All categories

3 years ago

Which pair of numbers is relatively prime? A. 102 and 321 B. 10 and 45 C. 3 and 51 D. 35 and 72

Mathematics

2 answers:

tamaranim1 [39]3 years ago

5 0

Which pair of numbers is relatively prime?


D. 35 and 72

Natali [406]3 years ago

3 0

Okay. I will list all the relatively prime numbers up to 331.
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101, 103,107,109,113,127,131,137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331.
Okay, so look at this list and see which match up.
For A. 102 and 312. Neither of these numbers are relatively prime.
For B. 10 and 45. Neither of these are relatively prime.
For C. 3 and 51. 3 is a relatively prime number, 51 is not.
For D. 35 and 72. Neither of these are relatively prime numbers.
But the answer would be D. because to get a relatively prime pair of numbers you have to have both of them not be divisible by the same number. 102 and 312 can be divided 2, so that's not the answer. 10 and 45 can be divided by 5, so that is incorrect. 3 and 51 can be divided by 3, so that is also incorrect. 35 and 72 cannot be divided by the same numbers.
So, the answer is D. 35 and 72.

You might be interested in

You cut a styrofoam ball in half for a project. Find the surface area of each half of the styrofoam ball.

uranmaximum [27]

Answer:

The question needs to state the radius of the styrofoam ball.

4 0

3 years ago

Suppose F⃗ (x,y)=(x+3)i⃗ +(6y+3)j⃗ . Use the fundamental theorem of line integrals to calculate the following.

Scorpion4ik [409]

In order to use the fundamental theorem of line integrals, you need to find a scalar potential function - that is, a scalar function f(x, y) for which

grad f(x, y) = F(x, y)

This amounts to solving for f such that

∂f/dx = x + 3

∂f/∂y = 6y + 3

Integrating both sides of the first equation with respect to x gives

f = 1/2 x ^2 + 3x + g(y)

Differentiating with respect to y gives

∂f/∂y = dg/dy = 6y + 3

Solving for g gives

g = ∫ (6y + 3) dy = 3y ^2 + 3y + C

and hence

f(x, y) = 1/2 x ^2 + 3x + 3y ^2 + 3y + C

(a) By the fundamental theorem, the integral of F along any path starting at the point P (1, 0) and ending at Q (3, 3) is

∫ F(x, y) • dr = f (3, 3) - f (1, 0) = 99/2 - 7/2 = 46

(b) Now we're talking about a closed path, so the integral is simply 0. We can verify this by checking the integral over the origin-containing paths:

• From the origin to P :

∫ F(x, y) • dr = f (1, 0) - f (0, 0) = 7/2 - 0 = 7/2

• From Q back to the origin:

∫ F(x, y) • dr = f (0, 0) - f (3, 3) = 0 - 99/2 = -99/2

Then the total integral is 7/2 + 46 - 99/2 = 0, as expected.

6 0

3 years ago

What is the poinet-slope form of the equation for the line in the graph?

Ne4ueva [31]

Answer:

$y -5 = \frac{9}{13}(x - 7)$

Step-by-step explanation:

Given :

Two points are given in graph (-6, -4) and {7, 5).

The point-slope form of the equation of a straight line is:

$y -y_{1} = m(x - x_{1})$ ------------(1)

Let $(x_{1}, y_{1})=(7,5)$ and $(x_{2}, y_{2})=(-6,-4)$

The slope of the line $m=\frac{y_{2}- y_{1}}{x_{2}- x_{1}}$

Put all known value in above equation.

$m=\frac{-4- 5}{-6- 7}$

$m=\frac{-9}{-13}$

$m=\frac{9}{13}$

The slope of the line $m=\frac{9}{13}$

We know m, and also know that $(x_{1}, y_{1})=(7,5)$ , so we put these value in equation 1.

$y -5 = \frac{9}{13}(x - 7)$

Therefore, the equation of the line is $y -5 = \frac{9}{13}(x - 7)$ .

6 0

2 years ago

Seiko spent $98.34 on a pair of shoes and 3 pairs of fancy shoestrings. The shoes cost $45.99. How much was EACH pair of shoestr

Marina86 [1]

Answer:

$17.45

Step-by-step explanation:

$17.45*3=52.35

$52.35+$45.99=$98.34

7 0

3 years ago

Let ax-by=c, where a,b,c>0. Rewrite the equation in slope-intercept form

Elis [28]

Here we are required to rewrite the equation ax-by=c, where a,b,c>0 In the slope-intercept form.

The slope-intercept form of ax-by=c is ;

y = (a/b)x - (c/b).

There a no. of ways to write the equation of a line; however, the most popular of these ways is the slope-intercept form.

The slope-intercept form usually takes the form ; y = mx + c.

Therefore, the equation ax-by=c can be rewritten thus;

ax - c = by
By divIDing both sides of the equation by b, we have ;
(a/b)x - (c/b) = y

Consequently, the slope-intercept form of ax-by=c is ;

y = (a/b)x - (c/b).
where , (a/b) is the slope(m)
and (-c/b) is the intercept(c).

Read more:

brainly.com/question/12184348

4 0

2 years ago