd is less than (or <) then the dvd

four more than the product of one and a number x

Answers

(X times 1) + 4 will be your answer

hope this helps

Hi there! I don't know if you want the answer or the equation, but I'll put both. :)

The equation would be "4 more" than 1*x. This would be (1 * x) + 4.

The answer to this expression would be x + 4.

Which function below is the inverse of f(x) = x2 − 9? ±square root of the quantity x plus 9 x squared over 9 ±three times the square root of x 1 over quantity x squared minus 9?

Answers

its the first answer

Answer:

Step-by-step explanation:

The first answer.

How do I solve this?? I'm lost

Answers

Your insight that the function values differ by 5 every time is very important. So your f(x) will contain 5x as a term. You have to find a constant to add or subtract to make sure f(1)=-2.

f(x) = 5x-7 does the job.

A recipe calls for of a cup of milk for 11 cookies. How many cups of milk are needed to make 99 cookies?

Answers

9 cups of milk would be needed to make 99 cookies
If 1 cup = 11 cookies then...
99 (cookies we need to make) divided by 11 (cookies each cup) we get 9.

I hope this helps!

9 cups of milk

1 cup for 11 cookies
9 cups for 99 cookies

Which operator is best to determine whether x contains a value in the range of 10 through 57?

Answers

to answer your question the choice is use "and"

the sum of the ages of carl and daria is twice as much as the difference between their ages. how old is daira if carl is nine years old and is
A) older than she?
b) younger than she?
Show your work using algebra

Answers

c + d = 2(c - d)
c = 9

9 + d = 2(9 - d)
9 + d = 18 - 2d
d + 2d = 18 - 9
3d = 9
d = 9/3
d = 3 <=== daira is 3 when carl is 9 years old and older then she

if carl is 9 years old and is younger then she ...I dont really understand this question....carl is 9 and daira is 3......possibly...their is a difference of 6 years in their ages....so if carl is 9 and younger then she, the daira is 6 years older ?? making her 9 + 6 = 15....not sure about this one ....the whole question throws me off

What is the equation of the following graph? Write it in both slope-intercept form and standard form.

Answers

x-intercept : (-2,0) and y-intercept (0,3)

slope = (3-0)/(0+2) = 3/2 = 1.5
b = 3

equation in slope-intercept form
y = 1.5x + 3

equation in standard form
1.5x - y = -3

Final answer:

The equation of the graph is y = 3x + 9 in slope-intercept form and 3x - y = -9 in standard form.

Explanation:

The equation of the graph can be written in slope-intercept form (y = mx + b) and standard form (ax + by = c).

Slope-intercept form: y = mx + bGiven slope (m) = 3 and y-intercept (b) = 9Substituting the values, the equation becomes: y = 3x + 9Standard form: ax + by = cRearranging the equation from slope-intercept form, we get: 3x - y = -9

Learn more about Equation of a straight line here:

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I need help of question #36

Answers

check the picture below.

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The difference of the squares of two positive consecutive even integers is 20 . find the integers. use the fact​ that, if x represents an even​ integer, then xplus 2 represents the next consecutive even integer.

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The difference of the squares of two positive consecutive even integers is 20 . find the integers. use the fact that, if x represents an even integer, then xplus 2 represents the next consecutive even integer.