8. The density (D) is related to the mass (M) and the volume (V) of a substance by the formula D=m/v

(a) Transpose the equation to make M the subject and hence find the mass when the volume is 12 and the density is 7. (2)

(b) Transpose the equation to make V the subject and hence find the volume when the mass is 3.4 and the density is 1.8.

M = 84

V = 1.89

Step-by-step explanation:

We are given the formula:

D = M/V

Where D is the density, M is the mass, and V is the volume of a substance.

(a) We'll use transposition to make M the subject of the equation.

To isolate M, we need to multiply by V on both sides of the equation:

D*V = M/V * V

The right side of the equation simplifies:

D*V = M

Now we swap sides:

M = D*V

Substituting the given values of V=12 and D=7:

M = 7 * 12 = 84

M = 84

(b) Now we must make V the subject of the equation:

D = M/V

Again, we multiply by V:

D * V = M

Now divide by D:

V = M/D

Substitute M=3.4, D=1.8:

V = 3.4/1.8

V = 1.89

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3

to find the perimeter of the rectangle this is the expression:

x-9+x-9+3x-4+3x-4=138

if we simplify it:

8x-26=138

remember, 138 is what it all adds up to

the length is 11.5cm

the width is 57.5cm

the area is 661.25cm^2

the answers might not be correct use at own risk