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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.

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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,

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

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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.