Here is a sequence of patterns made from dots.
Find an expression, in terms of n, for the number of dots in Pattern number n.

Answer:

a) 1/2

b) y = 0.5x + 2,5

c) k = -3

Step-by-step explanation:

Given are points T(3, 4) and U(7,6).

To find the gradient of TU, you look at the incline in value in the y-direction, divided by the incline in value in the x-diretion.

(Uy- Ty) / (Ux- Tx)

substitute the values given and you get:

(6-4) / (7-3)

2 / 4

This gives you the answer on question a) The gradient of TU = 1/2

Any line is of the form y = ax + b with a = the gradient found in answer a) an b is the the value on the y-coordinate on the y axis, where the line TU intersects with the y-axis.

The whole next part is my attempt to explain to you something about getting the answer for b. Sorry if it is so long, but please take the time to read the explanation, and I hope it will help you to understand what is going on.

The gradient of TU = 1/2 which means that if you start on any point on the line, and then you go 2 units to the right and 1 up you will end upon another point on the line. That is because the quotient is the same. 2/4 = 1/2 = 0,5/1

The last quotient, 0,5/1 , also has the resulting value of 0,5.

This means that if you start on any point on the line, and then you go 1 unit to the right and 0.5 up, you will be on another point on the line.

ATTENTION : This means also, that if you start on any point on the line TU, and then you go 1 unit to the LEFT and 0.5 DOWN, you will be on another point on the line TU. If you understand this, than you have learned something important!

We need to know where the line TU intersects with the y-axis, and now we can use this to find that value?

Since point T(3,4) lies 3 units to the right of the y-axis, we need to go 3 units to the LEFT. But remember the incline of 0.5/1 ... For every unit you go to the left you need to go 0,5 unit DOWN to remain on the line.

If you go 3vunits to the left, how many units do you need to go down?

3 * 0.5 units which is 1.5.

Point T has an y coordinate of 4 so ... what will the y coordinate be if you go 3 units to the left?

4 - (1.5) = 2.5

So now finally we can write down the answer to question b).

y = 0.5x + 2,5

c) (k, k+ 8) lies on the line TU. So substitute that in y = 0.5x + 2,5

y = 0.5 * ( x ) + 2,5

k+8 = 0.5 * ( k + 8 ) + 2,5

k+8 = 0.5*k + 4 + 2,5

Bring all k values to the left of the equality sign, and all number values to the right.

k - 0.5*k = 4 + 2,5 - 8

0.5*k = 6,5 - 8

0.5*k = -1,5

multiply left and right of the = sign by 2 and you get your answer on question c).

k = -3

Answer:

3:4

Step-by-step explanation:

Volume of cylinder A = V= π[tex]r^{2}[/tex]h = r,3 h,4 = [tex]\pi[/tex]36

Volume of cylinder B = V= π[tex]r^{2}[/tex]h = r,4 h,3 = [tex]\pi[/tex]48

Ratio of the volume = [tex]\frac{36}{48}[/tex]

= [tex]\frac{18}{24}[/tex]

= [tex]\frac{9}{12}[/tex]

= [tex]\frac{3}{4}[/tex]

= 3:4

Hope it helps!

Mark as brainliest!

Answer:

False

Step-by-step explanation:

See how the bottom of the line F(x) just drops off? That means there isn't an even decline, meaning even the inverse would have an uneven slope.

This line cannot be a function, no matter which way you turn it.

Answer:

false

Step-by-step explanation:

f is  on the Opisite side.

Answer:

4) BC=30.14

11)XZY≈47.5°

Step-by-step explanation:

4) we use cosine law because we have two length known and one angle known

BC²=AB²+AC²-2ABcos55°

BC²=23²+20²-2*23*20cos55°=908.6

BC=√908.6= 30.14 cm

11) we use cosinee law because three length known

cosXZY=(22²+20²-17²)/(2×22×20)

cosXZY=0.676

XZY^= cos^-1 0.676

XZY^=47.5°

Answer:

distance island dock to Dock A = 4.99 km

distance island dock to Dock K = 6.35 km

Step-by-step explanation:

Always make a scetch to visualize the situation.

You need to construct two triangle both with a streight angle, so you can use Pythagoras to calculate the unknown distances between the island dock L, and each of the other two docks A an K.

I chose to introduce an extra letter, the letter C. In total you have the letters A K L and the letter C.

The letter C has a streight angle of 90° between ACL and it has the same streight angle of 90° with KCL. It is crucial that you see that the distance of LC is exactly the same in triangle LAC and that LC has exactly the same distance in the other triangleLKC.

The distance between AK = 2.3 km.

I define the distance between K and point C as 2.3 + x, because the distance x is unknown.

KC = 2.3 + x

Further more, when you make a picture, you can see that the distance between A and point C = x.

From such a picture, it would show clearly, that K is further away in respect to L then point A. From the picture it would be clear that the angle of LKC is smaller then the angle of LAC, so LKC = 45° and LAC = 64°.

Because angle LKC = 45° and we choose C to have an angle of 90°, the TRIANGLE LKC must be a special triangle... In any triangle, the sum of the three angles together, must add up to 180° .

If that is true, then we have 45 + 90 + 45 (because that adds up to 180). Now that means triangle LKC must have two equal sides (because of the same angels of 45° ).

So we know the distance KC = LC and we already defined KC = 2.3 + x.

Now we know enough to solve the problem.

AK = 2.3 km

angle of LKC = 45°

angle of LAC = 64°

AC = x

KC = 2.3 + x

LC = KC

LC = 2.3 + x

Try to calculate the distance x by using tan. After that you can use Pythagoras to find the other distances.

tan(LKC) = ( LC ) / ( KC )

tan(LKC) = ( x+2.3 ) / ( x+2.3 )

That is not helpful. Let's try the other triangle...

tan(LAC) = LC / AC

tan(LAC) = ( x+2.3 ) / x

tan(64) = ( x+2.3 ) / x

Solve the equation which means you try to find the value for x.

x * tan(64) = ( x+2.3 )

tan(64) * x -x = 2.3

tan(64) * x - 1* x = 2.3

Try to get x outside of the braquets...

x* ( tan(64) - 1 ) = 2.3

x* (2.0503038415793 - 1 ) = 2.3

1.0503038415793 * x = 2.3

x = 2.3 / 1.0503038415793

x = 2.19

Now use Pythagoras a² + b² = c² in triangle LAC to find distance LA.

LA² = AC² + LC²

AC = x = 2.19

LC = 2.3 + x = 4.39

LA² = 2.19² + 4.39²

LA = SQRT( 4.79 + 20.16 )

LA = SQRT( 24.95 )

LA = 4.99 km

Now use Pythagoras a² + b² = c² in triangle LKC to find distance LK.

LK² = KC² + LC²

KC = 2.3 + x = 4.39

LC = 2.3 + x = 4.39

LK² = 4.39² + 4.39²

LK = SQRT( 20.16 + 20.16 )

LK = SQRT( 40.32 )

LK = 6.35 km

Answer:

She scored on 33 of them

Step-by-step explanation:

You take 150 and multiply it by .22. which is 22%

Answer: i think its b.

Step-by-step explanation:

Answer:

the median time for the 50 yard dash is 8 seconds

Step-by-step explanation:

hope this helps :)

Answer:

threee

Step-by-step explanation:

Answer: ([tex]\frac{-5 +\sqrt{5} }{2}[/tex], 0), ([tex]\frac{-5 -\sqrt{5} }{2}[/tex], 0)

Step-by-step explanation: Let me know if you need an explanation.

Answer: 16, rational

Step-by-step explanation: because its a real number

Answer: A

Step-by-step explanation:

Answer:

the correct answer i believe is A. :)

Answer:

D. 18.9 ÷ 9

Step-by-step explanation:

we need to divide

1.89 ÷ 0.9 but write it in different form

so ,we need to eliminate decimal from 0.9

as 0.9*10 = 9

thus,we multiply both  1.89 and  0.9 with 10, then we will have

(1.89*10) ÷ (0.9*10)

=> 18.9 ÷ 9

Thus, based on above calculation new look would be D. 18.9 ÷ 9

Answer:

The IQR describes the middle 50% of values when ordered from lowest to highest. To find the interquartile range (IQR), ​first find the median (middle value) of the lower and upper half of the data. These values are quartile 1 (Q1) and quartile 3 (Q3). The IQR is the difference between Q3 and Q1.

Step-by-step explanation:

hope this helps

correct me if this is wrong

Answer:

D

Step-by-step explanation:

Okay, so the best way to find is too plug in the answer choices.

to find the mean you: add all the numbers up and then, you divide it by however many numbers there are.

minimum meaning exactly 84 no greater!

Start with letter choice A

84+92+84+75+70+81=486

486/6=81 which is  below minimum

Next is letter choice B

84+92+84+75+70+84=489

84/6=81.5 which is below minimum

Next is letter choice C

84+92+84+75+70+95=500

500/6=83.3 which is below minimum

Next is letter choice D

84+92+84+75+70+99=504

504/6=84 which is the correct answer

pls mark me brainliest

Answer:$43

Step-by-step explanation:

65 -22 =43

Answer:

13

Step-by-step explanation:

We only need to pay attention to the x. We multiply 3 and 4 to get 12. Then we add 1 to get 13.

Answer:

13

Step-by-step explanation:

3x + 1

Let x = 4

3*4 +1

Multiply

12+1

13

Answer:

10% loss

Step-by-step explanation:

the difference = Rs. 5000 -Rs. 4500 = Rs. 500

Rs. 500/Rs. 5000*100%= 10%

Since it was reduction in price, it is 10% loss

Answer:

[tex]4000[/tex]

Step-by-step explanation:

[tex]8949-5324[/tex]

[tex]=3625[/tex]

Answer:

565.49 cm2

Step-by-step explanation:

The area of a circle is given by:

Area = pi * r^2

And the whole area represents a central angle of 2pi.

Then, to find the area of this sector, we just need to use a rule of three:

area of pi * r^2 -> central angle of 2pi

area of x -> central angle of 8pi/5

x * 2pi = pi * r^2 * 8pi/5

2x = r^2 * 8pi/5

x = r^2 * 4pi/5 = 15^2 * 4pi/5 = 565.49 cm2

Answer:180pi cm^2

Step-by-step explanation:

Cuz I got it right

Answer: 33

Step-by-step explanation:

there ages m and b.

m = b + 12

m - 17 = 4(b - 17) m = 4b - 51

3b = 63

b = 21

m = 21 + 12 = 33

Hope this helps :)

Answer: Michael is 33 years old.

Step-by-step explantation: Okay, think of it like this, Michael's age for right now is x since we still do not know Michael's age. Pay close attention to the first sentence. What does it say?  m = b + 2. Now pay attention to the second sentence. What does it say? m - 17 = 4 ⋅ (b = 17). Now, let's move on to the system of equations. As you can see here, the system of equations is

{m = b + 12

{m - 17  = 4 ⋅ (b - 17}.

Now for more equations.

m - 17 = 4b - 68

m = 4b - 68 + 17

m = 4b - 51

m - 4b = -51

-

b + 12 - 4b = -51, through the substitution from the first equation we saw

-3b = -51 - 12

3b = 51 + 12

b = 51/3 + 12/3

b = 17 + 4

b = 21

-

m = 33.

Answer:

15/4 OR 3 whole number 3/4

Step-by-step explanation:

Answer:

107.8

Step-by-step explanation:

1 decimal point is the tenths place, thus we have 107.8

Both matrices are 1 x 4 matrices. This notation says there is 1 row and 4 columns. The number of rows must match up, as well as the number of columns, in order for matrix addition to be possible. This is so the corresponding elements pair up and add together. For instance, the 5 and -2 pair up and add together for matrices A and C.

Answer:

c d

Step-by-step explanation:

no explanation

take out a minus from first two fractions

Answer:

1468 in³

Step-by-step explanation:

First get get the total volume of the rectangular prism:

length l = 10 in

width w = 15 in

height h = 10 in

diagonal d = 20.6155281 in

total surface area Stot = 800 in²

lateral surface area Slat = 500 in²

top surface area Stop = 150 in²

bottom surface area Sbot = 150 in²

volume V = 1500 in

Now get get the volume from the missing rectangular prism:

ength l = 4 in

width w = 4 in

height h = 2 in

diagonal d = 6 in

total surface area Stot = 64 in²

lateral surface area Slat = 32 in²

top surface area Stop = 16 in²

bottom surface area Sbot = 16 in³

volume V = 32 in³

So 1500in³- 32 in³ =1468 in³

Answer:

1468

Step-by-step explanation:

10*10*15 = 1500

1500 - (4*4*2) = 1468

1500-32=1468

Therefore the answer is 1468

Answer:

D. (2, 1)

Step-by-step explanation:

slope = 1/2

y-intercept = 0

Equation: y = 1/2 x

Choice A:

x = 0

y = (1/2)(0) = 0

Choice A does not work.

Choice B:

x = 1/2

y = (1/2)(1/2) = 1/4

Choice B does not work.

Choice C:

x = 1

y = (1/2)(1) = 1/2

Choice C does not work.

Choice D:

x = 2

y = (1/2)(1) = 1

Choice D works.

Answer: D. (2, 1)

Answer:

Just follow the guideline given below.

Step-by-step explanation:

To solve values of x by factoring, you need to follow these steps:

1. Move all terms to one side of the equation, usually the left, using addition or subtraction.

2. Factor the equation completely.

3. Set each factor equal to zero, and solve it.

4. List each solution from 3 as a solution to the original equation.

You usually end up with an answer like x =.. or x = ... and so on.

Answer:

y > [tex]\frac{5}{6}[/tex]

Step-by-step explanation:

Given

5y + 3 > - 7y + 13 ( add 7y to both sides )

12y + 3 > 13 ( subtract 3 from both sides )

12y > 10 ( divide both sides by 12 )

y > [tex]\frac{10}{12}[/tex] , that is

y > [tex]\frac{5}{6}[/tex]