At a school supply store, binders cost $5 and pencil pouches cost $2. In one day, 42 of these items are sold for total sales of $144. Which system represents this (b represents binders and p represents pencil pouches), and how many binders were sold?

Answer:

Step-by-step explanation:

the equation of a circle with a center at (0, 8) and a radius of 9.

To frame the equation of the circle we use center radius form of equation

Where (h,k) is the center and 'r' is the radius

Given center is (0,8) and radius = 9

h = 0 , k= 8 and r= 9

Plug in all the values

Answer:

Option A

Step-by-step explanation:

System of the inequalities is,

y ≥ 2x

y < x + 4

By satisfying these inequalities with the points given in the options we can get the answer.

Option (A). (2, 5)

y ≥ 2x

5 ≥ 2(2)

5 ≥ 4

True.

y < x + 4

5 < 2 + 4

5 < 6

True

Therefore, Option (1) is the answer.

Option (B) (1, 6)

y ≥ 2x

6 ≥ 2(1)

6 ≥ 2  

True.

y < x + 4

6 < 1 + 4

6 < 5

False.

Therefore, it's not the solution.

Option (C) (2, 3)

y ≥ 2x

3 ≥ 2(2)

3 ≥ 4

False.

y < x + 4

4 < 2 + 4

4 < 6

True.

Therefore, It's not the solution.

Option (D) (1, 5)

y ≥ 2x

5 ≥ 2(1)

5 ≥ 4

True.

y < x + 4

5 < 1 + 4

5 < 5

False.

Therefore, It's not the solution.

The additional information required to prove that the triangles are congruent using the ASAcongruence theorem is; ∠LNO ≅ ∠LNM

• We are given that;

△LON and △LMN share a common side LN.

This means that for both triangles LN = LN by reflexive property as LN is congruent to itself.

• Secondly, we are told that;

∠OLN and ∠NLM are congruent.

We can see that L is an included angle of the congruent side LN.

• Now, ASA congruency means Angle - Side - Angle. That means two congruent angles and the included side.

• Thus, we need one more angle of the included side LN.

We already have for L, and so the remaining angles that will make△LON and △LMN congruent are;∠LNO and ∠LNM.

Read more on ASA Congruence at; brainly.com/question/3168048

Answer:

The answer is ""

Step-by-step explanation:

Two angles will be congruent to each other in order to show ASA congruence between all the triangles. Its angle  is a common angle in both triangles As a result, we'll use the ASA congruence law to show that perhaps the triangles are congruent.