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2 years ago

X,y and z are three consecutive even numbers if y^2 - 2 = 2x + 5Z find x,y and z

Mathematics

2 answers:

Sindrei [870]2 years ago

8 0

Answer:

6, 8, 10

Step-by-step explanation:

x, y, z

y=x+2, z= x+4

y²- 2= 2x+5z
(x+2)²- 2= 2x+ 5(x+4)
x²+4x+4-2= 2x+5x+20
x²-3x-18=0

Solving the quadratic equation we get:

x=6, then y= 8, z= 10

x= -3 discarded as odd number

Rama09 [41]2 years ago

6 0

Answer:

6, 8, 10

Step-by-step explanation:

x y and z are three consecutive even numbers

it means that you can write y = x + 2

and z = y + 2 = x + 4

$y^2-2=2x+5z\\ (x+2)^2-2=2x+5(x+4)\\x^2+4x+4-2=2x+5x+20$

$x^2+4x+2=7x+20\\x^2+4x+2-7x-20=0\\x^2-3x-18=0\\(x+3)(x-6)=0(x=-3\ or \ x=6)$

so the solutions are

x = 6

y = 8

x = 10

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2 years ago

Three times one number added to five times another number is 54. The second number is two less than the first. Use a system of e

worty [1.4K]

Answer:

8 and 6

Step-by-step explanation:

If you use x for the first number, and y for the second, you get equations of 3x+5y=54 and x-2=y.

You can substitute the second equation into the first one to solve it. This gives 3x+5(x-2)=54.

The brackets can be expanded to 3x+5x-10=54. Collecting like terms makes it 8x-10=54.

Next, we add 10 to both sides. This gives 8x=64.

From there, we isolate the x by dividing both sides by 8, giving x=8.

To work out the second number, we can sub 8 for x in either equation (I'm using the second one as it's simpler).

This comes to y=8-2, therefore y=6.

**This content is simultaneous equations, which you may wish to revise. I'm always happy to help!

3 0

2 years ago

A box has a volume of 192 cubic inches, a length that is twice as long as its width, and a height that is 2 inches greater than

ruslelena [56]

Answer:

Therefore the dimension of the cuboid is 8 inches×4 inches ×6 inches.

Step-by-step explanation:

Cuboid : A cuboid is a three dimension shape. The length ,breadth and height of a cuboid are not same.

A cuboid has 6 faces.
A cuboid contains 8 vertices.
A cuboid contains 12 edges .
The total surface area of a cuboid is

= 2(length×breadth+breadth×height+length×height) square units

The dimension of a cuboid is written as length×breadth×height.

The volume is( length×breadth×height) cubic units

Given that the volume of the box is 192 cubic inches.

Let x inches be the width of the cuboid.

Since the length is twice as long as its width.

Then length = 2x inches

Again height is 2 inches longer than width.

Then height = (x+2) inches.

Therefore the volume of the cuboid is

$=[x\times 2x\times (x+2)]$ cubic inches

$=[2x^2(x+2)]$ cubic inches

$=(2x^3+4x^2)$ cubic inches

According to the problem,

$2x^3+4x^2=192$

$\Rightarrow 2x^3+4x^2-192=0$

$\Rightarrow 2(x^3+2x^2-96)=0$

$\Rightarrow (x^3+2x^2-96)=0$

$\Rightarrow x^3-4x^2+6x^2-24x+24x-96=0$

$\Rightarrow x^2(x-4) +6x(x-4)+24(x-4)=0$

$\Rightarrow (x-4)(x^2+6x+24)=0$

Therefore x=4

Since the all zeros of x²+6x+24 =0 is negative.

Therefore breadth = 4 inches

length=(2×4) inches=8 inches

and height = (4+2)inches = 6 inches.

Therefore the dimension of the cuboid is 8 inches×4 inches ×6 inches.

8 0

3 years ago

X,y and z are three consecutive even numbers if y^2 - 2 = 2x + 5Z find x,y and z​

X,y and z are three consecutive even numbers if y^2 - 2 = 2x + 5Z find x,y and z