Answer:
Associative Property
Step-by-step explanation:
Commutative: 35+(45+25) = (25+45)+35
Associative: 35+(45+25) = (35+45)+25
Distributive: cannot be done
hope this helps!
Answer:
The flagpole's shadow is 16.875 feet longer than the man's shadow
Step-by-step explanation:
The total length of the shadow is expressed by taking its actual length by a factor that depends on the position of the sun which is constant for the man too. The expression is as follows;
Height of the shadow=actual height of the flagpole×factor
where;
length of the flagpole's shadow=22.5 feet
actual height of the flagpole=32 feet
factor=f
replacing;
22.5=32×f
32 f=22.5
f=22.5/32
f=0.703125
Using this factor in the expression below;
Length of man's shadow=actual height of man×factor
where;
length of man's shadow=m
actual height of man=8 feet
factor=0.703125
replacing;
length of man's shadow=8×0.703125=5.625 feet
Determine how much longer the flagpole's shadow is as follows;
flagpoles shadow-man's shadow=22.5-5.625=16.875 feet
The flagpole's shadow is 16.875 feet longer than the man's shadow
The value of the expression is 
Explanation:
The expression is ![$2 \times[(12+2) \times 5]+\frac{3}{2}$](https://tex.z-dn.net/?f=%242%20%5Ctimes%5B%2812%2B2%29%20%5Ctimes%205%5D%2B%5Cfrac%7B3%7D%7B2%7D%24)
The value of the expression can be determined using the rule PEMDAS.
According to the PEMDAS rule, first we need to perform the operation which is within the parenthesis.
Thus, the expression becomes,

Multiplying the values within parenthesis, we have,

Using PEMDAS, we need to multiply the numbers.

Again using PEMDAS rule, divide the number,

Finally, using PEMDAS, let us add the values, we have,

Thus, the value of the expression is 
Assuming that the artist wants to paint 6 sides of the cube, the formula to count the surface area of the cube would be: 6* edge length^2. If the edge length is 10 feet, then the area would be:
area= 6*edge length^2
area= 6* 10^2 feet
area= 6*100feet^2= 600 feet^2
If one gallon of paint can be used for 350 feet^2, the amount of paint needed would be: 600feet^2/ (350ft^2/ gallon)= 1.71 gallon
9514 1404 393
Answer:
(x +6)^2 +(y -10)^2 = 225
Step-by-step explanation:
The standard form equation for a circle is ...
(x -h)^2 + (y -k)^2 = r^2
where the center is (h, k) and the radius is r.
The center of a circle is the midpoint of any diameter. The midpoint between two points is the average of their coordinates.
((-15, -2) +(3, 22))/2 = (-15+3, -2+22)/2 = (-6, 10)
The radius can be found using the distance formula, or by simply putting one of the given points in the equation for the circle to see what the constant (r^2) needs to be.
(x -(-6))^2 +(y -10)^2 = (-15-(-6))^2 +(-2-10)^2
(x +6)^2 +(y -10)^2 = 81 +144 = 225
The equation of the circle is ...
(x +6)^2 +(y -10)^2 = 225