Find the sum of the first n terms of the geometric sequence. n=5, a₁ =4, r = 3​

The function modelled for the given condition is [tex]y = -16x^{2} + 6x +22[/tex] and the time after which the skier is 5 feet above the water is 1.23 seconds.

A competitive water skier's heights y, x seconds after soaring off a ramp.

For x = 0, y = 22

for x = 0.25, y = 22.5

For x = 0.75, y = 17.5

For x = 1, y = 12

For x = 1.1, y = 9.24

The general equation of a quadratic equation is y = [tex]ax^{2} + bx +c[/tex]

Putting x = 0 and y = 22 in the equation, we get :

[tex]y = ax^{2} +bx +c[/tex]

c = 22

Now, putting x = 1 and y =12, we get,

12 = a*1 + b*1 + 22

a +b = 12 - 22 = -10 equation (1)

Putting x = 0.25, y = 22.5,

22.5 = a* [tex]22.5^{2}[/tex] +b*22.5 +22

506.25 a +22.5b = 0.5 equation(2)

Solving equation (1) and equation(2), we get :

a = -16 and b = 6 and c = 22

So, the quadratic equation becomes,

[tex]y = -16x^{2} + 6x +22[/tex]

Now, Time when the skier is 5 feet above the water,

[tex]x = \frac{3 +\sqrt{281} }{16} = 1.23 seconds[/tex]

Hence, the function modelled for the given condition is [tex]y = -16x^{2} + 6x +22[/tex] and the time after which the skier is 5 feet above the water is 1.23 seconds.

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1. The relationship as a function r = f(t) is: r = (9 - 2t)/9.

2. The numeric value at t = -9 is: f(-9) = 3.

3. The value of t for which f(t) = 5 is t = -18.

The relationship is given as follows:

9r + 2t = 9.

To write the relationship as a function of t, we have to isolate the variable r as a function of the variable t, hence:

9r = 9 - 2t

r = (9 - 2t)/9.

To find the numeric value at t = -9, we replace the lone instance of t in the relationship by -9, hence:

r = (9 - 2(-9))/9 = 27/9 = 3.

To find when f(t) = 5, we have to find t for which f(t) = 5, hence:

9r = 9 - 2t

2t = 9 - 9r

2t = 9 - 9(5)

2t = -36

t = -36/2

t = -18.

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The equation that generates the table is

y = (2/5)x + 4.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

Money Spent (x)      $0  $20  $40  $60

Pounds of Food (v)  4      12     20    28

We can have the following points from the table.

(0, 4), (20, 12), (40, 20), and (60, 28).

Now,

Choose two points:

(0, 4) and (20, 12)

m = (12 - 4) / (20 - 0)

m = 8 / 20

m = 2/5

Now,

(0, 4) = (x, y)

y = mx + c

4 = (2/5) x 0 + c

4 = c

c = 4

Now,

The equation is given as,

y = mx + c

y = (2/5)x + 4

The equation that generates the table is

y = (2/5)x + 4.

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25. doubled

26. doubled

27. increases 4 times

28. remains unchanged

29. increases 6 times

The value of P is $2,000.

The value of r is 2.8%

The value of n is 4.

The amount of money that Allision will have in 8 years is  $2,500.19.

When the account is compounded quarterly, it means that the amount invested and the interest that has already been earned would increase in value four times in a year. A compound growth rate can be modelled as an exponential equation.

The equation that can be used to determine the future value with quarterly compounding is:

S(t) = P( 1 + r /n)^(n x t)

Where:

S(t) = 2,000 x ( 1 + 0.028 / 4)^(4 x 8)

S(t) = 2,000 x 1.007^32 = $2,500.19

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Answer/Step-by-step explanation:

Use the given drawing and scale to find out how big the building is in real life. See image. Then use the scale they asked for to make the new drawing. See image.

Answer:

  240 cm by 288 cm

Step-by-step explanation:

You want the dimensions of a 150 cm by 180 cm poster enlarged by the ratio 8:5.

The enlargement ratio, expressed as a fraction, multiplies each of the original dimensions to get the new dimensions. The new dimensions are ...

  (8/5)·150 cm by (8/5)·180 cm = 240 cm by 288 cm

Answer of the given question are respectively,

[tex]-x^2y , 2w ,\\\\h^6 , -14a^5b^2\\x^6 , 4m^8\\9x^4/14 , y^2\\-5/x^2 , 1/2k\\7 , 1[/tex]

Exponent:

                          A quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression.

        Example:

                             [tex]2^3[/tex] = 2 × 2 × 2

Combine like term:

 1. [tex]9x^2y -10x^2y[/tex] = [tex]-x^2y[/tex]

 2. Subtract 6w from 8w

          8w -6w = 2w

Rule:

          [tex]x^{a} * x^{b} = x^{a+b} \\\\[/tex]

1.

        [tex]h^2 * h^4 = h^{2+4} \\ \\\\= h^6[/tex]              

2.  

        [tex](-2a^2b).(7a^3b)\\\\-14 a^{2+3} b^{1+1} \\\\= -14 a^5 b^2[/tex]

Rule:

       [tex](x^a)^b = x^{ab}[/tex]

  1.  [tex](x^2)^3 = x^6[/tex]

  2.

         [tex](-2m^3)^2 * m^2 \\\\4m^6*m^2\\\\4m^8[/tex]

Rule:

           [tex]x^a/x^b = x^{a-b}[/tex]

1.

   [tex]27x^5/42x\\\\= 9x^4 /14[/tex]

2.

          [tex](y^3)^2/y^4\\\\y^6/y^4\\\\y^2\\[/tex]        

Rule:

            [tex]x^{-a}= 1/x^a[/tex]

1.

    [tex]-5x^{-2} \\\\= -5/x^2[/tex]

2.

    [tex]4k^2/8k^3\\\\= k^{-1} /2\\\\= 1/2k[/tex]

Rule:

           [tex]x^0 =1[/tex]

1.

         [tex]7x^0\\\\= 7[/tex]

2.

         [tex](w^4)^2/w^8\\\\w^8/w^8\\\\w^0\\\\=1[/tex]

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For the given equation y  = 3x² -7x + 4 the vertex form is given by

( 7/6, -1/12).

As given in the question,

Equation is given by :

y  = 3x² -7x + 4

Standard form of the equation to get the vertex form is given by :

y = a ( x - h )² + k

Where ( h, k ) represents the vertex of the equation,

Now,

Simplify the given equation y  = 3x² -7x + 4 into standard form to get vertex form,

y  = 3x² -7x + 4

⇒ y = 3 [x² -2×(7/6)] + 4

⇒ y = 3 [ x² - 2×(7/6) + (49/36) - (49/36) ] + 4

⇒ y = 3 [ x² - 2×(7/6) + (49/36) ] - 3(49/36) + 4

⇒ y = 3 [x - (7/6)]² - (49/12) + 4

⇒ y = 3[x - (7/6)]² - (1/12)

Compare it with standard form ,

a = 3, h = (7/6) , k = -(1 /12)

Vertex form ( h, k) = ( 7/6 , -1/12 )

Therefore, for the given equation y  = 3x² -7x + 4 the vertex form is given by ( 7/6, -1/12).

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Answer:

[tex]\hat{y}=-0.29x+5.67[/tex]

Step-by-step explanation:

Given points on the scatter plot:

Plot the given points and draw a line of best fit (see attachment).

As the y-values decrease as the x-values increase, the slope of the line of best fit is negative.

From inspection of the plotted line of best fit, we can see that the y-intercept is approximately 5.7.

Therefore, the equation that is appropriate for the line of best fit is:

[tex]\boxed{\hat{y}=-0.29x+5.67}[/tex]

Answer:

y hat equals negative 29 hundredths times x plus 5 and 67 hundredths.

Step-by-step explanation:

i took the test :)

As Karen age is 52- year old and she is a female and her life insurance policy is for 20- years , then amount to be deducted from her life insurance paycheck is equal to $1317.

As given in the question,

Information given about Karen,

Age = 52- year old

Gender = female

Policy = 20 -year life insurance policy

Annual premium given per $1000 for coverage

Karen policy amount = $75,000

From the table it is given that,

Amount deducted per $1000 for 20year policy in the age limit of 48 -52

= $17.56

⇒ $1000 = $17.56

⇒ $75,000 = $( 17.56 × 75,000)/ 1000

                   = $1317.

Therefore, as Karen age is 52- year old and she is a female and her life insurance policy is for 20- years , then amount to be deducted from her life insurance paycheck is equal to $1317.

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Answer: x+3

Step-by-step explanation:

since it has the absolute value, it will be x+3 and you can graph that in your calculator!

A student 6ft tall is standing 20ft away from a 35ft tall flagpole.

The flagpole is 60ft away from a building.

From the students point of view, the flagpole is lined up perfectly with the top of the building.

What's the height of the building?

The new coordinates of House B and House C are
B' ( 3 , -5 ) and C' ( 4 , -4 ) respectively

What is Translation?

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

Given data ,

Let the 3 houses be A , B ,C

The coordinate of House A = A ( 1 , -1 )

​The coordinate of House B = B ( 1 , -2 )

The coordinate of House C = C ( 2 , -1 )

Now , the houses are relocated to new coordinates with

The new coordinate of House A = A' ( 3 , -4 )

The translation of Point A can be expressed in the form of x and y coordinate as there is a translation occurred with a scale factor

So ,

A ( x₁ , y₁ ) to A' ( x₂ , y₂ )

A ( 1 , -1 ) to  A' ( 3 , -4 )

x₂ = x₁ + 2

y₂ = y₁ - 3

From the figure , we can clearly see that the coordinates of the houses A , B and C are translated by a scale factor and the new coordinates are

x₂ = x₁ + 2

y₂ = y₁ - 3

Therefore ,

B ( x₁ , y₁ ) to B' ( x₂ , y₂ )

B' ( x₂ , y₂ ) = B' ( 3 , -5 )

C ( x₁ , y₁ ) to C' ( x₂ , y₂ )

C' ( x₂ , y₂ ) = C' ( 4 , -4 )

Hence , the new coordinates of House B and House C are B' ( 3 , -5 ) and C' ( 4 , -4 ) respectively

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The third graph or option 3 represents the function f(x) = - l x l - 2.

Given:

f(x) = - l x l - 2

Table

x            y = - l x l - 2

0            -2

1             -3

2            -4

3            -5

-1            -3

-2           -4

-3           -5

On plotting above points or the above points shown in figure 3 or third graph.

Therefore the third graph or option 3 represents the function f(x) = - l x l - 2.

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Answer:

I think it's 10 idek I just search it

The time it takes the object to attain maximum height is 2 seconds

To find the time it takes the object to attain maximum height, we have to use the quadratic equation to do so. The formula can be given as

t = -b/2a

But let's write and define our quadratic equation with it's variables.

S = 64t - 16t²

To attain maximum height;

t = -b/2a

a = -16, b = 64,c = 0

Substituting the values

t = -64/2(-16)

t = 2

The time is 2 seconds

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Step-by-step explanation:

1. 95+78 as its asking how many bools all together. 173 books

2. 305-98 ita asking how many miles LEFT.

The slope of the graph is 5.5.

Given:

During one hour of running, Jeff can run 5.5 miles. The number of miles Jeff runs and the number of hours are in a proportional relationship. This is represented by y=5.5x .

slope:

Slope is the steepness of a line as it moves from LEFT to RIGHT. Slope is the ratio of the rise, the vertical change, to the run, the horizontal change of a line. The slope of a line is always constant .

compare the y = 5.5x with standard equation y = mx + c

m = 5.5 and c =0

m is nothing but slope:

so slope m = 5.5

= 11/2.

Therefore The slope of the graph is 5.5.

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well, let's notice our tangent is positive, that only happens on the 1st and 3rd Quadrants

[tex]tan(t )=\cfrac{\stackrel{opposite}{3}}{\underset{adjacent}{4}}\hspace{5em} \textit{now let's find the hypotenuse} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{4^2 + 3^2}\implies c=5\hspace{5em} \stackrel{I~Quadrant}{cos(t)= \cfrac{\stackrel{adjacent}{4}}{\underset{hypotenuse}{5}}}\qquad \stackrel{III~Quadrant}{cos(t)=-\cfrac{4}{5}}[/tex]

Answer:

Step-by-step explanation:

The balance of the savings plan after 2 years will be=$7,410.85 at 3% compounded monthly.

The balance of the savings plan after 2 years will be=$7,407.95 at 3% compounded annually.

The formula you use to calculate this is:FV=P{[1 + R]^N - 1/ R}=FV OF $1 PER PERIOD, Where R=Interest rate per period, N=number of periods, P=periodic payment, FV=Future value.

By solving a linear equation we will see that there were 6 hours of labor.

We know that the total cost is composed by a fixed amount of $365 plus $89 per hour of labor, so if there are x hours of labor, the total cost will be:

c(x) =  $365 + x*$89

We know that the total cost is $899, then we can write the linear equation:

$899 = $365 + x*$89

$899 - $365 = x*$89

($899 - $365)/$89 = x = 6

So there were 6 hours of labor.

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The number of hours that are there in Jupiter is 9 hours.

The kilograms that a person weigh on the moon is 9kg.

It is important to note that there are 24 hours in a day. Therefore, when Jupiter day is about 3/8 of an earth day. The number of hours will be:

= 3/8 × 24

= 9 hours

Also, a person weight is about 1/6 of their weight on Earth. The kilograms that a person weigh on the moon if their weight on earth is 54kg will be:

1/6 × 54

= 9kg

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Answer:

[tex]33[/tex]

Step-by-step explanation:

Define functions:

[tex]r(x) = 2x+1\\s(x) = -x^2[/tex]

Substitute [tex]s(x)[/tex] into [tex]r(x)[/tex]:

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

Solve for value:

[tex]= 2((-4)^2)+1\\= 2(16) + 1\\= 32 + 1\\= 33[/tex]

** assuming that the function of [tex]s(x)[/tex] the x value is squared with the negative sign.

Answer:

x = 18. y = 54

Step-by-step explanation:

first we we figure out the degrees of the spot where N is.

(I know N references the line but ill be using it to call the spot)

72 + N = 90

subtract 72 from both sides

N = 18

So since opposite angles are the same

2x + N = 3x

2x + 18 = 3x

subtract 2x from both sides

18 = 1x

divide by 1 both sides

18 = x

______

now we add all the angles from the left sides to make 180

2x + N + 72 + y = 180

we know x is equal to 18 and N is also 18

2(18) + 18 + 72 + y = 180

simplify

36 + 18 + 72 + y = 180

add

126 + y = 180

subtract both sides by 126

y = 54

Answer:

P = $11233.08

Step-by-step explanation:

Another word for deposit is the principal and the compounded monthly indicates we're working with compound interest.

The formula for compound interest is:

[tex]A(t)=P(1+\frac{r}{n} )^{rt}[/tex], where P is the principal ("deposit"), r is the rate, n is the number of compounding periods, and t is the time.

Before solving, we will need to convert the percentage to a decimal (9.3% to 0.093) and remember that n = 12, since there are 12 months in a year.

Thus, we will need to solve for P to find Brad's deposit:

[tex]14832=P(\frac{0.093}{12})(^{12*3})\\14832=P(1.00775)^{36} \\14832=1.32038641P\\11233.07532=11233.08=P[/tex]

The slope of the function y = 2 + 34x is 34 and the y-intercept of the function y = 2 + 34x is 2.

First, let us understand the slope intercept form;

The slope intercept form is simply a way of writing a line's equation so that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are obvious.

We know that the slope intercept form of a line is y = mx + c where m is the slope of the line and b is the y-intercept of the line.

We are given:

y = 2 + 34x

y = 34x + 2

Compare with y = mx + c, we will get;

m = 34

b = 2

So, the slope is 34 and the y-intercept is 2.

Thus, the slope of the function y = 2 + 34x is 34 and the y-intercept of the function y = 2 + 34x is 2.

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Answer:

positive, positive, zero, zero, negative, negative, positive

Step-by-step explanation:

The derivative is positive when a function is increasing.

The derivative is zero when a function is neither increasing nor decreasing.

The derivative is negative when the function is decreasing.

Answer:

a. )

Step-by-step explanation:

There are 15 balls  ......  two are green with a star

2 out of 15 = 2/15 = .1333