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Delvig [45]
3 years ago
15

Prove that the sum of ab and ba is divisible by the sum of a and b

Mathematics
1 answer:
Likurg_2 [28]3 years ago
5 0

Answer:

It is divisible by 11 and (a + b) !

Step-by-step explanation:

Given a two digit number $ ab $, the digits written in reverse order is $ba $.

Note that a two digit number ab  = 10a + b.

For example: 24 = 10(2) + 4

Similarly, ba = 10(b) + a

Now, the sum of the numbers ab and ba = 10a + b + 10b + a

= 11a + 11b

= 11(a + b)

Hence, the sum of any two digit number ab and the reverse of the number ba,  is divisible by 11 and (a + b).

Hence, proved.

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I cannot understand this can you guys help
igor_vitrenko [27]
The mean is not the same thing as median
mean=78+81+85+87=331
mean=331/4=82.75
median is the middle number, but you have a par set of numbers, so your median will be the middle numbers 78,81,85,87 , which are 81+85=166, 166/2=83
83 is your median
5 0
3 years ago
Can someone answer with steps and explanation? Thanks.
Vika [28.1K]

Answer:

A dilation by a factor of three about Point T followed by a translation of two units downwards.

Step-by-step explanation:

When transforming functions, we will reflect/dilate the figure first and then translate it. This is directly from the order of operations.

Since we are trying to determine the transformation that was performed, we can try to map ΔS'T'U' onto ΔSTU. We can start by translating the figure and then determining any reflections/dilations.

First, we can translate ΔS'T'U' up two units to map T' onto T. This is represented by the black triangle in the image below. Let the black triangle be ΔS''T''U''. (T'' and T are the same point.)

Next, notice that from Point T'' to U'', we move nine units right and six units up.

From Point T to Point U, we move three units right and two units up.

Likewise, from Point T'' to S'', we move six units left and nine units up.

From Point T to Point S, we move two units left and three units up.

Therefore, to map ΔS''T''U'' onto ΔSTU, we dilate ΔS''T''U'' about Point T by a factor of 1/3.

Hence, by reversing the transformations, to acquire ΔS'T'U', we can see that we will dilate ΔSTU by a factor of three about Point T and then a perform a translation of two units downwards.

8 0
3 years ago
Mindy opens a bank account with $55 and start saving five dollars per week. Sean’s grandma gives him $100 for his birthday, but
sveticcg [70]

Answer:

3 weeks, $45

Step-by-step explanation:

So we can make an equation!

55+5x=100-10x

So solving for x,

X=3

4 0
3 years ago
If d is 55 degrees then what is F and E degrees. Explain how you know​
kipiarov [429]

Answer:

F=55

E=70

Step-by-step explanation:

The total degree of a triangle is 180.

So we have 180-55*2

E=180-110

E=70

8 0
3 years ago
What is the area of the following shape? Do not put units.
____ [38]

Answer:

Area = 30

Step-by-step explanation:

Add the two sides

8 + 4 = 12

Multiply that number by the height

12 × 5 = 60

Divide that number by 2

60 ÷ 2 = 30

4 0
2 years ago
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