The average length of time that three lawn-service mowers operate on a given day is 930 minutes. None of the mowers operates for

B. The correct ratio is sen α = BC/b. Step-by-step explanation: Trigonometric identities are utilized for resolving problems involving right angles. In any right-angled triangle, the side opposite to the angle is known as the opposite side, while the adjacent side runs parallel to the angle, ultimately leading to the longest side, called the hypotenuse.

The total is 4 boxes, as you don't count the.6 since it's not a complete box.

ANSWER

Initially, it was established that line p is parallel to line r.

To begin with the proof:

As stated in the prompt:

∠1 ≈∠5

∠1 and ∠5 are corresponding angles.

Utilizing the property of corresponding angles,

if two lines are intersected by a transversal such that the corresponding angles are

congruent, then those lines must be parallel.

In the diagram, q acts as the transversal.

Thus, based on this characteristic,

line p is parallel to line r.

Proof of 1(a)

REASON

Vertically opposite angle

When two lines intersect, the angles formed are referred to as vertically opposite angles.

Therefore,

∠4 and ∠1 are vertically opposite angles,

hence,

∠4 ≈∠1

Proof of 2(b)

REASON

Alternate interior angle

The angles situated on either side of the transversal, within the two lines, are termed alternate interior angles. When two parallel lines are crossed by a transversal, the alternate interior angles produced will be congruent.

Since line p is parallel to line r (as proven above)

and q is the transversal,

then

∠4 ≈∠5

Thus, it is established.

Proof of 3 (c)

Given that ∠4 ≈ ∠5 (as demonstrated above)

REASON

If two lines are intersected by a transversal such that the alternate interior angles are congruent, then those lines are parallel.

Thus, based on the previously mentioned property,

line p is parallel to line r.

Therefore, it is proven.

The unidentified quantity is the framed prints (517)

Every square meter of ceiling needs 10.75 tiles. To calculate the number of tiles needed for various ceiling areas: For a ceiling area of 1, it requires 10.75 tiles. For a ceiling area of 10, it requires 10.75 × 10, which equals 107.5 tiles. For an area of 100, it needs 10.75 × 100, totaling 1075 tiles. Consequently, that represents the necessary solution.