A college admissions office uses the following linear equation to predict the grade point average of an incoming student: x = 0.

Answer:

The 10th term in the geometric progression is 29.

Step-by-step explanation:

Given: In a geometric series, [T3 = 18] and [T6 = 486].

To find: The term [T10]?

Solution:

A geometric sequence takes the form [a, ar, ar^2,...]

Where, a represents the first term, and r denotes the common ratio.

The nth term is expressed as [Tn = a * r^(n-1)]

From the information provided: [T3 = a * r^2 = 18]

And [T6 = a * r^5 = 486]

By dividing the second equation by the first:

[(a * r^5) / (a * r^2)] = 486 / 18

[r^3 = 27]

Taking the cube root provides: r = 3.

Inserting r into one of the equations allows us to solve for a.

Substituting r gives: [T3 = a * r^2 = 18]

Thus, the first term is a = 2, and the common ratio is r = 3.

The 10th term in the geometric progression is computed as:

[T10 = a * r^(10-1)]

[Thus, T10 = 29.]

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.

Response:

15.9

Detailed explanation:

Initially, we need to determine how fast he skis in a minute without considering any speed increase.
To do that, we'll divide the total distance by the time.
960 divided by 5 equals 192.
Therefore, his speed is 192 meters per second.
Now, let's add 20 to this figure.
192 plus 20 equals 212.
Now, to calculate how far he can travel in 10 minutes, we multiply 212 by 10.
212 times 10 equals 2120.
Thus, Alex can cover 2120 meters in 10 minutes.