find the recursive formula of the arithmetic sequence
14,30,46,62

The equation of the parabola with vertex (2, -4) and directrix y = -6 is y = 0.25(x - 2)² - 4.

The equation of a parabola in vertex form is y = a(x - h)² + k, where (h, k) is the vertex, and a is a constant that determines the shape and direction of the parabola. Given the vertex (2, -4) and the directrix y = -6, we can determine the value of a using the formula a = 1 / 4(c), where c is the distance from the vertex to the directrix. Since the vertex lies two units above the directrix, the constant c = 2; hence, a = 1 / 4(2) = 0.25 or 1/4.

Thus, the equation of the parabola is y = 0.25(x - 2)² - 4.

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Answer:

( X -2 ) ^2 = 8(y +4)

Step-by-step explanation:

Answer:

the 2 in 270,413 is in the thousandths place. The 2 in 419,427 is in the tenths place

Hopes this helps

Answer:

10,000

Step-by-step explanation:

I did the test

Answer:

A = 102 cm^2

Step-by-step explanation:

This figure is a trapezoid.  The area is given by

A = 1/2 (b1+b2) *h  where b1 is the base and b2 is the top

b1 = 21   b2 = (6+7)  and h = 6

A = 1/2 (21+13) *6

A = 1/2 (34)*6

A = 102 cm^2

Answer:

He will cover 120 miles.

Step-by-step explanation:

K so provided is a picture of my work. I drew a unit rate table thing. Then off the side i calculated how fast he would need to go in 1 hour. So i could add it correctly. I hope this makes sense, if it doesnt just ask me lol

Answer:

Step-by-step explanation:

Alright, lets get started.

Suppose the distance to the park is d.

Suppose the speed is s.

Adam takes 4 hours to drive to park.

Applying speed, time , distance formula

[tex]time=\frac{distance}{speed}[/tex]

[tex]4=\frac{d}{s}[/tex]

[tex]s=\frac{d}{4}[/tex] .......................... equation 1

If the speed is 45 faster, time is 2.5 times less, means

[tex]\frac{4}{2.5}=\frac{d}{s+45}[/tex]

[tex]1.6=\frac{d}{s+45}[/tex]

Cross multiply

[tex]1.6(s+45)=d[/tex]

Plugging the value of s from equation 1

[tex]1.6(\frac{d}{4}+45)=d[/tex]

[tex]1.6*\frac{d}{4}+1.6*45=d[/tex]

[tex]0.4d+72=d[/tex]

[tex]0.6d=72[/tex]

[tex]d=\frac{72}{0.6}[/tex]

[tex]d=120[/tex]

So the distance is 120 miles.  :   Answer

Hope it will help :)

Answer:

 [tex]arc\ lenght=\pi[/tex]≈[tex]3.14[/tex]

Step-by-step explanation:

You need to use the formula for calculate the arc lenght:

[tex]arc\ length=2\pi r(\frac{C}{360})[/tex]

Where "C"  is the central angle of the arc in degrees and "r" is the radius.

You know that the measure of the radius of the circle is 4 inches and the central angle is 45 degrees, then you can substitute into the formula [tex]arc\ length=2\pi r(\frac{C}{360})[/tex].

Therefore, you get that  the measure of the arc length is:

[tex]arc\ length=2\pi r(\frac{C}{360})\\\\arc\ length=2\pi (4in)(\frac{45\°}{360})[/tex]

[tex]arc\ lenght=\pi[/tex]≈[tex]3.14[/tex]

Answer:

Pi Inches

Step-by-step explanation:

Answer:

The polynomial -gh⁴i + 3g⁵ is a binomial, since it has two terms

Degree of polynomial: degree of a polynomial is the term with highest of exponent.

Degree of binomial -gh⁴i + 3g⁵ = 6

1st term(-gh⁴i ) = (power of g = 1, power of h = 4, power of i = 1)

2nd term(3g⁵) = (power of g = 5)

the polynomial -gh⁴i + 3g⁵ is a 6 degree binomial.

Answer:

6,000

Step-by-step explanation:

every number 5 and over, you round it one number up. if youre rounding the thousands place, look at the hundreds place. if its 5 or over you round the thousands number up one then add the zeros.

Answer:

D, x = 3

Step-by-step explanation:

to know if a line is parallel, we need to know what kind of line x = 6 is

we can use the mnemonic VUX/HOY to determine the slope, the type of line, and which axis it corresponds to. VUX/HOY stands for:

Vertical line

Undefined slope

X axis

Horizontal line

0 is the slope

Y axis

according to this, the equation x = 6 is a vertical line

now we can start eliminating answer choices

A. a line containing the point (6,2)

the point lies on the line x = 6, as the x-coordinate in the ordered pair is 6. this  is not parallel to the line

B. y = 6

this intersects x = 6 and is not parallel

C. y = 4

this intersects x = 6 as well and is not parallel

D. x = 3

this leaves us with x = 3, which is a vertical line as seen by the equation and therefore x = 3 is our answer

Answer:

D, x = 3

Step-by-step explanation:

to know if a line is parallel, we need to know what kind of line x = 6 is

we can use the mnemonic VUX/HOY to determine the slope, the type of line, and which axis it corresponds to. VUX/HOY stands for:

Vertical line

Undefined slope

X axis

Horizontal line

0 is the slope

Y axis

according to this, the equation x = 6 is a vertical line

now we can start eliminating answer choices

A. a line containing the point (6,2)

the point lies on the line x = 6, as the x-coordinate in the ordered pair is 6. this  is not parallel to the line

B. y = 6

this intersects x = 6 and is not parallel

C. y = 4

this intersects x = 6 as well and is not parallel

D. x = 3

this leaves us with x = 3, which is a vertical line as seen by the equation and therefore x = 3 is our answer

Step-by-step explanation:

Answer:

10 1/2

Step-by-step explanation:\

dont change the whole number part

0.5 is the same as 1/2

so 10 1/2

Final answer:

To convert 10.5 to a fraction, express it as 105/10 and simplify it to 21/2.

Explanation:

When converting the decimal 10.5 to a fraction, we can view the number 10.5 as having one decimal place.

To express the decimal as a fraction, we put the decimal over its place value, which in this case is 10 since there is one decimal place (0.5 is in the tenths place).

Therefore, 10.5 can be expressed as 105/10.

However, this fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 5.

Thus, the simplified fraction for 10.5 is 21/2.

Answer:

(x+2) (x+6)

Step-by-step explanation:

x^2+8x+12

What 2 numbers multiply together to give you 12 and add together to give you 8

2*6 = 12

2+6 = 8

(x+2) (x+6)

Answer: (x+2) (x+6)

Step-by-step explanation: a p e x

Answer:50%

Step-by-step explanation:

Whenever you are trying to find the percentage  Use this euation for exmaple based off your question it would be

22*100/44

Answer:

First option: You start with $3 and save $1 each month.

In this case, the relationship is linear. So the corresponding equation is: y=x+3. Where 'x' represents the month. For example, the amount of money that you will have after 7 months is going to be: y = 7 + 3 = 10. (Ten dollars).

Second option: You save $3 the first month, and then each month the amount triples.

In this case, the relationship is exponential. If each month the amount triples, it means that the first month you have $3, the second month $9 and the third month $27. The equation that correctly models this situation is [tex]y=3^{x}[/tex]. For example, the amount of money that you will have after 7 months is going to be [tex]y=3^{7} = 2187[/tex] (2187 dollars)

Third option: Your total savings is 3 times the number of months multiplied by itself.

In this case, the relation is quadratic. So the equation that models this situation is: [tex]y=3x^{2}[/tex]. For example, the amount of money that you will have after 7 months is going to be [tex]y=3(7)^{2} = 147[/tex] (147 dollars)

✅✅✅✅ BONUS: The best option is the SECOND ONE ✅✅✅✅

The area of a square is length*width and since a square has the same side measurements, √1225 or 35 is one side. (35 * 35 = 1225)

There are 4 sides so 35*4 = 140ft² as the perimeter

I hope this helps!

Answer:

140 ft

Step-by-step explanation:

Here, A = 1225 ft² = s², where s represents the length of one side of the room.  Here, s = √( 1225 ft² ) = 35 ft.

Thus, the perimeter, P = 2L + 2W, is 4(35 ft) = 140 ft

Answer:

4$ for large 3$ for a small

Step-by-step explanation:

Answer:

(A) cost of one large popcorn is $4.

(B) cost of one small drink is $3.

Step-by-step explanation:

Given information:

Let the cost one of large popcorn [tex]=P[/tex]

And the cost of one small drink [tex]= D[/tex]

Now according to the given information the equations that can be formed are:

[tex]2P+4D=20\\2P+2D=14\\[/tex]

Now solving the above equation by elimination method:

[tex]4D-2D=20-14\\2D=6\\D=3[/tex]

So, the cost of one small drink is $3

Now, find the cost of one large popcorn is;

[tex]2P+4 \times 3=20\\2P=20-12\\P=4[/tex]

So, the cost of one large popcorn is $4

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Answer:

8

Step-by-step explanation:

20-1=19

19-3=16

16/2=8

Answer:

S= 8 Cans Of Soup

Step-by-step explanation:

Starts With- $20

Ends With- $1

20-1=$19

$19 spent in all

Buys gallon/ Or Gallons of milk :  1 Gallon= $3

$19-$3= $16   S=Cans of soup  1 can=$2        $16 ÷ $2= S

2, 4, 6, 8, 10, 12, 14, 16    S= 8 cans        $2×8=$16

1,  2, 3, 4, 5,   6,   7,   8

Answer: 5 cm

Step-by-step explanation: If you liked this answer check out my channel Saltygum and subscribe

Answer:

Step-by-step explanation:

Yes.  If the vertical line intersects the graph in only one place for each x value, the graph represents a function; if in two or more places, not.

the answers 11/6 which can't be reduced

To determine how long to leave $7500 in the bank at 6% interest compounded semi-annually to reach $16200, use the compound interest formula. Solving for t, time in years, yields approximately 11.9 years for the investment to grow to the desired amount.

To calculate how long the person must leave their money in the bank for it to grow from $7500 to $16200 with an interest rate of 6% compounded semi-annually, we'll use the formula for compound interest:

A = P(1 + \frac{r}{n})^{nt}

Where:

We are given:

Our goal is to solve for t, the time in years. Plugging the known values into the formula:

$16200 = $7500(1 + \frac{0.06}{2})^{2t}

Divide both sides by $7500:

2.16 = (1 + \frac{0.06}{2})^{2t}

Now take the natural logarithm of both sides:

ln(2.16) = ln((1 + \frac{0.06}{2})^{2t})

Use properties of logarithms to bring down the exponent:

ln(2.16) = 2t \cdot ln(1 + \frac{0.06}{2})

Divide both sides by 2ln(1 + \frac{0.06}{2}) to solve for t:

t = \frac{ln(2.16)}{2 \cdot ln(1 + \frac{0.06}{2})}

t = \frac{ln(2.16)}{2 \cdot ln(1.03)}

Using a calculator, we find t ≈ 11.9 years. Therefore, the person must leave the money in the bank for approximately 11.9 years to reach $16200.

To the nearest tenth of a year, the person must leave the money in the bank for approximately 13 years.

To find the time required for the investment to reach $16200, we can use the formula for compound interest:

[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]

Where:

- ( A ) is the amount of money accumulated after ( t ) years.

- ( P ) is the principal amount (the initial investment).

- ( r ) is the annual interest rate (in decimal form).

- ( n ) is the number of times interest is compounded per year.

- ( t ) is the time the money is invested for (in years).

Given:

- ( P = 7500 )

- ( A = 16200 )

- ( r = 0.06 ) (6% interest, converted to decimal)

- Interest is compounded semi-annually, so ( n = 2 )

We need to solve for ( t ):

[tex]\[ 16200 = 7500 \left(1 + \frac{0.06}{2}\right)^{2t} \][/tex]

[tex]\[ \frac{16200}{7500} = \left(1 + 0.03\right)^{2t} \][/tex]

[tex]\[ 2.16 = \left(1.03\right)^{2t} \][/tex]

Take the natural logarithm of both sides:

[tex]\[ \ln(2.16) = \ln\left(\left(1.03\right)^{2t}\right) \][/tex]

[tex]\[ \ln(2.16) = 2t \cdot \ln(1.03) \][/tex]

Now, solve for [tex]\( t \)[/tex]:

[tex]\[ t = \frac{\ln(2.16)}{2 \cdot \ln(1.03)} \][/tex]

[tex]\[ t \approx \frac{0.7693}{2 \cdot 0.0296} \][/tex]

[tex]\[ t \approx \frac{0.7693}{0.0592} \][/tex]

[tex]\[ t \approx 13 \][/tex]

So, to the nearest tenth of a year, the person must leave the money in the bank for approximately 13 years.

Check the picture below.

now, we know the base is a square, thus the length = width, namely L = w, so

[tex]\bf SA=2(Lw+Lh+wh)\implies \stackrel{\textit{since we know that L=w}}{380=2(ww+wh+wh)} \\\\\\ \cfrac{380}{2}=w^2+2wh\implies 190=w^2+2wh \implies 0=w^2+2wh-190 \\\\\\ 0=(w+19)(w-10)\implies w= \begin{cases} -19\\ \boxed{10} \end{cases}[/tex]

since the units must be positive, we can't use -19.

Final answer:

To find the largest width for the voting box, we need to consider its surface area. By setting up an equation and differentiating it with respect to the width, we can find the maximum width. The largest width for the box would be approximately 58.46 inches.

Explanation:

To find the largest width of the voting box, we need to consider its surface area. The surface area of a square-based box is given by 2lw + lh + wh, where l is the length, w is the width, and h is the height. We are given that the height is 4.5 inches, and we need to find the maximum width. The maximum surface area is 380 in2, so we can set up the equation as follows:

2lw + lh + wh = 380

Substituting the given height and rearranging the equation:

2lw + (4.5)(w) + (w)(w) = 380

Simplifying the equation:

2lw + 4.5w + w2 = 380

Since we are trying to find the maximum width, we can differentiate the equation with respect to w and set the derivative equal to zero:

d(2lw + 4.5w + w2)/dw = 0

2l + 4.5 + 2w = 0

Solving for w:

w = (380 - 4.5l)/2

Since the width should be the largest possible, we can substitute the maximum value of the length. Given that the box has a square base, the length and width are equal. Therefore, we substitute l = w:

w = (380 - 4.5w)/2

Simplifying the equation:

2w = 380 - 4.5w

6.5w = 380

w ~ 58.46 inches

Therefore, the largest width that the box could have is approximately 58.46 inches.

Answer:

30 degrees

Step-by-step explanation:

P+Q+R=180

80+70+Q=180

Q=30

PQR = angle Q

Answer:30 degrees!!

Step-by-step explanation:

happy Friday! :) hope this helps!

Answer:

Pretty sure its Quadratic

Step-by-step explanation:

Linear, needs to be in a straight line.

Quadratic, involving the second and no higher power of an unknown quantity or variable.

Exponential, (of an increase) becoming more and more rapid.

Answer:

[tex]\frac{WR}{v^2} =t[/tex]

Step-by-step explanation:

[tex]W = \frac{v^2t}{R}\\\\W\cdot R = v^2t\\\\\frac{WR}{v^2} =t[/tex]

oof did u ever find out the answer...

Answer:

The scatter plot that represents the data that is shown in the table is attached below.

Step-by-step explanation:

The given table represents the balance of bank account at the beginning of the past week was and how much it increased or decreased by the end of the past week.

In the scatter plot, x-axis represents the beginning balance in thousands of dollars and the y-axis represents the change in the bank account in hundreds of dollars.

From the table, it is clear that the points of scatter plot are (4,7), (7,5), (2,3), (3,4), (1,6), (5,3), (6,1) and (4,2).

Therefore the scatter plot that represents the data that is shown in the table is attached below.

For this case we must find the inverse of the following function:

[tex]f (x) = x ^ 2-1[/tex]

For them we follow the steps:

We change f (x) to y:

[tex]y = x ^ 2-1[/tex]

We exchange variables:

[tex]x = y ^ 2-1[/tex]

We solve for "y":

[tex]y ^ 2-1 = x[/tex]

We add 1 to both sides of the equation:

[tex]y ^ 2 = x + 1[/tex]

We apply square root to eliminate the exponent:

[tex]y = \pm \sqrt {x + 1}[/tex]

We change y by [tex]f ^ {- 1} (x)[/tex]:

[tex]f ^ {- 1} (x) =\pm \sqrt {x + 1}[/tex]

Answer:

Option D

Answer:

920

Step-by-step explanation:

Answer:The bottom rectangle is 15 x 20 = 300 square cm.

The top triangle is 1/2 x 20 x (8+8+15) = 1/2 x 20 x 31 = 1/2 x 620 = 310 square cm.

Total area = 300 + 310 = 610 square cms.

Answer:

After 9 movies they will have paid the same amount

Step-by-step explanation:

We must write an equation for Duke's expenses and an equation to represent Tennessee's expenses.

For Duke expenses we have:

A fixed expense of $ 111.60 per year

A variable expense of $ 4.00 for each movie.

The equation that represents the expenses is a linear equation like the one shown below

[tex]C = 111.60 + 4.00x[/tex]

Where C represents the cost and x the number of movies.

For Tennessee expenses we have:

A variable expense of $ 16.40 for each film.

The equation that represents the expenses is a linear equation like the one shown below

[tex]C = 16.40x[/tex]

Where C represents the cost and x the number of movies.

To know after how many movies have paid the same amount, we equate both equations and solve the variable x

[tex]111.60 +4.00x=16.40x\\\\16.40x - 4x = 111.60\\\\12.40x =111.60\\\\x =\frac{111.60}{12.40}\\\\x =9[/tex]

After 9 movies they will have paid the same amount

Answer:

You want to leave a 15% tip on a meal that cost $16.25.

First, convert the 15% to an actual number that can be used in a calculation. For percents,this is always done by simply dividing the percent (in this case 15%) by 100%.So, the conversational term "15%" becomes 15% / 100% = 0.15 in terms of a real mathematical number.

Second, you need to find out what 15% of your $16.25 meal cost is.This is always done by multiplying 0.15 by $16.25, or

0.15 x $16.25=$2.44.

So, the amount of tip you are going to leave is $2.44.

This makes the total cost of your meal (to write on your charge slip or other payment)

$16.25 + $2.44 = $18.69.

Answer:

$19.99

Step-by-step explanation:

16.25 + 3% tax + 20% tip

16.25 * 0.03 = .49

16.25 * .20 = 3.25

16.25 + .49 + 3.25 = $19.99

Answer:

$8.80

Step-by-step explanation:

In order to find the new price, you need to add 60% of the original price (5.50) to the original price. You have two options:

1) multiply $5.50*0.6 to get 60% of the original price. You would get $3.30. Then add $3.30+$5.50, which equals $8.80. This way takes longer but shows you all the steps.

2) The shorter way is to simply multiply $5.50*1.6, which also equals $8.80. This works because the "1" automatically adds the 5.50 to 60% of the original price, this way you don't have to multiply then add.

If you don't understand how the second way works or your teacher taught you #1, just do it the first way.

Final answer:

To find the new price after a 60% markup, you need to calculate 60% of the original price and then add it to the original price.

Explanation:

To find the new price after a 60% markup, you need to calculate 60% of the original price and then add it to the original price.

Step 1: Calculate 60% of $5.50. 60% is equivalent to 0.60, so multiply 0.60 by $5.50 to get $3.30.

Step 2: Add $3.30 to $5.50 to find the new price. $3.30 + $5.50 = $8.80.

Therefore, the new price of the item after the 60% markup is $8.80.

0.329 is rational, 127.5 is rational, -89 is rational rational