(1) ∠ABC = 65°, ∠DBE = 65°, ∠CBE = 115°, ∠ABD = 115°
(2) ∠ABC = 62°, ∠DBE = 62°, ∠CBE = 118°, ∠ABD = 118°
Solution:
(1) In the given image ABC and DBE are vertical angles.
<u>Vertical angle theorem:</u>
If two angles are vertical then they are congruent.
⇒ ∠ABC = ∠DBE
⇒ 3x° + 38° = 5x° + 20°
Arrange like terms one side.
⇒ 38° – 20° = 5x° – 3x°
⇒ 18° = 2x°
⇒ x° = 9°
∠ABC = 3(9°) + 38° = 65°
∠DBE = 5(9°) + 20° = 65°
Adjacent angles in a straight line = 180°
⇒ ∠ABC + ∠CBE = 180°
⇒ 65° + ∠CBE = 180°
⇒ ∠CBE = 115°
∠ABD and ∠CBE are vertical angles.
∠ABD = 115°
(2) In the given image ABC and DBE are vertical angles.
⇒ ∠ABC = ∠DBE
⇒ 4x° + 2° = 5x° – 13°
Arrange like terms one side.
⇒ 13° + 2° = 5x° – 4x°
⇒ 15° = x°
∠ABC = (4(15°) + 2°) = 62°
∠DBE = 5(15°) – 13° = 62°
Adjacent angles in a straight line = 180°
⇒ ∠ABC + ∠CBE = 180°
⇒ 62° + ∠CBE = 180°
⇒ ∠CBE = 118°
∠ABD and ∠CBE are vertical angles.
∠ABD = 118°
Answer:
<h2>
Larger number = 10</h2><h2>
Smaller number = 5</h2>
Step-by-step explanation:
Let larger number be x
Let smaller number be y
---> equation (i)
-----> equation (ii)
Equate equation (i) and (ii),
Move variable to L.H.S and change its sign:
Similarly, Move constant to R.H.S and change its sign
The difference sign (-) will be cancelled on both sides
Putting the value of y in equation (ii) in order to find the value of X ( larger number)
Plug the value of y
Calculate the product
Hence,
Smaller number = 5
Larger number = 10
Hope this helps..
Best regards!!
Given:
The inequality is
Where, c is the number of cars in the parking lot.
To find:
The graph for the given inequality.
Solution:
We have,
Here, the value of c can be any real number less than or equal to 7. But c is the number of cars, so c must be a non-zero integer.
Since, all the non-zero integer values less than or equal to 7 are included in the solution set, therefore, c = 0,1, 2,3,4, 5,6,7.
In the graph of the given inequality, there are close circles on 0,1, 2,3,4, 5,6,7 as shown in option D.
Therefore, the correct option is D.
Answer:
9.5
Step-by-step explanation:
There is no changeover in the first throw. The probability of each changeover is 1/2 and it doesnt depend on the other changeovers. The only thing that modifies each experiment is the result of the previous flip, but regardless of weather it was tails or heads, the probability will always be 1/2.
Since the coin is flipped 20 times and the first time there is no changeover, there are a total of 19 experiments. All of them independent and with probability 1/2. Therefore, the total amount of changeovers for 20 flips is a random variable with distribution Binomial B(19,0.5), the expected value of a Binomial B(n,p) is n*p. In this case, the expected value of changeovers for n=20 is 19*0.5 = 9.5.
