Find three consecutive even integers such that the sum of the squares of the first two is four less than twice the square of the third.

Answers

Answer 1

Answer:

the three consecutive even integers are -2, 0, 2

Step-by-step explanation:

Let the first even integer = n

Let the second even integer = n + 2

Let the third even integer = n + 4

From the given statement, we form the equation below

(n²) + (n + 2)²  + 4 = 2(n + 4)²

Expand this equation;

n² + (n + 2)(n + 2) +  4 = 2(n + 4)(n + 4)

n² + n² + 2n + 2n +  4 +  4 = 2(n² + 4n + 4n + 16)

2n² + 4n + 8 = 2(n² + 8n + 16)

2n² + 4n  + 8 = 2n² + 16n + 32

collect like terms together;

2n² - 2n² + 4n - 16n = 32 - 8

- 12n = 24

-n = 24/12

-n = 2

n = -2

Second integer = n + 2

                          = -2 + 2 = 0

Third integer = n + 4

                      = -2 + 4

                      = 2

Therefore, the three consecutive even integers are -2, 0, 2

Answer 2

The three consecutive even integers are -2, 0, 2

The calculation is as follows:

Let us assume the first even integer = n

Let us assume the second even integer = n + 2

Let us assume the third even integer = n + 4

Now

[tex](n^2) + (n + 2)^2 + 4 = 2(n + 4)^2\\\\n^2 + (n + 2)(n + 2) + 4 = 2(n + 4)(n + 4)\\\\n^2 + n^2 + 2n + 2n + 4 + 4 = 2(n^2 + 4n + 4n + 16)\\\\2n^2 + 4n + 8 = 2(n^2 + 8n + 16)\\\\2n^2 + 4n + 8 = 2n^2 + 16n + 32\\\\2n^2 - 2n^2 + 4n - 16n = 32 - 8\\\\- 12n = 24[/tex]

n = -2

Now  

Second integer = n + 2

= -2 + 2 = 0

And,  

Third integer = n + 4  

= -2 + 4

= 2

Learn more: brainly.com/question/17429689


Related Questions

Can somebody plz help!!
Marlena has a bag of coins the bag contains 8 quarters 10 dimes 4 nickels and 2 pennies she will randomly select a coin from the bag what is the probability that marlena will select a nickel? ​
A 1/12
B 1/3
C 1/6
D 1/5

Answers

The answer would be 4/24!! You add up all the numbers, 24. Then you see how many Nickels are in the bag, 4. So 4/24!!!

Evaluate the expression when m=25 and n=2

Answers

Answer:

what the expression, lmk in comments and then i will help you :)

Step-by-step explanation:

x^3 + 5x^2 + 2x + 10 = 0

Answers

Let's solve your equation step-by-step.

x3+5x2+2x+10=0

Step 1: Factor left side of equation.

(x+5)(x2+2)=0

Step 2: Set factors equal to 0.

x+5=0 or x2+2=0

x=−5

Answer:

x=−5

is a soup bowl a gallon quart pint or cup​

Answers

Answer:

their are different sizes of soup bowls

Pls be honest I’ll mark u

Answers

Answer:

C) 10

Step-by-step explanation:

The answer to this is 10.

How many 1 1/2 -pound loaves of bread can be made from 9 pounds of dough?

Answers

Answer:

6

Step-by-step explanation:

You divide 9 by 1 1/2.

9/45 how to simplify to it lowest term​

Answers

Answer:

1/5

Step-by-step explanation:

divide numerator and denominator by 9.

(Because that will go into both 9 and 45.)

9/45 = 1/5

Which notation describes {1, 2, 3}

Answers

first three natural numbers

First, three natural numbers notation describes {1, 2, 3}.

What is set notation?

In mathematics, set notation is essentially a list of numbers, things, or results. Curly brackets, often known as braces, are used for set notation. The items included between brackets are referred to as elements of a set and are not required to be in any particular order.

Given, a set  {1, 2, 3}

Since a set notation used to represent the elements of a set is the curly brackets { }. An example of a set is A = {a, b, c, d}. Here the set is represented with a capital letter, and its elements are denoted by small letters.

These given number best fit in the category of natural numbers.

Therefore, First, the notation for three natural numbers shows  {1, 2, 3}.

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A can of soup contains 1 1/4 cups. A serving is 1/2 of a cup. How many servings are in the
can?
1 3/4
3
21/2
2

Answers

Answer:

c 2 1/2

Step-by-step explanation:

Answer:

I think it is b. 3. Im not sure though.

Step-by-step explanation:

Why does 3x4 and 3x4 the same answer?

Answers

Answer:

bc the are both the same numbers. So the answer is 12. :>

Step-by-step explanation:

Answer:

because thay are the same problom

Step-by-step explanation:

3x4 is  12

In the figure, ΔABC~ΔADE. Find the length of line segment DE.

Answers

Answer:

13

Step-by-step explanation:

[tex]\triangle ABC \sim \triangle ADE => \frac{x}{x+10}=\frac{x+3}{x+16}=>x^{2}+16x=x^{2}+13x+30=>3x=30=>x=10\\DE=x+3=>DE=13[/tex]

A movie store sells DVDs for $16 each. What is the cost, "C", of "n" DVDs? Is the data Continuous or Discrete?


A. C = 16n; Continuous

B. C = 16 + n; Discrete

C. C = 16n; Discrete

D. C = 16 + n; Continuous

Answers

Answer: C = 16n; Discrete

Step-by-step explanation:

From the question, a movie store sells DVDs for $16 each. The cost, "C", of "n" DVDs will be calculated by multiplying $16 by n. This will be:

C = 16 × n

C = 16n

This is dicrete as the valuea that'll be gotten will take some particular values.


What is the approximate area of the shaded sector in the circle shown below? 145°
A. 34.6 in2
B. 4.68 in 2
C. 17.3 in2
D. 9.36 in2

Answers

Answer: 17.3 in 2

Step-by-step explanation

The approximate area of the shaded sector is 34.6 in2.

How to calculate the surface area of a composite figure?

Surface area are derived for some standard shapes like circle, triangle, parallelogram, rectangle, trapezoid, etc.

When some shape comes which isn't standard figure, then we find its area by slicing it (virtually, like by drawing lines) in standard shapes. Then we calculate those composing shapes' area and sum them all.

Thus, we have:

[tex]\text{Area of composite figure} = \sum (\text{Area of composing figures})[/tex]

That ∑ sign shows "sum"

We are given that;

Angle = 145°

Now,

The area of a sector of a circle is given by the formula A = (θ/360)πr2, where θ is the central angle in degrees and r is the radius of the circle. In this case, θ = 145° and r = 7 in.

Plugging these values into the formula, we get: A = (145/360)π(7)^2. Simplifying, we get: A = 0.4028π(49). Using a calculator, we get: A ≈ 34.6 in2.

Therefore, by the area the answer will be 34.6 in2.

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Which expression is equal to 27 when x = -6?
A (-x)2 - 9
B (-2x)2 - 120
C 10(-x) +33
D 3(x-4) + 3

Answers

Answer:

C

Step-by-step explanation:

i got C & D to both be -27 but I think I made a mistake in C w the negatives so I believe it is C.

I hope this helps, have a great day/ night :)

Please help I will mark brainleist if correct!!

Answers

The answer is b. 1/3, because the x value multiplied by 1/3 will equal the y value below it.

Under her cell phone plan, Lily pays a flat cost of $55.50 per month and $4 per
gigabyte. She wants to keep her bill at $63.10 per month. Write and solve an equation
which can be used to determine x, the number of gigabytes of data Lily can use while
staying within her budget.
equation:
answer x=

Answers

Answer:

Equation : y = 4x + 55.50

x = 1.9 gigabytes

Step-by-step explanation:

Given that:

Flat fee per month = $55.50

Cost per gigabyte = $4

Let,

x be the number of gigabytes.

y be the total cost

y = 4x + 55.50

Lily wants to keep her bill $63.10

63.10 = 4x + 55.50

63.10 - 55.50 = 4x

4x = 7.60

Dividing both sides by 4

[tex]\frac{4x}{4} = \frac{7.60}{4}\\x=1.9[/tex]

Hence,

Equation : y = 4x + 55.50

x = 1.9 gigabytes

Answer:

Equation: 4x+55.5=63.1

Answer: x=1.9

Sarah used 3 pound of blueberries to make 1 cup of jam. How many pounds of blueberries would she need
42
to make a cup of jam?

Answers

Answer:

126 pounds of blueberries

Step-by-step explanation:

1cup of jam=3pounds of blueberries

42cups of jam=?

42 X 3=126

A man needed to sell a car. He priced it at 3500 the first day. The second day he reduced the price by 15%. What was the price of the car after this reduction?

Answers

Answer:

Step-by-step explanation:b

Can someone help on how many dresses does Lucy sew in a hour?​

Answers

U multiply those fractions 12/28 and then u just simplify it
16/21
dresses

Explanation:
The ratio of time required to dresses made is
3/4•k hours: 4/7 • k dresses for any constant k.


Specifically, if we want 1 hour then the letter K will need to be 4/3.
.
So
4/7 x 3/4= 16/21 in an hour.

I hope this make sense LOL!

Which soap deal has the lowest price per ounce?



$5.50 for 13.0 oz


$5.75 for 14.0 oz


$3.45 for 3.5 oz


$5.25 for 12.0 oz

Answers

Answer:

The 5.75 for 14.0 oz

Step-by-step explanation:

Hope this helps, Have an amazing day!!!

Find the zeros of the function.

Enter the solutions from least to greatest.

f(x) = 5x^2 - 20

lesser x =

greater x =

Answers

Answer:

lesser x = -2

greater x = 2

Step-by-step explanation:

The values of a function f(x) are the values of x for which f(x) = 0.

In this question:

[tex]f(x) = 5x^2 - 20[/tex]

So, finding the zeros:

[tex]5x^2 - 20 = 0[/tex]

[tex]5x^2 = 20[/tex]

[tex]x^2 = \frac{20}{5}[/tex]

[tex]x^2 = 4[/tex]

[tex]x = \pm \sqrt{4}[/tex]

[tex]x = \pm 2[/tex]

So

lesser x = -2

greater x = 2

A delivery company has 18 vehicles in its fleet.

It has 8 vans and 10 trucks.

All 18 vehicles are on the road every working day.

The company is reviewing its fuel expenses and therefore

gathers some information about each type of vehicle.

Average distance Average distance

Type of vehicle

travelled ber day (in km) travelled per litre (in km) All the vehicles use the

Van

198

9

same type of fuel at

£1.29 per litre.

Truck

620

6.2

Use this information to work out the total fuel bill for 1 working day.

You must show all your working.

Answers

Answer: £1517.04

Step-by-step explanation:

The fuel expenses for the vans will be calculated as:

Vans:

Since the average distance travelled per day is 198km and the average distance travelled per litre is 9km, the van would use:

= 198/9

= 22 litres

Since there are 8 vans, they'll use:

= 22 × 8 = 176 liters

Trucks:

Since the average distance travelled per day is 620km and the average distance travelled per litre is 6.2km, the truck would use:

= 620/6.2

= 100

Since there are 10 trucks, they'll use:

= 100 × 10 = 1000 liters

The amount of liters for both the van and the truck will be:

= 176 liters + 1000 liters

= 1176 liters

The fuel cost will then be:

= 1176 × 1£1.29

= £1517.04

Michelle is working on a design for a new building. She has built a model of the building according to the client's specifications.
The height of the model is 15 inches, the slant height of the model is approximately 17 inches, and the base has a length of
14 inches and a width of 20 inches.
w
Note: picture not drawn to scale.
Michelle must order appropriate equipment to heat and cool the building, so she must use the model to determine how much
space there will be inside. What is the volume of her model? (Round to the nearest hundredth, if necessary.)
OA
5,600 cubic inches
OB
1,400 cubic inches
OC. 280 cubic inches
OD
980 cubic inches

Answers

Answer:

Step-by-step explanation:

980

Help please. Which polynomial represents the sum below? (20 points)

Answers

Answer:

b option ..............

At a local basketball game, all tickets are the
same price and all souvenirs are the same price.
Mr. Smith bought 2 tickets to this basketball game
and 1 souvenir for a total of $17.25. Ms. Lockhart
bought 5 tickets to the same game and 2 souvenirs
for a total of $42.00. How much was a ticket to
this game?

Answers

A - Mr. Smith

17.25 ÷ 3

= $5.75 ~ $6 Rounded-Off

B - Ms. Lockhart

42 ÷ 7

= $6

Each Ticket Costs approx. $6 Each

plz help!! Describe the transformation from the graph of f(x) = 3x + 4 to the graph of g(x) =f(x) + 2.

Answers

the transformation is translated 2 up

How much time required to complete a10days work if it could complete by 3 worker in 4days and 6worker in 3.05 days,if 5 workers is involved in it? please reply​

Answers

Answer:

This seems to be a linear relationship:

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

We know that 3 workers can complete the job in  4 days.

Then if we define W as the rate at which a single worker can complete the work, we have the ordered pair (3 workes, 4 days)

And we also know that 6 workers can finish the job in 3.05 days, then we also have the ordered pair (6 workers, 3.05 days)

Then using these two, we can find the slope of the line:

a = (3.05 days - 4 days)/(6 workers - 3 workers) = -0.35 days/worker.

Then we have the equation:

y = (-0.35 days/worker)*x + b

Where:

y represents the time to complete the job

x represents the number of workers.

b is the y-intercept, to find the value, we could just replace one of the points in the equation, for example with the point (3 workes, 4 days) we need to replace x by 3 workers, and y by 4 days:

4 days = (-0.35 days/worker)*3 workers + b

4 days = -1.4 days + b

4 days + 1.4 days = 5.4 days  = b

then the equation is:

y = (-0.35 days/workers)*x + 5.4 days.

Now we can find the number of days needed for 5 workers to finish the job, we just need to replace x by 5 workers:

y = (-0.35 days/workers)*5 workers + 5.4 days

y = 3.65 days.

is -9 greater thank or less than 8

Answers

It’s less than 8 because -9 is a negative and 8 is positive.

Jefferson is plotting the vertices of an isosceles triangle on a coordinate graph. He has plotted the two points shown. Where would he plot the three point?

Answers

Answer:

4,2

Step-by-step explanation:

Answer:

It is 4, 2

Step-by-step explanation:

Trust me

SOLVE FOR X AND Y !! WILL GIVE BRAINLIEST

Answers

Answer:

x=21, y=17

Step-by-step explanation:

180-42= 138

2x+138=180

2x= 42

x= 21

8y+2+2x=180

8y+2 + 42=180

8y= 136

y= 17

Answer:

x=21, y=68

Step-by-step explanation:

We're given that the quadrilateral on the left is a parallelogram as indicated by the arrow markings on the sides. We're also told that the angle on the right is 42 degrees. So, we can find the bottom right angle in the parallelogram by subtracting 42 from 180, because it forms a straight angle. 180-42 is 138. By the alternate interior angles theorem, 8y+2=138, because 138 is also the angle measure of the opposite corner. we also know that the bottom left angle in the parallelogram is the same as 2x. by the alternate interior angles theorem. Notice how the sides of the parallelogram with two arrow markings are parallel, which means that the bottom left angle and the 42 degree angle are congruent, or have the same measure, because of the parallel lines. This means that 2x=42, and the bottom left angle is 42. We can solve for x and y with simple algebra now. 8y+2=138, 8y=138-2, 8y=136, y=68. 2x=42, x=42/2, x=21. So, x is 21 and y is 68.

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