For the upcoming holiday season, Dorothy wants to mold 20 bars of chocolate into tiny pyramids. Each bar of chocolate contains 6

Answer:

Hours

Step-by-step explanation:

This is an incorrect figure.

Answer: x1 = 251/26, x2 = -111/26

Step-by-step explanation:

Greetings!

As illustrated in the diagram, the point you seek is where the two lines intersect.

This intersection point is found by solving the system of linear equations (both equations must be satisfied by the point):

You can approach solving it using the substitution method:

Then substitute x1 into equation 2 to resolve x2:

After which, utilize the x2 value to establish x1:

(0,1)(2,7)
Calculating the slope (m) gives: (7-1) / (2-0) = 6/2 = 3

The equation is represented as y = mx + b
where the slope (m) equals 3
Utilizing either of your coordinates... (0,1).... this implies x = 0 and y = 1
Substituting to solve for b, the y-intercept
1 = 3(0) + b
which simplifies to 1 = b

Thus, the equation you seek is: y = 3x + 1....or 3x - y = -1

Jerome's share of the total profit amounts to one-third. To determine the overall profit of the company, multiply his profit by 3.
If he earned $150,000, the calculation would be:
150,000 × 3 = $450,000

So, the total profit is $450,000.

The dot simply represents multiplication.

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.