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pochemuha
2 years ago
6

The number 55 is attached to the right of a two-digit number, and the resulting 4-digit number is divisible by 21. What could th

e 2-digit number be?
Mathematics
1 answer:
lesya [120]2 years ago
8 0
Your 2-digit number could be any of {11, 32, 53, 74, 95}.
  1155 = 21·55
  3255 = 21·155
  5355 = 21·255
  7455 = 21·355
  9555 = 21·455


_____
The smallest possible 4-digit number of interest is 1055. It has a remainder of 5 when divided by 21. Adding 100 to the number to make it be 1155 adds 100 mod 21 = 16 to the remainder, making it be 21 (or zero). Thus 1155 is the smallest 4-digit number of interest, and 11 is the corresponding 2-digit number. Of course, adding a multiple of 2100 to the 4-digit number will ensure that it remains divisible by 21. So, your 2-digit numbers are 21n+11 for n=0 to 4.
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Answer:

A number line goes from negative 10 to positive 10. An open circle appears at negative 9. The number line is shaded from negative 9 through positive 10.

Step-by-step explanation:

we have

-3x-7

Solve for x

Adds 7 both sides

-3x

-3x

Divide by -3 both sides

Remember that

When you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol

so

x> 27/(-3)\\x>-9

The solution is the interval (-9,∞)

therefore

A number line goes from negative 10 to positive 10. An open circle appears at negative 9. The number line is shaded from negative 9 through positive 10.

6 0
2 years ago
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A carpenter is building a rectangular bookcase with diagonal braces across the back, as shown. The carpenter knows that angle AD
Valentin [98]
Refer to the diagram shown below.

Let x = m∠ADB.

Because m∠BDC is 32° greater than m∠ADB, therefore
m∠BDC = x + 32°

Each angle of a rectangle is 90°, therefore
x + (x+32) = 90
2x + 32 = 90
2x = 58
x   = 29°
x+32 = 61°

Answer:
m∠BDC = 61°
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8 0
2 years ago
Scott wants to buy fencing to place around a circular rock garden. The diameter of the circle is 16 feet. Using 3.14 for π, Calc
denpristay [2]

Answer:

200.96 square feet

Step-by-step explanation:

The amount of fencing Scott will need to buy can be gotten by calculating the area of the circular rock garden .

Area of a circle is given by

Pi r^2

Where

r = radius

Given diameter of 16 feet

r = diameter/2

= 16/2

= 8 feet

Pi = 3.14

Therefore,

Area = 3.14 x 8^2

= 3.14 x 8 x 8

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The amount of fencing Scott will need to buy is 200.96square feet

5 0
2 years ago
Assume that a fair die is rolled. The sample space is , 1, 2, 3, 4, 56, and all the outcomes are equally likely. Find P8. Expres
liraira [26]

Answer:

P\left(8\right)=0

Step-by-step explanation:

Assuming that a fair die is rolled.

  • The sample space is 1, 2, 3, 4, 5, 6 and all the outcomes are equally likely.

Let  X  be the set of all possible outcomes. Let  A  be an outcome.

So, the probability that  A  occurs is:

                                                        P\left(A\right)=\frac{|A|}{|X|}

As the set of all possible outcomes of the roll of a single die is:

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Observe that

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So, the probability must be zero.

In other words,

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                         P\left(8\right)=\frac{0}{6}=0

Therefore,

                   P\left(8\right)=0

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