In a right triangle, angle A measures 20°. The side opposite angle A is 10 centimeters long. Approximately how long is the hypot

Answer:

For the first year, the total amount comes to $266, and with an hourly wage of $5.50, you can express this as the equation 5.50x=266

Step-by-step explanation:

Response:

• Marti is declared the winner

Step-by-step explanation:

Continuation of question:

• After 10 seconds, the race concluded. The winner is the racer farthest from the starting point. Which car deserves the title of winner? Use mathematical reasoning to support your conclusion.
• Table is attached

Solution

Greg

• Travel speed = 13 ft/s
• Initial position = 30.7 ft from the starting point after 2 seconds

Distance from the starting point after 10 seconds:

30.7 + 13*(10 - 2) = 30.7 + 13*8 = 30.7 + 104 = 134.7 ft

Marti

Travel speed = 16.5 ft/s

• Starting position = 2 ft from the beginning line

Distance from starting point after 10 seconds:

2 + 10*16.5 = 2 + 165 = 167 ft

• In comparing the distances from the start line, 134.7 ft against 167 ft, Marti is further from the start line and is thus declared the winner.

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.

(a) The multiplicative inverse of 1234 (mod 4321) is x so that 1234*x ≡ 1 (mod 4321). We can apply Euclid's algorithm:

4321 = 1234 * 3 + 619

1234 = 619 * 1 + 615

619 = 615 * 1 + 4

615 = 4 * 153 + 3

4 = 3 * 1 + 1

Now we will express 1 as a linear combination of 4321 and 1234:

1 = 4 - 3

1 = 4 - (615 - 4 * 153) = 4 * 154 - 615

1 = 619 * 154 - 155 * (1234 - 619) = 619 * 309 - 155 * 1234

1 = (4321 - 1234 * 3) * 309 - 155 * 1234 = 4321 * 309 - 1082 * 1234

This reduces to

1 ≡ -1082 * 1234 (mod 4321)

Thus, the inverse is

-1082 ≡ 3239 (mod 4321)

(b) Since both 24140 and 40902 are even, their GCD cannot equal 1, indicating no inverse exists.