A circle is cut into congruent sections and arranged to form a figure that approximates a parallelogram. Find the approximate height of the figure when its area is 42.25π square centimeters.

Approximate height of the figure is 6.5 cm.

Step-by-step explanation:

Area of a parallelogram = base × height

Area of a circle =

where r is the radius of the circle.

From the question, a circle was cut to approximate a parallelogram. Thus:

          area of the parallelogram = area of the circle =

Given that area of the circle is 42.25 square centimetres, which is the area of the figure, then;

        42.25  =

⇒     42.25 =

Find the square root of both sides, we have;

       r =

       r = 6.5

The radius of the circle is 6.5 cm.

From the figure, the radius of the circle is approximately equal to the height of the parallelogram. So that the height of the parallelogram is 6.5 cm.

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950