PLEASE HELP ME HURRY!!!!!!

5 ( 3x - 2) = 4 ( 2x + 1)

wariber [46]

Answer:

15x-2=8x+1

13x=9x

i think that's correct im not sure but i hope to help u :)

5 0

3 years ago

Read 2 more answers

Do the ratios 4/2 and 10/5 form a proportion? Yes or no

mars1129 [50]

Answer:

These are both 20 so that means that this is proportional, yes.

Step-by-step explanation:

Hi.

To figure this out we can do something called cross multiplying to find a cross product. If we do this and our two answers are equal then it is indeed a proportion.

Here is how we do this.

$\frac{4}{2}$ $\frac{10}{5}$

So basically what we are doing is multiplying across in a diagonal direction.

Diagonal meaning like a slash / .

So in this case we would multiply the 4 and the 5 , since they're diagonal from each other.

Do the same for the 2 and the 10.

So we have to multiply :

4 x 5

2 x 10

=

20

These are both 20 so that means that this is proportional, yes.

Hope this helps.

If you have any questions or concerns feel free to message me.

8 0

3 years ago

Use a triple integral to find the volume of the tetrahedron T bounded by the planes x+2y+z=2, x=2y, x=0 and z=0

Tanzania [10]

Answer:

Volume of the Tetrahedron T = $\frac{1}{3}$

Step-by-step explanation:

As given, The tetrahedron T is bounded by the planes x + 2y + z = 2, x = 2y, x = 0, and z = 0

We have,

z = 0 and x + 2y + z = 2

⇒ z = 2 - x - 2y

∴ The limits of z are :

0 ≤ z ≤ 2 - x - 2y

Now, in the xy- plane , the equations becomes

x + 2y = 2 , x = 2y , x = 0 ( As in xy- plane , z = 0)

Firstly , we find the intersection between the lines x = 2y and x + 2y = 2

∴ we get

2y + 2y = 2

⇒4y = 2

⇒y = $\frac{2}{4} = \frac{1}{2}$ = 0.5

⇒x = 2( $\frac{1}{2}$ ) = 1

So, the intersection point is ( 1, 0.5)

As we have x = 0 and x = 1

∴ The limits of x are :

0 ≤ x ≤ 1

Also,

x = 2y

⇒y = $\frac{x}{2}$

and x + 2y = 2

⇒2y = 2 - x

⇒y = 1 - $\frac{x}{2}$

∴ The limits of y are :

$\frac{x}{2}$ ≤ y ≤ 1 - $\frac{x}{2}$

So, we get

Volume = $\int\limits^1_0 {\int\limits^{1-\frac{x}{2}}_{y = \frac{x}{2}}\int\limits^{2-x-2y}_{z=0} {dz} \, dy \, dx$

= $\int\limits^1_0 {\int\limits^{1-\frac{x}{2}}_{y = \frac{x}{2}}{[z]}\limits^{2-x-2y}_0 {} \, \, dy \, dx$

= $\int\limits^1_0 {\int\limits^{1-\frac{x}{2}}_{y = \frac{x}{2}}{(2-x-2y)} \, \, dy \, dx$

= $\int\limits^1_0 {[2y-xy-y^{2} ]}\limits^{1-\frac{x}{2}} _{\frac{x}{2} } {} \, \, dx$

= $\int\limits^1_0 {[2(1-\frac{x}{2} - \frac{x}{2}) -x(1-\frac{x}{2} - \frac{x}{2}) -(1-\frac{x}{2}) ^{2} + (\frac{x}{2} )^{2} ] {} \, \, dx$

= $\int\limits^1_0 {(1 - 2x + x^{2} )} \, \, dx$

= ${(x - x^{2} + \frac{x^{3}}{3} )}\limits^1_0$

= 1 - 1² + $\frac{1^{3} }{3}$ - 0 + 0 - 0

= 1 - 1 + $\frac{1 }{3}$ = $\frac{1}{3}$

So, we get

Volume = $\frac{1}{3}$

7 0

3 years ago

How many real solutions exist for this system of equations? y = x^2 + 4 y = 4x

-BARSIC- [3]

Answer:

This system of equations has one real solution, (2, 8).

Step-by-step explanation:

Given:

y = x² + 4

y = 4x

1. Substitute the given value of y into y = x² + 4:

⇒ 4x = x² + 4

2. Solve for x (by factoring):

⇒ 4x = x² + 4

⇒ 0 = x² - 4x + 4

⇒ 0 = (x - 2)² [perfect square rule: a² -2ab + b² = (a - b)²]

⇒ 0 = (x - 2)² [take the square root of both sides]

⇒ $\sqrt{0} = \sqrt{(x - 2)^2}$

⇒ 0 = x - 2 [add 2 to both sides]

⇒ 0 + 2 = x - 2 + 2

⇒ 2 = x

3. Find the value of y by substituting the given value of x into y = 4x:

⇒ y = 4(2)

⇒ y = 8

4. Check your work:

⇒ y = x² + 4 and ⇒ y = 4x

⇒ 8 = 2² + 4 and ⇒ 8 = 4(2)

⇒ 8 = 4 + 4 and ⇒ 8 = 8 ✔

⇒ 8 = 8 ✔

Solution: (x, y) ⇒ (2, 8)

Learn more about solving system of equations:

brainly.com/question/19575460

brainly.com/question/27276129

5 0

2 years ago

Volume of a rectangular prism: V= Iwh ; Solve for I

bixtya [17]

V=lwh

divide both sides by wh
$\frac{V}{wh}=l$

4 0

3 years ago