There is a picture with the question can anyone help me.

Need help with my homework

Volgvan

Answer:

$\displaystyle y=\frac{16-9x^3}{2x^3 - 3}$

$\displaystyle y=-\frac{56}{13}$

Step-by-step explanation:

<u>Equation Solving</u>

We are given the equation:

$\displaystyle x=\sqrt[3]{\frac{3y+16}{2y+9}}$

i)

To make y as a subject, we need to isolate y, that is, leaving it alone in the left side of the equation, and an expression with no y's to the right side.

We have to make it in steps like follows.

Cube both sides:

$\displaystyle x^3=\left(\sqrt[3]{\frac{3y+16}{2y+9}}\right)^3$

Simplify the radical with the cube:

$\displaystyle x^3=\frac{3y+16}{2y+9}$

Multiply by 2y+9

$\displaystyle x^3(2y+9)=\frac{3y+16}{2y+9}(2y+9)$

Simplify:

$\displaystyle x^3(2y+9)=3y+16$

Operate the parentheses:

$\displaystyle x^3(2y)+x^3(9)=3y+16$

$\displaystyle 2x^3y+9x^3=3y+16$

Subtract 3y and $9x^3$ :

$\displaystyle 2x^3y - 3y=16-9x^3$

Factor y out of the left side:

$\displaystyle y(2x^3 - 3)=16-9x^3$

Divide by $2x^3 - 3$ :

$\mathbf{\displaystyle y=\frac{16-9x^3}{2x^3 - 3}}$

ii) To find y when x=2, substitute:

$\displaystyle y=\frac{16-9\cdot 2^3}{2\cdot 2^3 - 3}$

$\displaystyle y=\frac{16-9\cdot 8}{2\cdot 8 - 3}$

$\displaystyle y=\frac{16-72}{16- 3}$

$\displaystyle y=\frac{-56}{13}$

$\mathbf{\displaystyle y=-\frac{56}{13}}$

8 0

3 years ago

The extensions of the legs AB and CD of a trapezoid ABCD intersect at point E. Find the lengths of the sides of △AED if AB=5cm,

Lynna [10]

Answer:

AE = 15 cm; ED = 18 cm; AD = 15 cm (given)

Step-by-step explanation:

ΔBEC ~ ΔAED so ...

AD/BC = AE/BE = (BE+AB)/BE = 1 + AB/BE

Substituting given numbers (lengths in centimeters), we have ...

15/10 = 1 + 5/BE

1/2 = 5/BE

BE = 10

Similarly, ...

1/2 = 6/CE

CE = 12

Then the unknown sides are ...

AE = AB + BE = 5 + 10 = 15 . . . cm

ED = CE + CD = 12 + 6 = 18 . . . cm

8 0

3 years ago

Someone please help me !!! i need it by 7:30!! ammm!!!

AveGali [126]

Answer:

LON and MLN are both equal to 126 degrees,

since the angles with the value '4x + 7' and '7x - 35' degrees are equal to each other, you can rewrite it like this:

4x+7=7x-35

now, take the 7x away from both sides:

-3x+7=-35

then, subtract 7 from both sides:

-3x=-42

now, divide both sides by -3:

x=14

now that we know the value of x (14), we can plug it into the expressions.

4(14)+7=63

7(14)=63

add them together to find the angle MLN

and since the opposite angle (LON) is equal to MLN, they both = 126 degrees

hope this helped :)

8 0

2 years ago

When solving negative -1/3.(x − 15) = −4, what is the correct sequence of operations

FrozenT [24]

Answer:

x=27

Step-by-step explanation:

i would give you the steps but honestly, im tired of giving 20 steps for every problem i answer.

5 0

3 years ago

Factorise 1000a^2+27b^2

Ugo [173]

1000a+27b with 2 on top of the number

5 0

3 years ago