A dance studio charges $17 for the first ballet class a dancer takes and $11 for each class after that. what are the first four terms of an arithmetic sequence in which an is the total amount a dancer pays, in dollars, for taking n ballet classes?

Answer:

x = 18

Step-by-step explanation:

given y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the condition y = 15 when x = 9 , then

15 = 9x ( divide both sides by 9 )

[tex]\frac{15}{9}[/tex] = x , that is

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

y = [tex]\frac{5}{3}[/tex] x ← equation of variation

when y = 30 , then

30 = [tex]\frac{5}{3}[/tex] x ( multiply both sides by 3 to clear the fraction )

90 = 5x ( divide both sides by 5 )

18 = x

Answer:

x=30

Step-by-step explanation:

5=x/6

30=x

Answer:

A=34 B=20

Step-by-step explanation:

A: y=6(5)+4 (34)

B: y=45-(9(2)+7)

y= 45-(18+7)

y=45-25 (20)

Answer:

c = -13.78.

Step-by-step explanation:

21.2x + c  ≡ 5.3(4x - 2.6)

21.2x + c  ≡ 21.2x - 13.78

Equating constant terms:

c = -13.78.

Answer:

13.78

Step-by-step explanation:

21.2x + c = 5.3(4x - 2.6)

open the bracket

21.2x + c = 21.2x - 13.78

collect like terms

c + 13.78 = 21.2x - 21.2x

c + 13.78 = 0

c = -13.78

Answer:

The radius is 4.5cm.

Step-by-step explanation:

Circumference is the distance around the outside of a circle, the perimeter of the circle. Circumference formula is:

C = pi•d OR

C = 2•pi•r

Since we are looking for radius, use the second formula.

C = 2•pi•r

28.26 = 2pi•r

Divide by 2pi.

28.26/2pi = r

r = 4.5

The radius is 4.5 cm.

Answer:

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

The equation for slope is y2-y1/x2-x1 so put you numbers in and you get

-6-6/-9+5

-12/4

and then -3

Answer:

-3

Step-by-step explanation:

[tex]y=mx+b[/tex] is equation of a straight line.

Here, the slope is m.

[tex]m=\frac{y_{2}-y_{1} }{{x_{2}-x_{1}}} =\frac{-6-6}{-9-(-5)} =\frac{-12}{-4}=-3[/tex]

Answer:

12.7

Step-by-step explanation:

9^2+9^2=162

square root of 162 equals roughly 12.7

Use the pythagorean theorem

Answer:

27/2 in^3 or 13.5 in^3 as a mixed fraction

Step-by-step explanation:

V=whl

Simplify the following:

(1 + 1/2) (2 + 1/4)×4

Put 1 + 1/2 over the common denominator 2. 1 + 1/2 = 2/2 + 1/2:

(2/2 + 1/2) (2 + 1/4)×4

2/2 + 1/2 = (2 + 1)/2:

((2 + 1)/2) (2 + 1/4)×4

2 + 1 = 3:

3/2 (2 + 1/4)×4

Put 2 + 1/4 over the common denominator 4. 2 + 1/4 = (4×2)/4 + 1/4:

(3×4)/2 ((4×2)/4 + 1/4)

4×2 = 8:

(3 (8/4 + 1/4)×4)/2

8/4 + 1/4 = (8 + 1)/4:

(3×4)/2 ((8 + 1)/4)

8 + 1 = 9:

3/2×9/4×4

3/2×9/4×4 = (3×9×4)/(2×4):

(3×9×4)/(2×4)

(3×9×4)/(2×4) = 4/4×(3×9)/2 = (3×9)/2:

(3×9)/2

3×9 = 27:

Answer: 27/2 or 13.5 as a mixed fraction

Answer:

y-intercept = (-2,0)

Step-by-step explanation:

the "C" is the answer

The area of a 2D form is the amount of space within its perimeter. The total surface area of the rectangular prism is 203.2 units².

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or other quadrilaterals, multiply its length by its width.

The total surface area of a rectangular prism is given by the formula,

Total Surface Area = 2[(Length×width) + (Length×height) + (height×width)]

Given the length of the rectangular prism is 9cm, the width of a rectangular prism is 7.6 cm, and the height of the prism is 2 cm. Therefore, the total surface area can be written as,

[tex]\text{Total Surface Area} = 2[(9 \times 7.6) + (9 \times 2)+(2 \times 7.6)][/tex]

                              [tex]\rm = 2(68.4+ 18 + 2 \times 15.2)\\\\= 203.2\ cm^2[/tex]

Hence, the total surface area of the rectangular prism is 203.2 units².

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Answer:

12 1/6

It wants me to add more but there's nothing to add

Answer:

the answer is 75%

each dot represents 25% of the data

Below 345 meters are 3 points

so, 3 * 25% = 75%

Answer:

Step-by-step explanation:

the 2nd and 4th answers look good.  the 1st answer is correct as well.

To solve this look at the x axis and y axis,  the x axis is in inches, the y axis is in pounds.  So you know that as the distance increase per inch,  the force in pounds is increasing too.  

so the force applied is going up,   0.73 pounds , for each inch of travel ( or stretch) of the spring.  

Answer:

she should get in change $5.55

Answer:

It would be the last one

Step-by-step explanation:

Answer:

The surface area of cone = 54π cm²

Step-by-step explanation:

Given ;

Radius = 3 cm

slant height = 15cm

The surface area of cone = πr ( r + l )

=> π × 3 ( 3 + 15)

=> π × 3 ( 18)

=> 54 π cm²

Answer:

Option a

Explanation :

check out my attached work

Hope it helps, let me know if you have any questions !

Have a nice rest of your day :)

Step-by-step explanation:

The value of the term in the series will be equal to 3 + 12 +48 + 192 after calculation.

In mathematics, the summation is the addition of a sequence of any kind of numbers, called addends or summands.

Now we have a given term

[tex]\sum_{n=1}^{4} 3(4)^{n-1}[/tex]

By solving the above term;

[tex]\sum_{n=1}^{4} 3(4)^{n-1}=3(4)^{1-1}+3(4)^{2-1}+3(4)^{3-1}+3(4)^{4-1}[/tex]

[tex]\sum_{n=1}^{4} 3(4)^{n-1}=3(4)^0+3(4)^1+3(4)^2+3(4)^3[/tex]

[tex]\sum_{n=1}^{4} 3(4)^{n-1}=3 + 12 +48 + 192[/tex]

Hence the value of the term in the series will be equal to 3 + 12 +48 + 192 after calculation.

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Answer:

1. 3 + 12 +48 + 192

2. 255 edge

Step-by-step explanation:

Answer:

8a³b²c(9a²b - 4c)

Step-by-step explanation:

The GCF of 72 and 32 is 8.

72a^5b^3c - 32a^3b^2c^2 = 8a³b²c(9a²b - 4c)

Hey there!

12 1/2 * 4

= 12 1/2 * 4/1

= 12 * 2 + 1 / 2 * 4/1

= 24 + 1 / 2 * 4/1

= 25/2 * 4/1

= 25(4) / 2(1)

= 100 / 2

= 100 ÷ 2 / 2 ÷ 2

= 50 / 1

= 50

EASIER UNDERSTANDING….

= 25 + 25 + 25 + 25 / 2 + 0

= 50 + 50 / 2 + 0

= 100 / 2

= 100 ÷ 2

= 50

Therefore, your answer is: 50

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

[tex]0 = log_{10} 1[/tex]

Step-by-step explanation:

Base for the exponent and for the logarithm are the same!

10^0 is the exponential form where 10 is the base and 0 the exponent

[tex]log_{10} 1[/tex] is the logarithm form where 10 is the base

To solve [tex]log_{10} 1 =[/tex]   ask the question :

To what power should I raise the base 10 to obtain the number 1 ?

The answer to the power 0 therefore

[tex]log_{10} 1 = 0[/tex]

[tex]1 = 10^{0} -is-the- exponential -form\\0 = log_{10} 1 - is -the -logarithmic -form[/tex]

Answer:

The vertex of the function is (1.333, 4.667)

Step-by-step explanation:

1. Calculate -b / 2a. This is the x-coordinate of the vertex.

2. simply plug -b / 2a into the equation for x and solve for y.

[tex]Y = 3x^{2} - 8x + 10\\Compare with the form of y = ax^{2} + bx + c\\So that means a = 3, b = -8, and c = 10.[/tex]

Calculate -b/2a:

[tex]X = -(-8)/2(3)[/tex]

[tex]X = 8/6[/tex]

This is equal to 1.33 recurring

Plug 8/6 for x and solve for y:

[tex]Y = 3x^{2} - 8x + 10[/tex]

[tex]Y = 3(\frac{8}{6})^{2} - 8(\frac{8}{6}) + 10[/tex]

[tex]Y = \frac{48}{9} - \frac{64}{6} + 10\\[/tex]

This is equal to 4.66 reccuring.

The distance from the United States to Europe is 5200miles.

We have given that the,

There is a map of the world on the wall in Mr. Smith's classroom.

The scale on the map

lists 1 inch to 400 miles.

On his map, Mr. Smith measured 13 inches between the United States and Europe.

The value of one inch is 400 miles.

We have to determine the 13 inches in miles

We have given that

1inch=400miles

Therefore multiply both side by 13 so we get

13inches=13(400)miles

             =5200miles

Therefore we get, the distance from the United States to Europe is 5200miles.

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Answer:

5200

Step-by-step explanation:

If the scale on the map is 1 inch to 400 miles, and Mr. Smith measured 13 inches between the United States and Europe, we can find the distance in miles by multiplying the number of inches by the scale:

Distance in miles = Number of inches * Scale

Distance in miles = 13 inches * 400 miles/inch

Distance in miles = 5200 miles

Therefore, the distance from the United States to Europe, based on Mr. Smith's map, is 5200 miles.

Answer:

Step-by-step explanation:

22000-18700=3300

3300/22000x100=15%

Answer:

It is a 15 percent decrease

Step-by-step explanation:

Divide 18700 by 22000, and your answer will be 0.85 but its asking for the decrease, 100-85=15, so 15% is the decrease.

Answer:

It is attached

Step-by-step explanation:

Answer:

12.5

Step-by-step explanation:

.25 x 50= 12.5