The zoo sold 250 admission tickets on Tuesday. Some of the tickets were child tickets and the rest were adult tickets. A child's

Response:

Detailed explanation:

Given

Needed

Calculation

The expression becomes:

Combine similar terms

Thus:

Answer:

" Vertical angles are equal " ⇒ 2nd answer

Step-by-step explanation:

* Refer to the attached illustration

- Three lines intersect at point D.

- We have to identify the missing justification in step 3.

∵ Line FA intersects line EC at point D.

- When two lines cross, the angles created are referred to as

 vertical angles.

- By the vertical angles theorem, vertical angles are equal.

Thus, ∠ADC and ∠FDE are vertical angles.

Since vertical angles are equal

∴ ∠EDF ≅ ∠ADC

Thus, m∠EDF ≅ m∠ADC

Given that m∠EDF = 120°.

∵ m∠ADC is the sum of m∠ADB and m∠BDC.

Therefore, m∠ADB + m∠BDC = 120°.

∵ m∠ADB = (3x)° ⇒ given.

∵ m∠BDC = (2x)° ⇒ given.

Thus, 3x + 2x = 120 ⇒ combine like terms.

Thus, 5x = 120 ⇒ divide both sides by 5.

Thus, x = 24.

Column (1)                                                     Column (2)

m∠EDF = 120°                                               given

m∠ADB = 3 x                                                 given

m∠BDC = 2 x                                                 given

∠EDF and ∠ADC are vertical angles           definition of vertical angles

∠EDF is equal to ∠ADC                           vertical angles are equal

                                                                        equal  

m∠ADC = m∠ADB + m∠BDC                        angle addition principle.

m∠EDF = m∠ADC                                          definition of equality.

m∠EDF = m∠ADB + m∠BDC                         substitution.

120° = 3 x + 2 x                                               substitution.

120 = 5 x                                                         addition.

x = 24                                                           division.

∴ The missing justification is " vertical angles are equal "

- From the reasoning above, ∠ADC and ∠FDE are vertical angles and therefore they are equal according to the vertical angle theorem.

The general equation for exponential decay characterized by a half-life (T) is expressed as N(t) = N_0(1/2)^(t/T), where N(t) signifies the amount remaining at time t, N_0 stands for the initial amount (at t=0), and T denotes the half-life of the substance. The half-life of carbon-14 is about 5,730 years. When starting with 6 mg of carbon-14, the equation for the remaining amount after t years would be established.

Jay's bread has risen to 220% of its initial size. The question, as it stands, is incomplete. What is missing would clarify: Jay's bread increases to 11/5 of its original size after three hours. To determine the percentage of its original size: New bread size = units when dough is at 11/5 of its original size.

Part A

To identify the values of x that make 2x−1 positive

⇒ 2x - 1 > 0

⇒ 2x > 1

⇒ x >

As a result, for any x greater than , the expression 2x-1 is positive

Part B

To find values of y making 21−37 negative

⇒ 21-3y < 0

⇒ 21 < 3y

⇒ 7 < y

Thus, for all y values exceeding 7, the expression 21-3y is negative

Part C

To identify values of c that digit 5−3c greater than 80

⇒ 5-3c > 80

⇒ -3c > 75

⇒ -c > 25

⇒ c < -25

Therefore, for values of c less than -25, the expression 5-3c surpasses 80