Point B has coordinates ​(3​,2​). The​ x-coordinate of point A is negative 9. The distance between point A and point B is 15 units. What are the possible coordinates of point​ A?

The required explicit formula for the sequence is [tex]a_n = 9+(n+1)(-3)[/tex]. Option B is correct.

Given, an arithmetic sequance is given in the form of [tex]\left \{ {{a_1=9} \atop {a_n =a_{n-1}-3} \right.[/tex] .
Explicit formula for the sequence is to be determined.

Arithmetic progression is the sequence of numbers that have common differences between adjacent values.
Example,  1, 2, 3, 4, 5, 6. this sequence as n = 6 number with a = 1 (1st term)  and common differene d = 2- 1 = 1.

Given arithmetic sequance is in the form of [tex]\left \{ {{a_1=9} \atop {a_n =a_{n-1}-3} \right.[/tex]
From above expression
[tex]a_n-a_{n-1}= -3[/tex]
common difference (d) = -3
with d = -3 and [tex]a_1 = 9[/tex]
The equation for the nth term in an arithmetic sequence is given by
[tex]a_n =a +(n-1)d[/tex]
[tex]a_n = 9 +(n-1)(-3)[/tex]
The above expression is the explicit form of the arithmetic equation.

Thus, the required explicit formula for the sequence is [tex]a_n = 9+(n+1)(-3)[/tex]. Option B is correct.

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Answer: B) The heights of girls who live on a certain street in the city of Buffalo

Every answer choice starts with "the heights of all 14-year-old girls who", so we can ignore that part. Choice A describes the largest population while choice B describes the smallest population. In other words, choice A is very general and broad, while choice B is very specific and narrow. The more specific you get and the smaller the population is, the less likely its going to be normally distributed.

Answer:

42 Seats.

Step-by-step explanation:

If Arnold is in the second row and there are 5 rows behind him, there are 7 rows because 2 + 5 equals 7.

So then, you multiply 6 times 7 since there are 7 rows and 6 seats in each row. And that equals 42.

Answer:

b:42

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

Okay...um. Any number times 0 is 0 so the expression you choose should equal 0.

Answer:

Perimeter of the cross section = (10+4√5)inches = 18.9in

Area of the cross section= = 10√5 in²

Step-by-step explanation:

Find attached the diagrams used in solving the question

Dimensions of granite = 4in by 2in

Length = 4in

Breadth = 2in

Height = 5in

When granite is cut lengthwise along it's diagonal, the cross section formed by the cut will be a rectangle.

Perimeter of the cross section = 2(height+breadth)

Breadth = diagonal of the cross section

The diagonal of a rectangle divides the rectangle into two right angled triangles.

We would apply Pythagoras theorem to find the length of the diagonal

Hypotenuse ² = opposite ²+adjacent ²

Hypotenuse = length of diagonal

Hypotenuse ² = 2² + 4²

Hypotenuse ² = 4+16 = 20

Hypotenuse = √20 = 2√5

Perimeter of the cross section = 2(height+breadth) =2(5+2√5)

Perimeter of the rectangle = 10+4√5 inches = 18.9in

Area of the cross section= diagonal × height

Area of the cross section= 2√5 × 5

Area of the cross section= = 10√5 in²

Answer:

Correct option: C.

(Both Joey and Nolan)

Step-by-step explanation:

The step Joey did is:

Add 7x to both sides of the equation

Then, he got:

13x - 42 + 7x = 18 - 7x + 7x

20x - 42 = 18

The step Nolan did is:

Add 42 to both sides of the equation

Then, he got:

13x - 42 + 42 = 18 - 7x + 42

13x = 60 - 7x

So both of them used correctly the addition property of equality in the first step of their work.

Correct option: C.

Answer:

2.2

Step-by-step explanation:

Answer:

Car M:

50.4/2 = 25.2

car M uses up 1 gallon every 25.2 miles

Car P:

Just from the graph, you can see that it uses up 1 gallon every 30 miles

The two graphs vary the /miles slightly but it is around their zones of 25.2 and 30. It varies slightly because the cars may be traveling at a fast speed or slower speed thus using up more or less fuel by the time they've reached the recorded distances on the graphs.

Answer:

[tex]\frac{11}{13}[/tex]

Step-by-step explanation:

There are 4 aces and 4 kings.

[tex]\frac{8}{52} =\frac{2}{13}[/tex]

Now just subtract that from 1.

[tex]\frac{11}{13}[/tex]

Answer:

The answer is option D

Step-by-step explanation:

Just got it right on edge :)

Answer:

d

Step-by-step explanation:

Answer: 766.41m

Step-by-step explanation:

Hi, since the situation forms 2 right triangles (see attachment) we have to apply the Pythagorean Theorem for one triangle.  

c^2 = a^2 + b^2  

Where c is the hypotenuse of the triangle (in this case the diagonal distance between corners of the field, which is the distance between the posts if they are placed as far apart as possible ) and a and b are the other sides.  

Replacing with the values given:  

c^2 = 616^2 + 456^2  

c^2 = 379,456+207,936  

c^2 =587,392

c = √587,392

c = 766.41m

So, she is within the area serviced by the tower (20 miles)  

Feel free to ask for more if needed or if you did not understand something.  

Answer:

-5x^2-5x=+1

Step-by-step explanation:

Answer:

Step-by-step explanation:

area of side triangles=2(1/2×6×4)=24 units²

area of 3 rectangles=6×7+2(5×7)==42+70=112 units²

or=(6+5+5)×7=16×7=112 units²

Total surface area=24+112=136 units²

Answer:

C

Step-by-step explanation:

The y-intercept is at x=0, y=3.

Answer:

It will take 20 times for both cost to be same

Step-by-step explanation:

What we want to do here is to calculate the number of times it will take someone who’s wants to rent a boat by Billyboat will be able to rent Lisa boat.

The first thing to do here is calculate how much that is charged to rent Billyboats

That would be;

Let the number of times be n

so the amount will be

105 + 9.50n

Now, renting at 14.75 at n times would be 14.75n

Mathematically, we equate both

14.75n = 105 + 9.5n

14.75n - 9.5n = 105

5.25n = 105

n = 105/5.25

n = 20 times

Answer:

look on symbolab got my answer from there'

Step-by-step explanation:

Answer:

B. 32°

Step-by-step explanation:

Since two of the sides are 10 in length, then we can infer that ∠A and ∠C are congruent. So, both equal 74°. You add 74 + 74 + x = 180, x would equal 32°.

Answer:

B

Step-by-step explanation:

sum of angle in triangle is 180

and since its isosceles triangle, it means <C will be same with <A

so we know that A + C = 148.

so the value of B will be like this

B = 180° - (A+C)° = 180 - 148 = 32°

Answer:

The missing factor is (9s+1)

Step-by-step explanation:

The missing factor is (9s+1) because of the following

(9s^2 + s) + (18s+2)

If we factor out s from 9s^2+s, we get s(9s+1).

If we factor out 2 from 18s+2, we get 2(9s+1)

putting these together, we get s(9s+1) + 2(9s+1). Factoring out the common term of 9s+1, we get (9s+1)(s+2). therefore, the missing factor is 9s+1

Answer:

yes

Step-by-step explanation:

you see we need to make pairs and then we divide each one by square numbers and I have given picture

Answer:

Yes, the number 16,641 is a perfect square.

Step-by-step explanation:

16641 is the 129th perfect square number

__________________________________________

1 2 9    

1 1 66 41    

1        

22  66      

44      

249  22 41    

22 41    

258   0    

Number = 16641

Square Root = 129

________________________________

Step-1 :

Make pair of digits of given number starting with digit at one's place. Put bar on each pair.

1 66 41    

Step-2 :

Now we have to multiply a number by itself such that the product ≤ 1

Here 1×1=1≤1, So divisor is 1 and quotient is 1. Now do the division and get the remainder.

 1        

1 1 66 41    

1        

0        

Step-3 :

Now , we have to bring down 66 and quotient 1 is multiplied by 2 becomes 2, which is starting digit of new divisor

 1        

1 1 66 41    

1        

2  66      

Step-4 :

2 should be the digit at one's place of new divisor because when 22 is multiplied by 2 we get 44.

So new divisor is 22 and next digit of quotient is 2. Now do the division and get the remainder.

 1 2      

1 1 66 41    

1        

22  66      

44      

22      

Step-5 :

Now , we have to bring down 41 and quotient 12 is multiplied by 2 becomes 24, which is starting digit of new divisor

 1 2      

1 1 66 41    

1        

22  66      

44      

24  22 41    

Step-6 :

9 should be the digit at one's place of new divisor because when 249 is multiplied by 9 we get 2241.

So new divisor is 249 and next digit of quotient is 9. Now do the division and get the remainder.

 1 2 9    

1 1 66 41    

1        

22  66      

44      

249  22 41    

22 41    

0    

Answer: 129 (proof 129^2) = 16,641 or 129 x 129 = 16,641

______________________________

Second Solution shortcut:

A perfect square is a number that can be expressed as the product of two equal integers.

The only way to accurately calculate if a number is a perfect square is to find the factors. Before we go through the trouble of finding the factors, there is a quick trick you can use to help determine if you need even need to do the extra work.

Try these steps first:

A number that is a perfect square never ends in 2, 3, 7 or 8. If your number ends in any of those numbers, you can stop here because your number is not a perfect square.

Obtain the digital root of the number. The digital root essentially is the sum of all of the digits. If you're lost, don't worry, we'll go over each step in more detail below.

All possible numbers that are a perfect square have a digital root of 1, 4, 7, 9.

Let's try it...

Step 1:

What is the last number of 16,641? It is this number: 16641. The answer is 1. Is 1 in the list of numbers that are never perfect squares (2, 3, 7 or 8)?

Answer: NO, 1 is not in the list of numbers that are never perfect squares. Let's continue to the next step.

Step 2:

We now need to obtain the digital root of the number. Here's how you do it:

Split the number up and add each digit together:

1 + 6 + 6 + 4 + 1 = 18

If the answer is more than one digit, you would add each digit of the answer together again:

1 + 8 = 9

What is the digital root of number 16,641?

Answer: 9

Step 3:

So now we know the digital root of 16,641 is 9. Is 9 in the list of digital roots that are always a square root (1, 4, 7 or 9)?

Answer: YES, 9 is in the list of digital roots that are always perfect squares. We can conclude that 16,641 could be a perfect square!

Factoring

OK, so now we know that 16,641 could be a perfect square. We have to find the factors of the number to be sure.

Here are all of the factors of 16,641:

1 x 16,6413 x 5,5479 x 1,84943 x 387129 x 129

Highlighted in orange above is the factor combination that makes 16,641 a perfect square. Do you see why? A number can only be a perfect square if the product of two exactly the same numbers is equal to the original number.

Here's the proof: 129 x 129 = 16,641

Answer:

The TV has a length of 61.01" and a height of 34.32"

Step-by-step explanation:

The size of a TV is given by the length of it's diagonal, in this case the diagonal of the TV is 70". The ratio of the screen is 16:9, which means that for every 16 units on the length of the tv there are 9 inches on its height. The diagonal of the screen forms a right angle with the length and the width, therefore we can apply Pythagora's theorem as shown below:

[tex]diagonal^2 = height^2 + length^2\\\\height^2 + length^2 = (70)^2\\\\height^2 + length^2 = 4900[/tex]

Since the ratio is 16:9, we have:

[tex]9*length = 16*height[/tex]

[tex]length = \frac{16}{9}*height[/tex]

Applying this on the first equation, we have:

[tex]height^2 + (\frac{16}{9}*height)^2 = 4900\\\\height^2 + \frac{256}{81}*height^2 = 4900\\\\\frac{337}{81}*height^2 = 4900\\\\height^2 = \frac{4900*81}{337}\\\\height^2 = \frac{396900}{337}\\\\height^2 = 1177.744\\\\height = \sqrt{1177.744}\\\\height = 34.32[/tex]

[tex]length = \frac{16}{9}*34.32\\\\length = 61.01[/tex]

The TV has a length of 61.01" and a height of 34.32"

Answer:

Step-by-step explanation:

These are the values we will need:

  f(-5) = (-5)^2 -7(-5) +6 = 25 +35 +6 = 66

  f(4) = 4^2 -7(4) +6 = 16 -28 +6 = -6

  g(-5) = -5 -1 = -6

  g(4) = 4 -1 = 3

__

(f+g)(-5) = f(-5) +g(-5) = 66 +(-6)

(f+g)(-5) = 60

__

(f-g)(4) = f(4) -g(4) = -6 -3

(f-g)(4) = -9

Answer: not very sure but i think that may be 5

Step-by-step explanation:

Answer:

6.4

Step-by-step explanation:

By the Pythagorean Theorem:

[tex]c=\sqrt{5^2+4^2}= \\\\\sqrt{25+16}= \\\\\sqrt{41}\approx 6.4[/tex]

Hope this helps!

Answer:

To solve we need to use pythogorean theorm. So first we take the square of both giving us 25, 16. Then we add them and get 41. So the answer is squareroot of 41 and if you round you get 6.4

Answer:

(a)19.6 meters

(b) 1 seconds

(c)30.625 meters

Step-by-step explanation:

The height of the balloon is modeled by the equation:

[tex]h = -4.9t^2- 14.7t + 19.6[/tex]

(a)Since the balloon is thrown from the top of the house,  the height of the house is at t=0

When t=0

[tex]h(0) = -4.9(0)^2- 14.7(0) + 19.6\\h=19.6$ meters[/tex]

The height of the house is 19.6 meters.

(b)When the balloon hits the ground

Its height, h(t)=0

Therefore, we solve h(t)=0 for values of t.

[tex]h = -4.9t^2- 14.7t + 19.6=0[/tex]

[tex]-49t^2-147t+196=0\\-49(t^2+3t-4)=0\\t^2+4t-t-4=0\\t(t+4)-1(t+4)=0\\(t+4)(t-1)=0\\t+4=0$ or $t-1=0\\t=-4$ or t=1[/tex]

Therefore, the ball hits the ground after 1 seconds.

(c)To determine the maximum height, we take the derivative of the function and solve it for its critical point.

[tex]If$ h = -4.9t^2- 14.7t + 19.6\\h'(t)=-9.8t-14.7\\$Setting the derivative equal to zero$\\-9.8t-14.7=0\\-9.8t=14.7\\t=-1.5\\$Therefore, the maximum height, h(t) is:\\h(1.5) = -4.9(-1.5)^2- 14.7(-1.5) + 19.6\\=30.625$ meters[/tex]

Answer:

9 students

Step-by-step explanation:

5/9 of 18 is 10

Answer:

S(x)= 10+2^x

Step-by-step explanation:

The correct function which represents the number of members in the science club after x weeks is,

S (x) = 10 + 2ˣ

We have,

The science club is experiencing a growth in membership.

On average, they are seeing 2 new members sign up each week.

Here, they started with 10 members.

Hence, The function S (x) which represents the number of members in the science club after x weeks is,

S (x) = 10 + 2ˣ

Where, x is number of weeks.

Therefore, The function is,

S (x) = 10 + 2ˣ

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Answer:

Step-by-step explanation:

Statement A is closest to being correct.  To get the graph of g(x), we compress the graph of f(x) vertically due to multiplying f(x) by (1/4).

Answer:

C. The graph of g(x) is the graph of f(x) horizontally stretched by a factor of 4.

Step-by-step explanation:

a p e x

The answer choice which could be used to make a bow with the least amount remaining is; 1 2/5 yards.

It follows from the task content that the amount of ribbon remaining in each case can be evaluated as follows;

For 1 2/5 yards: 1 2/5 - 1 1/3 = 1/15. renders only 1/15 a yard to waste.

For 1 and 1/6 yards would render a waste of 1 1/6 yards since it is not possible to make a ribbon out of it.

1 2/10 yards would render a waste of 1 and 1/5 yards since it is not possible to make a ribbon out of it.

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