What is the recursive rule for this geometric sequence?

1, 3, 9, 27, ...

Enter your answers in the boxes.

Answer:

[tex]f(x)=33*(1.07)^x[/tex]

Step-by-step explanation:

Let f(x) be our exponential growth function representing growth after x years.

We are asked to find the exponential function that satisfies the given conditions: Initial value = 33, increasing at a rate of 7% per year.

Since an exponential growth function is in form: [tex]y=a*(1+r)^x[/tex], where a= initial value of function and r = growth rate in decimal form.

Given:

a=33  

r=7%.

Let us convert our given rate in decimal form.

[tex]7\text{ percent}=\frac{7}{100}=0.07[/tex]

Now let us substitute our given values in exponential function form:

[tex]f(x)=33*(1+0.07)^x[/tex]

[tex]f(x)=33*(1.07)^x[/tex]

Therefore, the exponential function that satisfies our given conditions will be [tex]f(x)=33*(1.07)^x[/tex].

Answer:

y = x^2 +3x-10

Step-by-step explanation:

If we know the roots of a quadratic function, we know that

y = (x -a) (x-b)  where a and b are the roots

y = (x-2 ) (x--5)

y = (x-2)(x+5)

We need to foil this out to get this in standard form of ax^2 + bx+c

FOIL  (x-2) (x+5)

First x*x:  x^2

outer : 5*x = 5x

inner:  -2x  = -2x

last :  -2*5  = -10

Add them up

x^2 +5x-2x-10

x^2 +3x-10

Final answer:

A quadratic equation in standard form with roots 2 and -5 is obtained by multiplying (x - 2)(x + 5), which simplifies to x² + 3x - 10 = 0.

Explanation:

To write a quadratic equation in standard form with integer coefficients that has roots 2 and -5, we use the fact that if α and β are roots of a quadratic equation, the equation can be written as:

ax² + bx + c = 0

Where:

The quadratic equation in standard form using the roots 2 and -5 is given by:

(x - 2)(x + 5) = 0

Expanding this we get:

x² + 5x - 2x - 10

Which simplifies to:

x² + 3x - 10 = 0

Thus, the quadratic equation with integer coefficients and roots 2 and -5 is x² + 3x - 10 = 0.

Answer:

2.  C. { 0, 1, 2}

3.  B. 53

6.  P = 14n + 10

Step-by-step explanation:

2.  The domain is the input values (or the x values)

The domain is { 0,1,2}

3.  f(x) = 5x+3

 where x is the number of minutes.  We will let x = 10

f(10 ) = 5*10 +3

       = 50+3

      = 53

53 cars will pass

6.  When we have 1 trapezoid, the perimeter is 5+5+8+6 = 24

When we have 2 trapezoids, the perimeter is 5+8+6+5+8+6 = 38

We add 14, when we add a second trapezoid

P = 14n + 10

p(1) = 14+10   Check for 1 trapezoid

p(2) = 14*2 +10 = 28+10 = 38    check for 2 trapezoids

2. You're given a function that maps 1 to 1, 0 to 0, and 2 to -1. The domain is the set of points that are given to the function as inputs, {1, 0, 2}, which is equivalent to the set listed in option C.

3. Evaluate [tex]f(x)[/tex] at [tex]x=10[/tex]:

[tex]f(10)=5(10)+3=50+3=53[/tex]

so the answer is B.

6. Each trapezoid in the chain contributes a copy of 8 and 6 (a total of 14), so that we should expect the total perimeter to contain [tex]14n[/tex]. The remaining two sides contribute a constant 10 regardless of [tex]n[/tex]. So the perimeter is given by the formula in D, [tex]P=14n+10[/tex].

Answer: 8.75

Step-by-step explanation: Divide 166.25 by 19

Mr Rice will purchase 8.75 ft of edging

if we derive equation for this question, then we have:

166.25 = 19Y

Y= [tex]\frac{166.25}{19 }[/tex]

Y= 8.75

To determine the lengths of edging Mr Rice will need to purchase, the total length of edging on the flower beds (166.25) will be divided by the total length of an edging being sold (19) i.e. 166.25 ÷ 19

= 166.25 ÷ 19

= [tex]\frac{166.25}{19 }[/tex]

= 8.75

Therefore, the total length of edging Mr Rice will need to purchase is 9 ft.

The above mathematical expression is a number problem, and was solved with the aid of division.

The term, division, is a basic arithmetic operation which deals with splitting or dividing two or more numerical values into different equal part.

In this case, it could be observed that the significant numbers that were divided are 166.25 and 19, resulting to 8.75. It is also a function of BODMAS (which is an order of operations).

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Answer:

Answer is B

Step-by-step explanation:

Answer:

y=5(x-3)^2 +50

Step-by-step explanation:

To find the value of x in the equation 4(px+1)=64, you divide by 4, simplify, and then divide 15 by p, resulting in x = 15/p. Substituting p=-5 gives x=-3.

To solve the equation 4(px+1)=64 and find the value of x in terms of p, we follow these steps:

Divide both sides of the equation by 4 to isolate the term with x: (px+1) = 64/4

Further simplify to get px + 1 = 16

Subtract 1 from both sides to get px = 16 - 1

Finally, divide by p to solve for x: x = (16 - 1) / p = 15/p

The value of x in terms of p is 15/p.

Substitute p = -5 into the equation to find the value of x when p is -5:

x = 15 / -5

x equals -3

Answer:

The point-slope form is y = 3/4x + 10 and the standard form is -3x + 4y = 40

Step-by-step explanation:

In order to find this equation in point-slope form, simply solve for the y value.

y - 4 = 3/4(x + 8)

y - 4 = 3/4x + 6

y = 3/4x + 10

Now to get to the standard form, solve for the constant, then rationalize the denominator.

y = 3/4x + 10

-3/4x + y = 10

-3x + 4y = 40

The equation of the same line in standard form is 3x - y = -9.

The equation of the same line in standard form is 3x - y = -9.

In point-slope form, y - 4 = (3/4)(x + 8). To convert this to standard form, we need to eliminate the fraction by multiplying both sides of the equation by 4. This gives us 4(y - 4) = 3(x + 8).

Simplifying, we have 4y - 16 = 3x + 24. Rearranging the terms, the equation in standard form is 3x - 4y = -40. To make it more standard, we can multiply all the terms by -1 to get -3x + 4y = 40. Finally, we divide all the terms by -1 to get the final equation of the line in standard form: 3x - y = -9.

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Answer:

(4,3,2)

Step-by-step explanation:

We can solve this via matrices, so the equations given can be written in matrix form as:

[tex]\left[\begin{array}{cccc}3&2&1&20\\1&-4&-1&-10\\2&1&2&15\end{array}\right][/tex]

Now I will shift rows to make my pivot point (top left) a 1 and so:

[tex]\left[\begin{array}{cccc}1&-4&-1&-10\\2&1&2&15\\3&2&1&20\end{array}\right][/tex]

Next I will come up with algorithms that can cancel out numbers where R1 means row 1, R2 means row 2 and R3 means row three therefore,

-2R1+R2=R2 , -3R1+R3=R3

[tex]\left[\begin{array}{cccc}1&-4&-1&-10\\0&9&4&35\\0&14&4&50\end{array}\right][/tex]

[tex]\frac{R_2}{9}=R_2[/tex]

[tex]\left[\begin{array}{cccc}1&-4&-1&-10\\0&1&\frac{4}{9}&\frac{35}{9}\\0&14&4&50\end{array}\right][/tex]

4R2+R1=R1 , -14R2+R3=R3

[tex]\left[\begin{array}{cccc}1&0&\frac{7}{9}&\frac{50}{9}\\0&1&\frac{4}{9}&\frac{35}{9}\\0&0&-\frac{20}{9}&-\frac{40}{9}\end{array}\right][/tex]

[tex]-\frac{9}{20}R_3=R_3[/tex]

[tex]\left[\begin{array}{cccc}1&0&\frac{7}{9}&\frac{50}{9}\\0&1&\frac{4}{9}&\frac{35}{9}\\0&0&1&2\end{array}\right][/tex]

[tex]-\frac{4}{9}R_3+R_2=R2[/tex] , [tex]-\frac{7}{9}R_3+R_1=R_1[/tex]

[tex]\left[\begin{array}{cccc}1&0&0&4\\0&1&0&3\\0&0&1&2\end{array}\right][/tex]

Therefore the solution to the system of equations are (x,y,z) = (4,3,2)

Note: If answer choices are given, plug them in and see if you get what is "equal to".  Meaning plug in 4 for x, 3 for y and 2 for z in the first equation and you should get 20, second equation -10 and third 15.

Answer:

C on edge

Step-by-step explanation:

: )

Answer:

.000167

Step-by-step explanation:

To get 1.67x10^-4  into standard from, we move the decimal to the left (the negative sign means to the left)  4 places.  That means we need to add 3 zero's.

.000167

[tex]\text{The formula of a midpoint:}\\\\\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)[/tex]

[tex]\text{We have}\\\\\text{endpoint}\ (-2,\ -14)\to x_1=-2,\ y_1=-14\\\\\text{midpoint}\ (-11,\ -20)\\\\\text{Therefore we have the equations:}\\\\\dfrac{-2+x_2}{2}=-11\qquad\text{multiply both sides by 2}\\\\-2+x_2=-22\qquad\text{add 2 to both sides}\\\\\boxed{x_2=-20}\\\\\dfrac{-14+y_2}{2}=-20\qquad\text{multiply both sides by 2}\\\\-14+y_2=-40\qquad\text{add 14 to both sides}\\\\\boxed{y_2=-26}\\\\Answer:\ \boxed{(-20,\ -26)}[/tex]

Final answer:

To find the other endpoint of a line segment when given the midpoint and one endpoint, use the formulas x2 = 2xm - x1 and y2 = 2ym - y1. For the given midpoint (-11, -20) and endpoint (-2, -14), the other endpoint is calculated to be (-20, -26).

Explanation:

To find the coordinates of the other endpoint of a segment when the midpoint and one endpoint are known, the midpoint formula can be used in reverse. For a line segment with endpoints (x1, y1) and (x2, y2) and midpoint (xm, ym), the coordinates of the midpoint are found by the formulas xm = (x1 + x2)/2 and ym = (y1 + y2)/2. If one endpoint is known, say (x1, y1) = (-2, -14) and the midpoint is (xm, ym) = (-11, -20), we can find the other endpoint (x2, y2) by rearranging the formulas: x2 = 2xm - x1 and y2 = 2ym - y1.

Calculating the values we get:

x2 = 2(-11) - (-2) = -22 + 2 = -20

y2 = 2(-20) - (-14) = -40 + 14 = -26

Therefore, the coordinates of the other endpoint are (-20, -26).

Answer:

18

Step-by-step explanation:

8x10= 18

Area of the rectangular cutting board is 80 square inches.

According to the problem,

∴ Area of the rectangle = (8 x 10) square inches

                                 = 80 square inches

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Answer:

Step-by-step explanation:

Set A: {32, 12, 24, 46, 18, 22, 14}

Mean =24 : Median =22:

Mean>Median hence positive skewed

Set B: {4, 12, 11, 14, 11, 5, 12, 13, 18, 14}

Mean =11.4 and median = 12

Mean <Median, hence negative skewed

Set C: {5, 4, 9, 12, 14, 26, 22, 18}

Mean=13.75 and median = 13

Mean >Median hence positive skewed

Set D: {1, 1, 1, 2, 2, 3, 3, 4, 5, 6}

Mean =2.8 Median = 2.5

Mean>Median Hence positive skewed

Wanna try 40?

Step-by-step explanation:

Answer:

The correct step will be [tex]5(\sqrt{164})=5(\sqrt{4*41})[/tex]

Step-by-step explanation:

We have been given that pond A has a radius of [tex]5\sqrt{(164)}[/tex] meters and radius of Pond B is [tex]\frac{(25\sqrt{200)}}{5}[/tex] meters. Todd simplifies the radius of pond A and we are asked to find out error in Todd's steps.

Step 1: [tex]5(\sqrt{100}+\sqrt{64})[/tex]

Since we know that [tex]\sqrt{ab}=\sqrt{a\times b}=\sqrt{a} \times \sqrt{b}[/tex]. We can see that Todd has made error in his very first step by splitting [tex]\sqrt{164}[/tex] as [tex]\sqrt{100+64}[/tex].

The correct step will be,

[tex]5(\sqrt{164})=5(\sqrt{4*41})[/tex]  

Therefore, the correct step 1 will be: [tex]5(\sqrt{4*41})[/tex].  

Now let us simplify our given radical expression.

[tex]5(\sqrt{4*41})=5(\sqrt{4}*\sqrt{41})[/tex]  

[tex]5\sqrt{4}*\sqrt{41}=5*2*\sqrt{41}[/tex]  

[tex]5*2*\sqrt{41}=10*\sqrt{41}[/tex]  

Therefore, our given radical expression simplifies to [tex]10*\sqrt{41}[/tex] meters.

The incorrect step in Todd's simplification is Step 1, which inaccurately breaks apart the square root of 164.

The step in Todd's simplification of the radius of Pond A that is incorrect is Step 1:

Incorrect Step 1: [tex]5(\sqrt{} 100 + \sqrt{ 64)[/tex]

This is incorrect because it suggests that √164 can be simplifed directly into the sum of the square roots of its components, which is not how square roots work.

The correct step should involve finding the prime factorization of 164 and then simplifying the square root.

Corrected Step 1: [tex]5\sqrt{} (4 x 41)[/tex]

Corrected Step 2: [tex]5(2\sqrt{} 41)[/tex]

Corrected Step 3: [tex]10\sqrt{} 41[/tex]

The fully simplified form of [tex]5\sqrt{} 164[/tex] meters would be [tex]10\sqrt{} 41[/tex] meters.

Answer:

C. $18673.25

Step-by-step explanation:  

Let us find cost of item after 7.7% of sales tax. The price after 7.7% of sales tax will be 17250 plus 7.7% of 17250.

[tex]\text{The cost of item after sales tax}=17250+(\frac{7.7}{100}\times 17250)[/tex]

[tex]\text{The cost of item after sales tax}=17250+(0.077\times 17250)[/tex]

[tex]\text{The cost of item after sales tax}=17250+1328.25[/tex]

[tex]\text{The cost of item after sales tax}=18578.25[/tex]

Therefore, the cost of item after 7.7% of sales tax will be $18578.25.

To find the total cost of item let us add registration fee ($95) to $18578.25

[tex]\text{The total cost of item}=18578.25+95[/tex]  

[tex]\text{The total cost of item}=18673.25[/tex]

Therefore, the total cost of item is $18673.25 and option C is the correct choice.

Answers:

Equation is 2*(2*W+W) = 102

Width is 17

Length is 34

=============================

Explanation:

L = 2*W because the length is twice the width

2*(L+W) = P is the perimeter formula

Replace P with the given perimeter (102). Also replace L with 2*W. Then isolate W

2*(L+W) = P

2*(2*W+W) = 102

2*(3W) = 102

6W = 102

6W/6 = 102/6

W = 17

If the width is W = 17, then the length is

L = 2*W = 2*17 = 34

So the width and length of this rectangle is 17 by 34

---------

Check:

P = 2*(L+W)

P = 2*(34+17)

P = 2*51

P = 102

Answer is confirmed

To find the length and width of a rectangle with given perimeter and lengths as twice of the width, first plug the length into the perimeter formula. Solve the resulting equation for width. Substitute this width into the length formula to get the length.

In this problem, we have a rectangle where the length (L) = 2 * width (W). Also, the perimeter of the rectangle (P) = 2L + 2W. The given perimeter is 102 inches.

Since L = 2W, substituting this equation into the formula for perimeter, we get P = (2*2W) + 2W = 102.

This simplifies to 6W = 102, and therefore W = 102 / 6 = 17 inches. Substituting the width back into the equation L = 2W, we find that the length (L) is 2 * 17 = 34 inches.

So, the width is 17 inches and the length is 34 inches.

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Answer:

12

Step-by-step explanation:

Answer: B

Step-by-step explanation:

The correct option is c.

The units of area are always square units because they are the product of two lengths dimensions. This could be square meters, square centimeters, or any other square unit.

The units of area are always square units. This is because area is defined as the product of two lengths dimensions. This applies whether you're calculating the area of a rectangle (length x width), a circle (pi x radius²), or any other shape. In the standard system of international units (SI), the base unit for length is meters, so area would be in square meters (m²). However, this can be adapted to any unit of length, such as centimeters, so area could also be measured in square centimeters (cm²).

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2,8   2+8=10

4,6    4+6=10

Can’t be more than 10$’s. The multiples of 2 are 2,4,6,8,10. So you’re answering which 2 numbers add up to 10$. If it’s anything higher than that it’s not a possible price and if it’s lower than that then she would have payed less which also isn’t possible.

Answer: 42°

Step-by-step explanation: In this problem, we're given that the measures of two complementary angles are in the ratio 7 to 8 and we're asked to find the measure of the smaller angle.

Since our two angles are in the ratio 7 to 8, let's represent the angles as 7x and 8x. We will call 7x an angle and 8x its complement. Now, remember that if two angles are complementary, then the sum of their measures is 90 degrees. So we can set up the equation 7x + 8x = 90.

Simplifying on the left side, we have 15x = 90.

Dividing both sides by 15, we find that x = 6.

So the measure of our first angle, 7x, is 7(6) or 42°.

The measure of its complement, 8x, is 8(6) or 48°.

Finally, notice that if we add our two angles together, we have 42 + 48 which equals 90 so our answer checks. This means that the smaller angle is 42°. Image is provided below.

Answer:

1. [tex]a_{n}=\frac{1}{3} a_{n-1}[/tex] where [tex]a_{1} =27[/tex]

2. [tex]2^{x+1}[/tex]

3. The domain is {-12,-8,0,1}. The range is {0,12,8}.

Step-by-step explanation:

1. The recursive formula is defined as an implicit way of writing the rule of a function or pattern. It is implicit because it uses previous terms to find the next term in the pattern. We multiply, add, subtract or divide a previous term by a constant value or expression to find the next. In this case, 27 becomes 9 through division by 3 or multiplication by 1/3. The pattern continues 9(1/3)=3 and so forth.

2. The function f(x) is an exponential and has a general form of [tex]y=ab^x[/tex]. We know f(x) is [tex]2^x[/tex]. The points of g(x) all changed from f(x) by shifting over to the left. This transformation occurred by [tex]2^{x+1}[/tex].

3. Domain is defined as the set of all x-values. Range is defined as the set of all y-values. The domain is {-12,-8,0,1}. The range is {0,12,8}.

Answer: ∠R = 137°

Step-by-step explanation:

The opposite angles of a quadrilateral are supplementary (equal to 180°).

Since ∠P and ∠R are opposite angles, their sum is 180°

∠P + ∠R = 180°

y + 3y + 8 = 180

4y + 8 = 180

4y = 172

y = 43

∠R = 3y + 8

     = 3(43) + 8

     = 129 + 8

     = 137

Answer:

The price of dinner before sales tax and tip is $60.

Step-by-step explanation:

Let the price of before sales tax and tip be x.

The amount of tip is 20% of the price of dinner. So, the amount of tip is

[tex]\frac{20}{100}x[/tex]

The amount of sales tax is 11% of the price of dinner. So, the amount of sales tax is

[tex]\frac{11}{100}x[/tex]

It is given that Zoe paid $18.60 in sales tax and tips for her dinner. Therefore the sum of tip and sales tax is $18.60.

[tex]\frac{20}{100}x+\frac{11}{100}x=18.60[/tex]

[tex]\frac{20+11}{100}x=18.60[/tex]

[tex]31x=1860[/tex]

[tex]x=60[/tex]

Therefore the price of dinner before sales tax and tip is $60.

Answer:

W = [tex]\frac{V}{LH}[/tex]

Step-by-step explanation:

given the formula V = LWH

to solve for W divide both sides by LH, hence

W = [tex]\frac{V}{LH}[/tex]

Answer:

the answer is B 2x-7

Step-by-step explanation:

-1 ║ 2               9                  7

                       -2                 -7

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

      2                7                  0

⇒ The Quotient is 2x + 7

Answer:

A: (-7x+10)(x-2)

Step-by-step explanation:

Given trinomial,

[tex]-7x^2-4x+20[/tex]

By middle term splitting,

[tex]=-7x^2-(14-10)x+20[/tex]

[tex]=-7x^2-14x+10x+20[/tex]  

[tex]=-7x(x+2)+10(x+2)[/tex]        

[tex]=(-7x+10)(x+2)[/tex]            

Since, further factorization is not possible,

Thus, the required factorized form of the given trinomial is,

[tex](-7x+10)(x+2)[/tex]    

Option A is correct.

Answer: There are 10 possible ways to get 3 heads. The probability of getting 3 heads from 5 flips would possibly be 10/32, or 5/16. I hope this helped! :)

Final answer:

The number of ways in which 3 heads can occur when 5 coins are flipped is 10. The number of ways in which 3 heads can occur when 6 coins are flipped is 20.

Explanation:

To calculate the number of ways in which 3 heads can occur when 5 coins are flipped, we can use the concept of combinations. The number of ways to choose 3 heads out of 5 coins is given by the formula C(5, 3), which is equal to 10. Therefore, there are 10 ways in which 3 heads can occur when 5 coins are flipped.

To calculate the number of ways in which 3 heads can occur when 6 coins are flipped, we can use the same concept. The number of ways to choose 3 heads out of 6 coins is given by C(6, 3), which is equal to 20. Therefore, there are 20 ways in which 3 heads can occur when 6 coins are flipped.

Answer:

226.50

Step-by-step explanation:

11.50*15=172.5(0)+4.50*12=54.0226.50

Answer:

It’s $226.50

Step-by-step explanation: