Consider directed line segment PQ. Point P is located at (-10,3). Point R, which is on segment PQ and divides segment PQ into a ratio of PR:RQ = 2:3, is located at (4,7). What are the coordinates of point Q?

Step-by-step explanation:

Let use have a interger,n

Thus three consectice intergers can be represented by

[tex]n[/tex]

[tex]n + 1[/tex]

[tex]n + 2[/tex]

Multiply, and we get

[tex]n(n + 1)(n + 2)[/tex]

[tex]n( {n}^{2} + 3n + 2)[/tex]

[tex]n {}^{3} + 3 {n}^{2} + 2n[/tex]

Then add the middle number, n+1.

[tex] {n}^{3} + 3n {}^{2} + 3n + 1[/tex]

We must prove that the middle number cubed = the equation.

Using the binomial theroem,

[tex](n + 1) {}^{3} = {n}^{3} + 3( {n}^{2} 1 {}^{1} ) + 3n( {1}^{2} ) + 1 {}^{3} [/tex]

[tex](n + 1 ){}^{3} = {n}^{3} + 3 {n}^{2} + 3n + 1[/tex]

So this is indeed true.

You can do the subsitue variables for n to prove it.

Answer:

You would expect to win the game 16 times.

Step-by-step explanation:

I set up a proportion for this :

2/7 = x/56

2(56) = 7x (cross multiply)

112 = 7x (multiply 2 and 56)

x = 16 (divide 7 from both sides)

:)

Answer:

-10x² - 7x + 7

Step-by-step explanation:

Subtract:

Remember: subtracting a negative number is adding that number

-Chetan K

Answer:

−

2

x

2

+

6

x

+

4

Explanation:

(

3

x

2

+

8

x

−

7

)

−

(

5

x

2

+

2

x

−

11

)

(

3

x

2

−

5

x

2

)

+

(

8

x

−

2

x

)

+

(

−

7

+

11

)

−

2

x

2

+

6

x

+

4

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Or if you prefer:

...

.

.

3

x

2

+

8

x

−

7

...

.

.

5

x

2

+

2

x

−

11

−−−−−−−−−−−−

←

Subtract

.

−

2

x

2

+

6

x

+

4

Step-by-step explanation:

have a good day

Answer: x = 5

Step-by-step explanation:

Replace x with 5: 5+3=8

This is true!

Step-by-step explanation:

-21=0.6k

divide both side by0.6=

-21\0.6=35

Hi!

I can help you with joy!

The first step in solving this equation is dividing both sides by -0.6:

-21:(-0.6)=-0.6k:(-0.6k)

35=k

k=35 (Answer)

_______________

Additional comment

* Whatever we do to one side, we do to the other.

** A negative number divided by a negative number is a positive.

______________

Hope it helps! Enjoy your day!

Ask me if you have any questions.

~Misty~

Answer:

D of course:

Step-by-step explanation:

Think about it,

50.54 is 50 estimated to the roundest digit, and 20.10 is 20 estimated. So we'll just do 50-20 which is 30

I hope this answers your concern :) Mark me brainliest if you want to (:

Answer:

-30

Step-by-step explanation:

50.54 - 20.10 = 30.44

Answer:

Let the denominator be x

x-18/x=2/5

5(x-18)=2x

5x-90=2x

3x=90

x=30

The fraction is 12/30

Hope it helps you!

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

d

Answer:

.22 chance next customer pays with credit card

Step-by-step explanation:

This is because there was in all 139 customers during that week, and 30/ 139 0.21582733812. This rounded to hundredth would be .22

Answer:

each of the four blocks weighs 12 ounces

Step-by-step explanation:

3 lbs = 3(16) or 48 ounces

48/4 = 12

each of the four blocks weighs 12 ounces

Answer:

1: x = 19 y = 16 ; 2. x = 5 y = -4

Step-by-step explanation:

To check your work plug the numbers back into one of the equations and see if it's true.

For example:
10(19)-9(16)=46

46=46

1. I distributed 3 to all the numbers so that 9y and -9y would cancel then you add like terms.

2. I distributed -4 to all the numbers so that 4x and -4x would cancel. Then add all like terms.

Once you get x or y plug it back into one problem to get the other variable.

Hope this helps!

#1

(2)×3

[tex]\\ \tt\hookrightarrow -6x+9y=30[/tex]--(3)

Subtracting eq(1) from (3)

[tex]\\ \tt\hookrightarrow -16x=-16[/tex]

[tex]\\ \tt\hookrightarrow x=1[/tex]

Put in eq(2)

[tex]\\ \tt\hookrightarrow -2+3y=10[/tex]

[tex]\\ \tt\hookrightarrow y=4[/tex]

#2

(2) ×4

[tex]\\ \tt\hookrightarrow 4x-8y=52--(3[/tex]

Subtracting eq(1) from (3)

[tex]\\ \tt\hookrightarrow -11y=44[/tex]

[tex]\\ \tt\hookrightarrow y=-4[/tex]

Put in eq(2)

[tex]\\ \tt\hookrightarrow x+8=13[/tex]

[tex]\\ \tt\hookrightarrow x=5[/tex]

Answer:

there are 2 swans to 1 monkey

Step-by-step explanation:

Function defines relationship between variables. The value of the f[g(x)] when the value of f(x)=6x+11 and g(x)=x²+6 is f[g(x)]= 36x²+47.

A function assigns the value of each element of one set to the other specific element of another set.

Given to us

f(x) = 6x + 11

g(x) = x² +  6

As we know the two functions, given to us f(x) = 6x + 11, therefore substitute the value of x as g(x) in order to find the value of f[g(x)] ,

[tex]f(x) = 6x + 11\\\\f[g(x)] = 6(x^2 + 6) + 11\\\\f[g(x)] = 6x^2 + 36 + 11\\\\f[g(x)] = 6x^2 + 47[/tex]

Hence, the value of the f[g(x)] when the value of f(x)=6x+11 and

g(x)=x²+6 is f[g(x)]= 36x²+47.

Learn more about Function:

https://brainly.com/question/5245372

The ordinates of the  linear system  is mathematically given as

C=(4,-6)

Question Parameters:

The equations

x - 4y = 28

2x + y = 2

Generally the equation for the linear system is mathematically given as

x - 4y = 28

2x + y = 2

Resolving the equations

x=4 and y=-6

Therefore

co ordinates are

C=(4,-6)

For more information on Graph

https://brainly.com/question/14375099

Answer:

Step-by-step explanation:

A: -1/3x+1

B: 1/4x -2

Answer:

Given Below.

question (a)

coordinates:

(0,1), (3,0)

slope:

[tex]\frac{0-1}{3-0}[/tex]

[tex]-\frac{1}{3}[/tex]

equation:

[tex]y - y1 = m(x - x1)[/tex]

[tex]y - 1 = -\frac{1}{3} (x-0)[/tex]

[tex]y = -\frac{1}{3}x+1[/tex]

question (b)

coordinates:

(0,-2) , (4, -1 )

slope:

[tex]\frac{-1--2}{4-0}[/tex]

[tex]\frac{1}{4}[/tex]

equation:

[tex]y - y1 = m(x - x1)[/tex]

[tex]y + 1 = \frac{1}{4} (x - 4)[/tex]

[tex]y=\frac{1}{4} x -1-1[/tex]

[tex]y=\frac{1}{4} x -2[/tex]

Answer:

6 ducks and 13 horses

Step-by-step explanation:

Let H and D be the numbers of Horses and Ducks, respectively.

We are told that:

H + D = 19

Our biology book confirms that:

1 horse = 4 legs, and

1 duck = 2 legs

[In most cases on Earth]

So we can say that:

4H + 2D = 64 legs

Rewrite

H + D = 19 as:   H = 19 - D

and then substitute:

4H +2D = 64 legs

4(19-D) +2D = 64 legs

76 - 4D + 2D = 64 legs

-2D = - 12

D = 6  [We have 6 ducks]

Then:

H + D = 19

H + 6 = 19

H = 13  [There are 13 horses]

=============================

Check:

Do 6 ducks and 13 horses have a total of 64 legs?

6*2 + 4*13 = 64?

12 + 52 = 64?

YES

Answer:

A) 9. B) 16

Step-by-step explanation:

Range is

12, 14, 15, 16, 17, 17, 21

so 21-12= 9

add all them up 12+14+15+16+17+17+21 = 112/7 = 16

Role plays are a strategy to understand the points of view of other people according to their thinking or the context in which they live.

An argument is a statement that is characterized by being very well supported by verifiable facts. When we want to defend our position, we must argue it through statements that validate our point of view.

According to the above, if we make a role play selecting to personify a historical character and defend his point of view on a specific topic, we must take into account:

These role plays are very important to learn more about the life of a historical figure or other person, because they make us aware of their way of thinking and how they have been influenced by different factors throughout their lives.

Learn more about point of view in: https://brainly.com/question/14834722

Answer:

1. The work place is a place for work, not for drinking and messing around. Please drink all you want on your own time or just accept the punishment.

2. I agree with ___ that alcohol is not tolerable and it isn't good for your work

3. I learned the owners sometimes have to make unpopular decisions for the good of their business and employees.

Answer: Option 2

The line starts at an x of -4, so the domain is from -4 to infinity since the arrow goes off the graph, meaning it keeps going. The line starts on a y of 2, and the line continues up with the arrow pointing slightly up, so the range is from 2 to infinity.

The domain is from left to right, and the range is down to up

Answer:

2.  {x | x ≥ −4}; {y | y ≥ 2}

Step-by-step explanation:

Let's try to determine the domain first. Look at the x values. The function begins at -4, so our possible domain values also begin at -4, and the values continue positively after -4.

Therefore, our domain is: Domain: {x ≥ -4}.

Or, we could assign our domain using interval notation: [-4,infinity).

Our range, or y values, begin at 2 and continue positively after 2.

Therefore, our range is: Range: {y ≥ 2}.

Again, we could use interval notation to assign our range: [2,infinity)

Therefore, the answer would be

2. {x | x ≥ −4}; {y | y ≥ 2}

Look at the picture to help you better understand

Step-by-step explanation:

a) Fred → 35 years old

James → J years old

(3 × J) - 1 = 35

3J - 1 = 35

b) the number of people (n) Anita can invite depends on her age (A) and you add (+) 2.

therefore, n= A +2

2.a) n represents the no of phones he sells.

so if he charges $10 for a phone, then

n × 10 will represent the amount of money he makes for the no of phones he sells. you are given that P represents the amount of money he makes from selling a phone which is 10N and also his weekly salary, $ 250. this is the amount of money he receives for the whole week.

Hence, 10n + 250 = P

ans: P= 10n + 250

b) the next week he sells 20 phones. he charges $10 per phone. then he will make $200 from selling the phones. but he will also receive his weekly salary, which is $250. total money he receives equals $450.

a better way to reach the answer is using the above equation:

P = 10n + 250, where n= 20

P= (10*20) + 250

P= $450

hope you understand this now,

s.

Answer:

4π/7 radians is 102.86°

Step-by-step explanation:

changing radian to degrees: 1 radian → [tex]\frac{180}{\pi }[/tex]

changing radians to degrees:

[tex]\dfrac{4\pi }{7} *\frac{180}{\pi }[/tex]

[tex]\dfrac{4*180}{7}[/tex]

[tex]\dboxed{102.86}[/tex]

[tex]\\ \rm\longmapsto \dfrac{4\pi}{7}\times \dfrac{180)(\pi}[/tex]

[tex]\\ \rm\longmapsto \dfrac{180(4)}{7}[/tex]

[tex]\\ \rm\longmapsto 720/7[/tex]

[tex]\\ \rm\longmapsto 102.8°[/tex]

From the recursive rule

[tex]a_n = a_{n-1}-13[/tex]

it follows that

[tex]a_{n-1}=a_{n-2}-13 \implies a_n = a_{n-2} - 2\times13[/tex]

[tex]a_{n-2}=a_{n-3}-13 \implies a_n = a_{n-3} - 3\times13[/tex]

and so on. Notice how the subscript on a on the right side and the coefficient multiplied by 13 add up to n (n - 2 + 2 = n; n - 3 + 3 = n; and so on). If we continue the pattern, we'll end up with

[tex]a_n = a_1 + (n-1)\times13[/tex]

so that the explicit rule for the n-th term in the sequence is

[tex]a_n = -2 + 13(n-1) \implies a_n = \boxed{13n-15}[/tex]

Answer:

22,100 for range

Step-by-step explanation:

To find range you subtract the lowest number from the highest number

Answer:

Step-by-step explanation:

Answer:

y = -3x + 5

Step-by-step explanation:

Answer:

The answer is B.

w + m > 224.

11w + 15m ≤ 2,876

Step-by-step explanation:

w + m > 224. There were more than (>) 224 who donated.

11w + 15m ≤ 2,876 No more than (≤) $2,876 was donated.

Hope that helps!

Answer:

(8.2 x 10^9) x (4.5 x 10^-5) = (8.2 x 4.5) x 10 ^(9 - 5) = 36.9 x 10^4 = 3.69 x 10^5

Step-by-step explanation:

Answer:

All the provided answers are incorrect

Step-by-step explanation:

Cross multiply and get

4(x + 5) = (-3)*11

4x + 20 = -33

4x = -33 - 20 = -53

x = -53/4 = -13 1/4

It’s -13 1/4

Step-by-step explanation: