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pogonyaev
3 years ago
8

Find an odd natural numbers x such that LCM (x, 40) = 1400​

Mathematics
1 answer:
vesna_86 [32]3 years ago
5 0

Answer:

Let x be odd such that LCM {x,40} = 1400 .

Since 1400 = 23×52×7 , then

x ∈ {5m×7n∣(m,n) ∈ {0,1,2}×{0,1}} .

By testing these values, we find that x = 175 .

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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
dalvyx [7]

Answer:

The answer is 2

Step-by-step explanation:

4 0
3 years ago
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In triangle abc, the perimeter is 36, and ab=ac. line ad is perpendicular to bc at the point d, and triangle abd's perimeter is
Musya8 [376]
Let x=ab=ac, and y=bc, and z=ad.

Since the perimeter of the triangle abc is 36, you have:

Perimeter of abc = 36
ab + ac + bc = 36
x + x + y = 36
(eq. 1) 2x + y = 36

The triangle is isosceles (it has two sides with equal length: ab and ac). The line perpendicular to the third side (bc) from the opposite vertex (a), divides that third side into two equal halves: the point d is the middle point of bc. This is a property of isosceles triangles, which is easily shown by similarity.

Hence, we have that bd = dc = bc/2 = y/2 (remember we called bc = y).

The perimeter of the triangle abd is 30:

Permiter of abd = 30
ab + bd + ad = 30
x + y/2 + z =30
(eq. 2) 2x + y + 2z = 60

So, we have two equations on x, y and z:

(eq.1) 2x + y = 36
(eq.2) 2x + y + 2z = 60

Substitute 2x + y by 36 from (eq.1) in (eq.2):

(eq.2') 36 + 2z = 60

And solve for z:

36 + 2z = 60 => 2z = 60 - 36 => 2z = 24 => z = 12

The measure of ad is 12.

If you prefer a less algebraic reasoning:

- The perimeter of abd is half the perimeter of abc plus the length of ad (since you have "cut" the triangle abc in two halves to obtain the triangle abd).

- Then, ad is the difference between the perimeter of abd and half the perimeter of abc:

ad = 30 - (36/2) = 30 - 18 = 12
4 0
3 years ago
Read 2 more answers
(ILL GIVE BRAINLIEST!!)<br><br><br> What is friction and when does it occur?
docker41 [41]

Answer:

Friction is a force that opposes motion between any surfaces that are touching. Friction occurs because no surface is perfectly smooth. Rougher surfaces have more friction between them. ... Friction produces heat because it causes the molecules on rubbing surfaces to move faster and have more energy

8 0
3 years ago
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Jynessa wants to order these fractions: 4/9, 2/3, 1/6, -2 1/2 What should she use as her common denominator?
IceJOKER [234]
4/9 , 2/3, 1/6, ....-2 1/2 = - 5/2

common denominator is 18
8 0
3 years ago
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Find the recursive rule, explicit rule, and f(20)
DiKsa [7]

Answer:

Recursive:

f(1)=35, f(n)=f(n-1)+10

Explicit:

f(n)=35+10(n-1)

And the 20th term is 225.

Step-by-step explanation:

We have the sequence:

35, 45, 55, 65.

Notice that each subsequent term is 10 more than the previous term.

Therefore, our common difference is (+)10.

Recursive Rule:

The standard format for the recursive rule is:

f(n)=a, f(n)=f(n-1)+d

Where a is the initial term and d is the common difference.

From our sequence, we know that a the initial term is 35.

And as determined, our common difference d is 10.

Substitute. Hence, our recursive rule is:

f(1)=35, f(n)=f(n-1)+10

Explicit Rule:

The standard format for the explicit rule is:

f(n)=a+d(n-1)

Where a is the initial term and d is the common difference. So, let’s substitute 35 for a and 10 for d. Hence, our explicit formula is:

f(n)=35+10(n-1)

Now, let’s find the 20th term. We will utilize the explicit rule since the recursive rule can get tedious. Substitute 20 for n because we would like to 20th term. Thus:

f(20)=35+10(20-1)

Evaluate:

\begin{aligned} f(20)&=35+10(19) \\ f(20)&=35+190 \\ f(20)&=225 \end{aligned}

Hence, the 20th term is 225.

5 0
2 years ago
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