A regular 10-sided polygon has a perimeter of 540 feet. What is
the length of one side?
A.540 feet
B.360 feet
C.270 feet
D.54 feet

Answer:

Width = 10 inches

Step-by-step explanation:

Given the perimeter of a rectangle of 68 inches, and a length that is 14 inches longer than its width.

We can establish the following values to help us solve for the width of a rectangle:

Perimeter (P) = 68 inches

Length (L) = 14 + W inches

Width (W) = unknown

P =  2(L + W)  ⇒ This is the same as P = 2L + 2W, except that 2 is factored out from the right-hand side.

Divide both sides by 2:

[tex]\displaystyle\mathsf{\frac{P}{2}\:=\:\frac{2(L\:+\:W)}{2}}[/tex]

[tex]\displaystyle\mathsf{\frac{P}{2}\:=L\:+\:W}[/tex]

Substitute the value of the Perimeter and the length (L) into the formula:

[tex]\displaystyle\mathsf{\frac{68}{2}\:=14\:+W\:+\:W}[/tex]

Combine like terms on the right-hand side, and simplify the left-hand side of the equation:

[tex]\displaystyle\mathsf{34\:=14\:+2W}[/tex]

Subtract 14 from both sides:

34 - 14 = 14 - 14 + 2W

20 = 2W

Divide both sides by 2 to solve for the width (W):

[tex]\displaystyle\mathsf{\frac{20}{2}\:=\:\frac{2W}{2}}[/tex]

W = 10 inches

Therefore, the width of the rectangle is 10 inches.

Verify whether the derived value for the width is correct:

P = 2L + 2W

68 = 2(14 + 10) + 2(10)

68 = 2(34) + 20

68 = 48 + 20

68 = 68 (True statement).  

Thus, the length of the rectangle is 34 inches, and the width is 10 inches.

Answer: √490  

Step-by-step explanation:

Answer:

Option D

Step-by-step explanation:

Step 1:  Determine the correct option

Option A, this option doesn't work because -3.46 is not greater than -2 1/3.  Although the number 3 is greater than 2, these numbers are negative therefore the bigger the negative number, the smaller the number actually is.

Option B, this option doesn't work because 16/5 is not greater than 6.  If we convert 16/5 into a decimal we get 3.2 and this number isn't bigger than 6.

Option C, this option doesn't work because once again it states that -3.46 is greater than -2 1/3 when in reality it's actually smaller.

Option D, this option does work because everything goes according the way it should.  -3.46 is smaller than -2 1/3 and -2 1/3 is smaller than -3/4 and -3/4 is smaller than 16/5 and 16/5 is smaller than 6.

Answer:  Option D

Answer:

Option B is the correct answer

Step-by-step explanation:

Given that

[tex]\sin \theta =\frac{-1}{\sqrt{2}}[/tex]

Value of sine function is negative in third and fourth quadrant

Hence this is true for

[tex]\theta =225^{0},315^{0}[/tex]

Option B is the correct answer

Answer:

help

Step-by-step explanation:

Answer:

(-5, -7)

Step-by-step explanation:

Answer:

[tex](-5,-7)[/tex]

Step-by-step explanation:

[tex]f(x)=2x+3[/tex]

[tex]g(x)=-4x-27[/tex]

[tex]2x+3=-4x-27[/tex]

[tex]6x+3=-27[/tex]

[tex]6x=-30[/tex]

[tex]x=-5[/tex]

[tex]f(-5)=2(-5)+3[/tex]

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

[tex]f(-5)=-7[/tex]

Therefore, the point of intersection is [tex](-5,-7)[/tex]

Answer:

  N is at -2 on the number line

Step-by-step explanation:

The location of point N can be found by writing the segment lengths as a proportion.

  ON : NP = 4 : 8

  8(ON) = 4(NP) . . . . . . . . "cross multiply"

  2(N -O) = (P -N) . . . . . divide by 4, show lengths ON and NP

  2(N -(-7)) = 8 -N . . . . . use given values of O and P

  3N = -6 . . . . . . . . . . . add N-14 and simplify

  N = -2 . . . . . . . . . . divide by 3

Point N is at -2 on the number line.

If the ratio of ON to NP is 4:8, point N lie on the -2 at the number line.

Point O is at -7.

Point P is at 8.

The ratio of ON to NP is 4:8.

The ratio 4:8 simplifies to 1:2. This means that ON is one-third of the total distance from O to P, and NP is two-thirds of the total distance.

The total distance from O to P is the sum of the distances between O and N, and between N and P.

As the ratio of ON to NP is 1:2, and the total distance is 15 (8 - (-7) = 15), we can set up the following equation:

ON/NP = 1/2

ON/(15 - ON) = 1/2

Now we can solve for ON:

2 × ON = 15 - ON

3 × ON = 15

ON = 5

So, ON is 5 units away from O.

Now O is at -7, point N is at -7 + 5 = -2 on the number line.

So, N is at -2.

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Answer:

1 1/2 pound

Step-by-step explanation:

If each coin weighs 3/4 ounces and she picked up 6 then you do 3/4 x 6/1 which equals 18/4 and since there is 16 ounces in a pound it simplifies to 1 2/4 or 1 1/2 pounds

Answer:

9 kg per 3 weeks = 3 kg per week

Therefore, after 4 weeks it is (4 * 3) kilograms or 12 kilograms

Step-by-step explanation:

Patterns are used to represent sequence of numbers.

The shape at the 50th position is a triangle

The pattern rule is given as: square, triangle, circle, oval.

The number of shapes (n) is given as:

[tex]n =4[/tex]

So, the 50th shape is calculated using the following absolute operator

[tex]Shape = 50\%4[/tex]

i.e. divide 50 by 4, and take note of the remainder.

When 50 is divided by 4, the remainder is 2

So, we have:

[tex]Shape =2[/tex]

This means that, the shape at the 50th position is the same shape at the 2nd position.

Hence, the shape is triangle

Read more about pattern at:

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Answer:

15 installments

Step-by-step explanation:

3900 = Σ [tex]\left \ {{x=n} \atop {x=1}} \right.[/tex]   400 - 20*(n - 1)

Answer:

Step-by-step explanation:

Assuming the density is the same for both lollipops, we can calculate what volume is required to make the 2158.7kg the same density of the smaller lollipop.  

Small Lollipop

r = 2cm

V=4 /3πr^3

V = 33.51 cm^3

Mass is 50 g in 33.51 cm^3, so the density is:

50g/(33.51 cm^3) = 1.492 g/cm^3

We have 2158.7kg in the larger lollipop.  That is 2158700 grams.

Find the volume required to contain 2158700 grams with a density of 1.492 g/cm^3.  :

       (2158700 grams)/(1.492 g/cm^3) = 1446775 cm^3

V=4 /3πr^3

1446775 cm^3 = (4/3)*π*r^3

r = 70.12 cm

Answer:

9/4

Step-by-step explanation:

Answer:

9/2.25 = 4

Step-by-step explanation:

9/x = 4

x = 9/4 or 2.25

Answer: to number 1 :The area of the square increases by 96% to number 2:  increase in width = 50%

Step-by-step explanation

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Explanation:

Roy spends 1/4 of his money on 3 pens and 6 notebooks. That means 3/4 of it is leftover.

2/3 of 3/4 = (2/3)*(3/4) = 1/2 of his money is spent on buying some unknown number of additional pens. We'll come back to this later.

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

In terms of cost,

1 pen = 3 notebooks

which is another way of saying 1 pen is the same price as 3 notebooks.

Multiply both sides by 2 to get

2 pens = 6 notebooks

Therefore, saying "3 pens + 6 notebooks" is the same as "3 pens + 2 pens = 5 pens" when just thinking about costs.

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

In short, Roy buying 3 pens and 6 notebooks is the same as him buying 5 pens. He spends 1/4 = 25% of his money on getting these 5 pens.

Multiply those two values by 2 to find that 50% = 1/2 of his money would allow him to get 10 pens.

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

Recall that at the end of the first section, we concluded that Roy spent 1/2 of his money on buying those unknown additional number of pens. Then the previous section mentioned that 1/2 of his money gets him 10 pens. Therefore, he must have bought 10 additional pens on top of the original 3 mentioned in the instructions.

Overall, he purchased 3+10 = 13 pens

Answer:

  13 pens

Step-by-step explanation:

If a pen costs 3 times the cost of a notebook, then the cost of 3 notebooks will equal the cost of a pen. The 6 notebooks that Roy bought are equivalent in cost to 2 pens, so 1/4 of Roy's money is the cost of 3+2 = 5 pens.

After the first purchase, Roy has (1 -1/4) = 3/4 of his money remaining. If he spends 2/3 of that on more pens, he will have spent ...

  (2/3)(3/4) = 2/4

of his money on more pens. We've already seen that 1/4 of his money buys 5 pens, so 2/4 will buy 10 more pens.

Roy bought 3 +10 = 13 pens altogether.

Answer:

Click the picture and u will see the answer.

#CarryOnLearning

The summation of the given function from 1 to 4 is 10.5x³.

The given parameters:

[tex]\Sigma \ x^3 \times \Delta x, \ \ \ \Delta x = 2 + \frac{i}{4} \\\\[/tex]

The summation of the given function from i = 1, to i = 4, is calculated as follows;

[tex]\Sigma \ x^3 \times \Delta x = x ^3 (2 + \frac{1}{4} ) + x ^3 (2 + \frac{2}{4} ) + x ^3 (2 + \frac{3}{4} ) + x ^3 (2 + \frac{4}{4} )\\\\= x^3(10\frac{1}{2} )\\\\=\frac{21}{2} x^3\\\\= 10.5x^3[/tex]

Thus, the summation of the given function from 1 to 4 is 10.5x³.

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Answer:

19 quarters and 13 nickles

Step-by-step explanation:

You have 32 coins in your pocket consisting of nickels and quarters with a total value of $5.40

How many nickels and quarters do you have?

Step 1: Setup Coin Value and Coin Total Equation:

Coin Value Equation → 0.05n + 0.25q = $5.40 where n = nickels and q = quarters

Coin Total Equation → n + q = 32

Step 2: Rearrange Coin Total Equation in terms of nickels (n)

n = 32 - q ← Revised Coin Total Equation

Step 3: Plug in our Revised Coin Total Equation for n into our Coin Value Equation:

0.05(32 - q) + 0.25q = $5.40

0.05(32) - 0.05(q) + 0.25q = $5.40

1.6 - 0.05q + 0.25q = $5.40

1.6 + (0.25 - 0.05)q = $5.40

1.6 + 0.2q = $5.40

Step 4: Subtract 1.6 from each side of the equation to isolate q

1.6 - 1.6 + 0.2q = $5.40 - 1.6

0.2q = 3.8

Step 5: Divide each side of the equation by 0.2 to isolate q

0.2q

0.2

=

3.8

0.2

q = 19

Step 6: Using our value for q, Solve for n using our Coin Total Equation:

n + 19 = 32

Subtracting 19 from both sides, we get n + 19 - 19 = 32 - 19

n = 13

Summarizing our word problem, we see that 19 quarters and 13 nickels adds up to $5.40

I know myself that the answer is 0.4

Answer:

2/5, 1/2, 6/10

Step-by-step explanation:

did problem

Answer:

1. 2/5

2. 1/2

3. 6/10

Step-by-step explanation:

Hope this helps

May I get braineist pls

Answer:

60 yards

Step-by-step explanation:

300 = 2(30 + w) + 2(w)

300 = 60 +2w + 2w

300 = 60 + 4w

240 = 4w

60 = w

Answer:

y = 6x - 3

Step-by-step explanation:

Answer:

a) 8/17

b) 4/17

c) 5/17

d) 48/187

Step-by-step explanation:

a) P(silver) = 16/34 = 8/17

b) P(blue) = 4/17

c) P(red) = 5/17

d) P(silver, not silver) = 8/17 × 18/33 = 144/561 = 48/187

The probability for each event are -

[A] -  8/34

[B] -  16/34

[C] -  10/34

[D] -  18/33

        P(A) = n(A)/n(S)

        where -

        n(A) = Number of outcomes favorable to event A.

       n(S) = Total number of outcomes

We have 16 silver cars, 8 blue cars and 10 red cars in a parking lot.

[A] -

P{silver} = 8/(16 + 8 + 10) = 8/34

[B] -

P{blue} = 16/(16 + 8 + 10) = 16/34

{C} -

P{red} = 10/(16 + 8 + 10) = 10/34

D) -

P{not silver} = 1 - 15/33 = 18/33

Therefore, the probability for each event are -

[A] -  8/34

[B] -  16/34

[C] -  10/34

[D] -  18/33

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Explanation:

x = Jose's speed in mph

x+35 = Kayla's speed since she drives 35 mph faster than Jose

Jose gets a 2.1 hour head start and it takes Kayla 1.2 hours to reach him. So this means Jose has been driving for 2.1+1.2 = 3.3 hours when Kayla reaches him. The distance he travels is

distance = rate*time

d = r*t

d = x*3.3

d = 3.3x

while Kayla's distance equation is

d = r*t

d = (x+35)*1.2

d = 1.2x+42

Since Kayla meets up with Jose at the 1.2 hour mark, this means the two distances they travel is the same. Set their distance expressions equal to one another. Solve for x.

3.3x = 1.2x+42

3.3x-1.2x = 42

2.1x = 42

x = 42/(2.1)

x = 20

Jose's speed is 20 mph, while Kayla's speed is x+35 = 20+35 = 55 mph.

Jose's fairly slow speed is probably due to a number of factors such as heavy traffic, icy roads, or poor visibility. Kayla probably got a bit of a break with more favorable conditions.

Since Jose travels at 20 mph and does so for 3.3 hours, he travels d = r*t = 20*3.3 = 66 miles. Kayla travels d = r*t = 55*1.2 = 66 miles as well. We get the same number each time to help confirm the answer.

Hi!

If they each got the same, then they each got 1/3 of the total $360. Therefore, we can divide 360 by 3. We can do this by dividing 36 by 3, 36/3, and that's 12. Then add the 0! 120.

Your sentence could be: "The amount of money each worker got can be represented by 360/3, which is $120."

Hope this helps! :D

Answer: Since Marcus hired 3 people and paid them $360 altogether, it should be easy to figure this out through dividing. 360/3 or 360 divided by 3 = 120. You can put three into 360 one-hundred and twenty times. So, your answer would be that each worker got $120.

Answer: 1 =.43, 2=.26, 3=.16 4=.33

Step-by-step explanation: So to find all these answers we have to know the total number of people in the chart 30. Then we have to find what info we need from the chart and divide it by the total number of people. I hope this helped I tried to make it simple.