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choli [55]
1 year ago
15

In the figure CD is the perpendicular bisector of AB . If the length of AC is 2x and the length of BC is 3x - 5 . The value of x

is ? ( see diagram ) please help and explain if possible :)

Mathematics
2 answers:
Dennis_Churaev [7]1 year ago
7 0

Answer

Find out the value of x .

To proof

SAS congurence property

In this property two sides and one angle of the two triangles are equal.

in the Δ ADC and ΔBDC

(1) CD = CD (common side of both the triangle)

(2) ∠CDA = ∠ CDB = 90 °

( ∠CDA +∠ CDB = 180 ° (Linear pair)

as given in the diagram

∠CDA  = 90°

∠ CDB = 180 ° - 90°

∠ CDB = 90°)

(3) AD = DB (as shown in the diagram)

Δ ADC ≅ ΔBDC

by using the SAS congurence property .

AC = BC

(Corresponding sides of the congurent triangle)

As given

the length of AC is 2x and the length of BC is 3x - 5 .

2x = 3x - 5

3x -2x =5

x = 5

The value of x is 5 .

Hence proved


Elanso [62]1 year ago
6 0

Answer with Step-by-step explanation:

We will prove the SAS congruence property

(In this property two sides and one angle of the two triangles are equal the, the two triangles are similar)

consider,  Δ ADC and ΔBDC

(1) CD = CD (common side of both the triangle)

(2) ∠CDA = ∠ CDB = 90 °

( since, ∠CDA +∠ CDB = 180 ° )

(3) AD = DB (as shown in the diagram)

Hence, Δ ADC ≅ ΔBDC

by using the SAS congurence property .

AC = BC

(Corresponding sides of the congruent triangle)

i.e. 2x = 3x - 5

    3x -2x =5

      x = 5

Hence, the value of x is 5

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4 0
1 year ago
Read 2 more answers
The inequality that will determine the number of months, x, that are required for the second phone to be less expensive is . The
ziro4ka [17]

<em>Question:</em>

<em>Sal is trying to determine which cell phone and service plan to buy for his mother. The first phone costs $100 and $55 per month for unlimited usage. The second phone costs $150 and $51 per month for unlimited usage. </em>

<em>The inequality that will determine the number of months, x, that are required for the second phone to be less expensive is . </em>

<em>The solution to the inequality is . </em>

<em>Sal’s mother would have to keep the second cell phone plan for at least months in order for it to be less expensive.</em>

Answer:

a. 150 + 51x < 100 + 55x

b. x > 12.5

c. At least 13 months

Step-by-step explanation:

Given

First Phone;

Cost = \$100

Additional = \$55 <em>(monthly)</em>

Second Phone;

Cost = \$150

<em />Additional = \$51<em> (monthly)</em>

<em></em>

Solving (a): The inequality

<em></em>

Represent the number of months with x

The first phone is expressed as:

100 + 55x

The second phone is expressed as:

150 + 51x

For the second to be less expensive that the first, the inequality is:

150 + 51x < 100 + 55x

Solving (b): Inequality Solution

150 + 51x < 100 + 55x

Collect Like Terms

51x-55x

-4x

Solve for x

x > -50/-4

x > 12.5

Solving (c): Interpret the solution in (b)

x > 12.5 implies 13, 14, 15....

Hence, She'll keep the second phone for a period of at least 13 months

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1 year ago
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