All categories

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

You might be interested in

Factor this polynomial 6x^2 + 19x – 7.

kondaur [170]

Answer:

(3x-1) (2x+7)

8 0

2 years ago

Is 152 points in 8 games<br> 171 points in 9 games equivalent

max2010maxim [7]

Answer:

Yes, they are equivalent.

3 0

2 years ago

When they arrived in Philadelphia, Tyler’s family took a taxi to a museum. The taxi charged $2.70 per mile, and they paid the dr

shtirl [24]

Answer:

5 miles

Step-by-step explanation:

To find how many miles it is from the train station to the museum we first have to subtract the tip from the total fair and you get 13.50 and then you divide 13.50 by 2.70 to get the number of miles and you get 5.

3 0

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