A sequence is defined as t1=1 and
t(n+1)=tn+3. which is the nth term of the
sequence ?
A) 3n-2
B) 4n-3
C) n^2-n+1
D) 5n-4
E) 6n-5


I need this for a test :(( in t1, the 1 is a subscript and in t(n+1) the (n+1) is a subscript.

Answer:

B

Step-by-step explanation:

In the right triangle with hypotenuse of 10 use the sine ratio to find x

sin20° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{10}[/tex]

Multiply both sides by 10

10 × sin20° = x, hence

x ≈ 3.4 ( to the nearest tenth ) → B

Answer:

The answer is 41.

Answer:

41

Step-by-step explanation:

Gabrielle's age = G

Mikhail's age = M

G = M - 15

G + M = 67

Substituting:

M - 15 + M = 67

2M = 82

M = 41

Mikhail is 41.

Answer: It was doubled in size and reflected across the X and Y axis.

Step-by-step explanation:

Answer:

(-1, 5.5)

Step-by-step explanation:

There are a number of techniques that can be used to solve a system of linear equations. Some of these techniques include;

Elimination method

Substitution method

Graphical method

In the graphical approach, we simply graph the linear equations on a cartesian plane. The solution to the system of equations is the co-ordinate of the point of intersection of the equations.

I use desmos graphing tool to graph the two equations;

y = -1/2x + 5

y = 1/2x + 6

From the attachment below, we can see that the lines intersect at (-1, 5.5)

Therefore, the solution to the given system of equations is (-1, 5.5)

Answer:

19/50

Step-by-step explanation:

.38 is equal to 38/100 so if you do half of that it is 19/50

Hope this helps!

Answer:

[tex]\frac{19}{50}[/tex]

Step-by-step explanation:

0.38 ← note 38 represents 38 hundredths, that is

0.38 = [tex]\frac{38}{100}[/tex] ← divide numerator/denominator by 2

       = [tex]\frac{19}{50}[/tex] ← in simplest form

43785 is not divisible by 2 because it's not an even number, and this also means it's not divisible by 10 because 10 = 2*5.

The sum of its digits is 4 + 3 + 7 + 8 + 5 = 27, which is divisible by 3 since 27 = 3*9, so 43785 is divisible by 3. We have 43785 = 3*14595.

It would be divisible by 9 if 14595 were also divisible by 3. That number has digital sum 1 + 4 + 5 + 9 + 5 = 24, which is divisible by 3, so 14595 is too and 14595 = 3*4865. So 43785 = 9*4865, and it is indeed divisible by 9.

14595 is clearly divisible by 5 because its ends with a 5.

Answer:

(6,-2)

Step-by-step explanation:

2x + 3y = 6

 x + y = 4

Multiply the second equation by -2 to eliminate x

-2(x+y) = -2*4

-2x-2y = -8

Add this to the first equation

2x + 3y = 6

-2x -2y = -8

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

       y = -2

Now we need to find x

x+y = 4

x-2 = 4

Add 2 to each side

x-2+2 = 4+2

x = 6

(6,-2)

Answer:

(6,-2)

Step-by-step explanation:

Given equations are [tex]2x + 3y = 6[/tex] and [tex]x + y = 4[/tex].

Solve 2nd equation  [tex]x + y = 4[/tex] for y

[tex]x + y = 4[/tex]

[tex]y = 4-x[/tex] ...(i)

Plug value of y from equation (i) into first equation  [tex]2x + 3y = 6[/tex]

[tex]2x + 3(4-x) = 6[/tex]

[tex]2x + 12-3x = 6[/tex]

[tex]12-x = 6[/tex]

[tex]-x = 6-12[/tex]

[tex]-x = -6[/tex]

[tex]x = 6[/tex]

Plug x=6 into equation (i)

[tex]y = 4-x[/tex]

[tex]y = 4-6[/tex]

[tex]y = -2[/tex]

Hence final answer is x=6, y=-2 or we can write that in (x,y) form as (6,-2)

since the point (4,13) is on the circle, then the distance from the center to it, is the radius of the circle.

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{13})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{[4-(-2)]^2+[13-5]^2}\implies r=\sqrt{(4+2)^2+(13-5)^2} \\\\\\ r=\sqrt{36+64}\implies r=\sqrt{100}\implies r=10 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-2}{ h},\stackrel{5}{ k})\qquad \qquad radius=\stackrel{10}{ r}\\[2em] [x-(-2)]^2+[y-5]^2=10^2\implies (x+2)^2+(y-5)^2=100[/tex]

It’s B

X•8 it the same as 8x

Answer:

  D. The constant 250 represents the average collection when no seniors ride.

Step-by-step explanation:

A -- the entire expression represents the driver's pay, not just the constant 250.

B -- collections continue to increase as x goes up, so 250 is the minimum, not the maximum.

C -- x is the number of seniors; 250 is in units of collections (dollars?), not numbers of seniors.

D -- indeed, 250 is the "y-intercept" of the expression, hence the collection when no seniors ride.

The value of the natural logarithm when x = 0.5 is rounded to the nearest hundredth is -0.69. So option B is correct.

When you raise a number with an exponent, there comes a result.

Let's say you get

a^b = c

Then, you can write 'b' in terms of 'a' and 'c' using a logarithm as follows

[tex]b = \log_a(c)[/tex]

'a' is called the base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'

Since x is lesser than 1, then the value of its natural logarithm must be negative.

The natural logarithm is a transcendental function and an irrational number, then it can be estimated by approximations.

ln ( 0.5) = -0.69

The value of the natural logarithm when x = 0.5 is rounded to the nearest hundredth is -0.69. So option B is correct.

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Answer:

Step-by-step explanation:

I can give you an answer, but I'm afraid it will only be true on paper.

Area = L * W

(x^2- 6x - 7) = L * (x - 7)

(x - 7)(x + 1) = L * (x - 7)

(x - 7)(x + 1)

=========     = L

(x - 7)

(x + 1) = L

The expression representing the length of a rectangle could vary depending on context, such as using graph measurements (Δx = 41 m), significant figures (1.25 cm), or scaling factors (4 inches × 2 = 8 inches).

To determine the expression that represents the length of a rectangle, we generally use the formula for the perimeter or area, depending on what information is available. In this case, information provided suggests different scenarios involving measurements and area calculations. From one scenario, the length of a rectangle is calculated using graph paper measurements, resulting in Δx = 41 m. In another scenario, we're given information about a rectangle's width being 1.25 cm with three significant figures.

In physics-related contexts, references to frame of reference and speed c suggest considering displacement in spacetime, though this might not relate directly to the geometrical dimensions of a rectangle. Lastly, one mention involves the scaling up by a factor, such as a square with side length doubled, resulting in a side length expression of 4 inches × 2 = 8 inches. Without further context, it is not possible to provide a definitive expression for the length of a rectangle.

Answer:

increase, appreciate, rise

Step-by-step explanation:

The words associated with expo GROWTH are

increase, appreciate, rise.

All the others are often but not always associated with expo DECAY.

Answer:

increase

rise

appreciate

They a;ll mean increase:)

Mark Brainlyest please

Check the picture below.

for "b", well, recall that the sum of all interior angles in a triangle is 180°.

for "a", "c" and "d", well, all those are just intercepted arcs.

Answer:

Associative property of addition

Step-by-step explanation:

We are given the statement [tex] ( a + b ) + c [/tex] and we are to determine whether which of the given answer options allows it to be written as [tex] c + ( a + b ) [/tex].

According to the associative property of addition, you can add the numbers regardless of how they are grouped.

Therefore, (a + b) + c = c + (a + b) is possible with associative property of addition.

The answer is commutative - addition!

The reason it is not associative is because while the direction changes, the parentheses does not move! In the associative, the parenthesis moves, but in (a + b) + c = c + (a + b), the parenthesis contains a + b in both of them. Also here is some picture proof. (Attached)

⭐ Answered by Hyperrspace (Ace) ⭐

⭐ Brainliest would be appreciated, I'm trying to reach genius! ⭐

⭐ If you have questions, leave a comment, I'm happy to help! ⭐

Answer:

The solution to this system is (4, 1/6).

Step-by-step explanation:

Please separate these two equations for clarity.  I like to write them in column format:

2.5y + 3x = 27

5x – 2.5y = 5

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

8x           = 32, and x = 4.

Subbing 4 for x in the second equation yields 5(4) - 2.5y = 5.

Then 20 - 2.5y = 5, or 15 = 2.5y.  Solving for y, we get y = 1/6.

The solution to this system is thus (4, 1/6).

Answer: The resultof adding the two equations is 3x= 32.  

The solution to the system is ( 4; 6).

Step-by-step explanation:

Hi, first we add the two equations.

2.5y + 3x =27

+

-2.5y +5x   = 5

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

8x= 32

The resultof adding the two equations is 3x= 32

the next step is solving the equation:

8x= 32

x=32/8

x= 4

Substituting the value of x in any of the original equations:

2.5y +3x= 27

2.5y +3(4) =27

2.5y +12=27

2.5y  = 27-12

2.5y = 15

y= 15/2.5

y=6

So, the solution to the system is ( 4; 6)

Feel free to ask for more if it´s necessary or if you did not understand something.

Answer:

i just need the points

Step-by-step explanation:

I think you are asking for 3 different ways of diving 100 pounds of potatoes into 5 and 2 pounds bags.

Alright:

I think you are asking for 3 different ways of diving 100 pounds of potatoes into 5 and 2 pounds bags.

Alright:

5 two pounds bags and 18 five pounds ones

10 two pounds bags and 16 five ones

15 two pounds bags and 14 five pounds ones

Answer:

arctan(2.6) = 68.96

Step-by-step explanation:

To find the arctan of 2.6, we are going to use calculator:

Then, we have that arctan(2.6) = 68.96.

The principal value of arctan(2.6) is 1.231 radians or approximately [tex]70.43^o[/tex].

The arctan function, also known as the inverse tangent function, is the inverse of the tangent function. It is denoted as arctan(x), atan(x), or tan^(-1)(x).

The arctan function takes a real number as input and returns the angle whose tangent is equal to that number. In other words, if y = arctan(x), then tan(y) = x.

In other words, the principal value of arctan refers to the primary angle within a specific range for which the tangent function yields a given value. In the case of arctan(2.6), we are seeking the principal angle whose tangent is equal to 2.6.

We can determine the principal value of arctan(2.6) to be approximately 1.231 radians or approximately [tex]70.43^o[/tex]. It is important to note that the angle can be expressed in either radians or degrees, depending on the desired unit of measurement.

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Answer:

y = -5x + 46

Step-by-step explanation:

We are trying to find an equation in y=mx+b form

Okay so we know two points on the graph,  from which we can get the slope (value of m) by the formula [tex]\frac{y_{2} -y_{1}}{x_{2}-x_{1}}[/tex]

plugging in the values:  [tex]\frac{6 -1}{8-9}[/tex]

the resulting slope is -5

to find our b value we can plug in one of our coordinants into the equation and solve for b

1 = -5(9) + b

1 = -45 + b

46 = b

so our equation in y = -5x + 46

Answer:

Hence final answer is [tex]x<-8[/tex] or [tex]x>\frac{1}{5}[/tex]

correct choice is B because both ends are open circles.

Step-by-step explanation:

Given inequality is [tex]\frac{x+8}{5x-1}>0[/tex]

Setting both numerator and denominator =0 gives:

x+8=0,  5x-1=0

or x=-8, 5x=1

or x=-8, x=1/5

Using these critical points, we can divide number line into three sets:

[tex](-\infty,-8)[/tex], [tex]\left(-8,\frac{1}{5}\right)[/tex] and [tex](\frac{1}{5},\infty)[/tex]

We pick one number from each interval and plug into original inequality to see if that number satisfies the inequality or not.

Test for [tex](-\infty,-8)[/tex].

Clearly x=-9 belongs to [tex](-\infty,-8)[/tex] interval then plug x=-9 into [tex]\frac{x+8}{5x-1}>0[/tex]

[tex]\frac{-9+8}{5(-9)-1}>0[/tex]

[tex]\frac{-1}{-46}>0[/tex]

[tex]\frac{1}{46}>0[/tex]

Which is TRUE.

Hence [tex](-\infty,-8)[/tex] belongs to the answer.

Similarly testing other intervals, we get that only [tex](-\infty,-8)[/tex] and [tex](\frac{1}{5},\infty)[/tex] satisfies the original inequality.

Hence final answer is [tex]x<-8[/tex] or [tex]x>\frac{1}{5}[/tex]

correct choice is B because both ends are open circles.

Answer:

[tex]x \:<\:-8[/tex] or  [tex]x \:>\:\frac{1}{5}[/tex].

Step-by-step explanation:

The given inequality is [tex]\frac{x+8}{5x-1} \:>\:0[/tex]

For this statement to be true, then we must have the following cases:

Case 1

[tex]x+8 \:<\:0\:and\:5x-1\:<\:0[/tex]

[tex]x \:<\:-8\:and\:x\:<\:\frac{1}{5}[/tex]

The intersection of these two inequalities is [tex]x \:<\:-8[/tex].

The solution to this first case is  [tex]x \:<\:-8[/tex].

Case 2

[tex]x+8 \:>\:0\:and\:5x-1\:>\:0[/tex]

[tex]x \:>\:-8\:and\:x\:>\:\frac{1}{5}[/tex]

The intersection of these two inequalities is [tex]x \:>\:\frac{1}{5}[/tex].

The solution to this second case is  [tex]x \:>\:\frac{1}{5}[/tex].

Therefore the solution to the given inequality is

[tex]x \:<\:-8[/tex] or  [tex]x \:>\:\frac{1}{5}[/tex].

The second option is correct

B I hope this help :)

The necessary conditions are: B. Opposite sides are parallel, A. Alternate interior angles, and D. Alternate interior angles are supplementary.

To prove that the opposite sides of a parallelogram are congruent, the following conditions are necessary:

1. **Opposite sides are parallel (Option B)**: This is a fundamental property of parallelograms. Parallel sides ensure that corresponding angles are congruent and alternate interior angles are congruent.

2. **Alternate interior angles (Option A)**: If the opposite sides are parallel, then alternate interior angles will be congruent. This property is essential in establishing the equality of corresponding sides.

3. **Alternate interior angles are supplementary (Option D)**: This property is crucial in proving the congruence of opposite sides. It guarantees that when opposite angles are equal, the opposite sides will also be equal.

Therefore, the correct options are A, B, and D. These conditions collectively ensure the congruence of opposite sides in a parallelogram.

For this question, set up an equation.  60 times what decimal is 27?

60x=60

x=0.45

Convert this decimal to a percentage by multiplying it by 100:

45%

For this question, set up an equation.  55% (or 0.55) times what number equals 22?

0.55x=22

*Divide both sides by 0.55*

x=40

Hope this helps!!

The equation that the drivers use to determine the time is  (1/7)n + (1/11)n.

What is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

Here, we have

Given: One delivery driver can complete a route in 7 h another can do the same route in 11 hours.

We have to determine the equation can the drivers use to determine time T in hours needed to complete the route when they work together.

We concluded that

= (1/7)n + (1/11)n

Hence, the equation that the drivers use to determine the time is  (1/7)n + (1/11)n.

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Answer:

x=3

Step-by-step explanation:

25x+57+x=45x

26x+57=45x

57=19x

x=57/19

x=3

ANSWER

x=96°

EXPLANATION

The sum of exterior angles of a polygon is 360°.

So we add all the exterior angles and equate to 360°

130°+134°+x=360°

264°+x=360°

x=360°-264°

x=96°

Answer:

0.50

Step-by-step explanation:

0.30 + 0.20 = 0.50

(That answer feels almost too easy so I am not positive. I would wait for other answers to come in before submitting for your quiz/homework)

Answer:

B.0.44

Step-by-step explanation:

0.3+0.2=0.5 that is the probability that the player will either throw the ball into

the basket or kick the ball through the goal

0.5-0.06=0.44

0.06 is the probability of the player doing both, but the question said not both so just minus it and there comes your answer.

Answer:

x = 20

Step-by-step explanation:

When two lines intersect they form two pairs of opposite angles which are also known as vertical angles.  Vertical angles are always congruent which means that they are equal.

Angle TRS = Angle VRW

x + 40 = 3x

x - x + 40 = 3x - x

40 = 2x

40/2 = 2x/2

20 = x

(20 + 40) = 3(20)

60 = 60

Answer:

x = 20

Step-by-step explanation:

The given angles are vertical and congruent, so

3x = x + 40 ( subtract x from both sides )

2x = 40 ( divide both sides by 2 )

x = 20

The equation for the annual driving cost, C, in terms of d, the number of miles driven is C = 0.125 d + 5000.

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .

Now it is given that,

annual cost of driving = $5000 per year

operating costs of car =  12.5 cents per mile = $0.125

Let total distance drive annually be dmile

So, operating costs of car annually  = $0.125 of total distance drive

⇒operating costs of car annually  = $0.125  of d

⇒operating costs of car annually  = $0.125 d

So,  equation for the annual driving cost, C, in terms of d, the number of miles driven is given as,

annual driving cost, C = operating costs of car annually + annual cost of driving

⇒ C = 0.125 d + 5000

Hence,The equation for the annual driving cost, C, in terms of d, the number of miles driven is C = 0.125 d + 5000.

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P(7) = 1/8 = 0.125 out of 1

The value of P(7) = 1/8 = 0.125

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.

We can predict only the chance of an event to occur i.e. how likely they are to happen, using it.

There are 8 possibilities, all equally spaced

each one has a probability of 1/8

landing on a 7 is one options

so the P(7) is 1/8

P(7) = 1/8 = 0.125 out of 1

Toss a coin 100 times, how many Heads will come up, Probability says that heads have a ½ chance, so we can expect 50 Heads.

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Answer:20/24

Step-by-step explanation:

To find the fraction of members that voted yes, we need to divide the number of members that voted yes by the total number of members.
Given:
- Total number of members (two dozen): 1 dozen is 12 members, so two dozen is 2 x 12 = 24 members.
- Number of members that voted 'yes': 20 members.
Now, to find the required fraction, we perform the following division:
Fraction of members that voted yes = (Number of members that voted 'yes') / (Total number of members)
                                   = 20 / 24
This fraction can be simplified to its lowest terms by dividing both the numerator (20) and the denominator (24) by their greatest common divisor (GCD), which is 4:
Simplified fraction = (20 ÷ 4) / (24 ÷ 4)
                    = 5 / 6
Therefore, the fraction of members that voted yes is 5/6.