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4 years ago

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What are the values the values of a and b?

1 answer:

Setler [38]4 years ago

4 0

The segment marked 20 is the geometric mean of the two pieces into which it splits the hypotenuse. You get the proportion

$\frac{20}{a} = \frac{21}{20}$

Solving,

$21a =(20)(20) \\ 21a = 400 \\ a = \frac{400}{21}$

To find b, use the fact that b is the geometric mean of the whole hypotenuse, 21 + a, and the part that is attached to it, a.

$\frac{b}{a} = \frac{21+a}{b}$

A little arithmetic shows that $21+a = \frac{841}{21}$ .

$\frac{b}{\frac{400}{21}} = \frac{\frac{841}{21}}{b} \\ b^2 = \frac{336400}{441} \\ b=\frac{580}{21}$

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Please Help.<br> Match the reasons to the statements given.

marishachu [46]

Answer:

1. Given

2. Diagonals of a parallelogram bisect each other.

3. Vertical angles are equal.

4. Definition of parallelogram.

5. If lines parallel, then alternate interior angles are equal.

6. ASA

7. CPCTE

Step-by-step explanation:

Statement 1:

The first statement is a parallelogram ABCD, which is already given in the question. So, reason 1 is: Given.

Statement 2:

BT and TD are equal because for a parallelogram, its diagonal bisect each other. Here, BD and AC are the diagonals of parallelogram ABCD. So, the diagonals bisect each other at T. Hence, $BT = TD$

Statement 3:

Angles 1 and 2 is a pair of vertical angles. A pair of vertical angles are always equal to each other.

Statement 4:

A parallelogram is a quadrilateral whose opposite sides are parallel and equal. Hence, $BC ||AD$ is because of the definition of a parallelogram.

Statement 5:

Angles 3 and 4 is a pair of alternate interior angles. If two lines are parallel, then the alternate interior angles are always equal.

Statement 6:

The triangles BET and DFT are now congruent because:

i.Angle- $\angle1=\angle2$

ii. Side - $BT = TD$

iii. Angle - $\angle3=\angle4$

Therefore, by ASA postulate the two triangles are congruent.

Statement 7:

As the two triangles are congruent, then their corresponding parts are also equal.

So, by CPCTE, $ET=FT$

5 0

3 years ago

Sendo A = (-1, 0, 1, 2) e B = (-2, -1, 0, 1, 2, 3, 4), verifique em cada caso se a lei dada define uma função de A com valores e

Eduardwww [97]

Answer:

A

Step-by-step explanation:

Because f(x) equals 4X

8 0

3 years ago

If the triangles are similar, only a, only b, both, or neither

Zarrin [17]

Answer:

B

Step-by-step explanation:

0.9/1=0.9

13.5/15=0.9

8/5=1.6

3 0

3 years ago

Suppose it is known from large amounts of historical data that X, the number of cars that arrive at a specific intersection duri

Andrew [12]

Answer:

a) P(x>8) = 0.3937

b) P(x = 2) =0.04661

Step-by-step explanation:

a) From to find the probabilty that in this specific time period, more than 8 cars arrive at the intesection, we use the probability function thus

P(x>8) = 1 - P(x≤8), Cause you can use the complement for calculate this probability , then:

P(x≤8) = $\frac{e^{-6}*6^{0} }{0!}+\frac{e^{-6}*6^{1} }{1!}+\frac{e^{-6}*6^{2} }{2!}+...$ , until x= 8, then you obtain:

P(x≤8)=0.6063 and

P(x>8) = 1 - P(x≤8)= 1-0.6063 = 0.3937

b) P(x=2)= $\frac{e^{-6}*6^{2} }{2!}$

P(x = 2) =0.04661

3 0

3 years ago

Anthony is an executive assistant. He makes $15.85 per hour. If he worked 47.50 hours this week, what is his (a) OT pay? What ab

alexdok [17]

Anthony's OT pay will be $118.875 and his overall pay will be $752.875.

Number of hours Anthony has to work in a week = 5 × 8 = 40 hours.

He worked for = 47.50 hours.

Overtime = 47.50 hours - 40 hours = 7.50 hours

Pay per hour = $15.85 / hour

Overtime pay (OT pay) = $15.85 × 7.50 = $118.875

Overall pay = $15.85 × 47.50 = $752.875

Therefore, Anthony's OT pay is $118.875 and his overall pay is $752.875.

Learn more about overtime pay here -

brainly.com/question/19022439

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5 0

2 years ago