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KiRa [710]
3 years ago
11

The sum of 4 consecutive even integers is -12. find the largest integer.

Mathematics
1 answer:
Ipatiy [6.2K]3 years ago
6 0

Answer:

The largest even integer is 0

Step-by-step explanation:

Given as :

The sum of four consecutive even number = - 12

Let The first even number = 2 x

The second even number = (2 x + 2)

The third even number = (2 x + 4)

The fourth even number = (2 x + 6)

<u>According to question</u>

sum of four consecutive even number = - 12

Or, 2 x + (2 x + 2) + (2 x + 4) + (2 x + 6) = - 12

Or, (2 x + 2 x + 2 x + 2 x) + (2 + 4 + 6) = - 12

Or, 8 x + 12 = - 12

Or, 8 x = - 12 - 12

Or, 8 x = - 24

∴  x = \frac{- 24}{8}

i.e  x = - 3

now, putting the value of x

The first even number = 2 × - 3 = - 6

The second even number = (2 × - 3 + 2) = - 6 + 2 = - 4

The third even number = (2 × - 3 + 4) = - 6 + 4 = - 2

The fourth even number = (2 × - 3 + 6) = - 6 + 6 = 0

So, The largest even integer = 0

Hence, The largest even integer is 0  Answer

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Answer:

x=2 and y=-1

Step-by-step explanation:

If two equations are given, we can solve one of the equation in terms of single variable and put it in the other equation which will further give the value of x and y.

For the given equations:

8x-5y=21              Equation:1

2x+9y=-5             Equation:2

Solving equation multiply equation 2 with 4 on both the sides

8x+36y=-20        Equation 3

Subtracting Equation:3 from Equation:1

8x-5y-(8x+36y)=21-(-20)\\8x-5y-8x-36y=21+20\\-41y=41\\y=-1

Putting value of 'y' in Equation:2 which will give the value of x

2x+9y=-5\\2x+9(-1)=-5\\2x-9=-5\\2x=4\\x=2

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Answer:

Part 1) d(x)=5(\frac{1}{3})^{x} ----> The y-intercept is the point (0,5), graph initially decreases rapidly and then decreases slowly

Part 2) g(x)=(\frac{2}{5})^{x} ----> The y-intercept is the point (0,1), graph initially decreases rapidly and then decreases slowly

Part 3) h(x)=(4)^{x} ----> The y-intercept is the point (0,1),graph initially increases slowly and then increases rapidly

Step-by-step explanation:

Part 1) we have

d(x)=5(\frac{1}{3})^{x}

Find the y-intercept

Remember that the y-intercept is the value of y when the value of x is equal to zero (initial value)

For x=0

Substitute

d(0)=5(\frac{1}{3})^{0}=5

The y-intercept is the point (0,5)

using a graphing tool

see the attached figure N 1

The graph initially decreases rapidly and then decreases slowly

Part 2) we have

g(x)=(\frac{2}{5})^{x}

Find the y-intercept

Remember that the y-intercept is the value of y when the value of x is equal to zero (initial value)

For x=0

Substitute

g(0)=(\frac{2}{5})^{0}=1

The y-intercept is the point (0,1)

using a graphing tool

see the attached figure N 2

The graph initially decreases rapidly and then decreases slowly

Part 3) we have

h(x)=(4)^{x}

Find the y-intercept

Remember that the y-intercept is the value of y when the value of x is equal to zero (initial value)

For x=0

Substitute

h(0)=(4)^{0}=1

The y-intercept is the point (0,1)

using a graphing tool

see the attached figure N 3

The graph initially increases slowly and then increases rapidly

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