Please help me with this

The first four terms of the sequence are 3, 7, 15, and 31. This sequence is represented using an explicit geometric formula.

A rule is defined such that its definition includes itself.

Example:

F(x) = F(x-1) + c

is one such recursive rule.

PART A:

State the first four terms of this sequence.

[tex]a_1 = 3\\\\a_n = 1+ 2a_{n-1}[/tex]

[tex]a_2 = 1+ 2a_{2-1}\\\\a_2 = 1+ 2a_{1}\\\\a_2 = 7\\\\a_3 = 1+ 2a_{2}\\\\a_3 = 15\\\\a_4 = 1+ 2a_{3}\\\\a_4 = 31\\[/tex]

PART B:

This sequence is represented using an explicit geometric formula.

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Answer:

the answer is 2.8

Step-by-step explanation:

Answer:

[tex]x=4[/tex]

Step-by-step explanation:

Given:

[tex]\frac{3x}{5} -0.5=1.9[/tex]

Add 0.5 to both sides

[tex]\frac{3x}{5} =2.4[/tex]

Multiply 5 from both sides

[tex]3x=12[/tex]

Divide both sides by 3

[tex]x=4[/tex]

Hope this helps

i wonder this is math problem or code word for treasure

Answer:

Step-by-step explanation:

(2x-15) = 45

Step-by-step explanation:

When two angles lie on a straight line, they are supplementary

what this mean is that the add up to equal 180 degrees

Mathematically, we have this as:

(2x-15) + 135 = 180

(2x-15) = 180-135

(2x-15) = 45

Answer:

0.4

Step-by-step explanation:

If we count up all of the colored squares, we will get 28. And if we count the non-colored squares we will get 72.

Now, we take 28 and we divide it by 72. This will get us 0.3888888. That number rounded up is 0.4.

Hope this helps and if it does, don't be afraid to give my answer a "Thanks" and maybe a Brainliest if it's correct?  

Answer:

This is an arithmetic sequence because there is a common difference of 4 between each term.

Add 4 to the last term to extend this arithmetic sequence

Step-by-step explanation:

Answer:

Step-by-step explanation:

9). Dimensions of the logo = 4 inch by 6 inch

   ∵ 12 inches = 1 feet

    ∴ 1 inch = [tex]\frac{1}{12}[/tex] feet

   Therefore, dimensions of the logo (in feet) will be,

   [tex]\frac{4}{12}[/tex] feet by [tex]\frac{6}{12}[/tex] feet  Or [tex]\frac{1}{3}[/tex] feet by [tex]\frac{1}{2}[/tex] feet

   Dimensions of the logo which are 6 times larger than the original one.

    Dimensions of the advertisement = [tex]\frac{6}{3}[/tex] feet by [tex]\frac{6}{2}[/tex] feet

                                                            = 2 feet by 3 feet

    Area of the advertisement = 2 × 3

                                                = 6 feet²

10). By the property of similar polygons,

     "Corresponding sides of two similar polygons are proportional"

     If the dimensions of two similar polygons are 'x' and 'kx'

     Ratio of the perimeter of two polygons = [tex]\frac{\text{Perimeter of the image polygon}}{\text{Perimeter of the original polygon}}[/tex] = k

     Ratio of area of two similar polygons = [tex]\frac{\text{Area of the image polygon}}{\text{Area of the original polygon}}[/tex] = k²

     Ratio of volumes of two similar polygons = [tex]\frac{\text{Volume of the image polygon}}{\text{Volume of the original polygon}}[/tex] = k³

the graph the represents the equation is C.

Answer:

the answer is a on the image i just did what they said and got it wrong

Step-by-step explanation:

Answer:

What is your definition of finance charge?

the interest is $105.24

3% of what he owes (the minimum) is $273.96

Step-by-step explanation:

$9,026.74

+9,026.74 * (.1399/12) = $105.2367438

($9,026.74 + $105.24)*(.03) = $273.96

Answer:

33.19

Step-by-step explanation:

$2846.89

$2846.89 * (.1399/12) = 33.189992583333333333333333333333

Finance Charge is $33.19

Answer:

I'll set up the problem and you can do the calculation

Step-by-step explanation:

we need to complete the squares to get the equation in the general form:

[tex] {(x - h)}^{2} + {(y - k) }^{2} = {r}^{2} [/tex]

where h = the x coordinate of the center

k = the y coordinate of the center

r = the radius

so looking at

[tex] {x}^{2} - 2x[/tex]

we can see that if use -1 as the constant we have

[tex] {(x - 1)}^{2} = {x}^{2} - 2x + 1[/tex]

doing the same for y

[tex] {y}^{2} - 4y[/tex]

we can use -2 as the constant (basically you that the s

quare of the y coefficient )

[tex] {(y - 2)}^{2} = {y}^{2} - 4y + 4[/tex]

so now we have to add or subtract the constant on the RHS to see what the square of the radius is according to the general form of the equation at the top

20 +1+4=25

Take the square root and you have the radius

Answer:

£455.13

Step-by-step explanation:

3% = .03

p = 530(1 *- .03)⁵

p = 530(.97)⁵

p = 455.129033621

Rounded

£455.13

Answer:

a) 0 seconds.

b) The stunt diver is in the air for 2.81 seconds.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]

[tex]\Delta = b^{2} - 4ac[/tex]

Height of the diver after t seconds:

[tex]h(t) = -4.9t^2 + 12t + 5[/tex]

a) How long is the stunt diver above 15 m?

Quadratic equation with [tex]a < 0[/tex], so the parabola is concave down, and it will be above 15m between the two roots that we found for [tex]h(t) = 15[/tex]. So

[tex]h(t) = -4.9t^2 + 12t + 5[/tex]

[tex]15 = -4.9t^2 + 12t + 5[/tex]

[tex]-4.9t^2 + 12t - 10 = 0[/tex]

Quadratic equation with [tex]a = -4.9, b = 12, c = -10[/tex]. Then

[tex]\Delta = 12^{2} - 4(-4.9)(-10) = -52[/tex]

Negative [tex]\Delta[/tex], which means that the stunt diver is never above 15m, so 0 seconds.

b) How long is the stunt diver in the air?

We have to find how long it takes for the diver to hit the ground, that is, t for which [tex]h(t) = 0[/tex]. So

[tex]h(t) = -4.9t^2 + 12t + 5[/tex]

[tex]0 = -4.9t^2 + 12t + 5[/tex]

[tex]-4.9t^2 + 12t + 5 = 0[/tex]

Quadratic equation with [tex]a = -4.9, b = 12, c = 5[/tex]. Then

[tex]\Delta = 12^{2} - 4(-4.9)(5) = 242[/tex]

[tex]x_{1} = \frac{-12 + \sqrt{242}}{2*(-4.9)} = -0.36[/tex]

[tex]x_{2} = \frac{-12 - \sqrt{242}}{2*(4.9)} = 2.81[/tex]

Time is a positive measure, so we take 2.81.

The stunt diver is in the air for 2.81 seconds.

Answer:

f(-2) = -3

Step-by-step explanation:

When x = -2 we want the value of y

We use the closed circle value ( open circle does not have a value)

f(-2) = -3

Answer: x = 28

Step-by-step explanation:

3x+10+3x+2=180

6x+12=180

6x=168

x = 28

Answer:

x=28

Step-by-step explanation:

Since both lines going up are parallel, we can label the angle to the left of the angle with the measure of 3x+10 3x+2. These angles are supplementary as they are on different sides of the same line. This means that:

(3x+10)+(3x+2)=180

6x+12=180

6x=168

x=28

It's is b cause it is and yeah

Answer:

a

Step-by-step explanation:

Answer:

Presently; Veeru is 15 and Neeru is 20

Step-by-step explanation:

Given

See comment for proper format of question

Let their present ages be x and y

So:

[tex]x : y = 3 : 4[/tex]

5 years time, the ratio will be:

[tex]x + 5: y + 5= 4 : 5[/tex]

Required

Their present ages

Express both ratios as fractions

[tex]x : y = 3 : 4[/tex] becomes

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

and

[tex]x + 5: y + 5= 4 : 5[/tex] becomes

[tex]\frac{x+5}{y+5} = \frac{4}{5}[/tex]

Make x the subject in: [tex]\frac{x}{y} = \frac{3}{4}[/tex]

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

[tex]x = 0.75y[/tex]

Cross multiply in [tex]\frac{x+5}{y+5} = \frac{4}{5}[/tex]

[tex]5(x + 5) = 4(y + 5)[/tex]

Substitute [tex]x = 0.75y[/tex]

[tex]5(0.75y + 5) = 4(y + 5)[/tex]

Open brackets

[tex]3.75y + 25 = 4y + 20[/tex]

Collect like terms

[tex]3.75y -4y = -25 + 20[/tex]

[tex]-0.25y = -5[/tex]

Divide by -0.25

[tex]y = 20[/tex]

Substitute [tex]y = 20[/tex] in [tex]x = 0.75y[/tex]

[tex]x = 0.75 * 20[/tex]

[tex]x = 15[/tex]

[tex]heres \: the \: answer \: i \: hope \: it \: help[/tex]

Answer:

[tex]10\frac{7}{18}[/tex]

Step-by-step explanation:

First revert it to improper fraction.

[tex]\frac{13}{2} +\frac{35}{9} \\\\[/tex]

Now put them to a common denominator.

[tex]\frac{187}{18}[/tex]

=> [tex]10\frac{7}{18}[/tex]

Answer:

y = -4x - 5

Step-by-step explanation:

Answer:

Step-by-step explanation:

a = 7 ;  b = 1 ;  c = -5

D = b² - 4ac

  = 1 - 4*7*(-5)

  = 1 + 140

  = 141

x =( - b ± √D ) / 2a

 = (-1 ± √141)/2*7

 = (-1±√141) / 14

[tex]a = \frac{-1+\sqrt{141} }{14}= \frac{-1+11.87}{14}= \frac{10.87}{14}=0.78\\\\b = \frac{-1-\sqrt{141}}{14}= \frac{-1-11.87}{14}= \frac{-12.87}{14}=3.59\\\\\\[/tex]

(a -4 )(b -4) = (0.78 - 4)(-3.59-4) = (-3.22)(-7.59)

= 24.4398

Answer:

last term is 1536

Value of the geometric series is 3,069

Step-by-step explanation:

took one for the team

There are 10 terms in the geometric series.

And, The first term of the series is, 3

We know that;

An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.

Given that;

The geometric series is,

⇒ S₁₀ = ∑ 3 (2)ⁿ⁻¹

Where, n is from 1 to 10.

Thus, We get;

There are 10 terms in the geometric series.

And, For first term;

Put n = 1;

⇒ S₁₀ = ∑ 3 (2)ⁿ⁻¹

⇒ S₁₀ = ∑ 3 (2)¹⁻¹

⇒ S₁₀ = ∑ 3 (2)⁰

⇒ S₁₀ = ∑ 3 × 1

⇒ S₁₀ = 3

Thus, The first term of the series is, 3

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Answer:

0.301

Step-by-step explanation:

Given that log 3 = .477 and log 6 =.778

Log 2

= log(6/3)

= log 6  - log 3

= 0.778 - 0.477

= 0.301

Hence the value of log 2 is 0.301

Answer:

Step-by-step explanation:544

Answer:

total weight of wheat and rice is 8 kg

Step-by-step explanation:

rice = [tex]3\frac{3}{2}[/tex]

=3*2+3/2

=9/2

wheat = [tex]2\frac{1}{2}[/tex]

=2*2+1/2

=5/2

total weight of wheat and rice = [tex]\frac{7}{2} + \frac{9}{2}[/tex]

since their denominator are same u can add numerators.

=7 +9/2

=16/2

=8

Answer:

D

Step-by-step explanation:

D

The correct function of the graph is,

⇒ f (x) = (x - 1) / (x - 3) (x + 1)

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The graph of function is shown.

Here, The graph is not defined at x = 3, and x = - 1.

Hence, By option;

The correct function of the graph is,

⇒ f (x) = (x - 1) / (x - 3) (x + 1)

Thus, The correct function of the graph is,

⇒ f (x) = (x - 1) / (x - 3) (x + 1)

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Answer:

(A) -3 ≤ x ≤ 1

Step-by-step explanation:

The given function is presented as follows;

h(x) = x² - 1

From the given function, the coefficient of the quadratic term is positive, and therefore, the function is U shaped and has a minimum value, with the slope on the interval to the left of h having a negative rate of change;

The minimum value of h(x) is found as follows;

At the minimum of h(x), h'(x) = d(h(x)/dx = d(x² - 1)/dx = 2·x = 0

∴ x = 0/2 = 0 at the minimum

Therefore, the function is symmetrical about the point where x = 0

The average rate of change over an interval is given by the change in 'y' and x-values over the end-point in the interval, which is the slope of a straight line drawn between the points

The average rate of change will be negative where the y-value of the left boundary of the interval is higher than the y-value of the right boundary of the interval, such that the line formed by joining the endpoints of the interval slope downwards from left to right

The distance from the x-value of left boundary of the interval that would have a negative slope from x = 0 will be more than the distance of the x-value of the right boundary of the interval

Therefore, the interval over which h has a negative rate of change is -3 ≤ x ≤ 1

Answer:

The probability is 0.5

Step-by-step explanation:

If there is a 50% chance of rain, then there is also a 50% chance of not rain.

Now let's write all the probabilities:

(just take the percentage and divide it by 100%)

Probability of rain: p = (50%/100%) =  0.5

probabiity for the squirrel to find food when it rains: q = (25%/100%) = 0.25

Then the joint probability, this is, the probability that rains and that the squirrel finds food, is equal to the product of these two probabilities, this is:

P1 = 0.5*0.25 = 0.125

And we also have the case where there is no rain.

Probability that does not rain: p' = (50%/100%) = 0.5

Probability that the squirrel finds food if doesn't rain: q = (75%/100%) = 0.75

The joint probability is:

P2 = 0.5*0.75 = 0.375

The total probability that the squirrel will find food is equal to the sum of the probabilities of the squirrel finding food if there is rain, and the probability of the squirrel finding food if there isn't rain, so the total probability is:

P = P1 + P2 = 0.125 + 0.375 = 0.5

Answer:

0.110

0.230

Step-by-step explanation:

Given :

In health :

Average salary, m = 51,541

Standard deviation, s = 11000

In Business :

Average salary, m = 53,901

Standard deviation, s = 15000

Since distribution is approximately normal ;

We can obtain the standardized scores and find the probability ;

Zscore = (x - mean) / standard deviation

Probability of earning salary if atleast $65,000

Health:

P(Z ≥ (65000 - 51541) / 11000) = P(Z ≥ 1.224) = 0.11048 (Z probability calculator)

Business :

P(Z ≥ (65000 - 53901) / 15000) = P(Z ≥ 0.740) = 0.22965 (Z probability calculator)

Hence, the probability of earning a starting salary of atleast $65,000 is :

Health = 0.11048

Business = 0.22965

Answer:

it's called the horizontal line

Step-by-step explanation:

also known as y=0