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2 years ago

What's bigger 20 or -25

Mathematics

1 answer:

pentagon [3]2 years ago

8 0

Answer:

I hope this helps you

Step-by-step explanation:

20 as it is a positive number

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A four-digit number N leaves a remainder of 10 when divided by 21, a remainder of 11 when divided by 23, and a remainder of 12 w

aksik [14]

Answer:

Step-by-step explanation:

There may be a formal way to solve simultaneous Diophantine equations, but I don't know what it is. So, I addressed this by solving them 2 at a time.

First of all, we want to find a relation between integers p and q such that ...

21p+10 = 23q +11

21p -23q = 1 . . . . . . subtract 23q+10

Using the extended Euclidean algorithm or trial and error or astute observation, we find that (p, q) = (11, 10) is a solution to this equation. Then we can write p and q as ...

p = 23n+11
q = 21n+10

for some integer n.

Then our original numbers become ...

21p+10 = 21(23n+11)+10 = 483n +241 . . . . for some integer n

For this to be a 4-digit number, we must have n such that

1000 ≤ 483n +241 ≤ 9999

1.6 < n < 20.2

Modulo 25, the number (483n+241) is ...

8n +16

and we want that value to be 12:

(8n +16) mod 25 = 12

(8n +4) mod 25 = 0 . . . . . subtract 12

4(2n+1) mod 25 = 0 . . . . factor out 4

For this to be true, we must have 2n+1 be a multiple of 25. The only value of n that is in the required interval [2, 20] is n=12.

When n=12, 483n+241 = 6037. The sum of digits of 6037 is 16.

3 0

2 years ago

Evaluate the expression. [(8 x 7) – 2): 9

frozen [14]

Answer:

☑ Answer is 6

Step-by-step explanation:

${ \tt{ \{(8 \times 7) - 2 \} : 9}} \\ = { \tt{(56 - 2) :9 }} \\ = { \tt{54 :9 }}$

» But this is a ratio, so it can be expressed in terms of fractions:

$= { \tt{ \frac{54}{9} }} \\$

» Divide both the denominator and numerator by 9:

${ \tt{ = \frac{54 \div 9}{9 \div 9} }} \\ \\ = { \tt{ \frac{6}{1} }} \\ \\ = 6$

6 0

2 years ago

Sin(-x)= -cos x for all values of x. True or false

kogti [31]

Answer:

That's incorrect. The simplest way to show this is by evaluating the functions at a given point. Let's say x=0, then:

Sin(-x) = Sin(0) = 0

-cos x = -cos (0) = -1

Therefore, Sin(-x)≠-cos x.

5 0

3 years ago

Read 2 more answers

Cubed root x cubed root x2

Yuki888 [10]

Answer:

Final answer is $\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=x$ .

Step-by-step explanation:

Given problem is $\sqrt[3]{x}\cdot\sqrt[3]{x^2}$ .

Now we need to simplify this problem.

$\sqrt[3]{x}\cdot\sqrt[3]{x^2}$

$\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}$

Apply formula

$\sqrt[n]{x^p}\cdot\sqrt[n]{x^q}=\sqrt[n]{x^{p+q}}$

so we get:

$\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=\sqrt[3]{x^{1+2}}$

$\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=\sqrt[3]{x^{3}}$

$\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=x$

Hence final answer is $\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=x$ .

7 0

2 years ago

To determine the number of trout in a lake, a conservationist catches 180 trout, tags them and throws them back into the lake.

GaryK [48]

The ratio of the trout with tags that are caught and the total trout with tags is first calculated.

r = 12 trout / 180 trout = 1/15

Then, we divide the number of trouts caught without tag by the value obtained above.

N = (48 - 12) / (1/15) = 540

Then, we add the number obtained above and 180.
T = 540 + 180 = 720

ANSWER: 720

3 0

3 years ago