The sum of the measures of the interior angles of the polygon below is 1800°

Answer:

1225.56 kg

Step-by-step explanation:

1 stone = 14 slugs

1 slug = 14.59 kg

[tex]\text{6 stones} ( \dfrac{14 slug}{1 stone})(\dfrac{14.59 kg}{1 slug})[/tex]

numerator 6 * 14 * 14.59 = 1225.56 kg

denominator = 1

Answer 1225.56 kg in 6 stones

NOTES:

1)⇒    A + B + C = 180°

       A + B + C = π

       A + B        = π - C

2)⇒⇒ sin (A + B) = sin (π - C)

                         = (sin π)(cos C) - (sin C)(cos π)

                          = (0)(cos C) - (sin C)(-1)

                          = 0 - (-sin C)

                          = sin C

3)⇒⇒⇒cos (A + B) = cos (π - c)

                            = (cos π)(cos C) + (sin π)(sin C)

                            = (-1)(cos C) + (0)(sin C)

                            = - cos C              

4)⇒⇒⇒⇒ sin 2A + sin 2B = 2 sin (A + B) cos (A - B)

PROOF (from left side):

sin 2A + sin 2B + sin 2C    =    4 sin A sin B sin C

2 sin (A + B) cos (A - B) + sin 2C     refer to NOTE 4

2 sin (A + B) cos (A - B) + 2 sin C cos C  double angle formula

2 sin C cos (A - B) + 2 sin C cos C   refer to NOTE 2

2 sin C [cos (A - B) + cos C]     factored out 2 sin C

2 sin C [cos (A - B) - (cos(A + B)]   refer to NOTE 3

2 sin C [2 sin A sin B]           sum/difference formula

4 sin A sin B sin C      multiplied 2 sin C by 2 sin A sin B

Proof completed: 4 sin A sin B sin C   =   4 sin A sin B sin C

Answer:

1. 756 / 108 = 7 inches (the width of the first roof);

2. 954 / 106 = 9 inches (the width of the second roof);

Step-by-step explanation:

The smallest possible whole number length for the third side of a triangle with sides of length 20 and 2, based on triangle inequalities, is 19.

The subject of your question revolves around triangle inequalities, a fundamental concept in geometry. Triangle inequalities state that the length of any one side of a triangle must be less than the sum of the lengths of other two sides. In this case, you have two sides of lengths 20 and 2. This means the third side must be less than 22 but more than 18 (since it also needs to be more than the difference of two sides).

However, your question asks for the smallest whole-number length possible for the third side. Hence, the smallest possible whole number length for the third side of the triangle is 19.

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The smallest possible whole-number length for the third side of the triangle is 18.

To determine the smallest whole-number length for the third side of a triangle with sides of length 20 and 2, one must consider the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.Let's denote the lengths of the sides as [tex]\( a \), \( b \), and \( c \)[/tex] , where [tex]\( a = 20 \) and \( b = 2 \)[/tex]  . We are looking for the smallest whole number [tex]\( c \)[/tex]  that satisfies the triangle inequality theorem:  

1. [tex]\( a + b > c \)2. \( a + c > b \)3. \( b + c > a \)[/tex] . Substituting the known values of [tex]\( a \) and \( b \), we get: 1. \( 20 + 2 > c \)[/tex]

2.[tex]\( 20 + c > 2 \)[/tex]

3. [tex]\( 2 + c > 20 \)[/tex] From inequality 1, we have: [tex]\( 22 > c \)[/tex] This means [tex]\( c \[/tex] must be less than 22.From inequality 2, we have:[tex]\( 20 + c > 2[/tex]  Since [tex]\( c \)[/tex]  is a positive number, this inequality will always hold true for any positive \( c \).From inequality 3, we have:[tex]\( 2 + c > 20 \)[/tex].  Solving for  [tex]\( c[/tex] , we get: [tex]\( c > 18[/tex]) .Since  [tex]\( c \)[/tex] must be a whole number and the smallest whole number greater than 18 is 19, one might initially think that the smallest possible length for [tex]\( c \)[/tex]  is 19. However, we must also consider that [tex]\( c \)[/tex]  must be less than the sum of the other two sides (inequality 1). The smallest whole number less than 22 is 21, but since [tex]\( c \)[/tex] cannot be equal to [tex]\( a \)[/tex]  or [tex]\( b[/tex]) (as this would not form a triangle), the next smallest whole number is 20, which is also not possible as it would make two sides equal and the triangle degenerate. Therefore, the next smallest whole number is 19. However, we must also consider that for a valid non-degenerate triangle, the difference between the lengths of any two sides must be less than the length of the third side. Since  [tex]\( a = 20 \) and \( b = 2 \)[/tex] , the difference between  [tex]\( a \). and \( b \)[/tex] is 18, which means [tex]\( c \)[/tex] must be greater than 18 to satisfy this condition.Thus, the smallest possible whole-number length for the third side [tex]\( c \)[/tex] is 19, but since we are looking for the smallest whole number greater than 18, the correct answer is actually 18, as it is the smallest whole number that satisfies all the conditions of the triangle inequality theorem and the condition that the difference between the lengths of any two sides must be less than the length of the third side.

Answer:

B. Rhombus

Step-by-step explanation:

A rombus has four congruent sides and has 2 equal pairs of angles, the rhombus has 4 equal sidesd that are conected by 4 suplemmentary angles between them, in the end the sum of the inner angles is 360 like in every polygon.

Answer:

The correct answer option is a. 14∑1 (-28+3n)

Step-by-step explanation:

The summation notation for the given series is 14∑1 (-28+3n) where [tex]i[/tex] (the index of summation or the lower limit of summation) is 1 and [tex]n[/tex] (the upper limit of summation) is 14.

Putting in the values of the limit from 1 to 14 in the notation to get the first 14 terms of the series:

[tex]-28+3(1)=-25\\\\-28+3(2)=-22\\\\-28+3(3)=-19\\\\-28+3(4)=-16\\\\-28+3(5)=-13\\\\-28+3(6)=-10\\\\-28+3(7)=-7\\\\-28+3(8)=-4\\\\-28+3(9)=-1\\\\-28+3(10)=2\\\\-28+3(11)=5\\\\-28+3(12)=8\\\\-28+3(13)=11\\\\-28+3(14)=14\\[/tex]

Therefore, first option is the correct one.

Answer:

A is the correct one hope ive been of help

Answer: weclome

Step-by-step explanation:

Average movie ticket prices in the united states are, in general, lower than other countries. It would cost in $77.87 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost $73.83. How much does an average movie ticket cost in each of these countries?  

Let ticket in japan cost x

Let ticket in Switzerland cost y  

3x+2y=77.87 ------1

3y+2x=73.83------2  

Subtract the equations  

x-y= 4.04 ---4

3y+2x=73.83------5

Answer:

Step-by-step explanation:

Average movie ticket prices in the united states are, in general, lower than other countries. It would cost in $77.87 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost $73.83. How much does an average movie ticket cost in each of these countries?  

Let ticket in japan cost x

Let ticket in Switzerland cost y  

3x+2y=77.87 ------1

3y+2x=73.83------2  

Subtract the equations  

x-y= 4.04 ---4

3y+2x=73.83------5

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Answer:

The vertices of A'B'C are  A'(-1,2), B'(-4,6) and C'(-4,2).

Step-by-step explanation:

Triangle ABC has vertices at A(1, 2) B(4, 6) and C(4, 2).

If a figure reflected over x-axis, then

[tex](x,y)\rightarrow (x,-y)[/tex]

Therefore the vertices of triangle ABC after reflection over x-axis are:

[tex]A(1,2)\rightarrow A'(1,-2)[/tex]

[tex]B(4,6)\rightarrow B'(4,-6)[/tex]

[tex]C(4,2)\rightarrow C'(4,-2)[/tex]

Rotation 180 degrees about the origin is defined as

[tex](x,y)\rightarrow (-x,-y)[/tex]

Therefore the vertices of triangle ABC after reflection over x-axis followed by rotated 180 degrees about the origin are:

[tex]A(1,-2)\rightarrow A'(-1,2)[/tex]

[tex]B(4,-6)\rightarrow B'(-4,6)[/tex]

[tex]C(4,-2)\rightarrow C'(-4,2)[/tex]

Therefore the vertices of A'B'C are  A'(-1,2), B'(-4,6) and C'(-4,2).

Answer:

C

Step-by-step explanation:

If ur not trying to look at all that but you should

Answer:

The point of change is the point (1,9)

Step-by-step explanation:

The first derivative of the function equated to zero will give you the point where the function changes.

Therefore, to solve this problem find the first derivative of f (x)

[tex]f '(x) = 3*3(x-1)^{3-1}\\\\f '(x) = 9(x-1)^2[/tex]

Now we equate the derivative to 0.

[tex]9 (x-1)^ 2 = 0\\\\x = 1[/tex]

Then the derivative of the function is equal to 0 when x = 1. This means that the concavity of the function changes in x = 1.

When [tex]x = 1, y = 3(1-1) ^ 3 +9\\\\x =1, y = 9.[/tex]

Then the point of change is the point (1,9)

Answer:

The point of inflection is (1,9)

Step-by-step explanation:

We have following  given function

[tex]f(x)=(x-1)^{3} +9[/tex]

The point at which the function changes its curvature is defined by the point of inflection.

To find point of inflection we set 2nd derivative to 0

[tex]f''(x)= 0[/tex]

The first derivative is given by

[tex]f'(x)= \frac{d}{dx} [(x-1)^{3} +9][/tex]

[tex]f'(x)= 3(x-1)^{2}[/tex]     ( using chain rule  and derivative of constant is 0)

now again we take 2nd derivative

[tex]f''(x)=3(2(x-1))[/tex]

[tex]f''(x)=6(x-1)[/tex]

now we equate 2nd derivative to 0

[tex]6(x-1)=0\\x-1=0\\x=1[/tex]

hence point of inflection is at x=1

now we find y coordinate of point of inflection by plugging x=1 in f(x)

[tex]y=f(1)=(1-1)^{3} +9 =9[/tex]

Hence the point of inflection is (1,9)

Answer:

The equation of this line would be y = -6

Step-by-step explanation:

In order to find this, we must first find the slope. For that we use the two points and the slope equation.

m(slope) = (y2 - y1)/(x2 - x1)

m = (-6 - -6)/(7 - 3)

m = 0/4

m = 0

Given that slope, we can use it along with a point in point slope form. From there we can solve for y and get the equation.

y - y1 = m(x - x1)

y + 6 = 0(x - 7)

y + 6 = 0

y = -6

Final answer:

To find the equation of a line passing through given points, calculate the slope, use the point-slope formula, and simplify to obtain the final equation. In this case, the line passing through (7,-6) and (3,-6) results in the equation y = -6.

Explanation:

To find the equation of the line passing through the points (7,-6) and (3,-6):

Calculate the slope (m) using the formula: m = (y₂ - y₁) / (x₂ - x₁)

Substitute one of the points and the slope into the point-slope formula: y - y₁ = m(x - x₁)

Simplify the equation to get the final answer: y = mx + b

The equation of the line passing through those two points is y = -6.

The Kansas City Royals won approximately 78.57% of their playoff games in 2014.

To find the percentage of games won by the Kansas City Royals, we divide the number of games they won by the total number of games played and then multiply by 100. In this case, the Royals won 11 out of 14 playoff games in 2014. So the percentage of games they won is:

Percentage = (Number of games won / Total number of games) x 100

= (11 / 14) x 100 = 78.57%

Therefore, the Royals won approximately 78.57% of their playoff games in 2014.

x-2y=6

-2y=-x+6

2y=x-6

y=0.5x-3

Parallel=same slope

y=0.5x+5

Answer:

If we are to treat these as two ordered pairs, then the rate of change is 1.25.

Step-by-step explanation:

To find this, use the slope equation with the ordered pairs.

m(slope) = (y2 - y1)/(x2 - x1)

m = (11 9/16 - 9 1/16)/(12 - 10)

m = (2 8/16)/2

m = 2.5/2

m = 1.25

Now we know that this could be a function since we have a constant slope.

The rate of change between these two sets of measurements is 1 1/4 inch. Additionally, the relation is indeed a function because each x-value corresponds to exactly one y-value.

The rate of change in a relationship between two variables is a measure of how much one variable changes in relation to a change in the other variable. Here, we are dealing with pairs of measurements in inches. To find the rate of change, we subtract the y-values (the second number in each pair) and divide by the difference of the x-values (the first number in each pair).

We calculate as follows: (11 9/16 - 9 1/16) / (12 - 10), which simplifies to 2 1/2 / 2 or 1 1/4.

The relation is indeed a `function` because each input (x-value) corresponds to exactly one output (y-value). In other words, if you insert a particular measurement of the x-value into this relationship, you will always get the same corresponding y-value. In the context of mathematical functions, this is known as the vertical line test.

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Answer:

y = -2x + 25/2

Step-by-step explanation:

Slope intercept form is y = mx + b.

You must solve the equation for y.

4x + 2y = 25

Subtract 4x from both sides.

2y = -4x + 25

y = -2x + 25/2

Answer:

solution given:

4x+2y=25

we know that

slope intercept form is

y=mx+c

so

4x+2y=25

2y=-4x+25

y=-4/2 x+25/2

y=-2x+25/2 is a required answer.

We are given that revenue of Tacos is given by the mathematical expression [tex]-7x^{2}+32x+240[/tex].

(A) The constant term in this revenue function is 240 and it represents the revenue when price per Taco is $4. That is, 240 dollars is the revenue without making any incremental increase in the price.

(B) Let us factor the given revenue expression.

[tex]-7x^{2}+32x+240=-7x^{2}+60x-28x+240\\-7x^{2}+32x+240=x(-7x+60)+4(-7x+60)\\-7x^{2}+32x+240=(-7x+60)(x+4)\\[/tex]

Therefore, correct option for part (B) is the third option.

(C) The factor (-7x+60) represents the number of Tacos sold per day after increasing the price x times. Factor (4+x) represents the new price after making x increments of 1 dollar.

(D) Writing the polynomial in factored form gives us the expression for new price as well as the expression for number of Tacos sold per day after making x increments of 1 dollar to the price.

(E) The table is attached.

Since revenue is maximum when price is 6 dollars. Therefore, optimal price is 6 dollars.

Answer:

69

Step-by-step explanation:

23 times 3

Using exterior angle formula, you get that ∠CAD=36+123=159°

Exterior angle formula says that the angles facing CAB (ACB and ABC) sum to CAD.

[tex]\displaystyle\\(x-4)^2=49\\\\(x-4)^2-49=0\\\\(x-4)^2-7^2=0\\\\(x-4-7)(x-4+7)=0\\\\(x-11)(x+3)=0\\\\x-11 = 0~~~\text{or}~~~x+3=0\\\\x-11=0~~~\implies~~~\boxed{x_1=11}\\\\x+3=0~~~\implies~~~\boxed{x_2=-3}\\\\\boxed{\bf The~solutions~are:~~x =11~~\text{or}~~x =-3}[/tex]

Answer:

[tex]\frac{70+71+72+x}{4}\geq 73[/tex]        

[tex]x\geq 79[/tex]

Step-by-step explanation:    

Let x be the height of 4th plant purchased by Millie.

We have been given that Millie needs the average height of the plants she is buying to be at least 73 inches. She has selected three plants that are 70, 71 and 72 inches tall.

So the average of 4 plants purchased by Millie will be: [tex]\frac{70+71+72+x}{4}[/tex]

We can represent this information in an inequality as: [tex]\frac{70+71+72+x}{4}\geq 73[/tex]        

Therefore, our desired inequality will be [tex]\frac{70+71+72+x}{4}\geq 73[/tex].

Now let us solve our inequality by multiplying both sides of inequality by 4.

[tex]4*\frac{70+71+72+x}{4}\geq 4*73[/tex]  

[tex]70+71+72+x\geq 292[/tex]    

[tex]213+x\geq 292[/tex]

[tex]x\geq 292-213[/tex]    

[tex]x\geq 79[/tex]      

Therefore, the height of 4th plant purchased by Millie must be at least 79 inches.

Answer:

53 minutes.  

Step-by-step explanation:

We have been given that Payton leaves  to go on an 85 minute bike ride at 3:27 pm.

Let us find when Payton will finish biking by 85 minutes after 3:27 pm.

Since 85 minutes equals to 1 hour and 25 minutes. 1 hour after 3:27 pm will be 4:27 pm. Now let us add 25 minutes to 4:27 pm.

So Payton will finish biking at 4:(27+25) pm= 4:52 pm.

Payton's family eats dinner at 5:45 pm. Now let us find remaining time between dinner and 4:52 pm.

[tex]\text{Minutes between dinner and finishing bike ride}=5:45 pm- 4:52 pm[/tex]  

[tex]\text{Minutes between dinner and finishing bike ride}=53[/tex]  

Therefore, Payton have 53 minutes between finishing her bike ride and eating dinner.  

Answer:

tan C = 1/2

Step-by-step explanation:

The tan function in a right triangle is the opposite side over the adjacent side

tan C = 11/22

We can divide the top and bottom by 11

tan C = 1/2

Answer: Tan(C) = 1/2

Step-by-step explanation:

For a triangle rectangle, we have the relation, for an angle θ.

Tan(θ) = Opposite cathetus/Adjacent catethus.

Here, the opposite cathetus to C is equal to 11 units

The adjacent cathetus to C is 22 units.

Then we have Tan(C) = 11/22 = 1/2

and we can not simplify it anymore, so this is the answer.

Final answer:

The domain restrictions of the expression [tex]g^2[/tex] are the same as the domain restrictions for the variable g.

Explanation:

The domain restrictions of the expression [tex]g^2[/tex], can vary depending on the context in which it is used.

However, in general, the domain restrictions for this expression would be the same as the domain restrictions for the variable g.

This means that any values that make g undefined or result in a complex number would also be restrictions for [tex]g^2.[/tex]

For example, if g cannot be negative due to a square root operation, then the domain restrictions for [tex]g^2[/tex] would also exclude any negative values of g.

Answer: D

Step-by-step explanation:

End behavior is determined by two factor:

1. Coefficient - determines right side:

2. Degree - determines left side:

******************************************************************************************

-x³ + 2

Leading coefficient is NEGATIVE, so right side goes to -∞ (decreases)

Degree is ODD, so left side is opposite of right side → goes to +∞ (increases)

w - width

2w - length

60 - perimeter

w + w + 2w + 2w = 6w - perimeter

The equation:

6w = 60    divide both sides by 6

w = 10 → 2w = 2 · 10 = 20

The area: A = width × length

A = (10)(20) = 200

Answer:

It would cost $39.95 in a month when you use the internet for 14 hours.

Step-by-step explanation:

Suppose, the internet is used for [tex]x[/tex] hours and the monthly total cost is [tex]y[/tex] dollars.

The internet company charges $4.95 per month plus $2.50 for each hour of use.

That means, fixed cost is $4.95 per month and the cost for [tex]x[/tex] hours of use [tex]= \$2.50x[/tex]

So, the linear equation in slope intercept form to model the situation will be:  [tex]y=2.50x+4.95[/tex]

Now, if [tex]x= 14[/tex] hours, then [tex]y=2.50(14)+4.95=39.95[/tex]

So, it would cost $39.95 in a month when you use the internet for 14 hours.

If Tonya bought 10 pears and spent a total of $10.00 in expression 0.50a+0.65p represents the total cost of a apples and p pears then Tonya bought 7 apples.

Let's use the information provided to set up an equation and solve for the number of apples (a) that Tonya bought.

Cost of pears (p) = $0.65 each

Cost of apples (a) = $0.50 each

Total cost = $10.00

We are told that Tonya bought 10 pears. So, the cost of 10 pears would be:

Cost of 10 pears = 10 * $0.65 = $6.50

Now, we can set up an equation to represent the total cost of apples and pears:

Total cost = 0.50a + 0.65p

We know that the total cost is $10.00 and the cost of 10 pears is $6.50:

$10.00 = 0.50a + $6.50

Now, let's solve for 'a' (the number of apples):

Subtract $6.50 from both sides:

$10.00 - $6.50 = 0.50a

$3.50 = 0.50a

Now, divide both sides by 0.50 to solve for 'a':

a = $3.50 / $0.50

a = 7

Tonya bought 7 apples.

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