A small pebble has a mass of about 20 L b. 20 ml 20 g 20 kg d.

If r and s are positive integers, is \small \frac{r}{s} an integer? (1) Every factor of s is also a factor of r. (2) Every prime

Yuri [45]

Answer:

If statement(1) holds true, it is correct that $\small \frac{r}{s}$ is an integer.

If statement(2) holds true, it is not necessarily correct that $\small \frac{r}{s}$ is an integer.

Step-by-step explanation:

Given two positive integers $r$ and $s$ .

To check whether $\small \frac{r}{s}$ is an integer:

Condition (1):

Every factor of $s$ is also a factor of $r$ .

$r \geq s$

Let us consider an example:

$s = 5^2 \cdot 2\\r = 5^3 \cdot 2^2$

$\dfrac{r}{s} = \dfrac{5^3\cdot2^2}{5^2\cdot2} = 10$

which is an integer.

Actually, in this situation $s$ is a factor of $r$ .

Condition 2:

Every prime factor of s is also a prime factor of r.

(But the powers of prime factors need not be equal as we are not given the conditions related to powers of prime factors.)

Let

$r = 2^2\cdot 5\\s =2^4\cdot 5$

$\dfrac{r}{s} = \dfrac{2^3\cdot5}{2^4\cdot5} = \dfrac{1}{2}$

which is not an integer.

So, the answer is:

If statement(1) holds true, it is correct that $\small \frac{r}{s}$ is an integer.

If statement(2) holds true, it is not necessarily correct that $\small \frac{r}{s}$ is an integer.

8 0

4 years ago

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Craig's Bakery re

soldi70 [24.7K]

Answer:

a. 311 hours

b. i. $3,100 in receipts

ii. $2,799 in expenses.

Step-by-step explanation:

a. The company is making $10 per hour and spending $9 an hour. Their profit is therefore:

= 10 - 9

= $1 per hour

Since they spent $311 on the new equipment, the amount of time it would take for them to make this back is:

= 311 / 1

= 311 hours

b. In 311 hours, the total receipts would be:

= 311 * 10

= $3,110

The expenses would be:

= 311 * 9

= $2,799

8 0

3 years ago

John is making himself a lunch. He has three different soups to choose from, four kinds of soda, and three different kinds of fr

Levart [38]

3*4*3=36 so the answer is 36

3 0

3 years ago

Felisa read the first 60 pages of a book in 3 days. She reads the last 90 pages in 6 days. Are these reading rates equivalent? E

Montano1993 [528]

No, because
60/3 = 20
90/6= 15
Both of the answers aren’t equivalent.

3 0

3 years ago

Please help 25 points and brainliest

-BARSIC- [3]

Answer:

1a. 8

1b. AB & BC

1c. AC

2. $\sqrt{52}$ miles

3. NO

Step-by-step explanation:

1a. AC is your hypotenuse which is C² and BC is B², so we plug it in the equation.

A²+6²=10²

A²+36=100

A²=64

A= $\sqrt{64}$

A=8

1b. Legs are the two shorter sides, AB & BC, which are 6 & 8 respectively.

1c. The hypotenuse is the longest side AC

2. Make lines that make the graph for a triangle with a line. My graph is linked below. Then counts the points, AC=6, BC=4, then use the pythagorean therom.

6²+4²=X²

36+16=52

$\sqrt{52}$ =X

3. 15²+17²=19²

514=361

not possible

so it is not a right triangle

7 0

3 years ago