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Lelechka [254]
3 years ago
10

A transversal intersects two lines and forms a pair of same side interior angles that measure 36° and 4 times that measure. Prov

e that the lines are parallel. Please answer now I need it desperately. thx.

Mathematics
1 answer:
MAXImum [283]3 years ago
7 0

Answer:

The addition of the same side interior angles is equal to 180°

Step-by-step explanation:

If the addition of the same side interior angles is equal to 180°, then the lines are parallel. One angle measure 36°, the other angle measures 4*36° = 144°. The addition gives 36° + 144° = 180°.

See picture attached; given that m║n then ∠1 ≅ ∠4 and ∠2 ≅ ∠3. Also, ∠1 + ∠3 = ∠2 + ∠4 = 180°; combining, we get ∠1 + ∠2 = 180°, where ∠1 and ∠2 are same side interior angles. This conclusion was gotten because we knew that m and n were parallel.

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OlgaM077 [116]
If you would like to solve the equation 7 * x = 42, you can calculate this using the following step:

7 * x = 42    /7
x = 42 / 7
x = 6

The correct result would be A. x = 6.
8 0
3 years ago
Read 2 more answers
Two dice are rolled. Use the complement rule to find that the probability that the sum of the dice is less than 10.
Katarina [22]

Answer:

\dfrac{5}{6}

Step-by-step explanation:

When two dice are rolled, the sample space is

\begin{array}{cccccc}(1,1)&(1,2)&(1,3)&(1,4)&(1,5)&(1,6)\\(2,1)&(2,2)&(2,3)&(2,4)&(2,5)&(2,6)\\(3,1)&(3,2)&(3,3)&(3,4)&(3,5)&(3,6)\\(4,1)&(4,2)&(4,3)&(4,4)&(4,5)&(4,6)\\(5,1)&(5,2)&(5,3)&(5,4)&(5,5)&(5,6)\\(6,1)&(6,2)&(6,3)&(6,4)&(6,5)&(6,6)\end{array}

In total, 36 outcomes

First, find the probability that the sum is 10 or greater:

All favorable outcomes

10: (4,6),\ (5,5),\ (6,4)

11: (5,6),\ (6,5)

12: (6,6)

In total, 6 outcomes.

The probability that the sum is 10 or greater is

P(A)=\dfrac{6}{36}=\dfrac{1}{6}

Use the complement rule to find that the probability that the sum of the dice is less than 10:

P(A^C)=1-P(A)=1-\dfrac{1}{6}=\dfrac{5}{6}

6 0
3 years ago
In a servey of 80 people ,it was found that 60 liked oranges only and 10 liked both oranges and apples.The nuber of people who l
I am Lyosha [343]

Answer:

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Step-by-step explanation:

servey=80 people

70= answered the servey

so we should take the difference:-

80–70= 10

Hope I got the right answer!

4 0
3 years ago
An urn contains 3 red and 7 black balls. Players and withdraw balls from the urn consecutively until a red ball is selected. Fin
Sliva [168]

Correct question:

An urn contains 3 red and 7 black balls. Players A and B withdraw balls from the urn consecutively until a red ball is selected. Find the probability that A selects the red ball. (A draws the first ball, then B, and so on. There is no replacement of the balls drawn).

Answer:

The probability that A selects the red ball is 58.33 %

Step-by-step explanation:

A selects the red ball if the first red ball is drawn 1st, 3rd, 5th or 7th

1st selection: 9C2

3rd selection: 7C2

5th selection: 5C2

7th selection: 3C2

9C2 = (9!) / (7!2!) = 36

7C2 = (7!) / (5!2!) = 21

5C2 = (5!) / (3!2!) = 10

3C2 = (3!) / (2!) = 3

sum of all the possible events = 36 + 21 + 10 + 3 = 70

Total possible outcome of selecting the red ball = 10C3

10C3 = (10!) / (7!3!)

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The probability that A selects the red ball is sum of all the possible events divided by the total possible outcome.

P( A selects the red ball) = 70 / 120

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7 0
3 years ago
The temperature is 2 degrees and drops to -15 degrees overnight. Write and then evaluate a subtraction expression to determine t
KiRa [710]

Answer:

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Step-by-step explanation:

Given that:

Initial temperature = 2 degrees

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To Determine:

The change in temperature.

Solution:

First of all, let us have a look at the method for calculating the change in any quantity.

Let the initial quantity = a

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Here, we are given the quantity as temperature.

where a = 2 degrees and

b = -15 degrees

Therefore, the change in temperature = -15 - 2 = \bold{-17} <em>degrees</em>

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