A, B and C are three similar shapes. The surface area of shape A is 4 cm2
.
The surface area of shape B is 25 cm2
.
The ratio of the volume of shape B to the volume of shape C is 27 : 64.
Work out the ratio of the height of shape A to the height of shape C.
Simplify your answer, and give it in the form A : C.

+explanation pleasee :)

Explanation

Shape A has surface area 4 cm^2

Shape B has surface area 25 cm^2

The ratio of the surface areas, from A to B, is 4:25

Apply the square root to both parts and we get 2:5 as the ratio of the corresponding sides. If shape A has a height of 2, then shape B will have a corresponding height of 5. I recommend drawing out two squares with these properties to see that their areas form the ratio mentioned above.

The ratio of the volume of shape B to shape C's volume is 27:64. Apply the cube root to both parts to get 3:4. This means if the height of shape B is 3, then the corresponding height on shape C is 4.

We found these ratios for the sides

The goal is to find the ratio A:B:C which ties all three shapes together showing how they all connect in terms of their corresponding sides.

Note how in A:B = 2:5 we have B = 5, but in B:C = 3:4 we have B = 3. We cannot combine the two ratios in this form since the B terms don't match.

The good news is that we can apply scaling to get the B values to match up

The ratio 2:5 is equivalent to 6:15 after multiplying both parts by 3

The ratio 3:4 is equivalent to 15:20 after multiplying both parts by 5.

The multipliers 3 and 5 are used because note how 15 is the LCM of those previous B values mentioned.

After scaling those ratios, we have

From here, we can quickly see that A:B:C = 6:15:20. This is possible because the '15's match up for the B terms.

If shape A has a height of 6, then shape B has a height of 15, and C has a height of 20. All of these heights correspond to one another.

Then we just erase out the B part to conclude A:C = 6:20 which reduces to A:C = 3:10 after dividing both parts by 2.

the answer is 175.4379

step-by-step explanation:

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!