Which expression is equivalent to (4x + 7y) + 5z? a) 4x + (7y + 5z) b) 4x(7y + 5z) c) 11xy + 5z d) 16xyz

(A) 4x+(7y+5z).

Step-by-step explanation:  The given expression is (4x+7y)+5z.

For the set of real numbers, we have the following associative property-

If a, b and c are any three real numbers, then  

Applying this associative property of real numbers, we can write

So, options (B), (C) and (D) are incorrect.

Thus, the correct option is (A).

d) 30 units^2

area of rectangle = l × b

we know,

length = 10 unit

breadth = 3 unit

applying the formula,

= l × b

= 10 × 3

= 30 unit^2

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m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°