Answer:x=17
Step-by-step explanation:
Set 6x+5+5x-12 equal to 180
Simplify into 11x-7=180
Add 7 to both sides to get 11x=187
Divide both sides by 11 to get x=17
<h2>
Dimension of box is 2 m x 2 m x 1.33 m</h2>
Step-by-step explanation:
Let a be base side and h be the height.
Volume of box, V = a²h
The sides of the box will cost $3 per m² and the base will cost $4 per m². Cost for making is $48.
That is
4a² + 3 x 4 x a x h = 48
4a² + 12 a x h = 48
a² + 3 ah = 12

So volume is

At maximum volume we have derivative is zero,

Negative side is not possible, hence side of square base is 2m.
Substituting in a² + 3 ah = 12
2² + 3 x 2 x h = 12
h = 1.33 m
Dimension of box is 2 m x 2 m x 1.33 m
Answer: 500%
Step-by-step explanation:
It is growing because the base is greater than 1 and the exponent has a positive sign
Answer:
B. 40 meters
Step-by-step explanation:
— Estimating
The rectangle enclosing the path has sides of length 9 m and 14 m, so its perimeter is 2(9+14) = 46 m. The distance covered will be shorter than that.
The distance from A to C is longer than the distance from D to C, so we know the distance will be longer than 2·14+9 = 37 m.
Only one answer choice fits in the range 37 < d < 46.
____
— Detailed calculation
The distance from B to C is the hypotenuse of a right triangle with sides 9 and 12. You will recognize that these side lengths are 3 times the side lengths of a 3-4-5 right triangle, so the hypotenuse distance is 3·5 = 15 meters.
The circuit length is ...
AB +BC +CD +DA = 2 + 15 + 14 + 9 = 40 . . . . meters
Answer:

Step-by-step explanation:
Given
Age 11 Age 12 Total
Girls 3 5 8
Boys 1 3 4
Required

The number of aged 12 children is:


The total number of children is:

So, we have:


Simplify
