If a and b represent numbers, which of the following statements represents the commutative property of multiplication? a + b = b + a a · b = b · a a + 0 = a a · 1 = a

The commutative property of multiplication states that the numbers can be multiplied in any order.

a+b = b+a : Commutative property of addition

a*b = b*a : Commutative property of multiplication

a+0=a : Additive identity property  

a*1 =a : Multiplicative identity property  

Answer : a*b =b*a

a · b = b · a

Step-by-step explanation:

Commutative property of multiplication states that the order of multiplication in real numbers does not matter,

I.e.

m × n = n × m

∀ m, n ∈ R

Thus, the correct option that represents the commutative property of multiplication is,

a · b = b · a

Note :

a + b = b + a represents commutative property of addition,

a + 0 = a represents the additive identity property,

a . 1 = a represents the multiplicative identity property.

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west