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 factor of s is also a prime factor of r.

Answer:

6

Step-by-step explanation:

Hello, we can use the Remainder Theorem, so the remainder is P(-1)

[tex]P(-1)=3+2+2-1=6[/tex]

Thanks

Answer:

2⋅(x  3  −5)

________

      5

​  

Step-by-step explanation: I hope this really help!

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x3"   was replaced by   "x^3".  

STEP

1

:

           x3

Simplify   ——

           5  

Equation at the end of step

1

:

      x3      

 (2 • ——) -  2

      5      

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  5  as the denominator :

        2     2 • 5

   2 =  —  =  —————

        1       5  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

2x3 - (2 • 5)     2x3 - 10

—————————————  =  ————————

      5              5    

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  2x3 - 10  =   2 • (x3 - 5)  

Trying to factor as a Difference of Cubes:

3.2      Factoring:  x3 - 5  

Theory : A difference of two perfect cubes,  a3 - b3 can be factored into

             (a-b) • (a2 +ab +b2)

Proof :  (a-b)•(a2+ab+b2) =

           a3+a2b+ab2-ba2-b2a-b3 =

           a3+(a2b-ba2)+(ab2-b2a)-b3 =

           a3+0+0+b3 =

           a3+b3

Check :  5  is not a cube !!

Ruling : Binomial can not be factored as the difference of two perfect cubes

Polynomial Roots Calculator :

3.3    Find roots (zeroes) of :       F(x) = x3 - 5

Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  1  and the Trailing Constant is  -5.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,5

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -6.00      

     -5       1        -5.00        -130.00      

     1       1        1.00        -4.00      

     5       1        5.00        120.00      

Polynomial Roots Calculator found no rational roots

Final result :

 2 • (x3 - 5)

 ————————————

      5      

Answer:

2⋅(x  3  −5)

________

     5

Step-by-step explanation:

Answer:

A is the true proportion

Step-by-step explanation:

3/4 = 9/12 = 36 = 36

Answer:

35

Step-by-step explanation:

Brianna=x

Justin=x+10

Hannah=2(x+10)

x+x+10+2x+20=130

4x+30=130

4x=130-30

4x=100

x=25

Justin =x+10 = 25+10=35

Answer:

The answer is 1

Step-by-step explanation:

You replace the x with 4 making it 4-2/2=1

Answer:

x = 40

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the 3 given angles and equate to 180

2x + x + [tex]\frac{3x}{2}[/tex] = 180 ( multiply through by 2 to clear the fraction )

4x + 2x + 3x = 360 , that is

9x = 360 ( divide both sides by 9 )

x = 40

Answer:

3x^3+ 12x^2-15x

Step-by-step explanation:

First, you would have to distribute the 3x to everything in the parentheses. So you can write it out as (3x*x^2)+(3x*4x)+(3x*5). Solving this will give you the answer. We'll start off with (3x*x^2). Because we are MULTIPLYING, this part will equal to 3x^3. There is ONE x with 3x (think of it as 3x^1) and 2 x's in x^2, having a total of 3 x's, or x^3. Since the 3 is being multiplied as well, we can write it as 3x^3.

Second, we will solve (3x*4x). We are multiplying, so first we multiply 3*4 and then x*x. 3*4 is 12 and x*x is x^2.  There are 2 x's being mutipled by each other, so the x becomes squared. Now we finish and multiply 12*x^2 wich is 12x^2.

Lastly, we solve (3x*5). 3x is being multiplied 5 times which gives us 15x.

I hope this helped :)

Answer:

a^2 - 6a + 6

Step-by-step explanation:

6−a(4−a)−2a =

6+a2+−4a+−2a

6+a2+−4a+−2a

(a^2)+(−4a+−2a)+(6)

a2+−6a+6

=a^2−6a+6

Answer:

x=-4

Step-by-step explanation:

Filp the sign

The reflection of the line x = 4 will be x = -4.

Reflection is basically a mirror image of the shape, in which the image of a given figure changes accordingly to a given line or axis.

The given equation of line,

x = 4.

The reflection of the line x = 4 will be x = -4.

The reflected graph is shown below.

To learn more about Reflection on:

https://brainly.com/question/15487308

#SPJ2

Answer:

x=49

Step-by-step explanation:

Let's solve your equation step-by-step.

1

8

x−

49

8

=0

Answer:

x=49

Answer:

30.2

Step-by-step explanation:

5.2 - 3y + 7

Let y= -6

5.2 -3(-6) +7

5.2 +18 +7

30.2

Just substitute and solve.

5.2 - 3(-6) + 7

5.2 - (-18) + 7

23.2 + 7

30.2

Best of Luck!

Answer:

0

Step-by-step explanation:

Given

a + 7(a + b) - 8(a + b) + b ← distribute both parenthesis

= a + 7a + 7b - 8a - 8b + b ← collect like terms

= a + 7a - 8a + 7b - 8b + b

= 0

Answer:

0

Step-by-step explanation:

a+7a+7b-8a-8b+b

combining like terms

a+7a-8a+b+7b-8b

8a-8a+8b-8b

0

Answer:

15a

Step-by-step explanation:3times3times3times3times3

Answer:

x=0

Step-by-step explanation:

7x+(-7)=9x-7

Add 7 to each side

7x+(-7)7=9x-7+7

7x = 9x

Subtract 7x from each side

7x-7x = 9x-7x

0 = 2x

Divide by 2

0 = 2x/2

0 = x

Hello,

I hope you and your family are staying safe and healthy!

Answer: 0

Step-by-step explanation:

[tex]7x + (-7) = 9x - 7[/tex]

[tex]7x - 7 = 9x - 7[/tex]

Now susbtract [tex]9x[/tex] from both sides

[tex]7x -7 - 9x = 9x - 7 - 9x\\-2x - 7 = -7[/tex]

Then add 7 to both sides

[tex]-2x - 7+7=-7+7\\2x=0[/tex]

[tex]x = \frac{0}{-2} \\x = 0[/tex]

--------------

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Answer: 130°

Step-by-step explanation:

Concept to know:

Linear pair: two angles that forms one line

One line: 180°

-------------------------------------------------------------

x+50=linear pair

x+50=180

     x=130°

Hope this helps!! :)

Please let me know if you have any question

Answer:

k = 2

Step-by-step explanation:

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Step 1: Replace variables

[tex]\frac{(k+3)-2}{3+1} =\frac{3}{4}[/tex]

Step 2: Combine like terms

[tex]\frac{k+1}{4} =\frac{3}{4}[/tex]

Step 3: Solve for k

k + 1 = 3

k = 2

Answer:

k=2

Step-by-step explanation:

The slope is 3/4

The slope formula is (y1-y2)/(x1-x2)

We can plug the values in

(2-k-3)/(-1-3)=3/4

Combine like terms

(-1-k)/-4=3/4

Cross multiply

-12= -4 - 4k

-8=-4k

k=2

Hope this helps!

Answer:

108

Step-by-step explanation:

There are 31 students in the pep band. One third of students in the marching band signed up, and 5 changed their mind. 31 + 5 = 36, and 36 x 3 = 108. 36 is one third of 108 and there are 108 students in the marching band.

Answer:

12 ft^2

Step-by-step explanation:

48 inches needs to be converted to ft

12 inches = 1 ft

48/12 = 4 ft

36 inches needs to be converted to ft

12 inches = 1 ft

36/12 =3 ft

Find the area

4 ft * 3 ft = 12 ft^2

Answer:

4(1/2x+6)=48

Step-by-step explanation:

half a number= 1/2x

is= equal

Answer:

47

Step-by-step explanation:

Ok first lets do this with small numbers like 10 and 5. How many integers are between 10 and 5? which does not include 10 or 5. You do 10 minus 5 which is 5, but if you count how many integers are between them with your fingers you get 4.

so now you know to get the integers between 2 large numbers you subtract like normal then you mines a 1.

so 63 - 15 - 1 = 47

There are 47 integers between 15 and 63

Hope this helps :)

There have been 47 integer arithmetic in the range of 15 to 63.

Number of integer between two number = Highest number - Lowest number - 1

So,

Number of integer between 15 and 63

63 - 15 - 1

63 - 16= 47

So,

Number of integer between 15 and 63  = 47

Learn more:

https://brainly.com/question/13212492?referrer=searchResults

Answer:

I guess that you want to find the profit:

We have two equations:

the cost equation:

C(x) = -0.1*x^2 + 100.

And the selling equation, that is a vertical stretch of the cost equation by a factor of 1.4:

S(x) = 1.4*C(x) = 1.4*( -0.1*x^2 + 100.) = -0.14*x^2 + 140

Now, whit those two equations we can find the profit equation, that is defined as the difference between the selling price, and the cost:

P(x) = S(x) - C(x) = 1.4*C(x) - C(x) = (1.4 - 1)*C(x) = 0.4*C(x).

Then the profit is 0.4 times the initial cost.

P(x) = 0.4*( -0.1*x^2 + 100.) = -0.04*x^2 + 40

Answer:

D. S(C(x))= –0.14x^2+140; $108.50

Step-by-step explanation:

Cause the others are wrong

Answer:

True

Step-by-step explanation:hi

Answer:

5 units

Step-by-step explanation:

Annie is located at (6,-20) and Barbara is located at (1, 14) and they meet at a point equidistant to their current locations.

This means that they have to meet at the midpoint between their two locations. Let the coordinate of the midpoint be (x,y) hence:

[tex]x=\frac{x_1+x_2}{2}=\frac{6+1}{2} =\frac{7}{2}[/tex]

[tex]y=\frac{y_1+y_2}{2}=\frac{-20+14}{2} =-3[/tex]

The point at which they met is at (7/2, -3). Charlie location is at (7/2, 2). Hence the distance upward that they have to move = 2 - (-3) = 5 units

They have to move 5 units upwards

Answer:

Hey there!

The equation is y=-3/4x+6. (Note the 3/4 is negative because the line has a negative slope.

Let me know if this helps :)

Answer:

[tex]\huge \boxed{y=-\frac{3}{4}x+6 }[/tex]

Step-by-step explanation:

Two points are (0, 6) and (8, 0)

Finding the slope.

m = (y2-y1)/(x2-x1)

m = (0-6)/(8-0)

m = -6/8

m = -3/4

The y-intercept is 6.

y = mx + b

m = slope

b = y-intercept

y = -3/4x + 6

Answer:

Answer : -69

Step-by-step explanation:

-5 - 3x - x- (-16)

= -5 -3 ×(20) - 20 -( -16)

= -5 - 60 -20 +16

= -85 + 16

= -69.

Hope it helps,

Mark it as Brainliest.

Correct question is;

Ms. Ironperson lives due east from the shawarma mediterran grill and Mr. Thoro lives due south. Both leaves at the same time, ms.Iron person traveling at 50 mph and mr. Thoro at 60 mph. Calculate when they would be 400 miles apart and how long would it take to happen

Answer:

They will be 400 miles apart when Ms. Ironperson has covered 256 miles and Mr. Thoro has covered 307 miles after 5.12 hours

Step-by-step explanation:

Since Ms. Ironperson lives due east from the shawarma mediterran grill and Mr. Thoro lives due south,then the distance between them will be the hypotenuse of a right angle triangle.

Now, we are told that Ms. Ironperson is traveling at 50 mph and that Mr. Thoro is traveling at 60 mph.

Thus, if we want to find when they would be at 400 miles apart, it means we have to find the distance Ms. Ironperson and Mr. Thoro would have covered after a time "t".

Thus,

Ms. Ironperson covered 50t miles

Mr. Thoro covered 60t miles

Therefore, since their location forms a right angled triangle, then we can use pythagoras theorem and we have;

(50t)² + (60t)² = 400²

This gives;

2500t² + 3600t² = 160000

6100t² = 160000

t² = 160000/6100

t = √(160000/6100)

t ≈ 5.12 hours

Thus, for Iron person, distance covered is: 50 × 5.12 = 256 miles

For Mr. Thoro, distance covered is: 60 × 5.12 ≈ 307 miles.

They will be 400 miles apart when Ms. Ironperson has covered 256 miles and Mr. Thoro has covered 307 miles after 5.12 hours

Mean: 52.2 because its the average of all the numbers

Range: 2   because (60-58)

Median: 53 because its in the middle of all the numbers

Mode : None

Answer:

Commutative Property  

Associative property

Additive inverse  

Identity property

Step-by-step explanation:

In a  commutative property multiplication and addition which posses commutative property takes place without considering the order of arrangement of data

12.2 + 18.6 + –4.3 + (–18.6)

12.2 + –4.3 + 18.6 + (–18.6)

The second step results into the presence of a commutative property.

The next step 12.2 + –4.3 + [18.6 + (–18.6)] is an associative property because here, re-grouping of numbers which gives the same result takes place

[18.6 + (–18.6)] is an additive inverse since the result is zero. Additive inverse occurs when the addition of a number to another number results into zero

12.2 + –4.3 + (0)   is an Identity property

Identity property occurs when the addition of any number with zero eventually resulted into that number.

Answer:

Commutative Property  

Associative property

Additive inverse  

Identity property

Step-by-step explanation: