The graphs below show measurements from cubes with different side lengths. Which pairs of variables have a linear relationship?

To determine the values of b that fulfill 3(2b+3)^2 = 36

we start with
3(2b+3)^2 = 36
Divide both sides by 3
(2b+3)^2 = 12
Next, take the square root of both sides
(2b+3)} = (+ /-) \sqrt{12} \\ 2b=(+ /-) \sqrt{12}-3

b1=\frac{\sqrt{12}}{2} -\frac{3}{2}
b1=\sqrt{3} -\frac{3}{2}

b2=\frac{-\sqrt{12}}{2} -\frac{3}{2}
b2=-\sqrt{3} -\frac{3}{2}
Thus,

the solutions for b are
b1=\sqrt{3} -\frac{3}{2}
b2=-\sqrt{3} -\frac{3}{2}

The response is A

I hope this information is useful.

The toddler weighs 12.5 kg.

In-depth explanation:

The formula for gravitational potential energy is Ep=mgh where;

Ep=gravitational potential energy

m=mass of an object

g=gravitational field strength

h=height in meters

Given that; h= 1.5m, Ep=187.5J, g=10 N/kg then finding m;

Ep=mgh

187.5=m*10*1.5

187.5=15m

187.5/15 =15m/15

m=12.5 kg

Learn More

• Gravitation potential energy:

Keywords: Mass, gravitational potential energy

The choice is the first one (positive)

Answer:

i) A total of 40320 different arrangements

ii) For the initial 3 spots, there are 336 different combinations.

Step-by-step explanation:

Given: The total finalists = 8

The count of boys = 3

The count of girls = 5

To determine the number of sample point in the sample space S for possible arrangements, we calculate the factorial of 8!

The number of possible arrangements equals 8!

= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8

= 40320

ii) Among the 8 finalists, we must select the first 3 spots. The sequence matters, hence we utilize permutation.

nPr =

Here n = 8 and r = 3

Substituting n = 8 and r = 3 into the formula, we arrive at

8P3 =

=

= 6.7.8

= 336

Thus, there are 336 different arrangements for the first 3 spots.