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3 years ago

Find the value of x. Give reasons to justify your solution. C ∈ AE

Mathematics

1 answer:

saw5 [17]3 years ago

7 0

Answer:

x = 11º

Step-by-step explanation:

1. Notice Parallel Lines

2. Understand Angle Relationships When Parallel Lines Are Present (e.g., alternate interior/exterior)

3. ∠CAB ≅ ∠DCA ∴ m∠CAB = 33º

4. Use exterior angle theorem: the sum of non-adjacent angles of the same triangle which the exterior angle is drawn is equal to the measure of that angle.

5. Therefore write and solve the equation 2x + 33º (sum of non-adjacent interior angles) = 5x (exterior angle).

2x + 33 = 5x (C.L.T or Combine Like Terms)
3x = 33 (inverse operations; divide by 3)
x = 11º (remember to apply units)

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Consider the diagram.

Dima020 [189]

Answer:

AB = 9

Step-by-step explanation:

Given that line, l is a perpendicular bisector of line segment AC. It intersects line segment AC at point B.

So, we can conclude that AB = BC ............ (1)

Also given that the length of line segment BC is 9.

Now, from equation (1) we can say that, AB = 9.

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2 years ago

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Jonah drives from his car to and from work. The total length of the trip to and from work is 19.2 miles. In August, Jonah worked

natita [175]

ANSWER

The total length of the trip to and from work in August is

$403.2 \: miles$

EXPLANATION

The total length of the trip to and from work is

$19.2 \: miles$

If Jonah worked 21 days in August,

Then, the total length of the trip to and from work is
$= 21 \times 19.2 \: miles$

Change the decimal to fraction and multiply,

$= 21 \times \frac{192}{10} miles$

$= \frac{21 \times 192}{10}$

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3 years ago

A husband and wife can complete a certain task in 1 and 2 hours respectively. Their children, Rae and Herman, can complete the s

hodyreva [135]

Answer:

1:2 and 4:6 which equal 3:10

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3 years ago

2 x — = ----- 7 x + 10 x = ???

valentina_108 [34]

9514 1404 393

Answer:

x = 4

Step-by-step explanation:

Maybe you want to find x such that ...

2/7 = x/(x +10)

2(x +10) = 7x . . . . . . multiply by 7(x+10)

20 = 5x . . . . . . . . . . subtract 2x, simplify

4 = x . . . . . . . . . . . . divide by 5

_____

Additional comment

You can almost solve this "by inspection" if you recognize the difference of the denominator and numerator is 5 on the left and 10 on the right. If you multiply the fraction on the left by 2/2, you get 4/14, the values in x/(x+10) in the fraction on the right.

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2 years ago