Find the missing side
V=252ft3
7ft , 3ft , ??ft

The pattern is [tex]n^2-2n[/tex]

And, the 8th term of the pattern is 48.

Given that,

Based on the above information, the calculation is as follows:

1 2 5 10 17

Here second number is calculated by adding 1, the third number is calculated by adding 3, the fourth number is calculated by adding 5, and the last number is calculated by adding 7

So,  

+1 +3 +5 +7

+2 +2 +2

Now  

[tex]2\div 2=1[/tex]

Therefore it starts with [tex]n^2[/tex]

[tex]n^2[/tex] = = 1 4 9 16 25  

-0 -2 -4 -6 -8

-2 -2 -2 -2

Therefore we have -2n

Now  

The 8th term should be

[tex]= 8^2- 2\times 8[/tex]

= 64-16

= 48

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Problem 5

x = number of songs downloaded

MyTunes charges $2.50 per song, so you pay 2.50*x dollars if you download x songs. If M is the cost of using MyTunes, then M = 2.50*x.

Let G be the cost of using Great Songs. The equation here is G = 1.50*x+50. We have 1.50*x representing the cost of downloading x songs (at 1.50 dollars a piece) plus the membership fee of $50. So the total cost here is 1.50x+50 dollars.

We want to find out when Great Songs is a better deal, so we want to determine what x values make G smaller than M

(Great Songs Cost) < (MyTunes Cost)

G < M

1.50x+50 < M ................................... replace G with 1.50x+50

1.50x+50 < 2.50x ............................. replace M with 2.50x

1.50x+50-1.50x < 2.50x-1.50x ....... subtract 1.50x from both sides

50 < 1.00x

50 < x

x > 50

If you download more than 50 songs, then Great Songs will be the better deal since it will be the cheaper plan.

-24-1/8p=3/8p

Rewrite as

3/8p=-24-1/8p

Add -1/8p both sides

1/2p= -24

Multiply 2 to each side

P= -24(2)

P=-48

The value of p is 48 for the equation 24 - 1/8p = 3/8p.

To solve this equation -24 - 1/8p = 3/8p.

24 - 1/8p = 3/8p.

Subtract 24 on both side,

24 - 1/8p -24 = 3/8p - 24,

- 1/8p = 3/8p - 24

Add 1/8p on both side,

1/8/p - 1/8p = 3/8p - 24 + 1/8p

0 = 1/2p -24

24 = 1/2p

p = 48.

Therefore, the value of p is 48.

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Answer:

The rule transforms the quadrilateral ABCD to quadrilateral A'B'C'D' is given by

D.(-x,y-4).

Step-by-step explanation:

Given quadrilateral ABCD  transform into new quadrilateral A'B'C'D.

The transformation is a  special rule by which to determine the coordintae of  image point of any coordinate of given point . The transformation can be rotation, reflection, dialtion etc.

In given figure of qudrilateral ABCD

Coordinate of A (-5,4)

Coordinate of B(0,1)

Coordinate of C (-4,0)

Coordinate of D (-6,2)

In II figure  of quadrilateral A'B'C'D

Coordinate of A' (5,0)

Coordinate of B' (0,-3)

Coordinate of C' (4,-4)

Coordinate of D' (6,-2)

Then we can see that coordinate of A (-5,4) change into A' (5,0)

It means x change into -x and y change into y-4

Similarly in same  way  B (0,1) change into B'(0,-3)

C(-4,0) change into C'(4,-4)  and D( -6,2) change into D'(6,-2)

[tex]\frac{-9.5}{10}[/tex] is halfway between [tex]\frac{-9}{10}[/tex] and [tex]\frac{10}{10}[/tex].

hope that helps :)

A is twice ( 200%) lager than b

You're slope intercept form is: y = mx + b, in which:

m = slope

b = y-intercept

Plug in the -3 for m, and 7 for b

y = -3x + 7 is your slope-intercept form.

hope this helps

Volume of cylinder= /pi r square h

Taking /pi as 22/7

r= diameter/2

=5m

h=24m

V= 22/7*5 square*24

V=22*25*24/7

V=13200/7

V=1885.7 m cube

Answer

Find out the how many fertilizer she used for a 450-foot row of vegetables.

To proof

let us assume that the fertilizer would she use for a 450-foot row of vegetables be x.

As given

Cala uses 2 pounds of Feed-All fertilizer for a 100 foot row of vegetables at her farm.    

than the equation becomes

[tex]x = \frac{2\times450}{100}[/tex]

solving the above

x = 9 pound

Therefore 9 pound are used  for a 450-foot row of vegetables.

Hence proved

Answer:

No, Sara can only cut 8 equal-sized pieces with maximum longitude and no wood left over.

Step-by-step explanation:

For finding which longitude meets the requirements (to be the longest with no wood left over) we must decompose 18 and 30 in their prime factors.

For doing so, we look for the prime numbers that divide 18 and 30, as follows

18 | 2              30 | 2

9  | 3               15 | 3

3  | 3                5 | 5

1                       1

Thus 18=2*3*3, and 30=2*3*5.

The maximun number that divides both 18 and 30 must be 2*3=6, because these are the prime numbers that both decompositions have in common.

6 represents the maximum longitude for a piece of wood with no leftovers.

Since 18/6=3, and 30/6=5, we can only obtain 5+3=8 wood pieces from the boards.

Of course, we can cut in a half the 8 pieces obtaining 16 equal-sized pieces of wood, but unfortunately, they won't be the longest pieces possible.

A system of linear equations can be set up with x representing the first number and 4x representing the second number, which is four times the first. Solving the equation x + 4x = 35 gives us x = 7, and the second number is 28.

To solve the problem where one number is four times another and their sum is 35, we can set up a system of two linear equations. Let's call the first number x and the second number, which is four times the first, 4x. According to the problem, x + 4x = 35.

Now we can simplify the equation:

So the first number is 7. To find the second number, we multiply 7 by 4, which is 28. To check our work, we add the two numbers and confirm they sum to 35: 7 + 28 = 35.

The reasoning behind why it equals 19 is because you use PEMDAS (aka: Order Of Operations). When you solve, you solve in the same order PEMDAS, so you first solve the parenthesis. Next, you'd solve exponents, but in this case, there are none. So, you solve the multiplication and/or division (from left to right). Finally you'd solve completely, by adding and subtracting (from left to right). Doing all these steps would give you your answer of 19.

I hope this helps!

[tex]52-2x=4\\\\2x=48\\\\x=24[/tex]

Answer: x = 24

Step-by-step explanation:

52 - 2x = 4

-52          -52

__________

-2x = -48

___   ___

-2        -2

x = 24

hope this helps! ❤ from peachimin

Kelly's average speed is greater. Paula: ~0.026 miles per minute, Kelly: ~0.156 miles per minute. Kelly's average speed is higher.

To compare their average speeds, let's first convert their distances to the same unit. Since 8 kilometers is equal to 5 miles, we can use this conversion to make both distances consistent.

Kelly ran 10 kilometers, which is [tex]\( \frac{10}{8} \times 5 = \frac{25}{4} \)[/tex] miles.

Now we can compare their average speeds:

Paula's average speed = [tex]\( \frac{10 \text{ miles}}{65 \text{ minutes}} \)[/tex]

Kelly's average speed = [tex]\( \frac{\frac{25}{4} \text{ miles}}{40 \text{ minutes}} \)[/tex]

Now, let's calculate both:

Paula's average speed:

[tex]$\begin{aligned} & \text { Paula's average speed }=\frac{10 \text { miles }}{65 \text { minutes }} \times \frac{1 \text { hour }}{60 \text { minutes }} \\ & =\frac{10}{65} \times \frac{1}{60} \text { miles per minute } \\ & \approx \frac{1}{39} \text { miles per minute }\end{aligned}$[/tex]

Kelly's average speed:

[tex]$\begin{aligned} & \text { Kelly's average speed }=\frac{\frac{23}{4} \text { miles }}{40 \text { minutes }} \times \frac{1 \text { hour }}{60 \text { minutes }} \\ & =\frac{\frac{25}{4}}{40} \text { miles per minute } \\ & =\frac{25}{4} \times \frac{1}{40} \text { miles per minute } \\ & =\frac{25}{160} \text { miles per minute }\end{aligned}$[/tex]

Now, we can compare the two speeds. Since both speeds are in miles per minute, we can directly compare them.

[tex]\[ \frac{1}{39} \text{ miles per minute} \approx 0.0256 \text{ miles per minute} \][/tex]

[tex]\[ \frac{25}{160} \text{ miles per minute} \approx 0.15625 \text{ miles per minute} \][/tex]

Kelly's average speed is greater than Paula's average speed.

Therefore, Kelly has the greater average speed.

The complete question is here:

Paula and Kelly are comparing their running times. Paula completed a 10-mile run in 65 minutes. Kelly completed a 10-kilometre run in 40 minutes. Given that 8 kilometres are equal to 5 miles, which girl has the greater average speed?

Answer:

Step-by-step explanation:

+y = -18

-y = -18

By dividing the total budget ($350) by the cost per hour ($45), we can tell that the family can rent a jet ski for 7 hours.

This problem involves a simple division process. Given that, the rental fee for jet ski is $45.00 per hour and your family has allocated $350 for this. We can solve this problem by dividing the total budget by the cost per hour.

So, $350 ÷ $45 = 7.777. But since we can't rent a jet ski for partial hours, we only consider the whole number. Hence, Your family can rent a jet ski for 7 hours with a budget of $350.

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Given

Annual fixed costs for a product are $75,000.

The product i sells for $6

it costs $2 in variable costs to make each product.

the variable cost per unit goes up to $2.50

find out how many units will the annual break-even point for the product change .

To proof

FORMULA

Break even = Fixed cost ÷  Contribution margin per unit

where

Contribution margin per unit = sale price - variable price

Take two cases

Case first

fixed costs for a product =  $75,000

product itself sells =  $6

variable costs  = $2

put all the value in the above equation

we get

Contribution margin per unit = 6 - 2

                                               = 4

[tex]Break even (say B1 ) = \frac{75000}{4}[/tex]

                                        = 18750 units

CASE SECOND

 the variable cost per unit goes up to $2.50

put value inthe formula

Contribution margin per unit = 6 - 2.50

                                               = 3.5

[tex]Break even (say B2 ) = \frac{75000}{3.5}[/tex]

we get

Breakeven (sayB2) = 21428.6 unit

change in the break even product = B2- B1

                                                         = 21428.6 - 18750

                                                        =  2678.6 unit

Hence proved

The annual break-even point for the product will increase by approximately 2,679 units if the variable cost per unit goes up to $2.50.

To determine the break-even point, we need to calculate the number of units that need to be sold in order to cover the fixed costs. The formula to calculate the break-even point is:

Break-Even Point = Fixed Costs / (Selling Price per Unit - Variable Cost per Unit)

In this case, the fixed costs are $75,000, the selling price per unit is $6, and the variable cost per unit is $2.

To find the current break-even point, we can substitute these values into the formula:

Break-Even Point = $75,000 / ($6 - $2) = $75,000 / $4 = 18,750 units

If the variable cost per unit goes up to $2.50, we can substitute this new value into the formula to find the new break-even point:

Break-Even Point = $75,000 / ($6 - $2.50) = $75,000 / $3.50 = 21,428.57 units

Therefore, the annual break-even point for the product will increase by approximately 2,679 units if the variable cost per unit goes up to $2.50.

the factors are: 1,2,4,5,10,20. So Therefore there are 6 factors.

Prime numbers have only one rectangular array. Numbers with four factors have two types of rectangular array: 8 has 1 x 8 and 2 x 4. Numbers with six factors have three rectangular arrays: 20 has 20 x 1, 10 x 2, and 5 x 4.

1 day = 24 hours.

7 days x 24 hours per day = 168 hours

1 hour = 60 minutes.

168 hours x 60 minutes per hour = 10,080 total minutes.

195 pages / 10,080 minutes = 0.019 = 0.02 pages/min.

The answer is A.

The answer is A

This is because 7 days is equivalent to 10080 minutes.

To get the number of pages read per minute, divide 195 by 10080 to get approximately 0.02

Answer: 60 mph

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

Explanation:

R*T = D is the same as D = R*T

The D value is unknown, but it is the same for both cars since each car traveled the same distance.

The rate or R value for car A is some unknown x. For car B, R = x+15 because it traveled 15 mph faster than car A.

For car A, T = 2. For car B, T = 1.5

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

The equation for car A is going to be D = x*2 or D = 2x. Note how I replaced R and T with x and 2 respectively.

The equation for car B is D = (x+15)*1.5 which distributes and simplifies to D = 1.5x+22.5

Because we're dealing with the same D value for both equations, we can equate the two right hand sides and solve for x

D = 2x

1.5x+22.5 = 2x ..... replace D with 1.5x+22.5

22.5 = 2x-1.5x

22.5 = 0.5x

0.5x = 22.5

x = 22.5/0.5

x = 45

So car A's speed was 45 mph. Add on 15 to get

x+15 = 45+15 = 60

which is car B's speed

side note: car A travels a distance of D = R*T = 45*2 = 90 miles; while car B travels a distance of D = R*T = 60*1.5 = 90 miles. Both cars traveling the same distance helps us confirm we have the right answer.

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

So this is why the final answer is 60 mph

When converting a number from scientific notation with a negative exponent to standard notation, the result is a decimal number less than one. The scientific notation's negative exponent indicates how many places to move the decimal point to the left in the standard form.

When the scientific notation of a number has a negative exponent, it signifies that the standard notation of the number will be a decimal less than one. For example, if the scientific notation is 3.5 × 10-4, then the standard notation would be 0.00035. This transition is made by moving the decimal point to the left instead of to the right, which would be the case with a positive exponent. Each step the decimal point moves to the left corresponds to one negative power of ten.

In standard notation, the number is expressed in its regular decimal form without any exponents. For very small numbers, a negative exponent in scientific notation helps to simplify and make the representation more readable.

For instance, the size of a virus might be about 0.000000025 meters. In scientific notation, this is written as 2.5 × 10-8 meters. Converting this back to standard notation, we'd move the decimal point to the right eight places, giving us the small standard number mentioned before.

4,285.714%

unless you need it siplified?

Answer:

4285.714%

Step-by-step explanation:

Multiply 42.85714 by 100 to convert to percent:

42.85714 × 100 = 4285.714 %

Hope this helps :-)

A lower temperature suggests a subtraction.

Wake up temperature: 102° F

Temperature two hours later: 3° F lower, or -3° F

Temperature two hours later: 102° F - 3° F = 99° F

Answer: 99° F

Judging from the graph (attached), there is one negative and one positive zero. Since this is a 4-th order polynomial, it has 4 zeros in total. So there are 2 complex zeros with imaginary components.

Step 1. Divide both sides by 2

2x + 1 = 26/2

Step 2. Simplify 26/2 to 13

2x + 1 =13

Step 3. Subtract 1 from both sides

2x = 13 - 1

Step 4. Simplify 13 - 1 to 12

2x = 12

Step 5. Divide both sides by 2

x = 12/2

Step 6. Simplify 12/2 to 6

x  = 6

14 / 426 = 0.09389

Hope this helps!

7/213 in fraction and 0.03286384977 in decimal form

Final answer:

The inequality 4 − d < 4 + d solves down to d > 0, meaning any positive number for d will satisfy the inequality. We achieve this by eliminating like terms and isolating the variable on one side.

Explanation:

To solve the inequality 4 − d < 4 + d, we want to find the values of d that make the inequality true. We can do so by following these steps:

Subtract 4 from both sides of the inequality to simplify it: 4 − d − 4 < 4 + d − 4, which simplifies to −d < d.

Add d to both sides to get all the d terms on one side: −d + d < d + d, which simplifies to 0 < 2d.

Divide both sides by 2 to solve for d: 0 / 2 < 2d / 2, which simplifies to 0 < d.

The solution to the inequality is d is greater than 0. In other words, any positive number for d will satisfy the inequality.