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3 years ago

In the figure, AC and BD bisect each other. Complete the statements to prove that quadrilateral ABCD is a parallelogram.

Mathematics

2 answers:

Dmitriy789 [7]3 years ago

6 0

Answer:

1. Vertical Angles Theorem

2. Converse of Alternate Interior Angles Theorem

Step-by-step explanation:

<u>First option:</u>

Lines AC and BD intersect at point E. Angles AEB and CED are opposite angles formed when these two lines intersect and are called vertical angles. By vertical angles theorem, these angles are congruent. So,

Vertical Angles Theorem

<u>Second option:</u>

$\triangle BEC\cong \triangle DEA$ by SAS postulate, then

$\angle CBE\cong \angle ADE$ as corresponding sides of congruent triangles.

Converse of Alternate Interior Angles Theorem states that if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel.

So, $\overline{BC}\cong \overline{AD}$ by

Converse of Alternate Interior Angles Theorem

loris [4]3 years ago

6 0

Answer:

1.B 2.B

Step-by-step explanation:

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Ronnie’s Rentals charges $25 plus $15 per to rent a chain saw for 5 hours. Write an expression to show how you could calculate t

iragen [17]

Answer:

The expression of total amount David paid is

y=25+ 15x

where y represents total amount in dollar, x is time in hour.

The total amount that David paid is $100.

Step-by-step explanation:

Given that,

Ronnie's Rentals charges $25 plus $15 per hour to rent a chain for 5 years.

Let

Ronnie's rents a chain for x hours.

Given that,

Rental charge of a chain for 1 hour is $15

Rental charge of a chain for 2 hour is $(15+15) = $30 = $(2×15)

Rental charge of a chain for 3 hour is $(15+15+15) = $45 = $(3×15)

From the above we conclude that,

∴Rental charge = Time ×$15

Rental charge of a chain for x hour is = $(x.15)=$15x

The expression of total amount David paid is

y=25+ 15x

where y represents total amount in dollar, x is time in hour.

Now plugging x= 5 in the above expression

y= 25 + (15×5)

=$100

The total amount that David paid is $100.

5 0

4 years ago

In a particular year, the mean score on the ACT test was 22.5 and the standard deviation was 5.3. The mean score on the SAT math

RideAnS [48]

Question is incomplete ; The questions solved were picked from similar questions but different parameters. However, the solution pattern are exactly the same.

Answer:

- 0.0943

- 0.386

30.185

Step-by-step explanation:

Given :

ACT:

Mean score, m = 22.5

Standard deviation, σ = 5.3

SAT :

Mean score, m = 526

Standard deviation, σ = 101

1.)

Zscore for ACT score of 22:

Since the distribution is normal ; we use the relation ;

Zscore = (score - mean) / standard deviation

Score = 22

Zscore = (22 - 22.5) / 5.3 = - 0.0943

B.)

Zscore for SAT of 487

Zscore = (score - mean) / standard deviation

Score = 487

Zscore = (487 - 526) / 101 = - 0.386

C.)

ACT score, for ACT Zscore of 1.45

Zscore = (score - mean) / standard deviation

ZScore = 1.45

1.45 = (score - 22.5) / 5.3

1.45 * 5.3 = (score - 22.5)

7.685 = score - 22.5

Score = 7.685 + 22.5

Score = 30.185

7 0

3 years ago

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melomori [17]

Answer:

REFER TO ATTACHMENT.

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3 years ago

Solve the equation for x.<br>3x = 12. A 1/4. B 4

Law Incorporation [45]

Answer:

option B

Step-by-step explanation:

$3x = 12$

$x = \frac{12}{3}$

$x = 4$

8 0

4 years ago

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allsm [11]

Answer:

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3 years ago