Given the recursive sequence defined by:
tn=5tn-1 + 3tn-2
with ti=2 and t2 = 4
Which of the following would be the first 5 terms of the sequence?

Answer: 12x + 9

Step-by-step explanation:

Given

(6 + 5x) + (7x + 3)

Put like terms together

=5x + 7x + 6 + 3

Combine like terms

=[tex]\boxed {12x+9}[/tex]

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Answer:

35/36  or about 0.972

Step-by-step explanation:

The probability of rolling the same number

first die 6/6

second die 1/6

third die 1/6

1(1/6)(1/6) = 1/36

so there is a 35/36 chance that you will not get it done on the first roll and need to attempt at least one more time.

Step-by-step explanation:

since < 5 = < 8, so,

< 7 = < 6 = 29°

and < 5 = 90° - 29° = 61°

Answer:

149+(13x+5)=180

154+13x=180

13x=26

x=2

Answer:

see explanation

Step-by-step explanation:

The 2 angles are adjacent on a straight line and sum to 180° , then

149 + 13x + 5 = 180 , that is

154 + 13x = 180 ( subtract 154 from both sides )

13x = 26 ( divide both sides by 13 )

x = 2

Then

unknown angle = 13x + 5 = 13(2) + 5 = 26 + 5 = 31°

[tex]\{(x,y) | \ \ x+y = c, \ c \in \mathbb{R}\}[/tex]

Explanation:

The notation for choice A basically says "we have a line of the form x+y = c where c is a real number". Then points on the line in the form (x,y) will form a particular partition. A partition is where we break a set up into non-overlapping subsets and there are no gaps. Think of it like breaking up a house into multiple rooms. Each room is a subset of the house. There are no gaps or overlaps (ignore the regions in the walls).

Take note that if a point is on a line like x+y = 5, then it cannot be on any other line of the form x+y = c, where c is not equal to 5. Something like (x,y) = (2,3) is on x+y = 5 and not on any other line. If c is allowed to be any real number, then x+y = c will be able to partition the real numbers.

Put another way, we can pick any real number we want (aka the number c) and break it down into a sum of x and y values. Such a sum cannot yield any other c value. So going back to the house/room analogy, any particular (x,y) ordered pair will belong to one and only one room.

Let's look at an example of a non-answer. Choice B is not correct because it is perfectly possible to have circles intersect. Intersecting circles share at least one common point. Those common points are what break the idea of partitions. This idea also means choice C is false as well.

Choice D can be ruled out because the notation should be (x,y) in R2 and not simply R.

The collections of subsets of the plane, R2 is (a) {{x,y) : x + y = c} : c ∈ R}

If X is a subset of Y then all the elements of A also contained in B.

According to the given statement we have o determine which of the following collections of subsets of the plane R2.

R2 defines a two dimension plane.

x+y = c where c is a real number.

Then points on the line in the form (x,y) will form a particular partition. A partition is where we break a set up into non-overlapping subsets and there are no gaps. Think of it like breaking up a house into multiple rooms. Each room is a subset of the house.

Take note that if a point is on a line like x+y = 7, then it cannot be on any other line of the form x+y = c, where c is not equal to 7. Something like (x,y) = (3,4) is on x+y = 7 and not on any other line.

B. Is not correct because it is perfectly possible to have circles intersect. Intersecting circles share at least one common point. Those common points are what break the idea of partitions.

C. is false as well

D. Is ruled out because the notation should be (x,y) in R2 and not simply R.

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Answer:

5

Step-by-step explanation:

(4k + 2) ÷ 10

(4(12) + 2) ÷ 10

(48 + 2) ÷ 10

(50) ÷ 10

= 5

Hope this helps!! <3

The solution to the expression (4k + 2 ) ÷ 10 when k = 12 is 5

From the given expression, we are to solve for (4k + 2) ÷ 10

When

What we are going to do is that we will replace k with 12 wherever we see (k) in the expression given

∴

= (4k + 2 ) ÷ 10

= (4(12) + 2 ) ÷ 10

= (48 + 2) ÷ 10

= (50) ÷ 10

= 5

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Answer:

An additional assumption is that a is not negative.

Step-by-step explanation:

If a could be negative, then:

(-7)^2 < 3^2  would be false because

49 is not greater than 9

Step-by-step explanation:

The circumcenter is the centre of the circumcircle. All the vertices of a triangle are equidistant from the circumcenter.In an acute-angled triangle, circumcenter lies inside the triangle. In an obtuse-angled triangle, it lies outside of the triangle.

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[tex]3^{2c} + 1 = 28\times3^c - 9 \implies 3^{2c} - 28\times3^c = -10[/tex]

Complete the square on the left side:

[tex]3^{2c} - 28\times3^c = \left(3^{2c}-28\times3^c+14^2\right)-14^2 = \left(3^c-14\right)^2 - 196[/tex]

Then the equation becomes

[tex]\left(3^c-14\right)^2 - 196 = -10 \\\\ \left(3^c-14\right)^2 = 186 \\\\ 3^c - 14 = \pm\sqrt{186} \\\\ 3^c = 14\pm\sqrt{186}[/tex]

Both 14 + √186 and 14 - √186 are positive numbers, so we can take the logarithm (base 3) of both sides without issue:

[tex]\log_3\left(3^c) = c = \log_3\left(14\pm\sqrt{186}\right)[/tex]

Then in increasing order, the solutions are

c = log₃(14 - √186), c = log₃(14 + √186)

Answer:

[tex]sum \: of \: exterir \: anges \: for \: a \: polygon = 360 \\ 5x - 5 + x + 4x - 5 + 4x + 20 = 360 \\ x \: terms \: togather \\ 5x + x + 4x + 4x - 5 - 5 + 20 = 360 \\ 14x + 10 = 360 \\ 14x = 360 - 10 \\ 14x = 350 \\ x = \frac{350}{14} = 25 \\ x = 25 \\ thank \: you[/tex]

Answer:

SUM OF EXTERIOR ANGLES=360

Step-by-step explanation:

5x-5+4x-5+4x+20+x=360

14x+10=360

14x=350

x=350/14

x=25

Answer:

4.3

Step-by-step explanation:

Answer:

g^-1(x)=x/2+3/2

Step-by-step explanation:

Hello :D

£1.45 + £2.85 = £4.30

£4.30 + £1.95 = £6.25

£6.25 to the nearest pound = £6.00

Answer: Selling fees = £6 (rounded to the nearest pound)

Step-by-step explanation:

Given information

Insertion fee = £1.45

Enhanced advert = £2.85

Selling fee = £1.95

Given expression deducted from the given information

Total = insertion + enhanced advert + selling

Substitute values into the expression

Total = (1.45) + (2.85) + (1.95)

Simplify by addition

Total = 4.3 + (1.95)

Total = 6.25

[tex]\boxed{Total=6}[/tex]

Hope this helps!! :)

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Answer:

40

Step-by-step explanation:

Answer:

1/2 pound

Step-by-step explanation:

Answer:

2 cups is equal to 0.5 pounds.

Step-by-step explanation:

4 divided by 2 is 2 and 1 pound divided by 2 is 0.5.

The fraction that represents the total number of seats occupied during the three days is 1.

The total number of seats in the auditorium is 200.

On day 1, 40% of the seats were occupied. So, 40/100 * 200 = 80 seats were occupied on day 1.

On day 2, 35% of the seats were occupied. So, 35/100 * 200 = 70 seats were occupied on day 2.

On day 3, 25% of the seats were occupied. So, 25/100 * 200 = 50 seats were occupied on day 3.

The total number of seats occupied during the three days is 80 + 70 + 50 = 200 seats.

The fraction that represents the total number of seats occupied during the three days is 200/200 = 1.

Here is the solution in mathematical form:

Let x be the fraction that represents the total number of seats occupied during the three days.

Then, x * 200 = 80 + 70 + 50

x = (80 + 70 + 50) / 200

x = 1

Therefore, the answer is 1.

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Answer:

x=20

Step-by-step explanation:

3^x=243^4

3^x=(3^5)^4

3^x =3^20

x=20

9514 1404 393

Answer:

  T, T, F, F, T

Step-by-step explanation:

First of all, it is helpful to know ...

  √8 ≈ 2.8284

  √7 ≈ 2.6458

Now you can check the inequalities:

0, 1, 2, and √7 are left of √8 on a number line, so are all less than √8.

3 and 8 are right of √8 on a number line, so are greater than √8.

Answer:

T, T, F, F, T.

Step-by-step explanation:

Person above is correct!!

Answer:

it's A or C

Step-by-step explanation:

because if it was be it would round to .19 but c and a round to .18

Answer:

$8,000

Step-by-step explanation:

8,375.79 < 8,500 so it will round to 8,000

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Answer:

[tex]\displaystyle \cos(\theta) = \frac{\sqrt{7}}{4}[/tex].

[tex]\displaystyle \tan(\theta) = \frac{3\sqrt{7}}{7}[/tex].

Step-by-step explanation:

By the Pythagorean identity, for any given angle [tex]\theta[/tex], [tex]\sin^{2}(\theta) + \cos^{2}(\theta) = 1[/tex].

Given that [tex]\displaystyle \sin(\theta) = 3/4[/tex], solve this equation for [tex]\cos(\theta)[/tex].

[tex](\sin(\theta))^{2} + (\cos(\theta))^{2} = 1[/tex].

[tex]\displaystyle \left(\frac{3}{4}\right)^{2} + (\cos(\theta))^{2} = 1[/tex].

[tex]\begin{aligned} \cos(\theta) &= \sqrt{1 - \frac{9}{16}} \\ &= \sqrt{\frac{7}{16}} \\ &= \frac{\sqrt{7}}{4} \end{aligned}[/tex].

The tangent of an angle is equal to the ratio between the sine and cosine of that angle. In this question:

[tex]\begin{aligned} \tan(\theta) &= \frac{\sin(\theta)}{\cos(\theta)} \\ &= \frac{3/4}{\sqrt{7}/4} \\ &= \frac{3}{\sqrt{7}} \\ &= \frac{3\sqrt{7}}{7}\end{aligned}[/tex].

Answer:

-1/2  ,  3

Step-by-step explanation:

In order to find the roots of the function 2x² - 5x - 3  

We have to solve the quadratic equation :

2x² - 5x - 3 = 0

Calculating the discriminant Δ :

Δ = b² - 4ac

  = (-5)² - 4(2)(-3)

  = 25 + 24

  = 49

Then

√Δ = √49 = 7

Determining the Zeros :

[tex]x=\frac{-b+\sqrt{b^{2}-4ac} }{2a} = \frac{5+7} {2 \times (2)} =\frac{12}{4} =3[/tex]

or

[tex]x=\frac{-b-\sqrt{b^{2}-4ac} }{2a} = \frac{5-7} {2 \times (2)} =\frac{-2}{4} =\frac{-1}{2}[/tex]

Answer:

-4/21

Step-by-step explanation:

-3/5×20/63

-3×4/63

-4/21

Answer:

-20 -d

Step-by-step explanation:

-(20+d)

Distribute he minus sign

-20 -d

Answer:

5

Step-by-step explanation:

you have to replace 2 were there's x in the function

f(2)=3(2)-1

=6-1

=5

I hope this helps

Step-by-step explanation:

Using the properties of logarithms, the left side of the equation becomes

[tex]\log{3x^3} - \log{x^2} = \log{3x}[/tex]

while the right hand side becomes

[tex]\log{27} - \log{x} = \log{\frac{27}{x}}[/tex]

so we end up with

[tex]3x^2 =27 \Rightarrow x = 3[/tex]

475,805 rounded to the nearest ten thousand would be 476,000.

Answer:

The perimeter of it is going to be 50

Step-by-step explanation:

This is because when finding the perimeter you add up all the sides so

14 + 12 + 18 + 6 = 50

Answer:

50 m

Step-by-step explanation:

Perimeter

= Sum of the length of all sides

= 14 m + 12 m + 6 m + 18 m

= 50 m