All categories

2 years ago

Find three consecutive even integers if three times the first integer is two times the third.

Mathematics

2 answers:

drek231 [11]2 years ago

6 0

Using a system of equations, it is found that the three consecutive even integers are -8, -6 and -4.

<h3>What is a system of equations?</h3>

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the three consecutive even integers are represented by:

n, n + 2, n + 4

The first integer is two times the third, hence:

n = 2(n + 4)

2n + 8 = n

n = -8

Thus:

n = -8

n + 2 = -8 + 2 = -6

n + 4 = -8 + 4 = -4

The integers are -8, -6 and -4.

To learn more about system of equations, you can take a look at brainly.com/question/26650649

iren [92.7K]2 years ago

5 0

Answer:

8,10,12

Step-by-step explanation:

Step-by-step explanation:

Smallest Integer = 2x - 2

Middle integer = 2x

Largest integer = 2x + 2

All three are every

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

6x - 6 = 4x + 4 Add 6 to both sides

6x = 4x + 6 + 4 Combine

6x = 4x + 10 Subtract 4x from both sides

6x-4x = 10 Combine

2x = 10 Divide by 2

x = 10/2

x = 5

2x - 2 = 2*5 - 2 = 8

2x = 10

2x+2 12

3*8 = 2*12

24 = 24

So the answers are correct.

You might be interested in

What is the answer to 3/4x+16=22

raketka [301]

x=8 would be the answer.

6 0

3 years ago

Read 2 more answers

In a race, 41 out of the 50 bicyclists finished in less than 38 minutes. What percent of bicyclists finished the race in less th

storchak [24]

For left put 2 on each
On the box over 100 put 82, and put 82 in the box on the right

5 0

3 years ago

Read 2 more answers

6.371 in lowest terms

kozerog [31]

Well you would have to round this 5 and above goes up. Since 1 is lower than 5 that would leave you at 6.37. 7 rounds up so that would change to 6.4. Lastly 4 would round down, So that would leave you with 6. Now 6 is the simplest form but if your looking for rounded to the nearest tenth the answer would be 6.4. If your looking for rounded to the nearest 100th place 6.37. But over all simplest form is 6.

5 0

3 years ago

What is the value of cos(150°)?

baherus [9]

ANSWER

$-\frac{\sqrt[]{3}}{2}$

EXPLANATION

Given

$\begin{gathered} \cos \text{ 150} \\ \end{gathered}$

We can find cos 150 by using

$\begin{gathered} \cos (180-\theta)=-\cos \theta \\ \Rightarrow\cos (180-\theta) \\ =-\cos 30 \end{gathered}$

recall that

$\begin{gathered} \cos 30=\frac{\sqrt[]{3}}{2} \\ \end{gathered}$

Hence,

$\begin{gathered} \cos 150=-\cos 30 \\ =-\frac{\sqrt[]{3}}{2} \\ \end{gathered}$

Therefore, the value of cos 150 is

$-\frac{\sqrt[]{3}}{2}$

4 0

1 year ago

The length of a side of a triangle is 36. A line parallel to that side divides the triangle into two parts of equal area. Find t

sp2606 [1]

Answer:

Length of DE is : 18√2 units

Step-by-step explanation:

The length of a side of a triangle is 36.

To calculate : The length of the segment DE

Now, the two parts of triangle have equal area ∴ Area(ADE) = Area(BDEC)

$\implies Area(ADE)=\frac{1}{2}\times Area(ABC) \\\\\implies \frac{Ar(ADE)}{Ar(ABC)}=\frac{1}{2}$

In ΔABE and ΔABC,

∠A = ∠A (Common angles)

∠ABE = ∠ABC (Corresponding angles are always equal)

By AA postulate of similarity of triangles, ΔABE ~ ΔABC.

Hence by area side proportionality theorem

$\frac{Ar(ADE)}{Ar(ABC)}=(\frac{DE}{BC})^2\\\\\implies \frac{1}{2}=\frac{DE^2}{36^2}\\\\\implies DE^2=\frac{36^2}{2}\\\\\bf\implies DE=18\sqrt{2}\textbf{ units}$

Hence, length of DE is 18√2 units

8 0

3 years ago

Find three consecutive even integers if three times the first integer is two times the third.​

Find three consecutive even integers if three times the first integer is two times the third.