Math <br> Need to find volume <br> Fractions

The product of 3 consecutive even integers is equal to the cube of the first plus the square of the second plus twice the square

algol [13]

Answer:

6, 8 and 10 and -2, 0, 2

There are two roots x = -2 and 6,

but the since I don't believe 0 is an even number the answer is 6, 8 and 10

I was incorrect according to G0ggle zero is an even number so another answer is -2, 0, 2

Step-by-step explanation:

read the question and convert the English to mathematics

x, y and z even consecutive number

y = x+2

z = y+2 = x+4

and

xyz = x³ + y² + 2z² substitiute x terms in for y and z

x(x+2)(x+4) = x³ + (x+2)² + 2(x+4)² solve for x by graphing on DEMOS

x = -2, 6 solved algebraically below

x = -2 y=0 z=2

x = 6 y=8 z=10

Checked both answers

xyz = x³ + y² + 2z²

-2(0)2 = -8 + 0 + 8 when x = -2

0 = 0

and

6(8)(10) = 6³ + 8² +2(10)² when x = 6

480 = 216+64+200

= 480

x(x+2)(x+4) = x³ + (x+2)² + 2(x+4)² solved algebraically

(x²+2x)(x+4) = x³ + x² +4x +4 + 2x² + 16x + 32

x³ + 6x² + 8x = x³ + x² +4x +4 + 2x² + 16x + 32

x³ + 6x² + 8x = x³ + 3x² + 20x + 36

3x² - 12x - 36 = 0 factor out the 3

3[x² - 4x - 12] = 0

3(x+2)(x-6) = 0 x = -2 and -12

6 0

2 years ago

Can you help me create a polynomial function matching the criteria on the left please and thanks

Olenka [21]

Answer:

$f(x) = \dfrac{1}{8}(x + 4)^2(x + 1)(x - 3)$

Step-by-step explanation:

From inspection of the graph, we can see that the curve intercepts the x-axis at (-4, 0), (-1, 0) and (3, 0)

Therefore,

x = -4 ⇒ x + 4 = 0

x = -1 ⇒ x + 1 = 0

x = 3 ⇒ x - 3 = 0

Because (-4, 0) touches the x-axis, then (x + 4)² will be a factor

So (x + 4)², (x + 1) and (x - 3) are all factors of the polynomial

$\implies f(x) = \dfrac{1}{n}(x + 4)^2(x + 1)(x - 3)$

If we multiply the constants, this will give us the y-intercept:

⇒ 4² x 1 x -3 = -48

From inspection of the graph, the y-intercept is -6

So to get from -48 to -6 we need to multiply -48 by 1/8

Therefore, n = 1/8

$\implies f(x) = \dfrac{1}{8}(x + 4)^2(x + 1)(x - 3)$

7 0

2 years ago

Read 2 more answers

A circle with radius of 3cm sits inside a circle with radius of 11 cm? What is the area of the shaded region?

garri49 [273]

Answer:

3cm = 28.26

11cm = 379.94

3 x 3 x 3.14 = 28.26

11 x 11 x 3.14 = 379.94

hope this helps

8 0

3 years ago

Which graph represents a linear function?

pshichka [43]

Answer:

y + 2x = 10 (third option)

Step-by-step explanation:

We can see that every time x increases by one, y increases by -2, meaning that the slope is -2.

We also know that the y-intercept is 10 because that is the value of y when x is equal to 0.

Now, we can create the equation using the slope-intercept form (y = mx + b, where m is the slope and b is the y-intercept).

y = -2x + 10

If you look at the third option, that equation is just a rearranged form of our equation (y + 2x = 10).

This means that the third option is correct.

7 0

2 years ago

Read 2 more answers

Please help me with this.

masya89 [10]

Answer:

a) 48 b) 132 c) 180 d) 228 e) 312

Step-by-step explanation:

3 0

2 years ago

Math Need to find volume Fractions