Sarah and her children went into a movie theater and she bought $35.50 worth of drinks and candies. Each drink costs $5 and each

To obtain a complete response, the diagram would be essential. However, to approximate the solution, I'd calculate the distances from her home to her school and combine that with the stretch from school to work, and finally, from work back home. If there’s no information regarding the distance from work to home, I’d simply double the traveled distance already accounted for.

The weight of an orangutan is 64.5 kilograms

Solution:

It is stated that the orangutan's weight is 142 pounds

Additionally,

1 kilogram is approximately 2.2 pounds

We will now convert 142 pounds into kilograms

1 kilogram = 2.2 pounds

As a result, 142 pounds translates to

When rounding to the nearest tenth, we obtain 64.5 kilograms

Therefore the mass of the orangutan is 64.5 kilograms

Answer:

x = -4/45

Step-by-step breakdown:

180x=2(30÷3)+17-5•11+2÷1

We first need to simplify the right side.  The initial step involves the parentheses

180x=2(10)+17-5•11+2÷1

Next, we multiply and divide, proceeding from left to right after the equals sign.

180x=20+17-5•11+2÷1

180x=20+17-55+2÷1

180x=20+17-55+2

Next, we add and subtract, moving from left to right in relation to the equals sign.

180x=37-55+2

180x =-18+2

180x = -16

Then divide each side by 180

180x/180 = -16/180

x = -4/45

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.