The length x of a rectangle is decreasing at the rate of 5 cm/min and the width y is increasing at the rate of 4 cm/min. When x = 8 cm and y = 6 cm, find the rate of change of

(i) the perimeter.

(ii) area of rectangle.

Given:

A 7-sides regular polygon.

To find:

The sum of the interior angles of the given regular polygon.

Solution:

The formula for the sum of the interior angles of a regular polygon is:

[tex]Sum=180^\circ(n-2)[/tex]

Where, n is the number of sides of the regular polygon.

The given regular polygon has 7 sides. Putting [tex]n=7[/tex] in the above formula, we get

[tex]Sum=180^\circ(7-2)[/tex]

[tex]Sum=180^\circ(5)[/tex]

[tex]Sum=900^\circ[/tex]

Therefore, the sum of the interior angles of the given regular polygon is 900 degrees.

Answer:

5x+4

Step-by-step explanation:

5x + 6 - 2

5x + 4

Answer:

Step-by-step explanation:

he needs 10 inches of each color to make the wreath

10

+ 10

+ 10

+ 10

= 40

40 inches of ribbon

Answer:

vertices in total will coincide = 1174/2 = 587

Step-by-step explanation:

1st polygon: 1174 sides, 1174 vertex, arc for between 2 vertex= 360°/1174 (arc1)

2nd polygon: 2935 sides, 2935 vertex, arc for between 2 vertex= 360°/2935 (arc2)

360°/1174 = (360°/2935) x (5/2)  (every 2.5 arc2 = 1 arc1)

It means every 5 arc2 = 2 arc1, this is the 2nd vertex coincide

vertices in total will coincide = 1174/2 = 587

check: 2935/5 = 587

9514 1404 393

Answer:

Step-by-step explanation:

We assume the given ratios are proportional. I find it easiest to write the proportion with the unknown in the numerator.

a) dollars/ounces = x/17 = 7/20

Multiply by the inverse of the coefficient of x to solve.

  x = 17(7/20) = 5.95 . . . dollars

__

b) bushels/acres = x/9.6 = 225/3

  x = 9.6(225/3) = 720 . . . bushels

Answer:

28

Step-by-step explanation:

280 divided by 10 = 28

Answer:

They can be seated in 10,080 ways.

Step-by-step explanation:

Arrangements of n elements:

The number of possible arrangements of n elements is given by:

[tex]A_n = n![/tex]

In this question:

In each end, the two admirals, so 2 possible outcomes.

In the middle seats, arrangements of 7 elements(3 generals, 4 lieutenants). So

[tex]2A_{7} = 2*7! = 10080[/tex]

They can be seated in 10,080 ways.

The number of ways they can be seated is 10,080 ways.

The number of possible ways fof arranging n elements is given as:

P = n!

According to the question, there are 2 admirals! 3 generals and 4 lieutenant.

In each end, the two admirals, so 2 possible outcomes.

In the middle seats, arrangements of 7 elements(3 generals, 4 lieutenants). Hence the required number of combination will be given as:

Number of ways = 2*7!

Number of ways = = 100802

Hence the number of ways they can be seated is 10,080 ways.

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The domain of the function f(x, y, z) = ln(144 − 9x² − 16y² − z²) is x ∈ (-4, 4), y ∈ (-3, 3) and z ∈ (-12, 12) which forms an ellipsoid.

Domain of a function is the set of all values possible for the input parameters for real output parameter or output parameter in given range.

Given the function as f(x, y, z) = ln(144 − 9x² − 16y² − z²)

For f(x, y, z) to be real, the function 144 − 9x² − 16y² − z² should be greater than 0. So,

144 − 9x² − 16y² − z² > 0

9x² + 16y² + z² < 144

x²/ 4² + y²/ 3² + z²/ 12² < 1

Therefore, the domain is an ellipsoid.

Therefore x ∈ (-4, 4)

y ∈ (-3, 3)

z ∈ (-12, 12)

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The correct solutions for this question are as:

(A) Bearing of B from A = 72°

(B) Bearing of B from C = 342°

(C) Bearing of A from B = 252°

(D) Bearing of A from C = 293°

Step by step solution:

(A) Bearing of B from A:

= 72° (Given in question)

(B) Bearing of B from C: = 342°

Solution:

As sum of co-interior angles is 180° , i.e.  ∠NBC +∠NCB =180°

so, 162° + ∠NCB = 180°

     ∠NCB = 180°-162°

     ∠NCB = 18°

reflexive angle NCB =360° - ∠NCB

reflexive angle NCB = 360° - 18°

reflexive angle NCB = 342°

So, bearing of B from C: = 342°

(C) Bearing of A from B: = 252°

Solution:

First extend the line AB to any point (let's say "X")

So, ∠NBX = 72°   [BY USING CORRESPONDING ANGLES]

Bearing of A from B = ∠NBX + 180°

Bearing of A from B =72° + 180°

Bearing of A from B =252°

(D) Bearing of A from C: = 293°

Solution:

Bearing of A from C= 360° - (∠BCA + ∠BCN)

Bearing of A from C= 360° - (49° + 18°)

Bearing of A from C= 360° - (67°)

Bearing of A from C= 293°

Important Points for "Bearing of Angles":

A bearing is an angle that is calculated clockwise from the north. A traverse should be regarded as anticlockwise unless differently stated or obvious from the bearings.

The angle between two lines cannot be directly read using a regular compass. By tracking the two lines bearings away from their point of confluence, the angles can be found.

Two angles—an inner angle and an exterior angle—are created when the two lines converge at a place. These two angles add up to a 360° angle.

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Answer:

Refer to step-by-step

Step-by-step explanation:

Prove that, [tex]\lim_{x \to \22} 2^{x}=4[/tex]

Plug in the value of 2 into the limit.

[tex](2)^{2}=4[/tex]

Thus we proved the limit.

Answer:

Yes, 1/4 and 4/16 are equivalent

Step-by-step explanation:

1/4 = 0.25

4/16 = 0.25

Answer:

5/14 * 5/14

Step-by-step explanation:

Answer:

The appropriate answer is option b (0.0228).

Step-by-step explanation:

The given values are:

Random sample,

[tex]n=100[/tex]

Average length of time,

[tex]\bar{x}=3.1 \ minutes[/tex]

Waiting time,

[tex]\mu=3 \ minutes[/tex]

Standard deviation,

[tex]\sigma=0.5[/tex]

Now,

The test statistics will be:

⇒  [tex]z=\frac{(\bar{x}-\mu)}{\frac{\sigma}{\sqrt{n} } }[/tex]

On substituting the values, we get

⇒     [tex]=\frac{(3.1-3)}{\frac{0.5}{\sqrt{100} } }[/tex]

⇒     [tex]=\frac{0.1}{0.05}[/tex]

⇒     [tex]=2[/tex]

hence,

⇒  [tex]P(z >2 ) = 1 - P(z <2 )[/tex]

By using the table,

⇒                 [tex]=1-0.9772[/tex]

⇒                 [tex]=0.0228[/tex]

The marginal average cost is -1 and The marginal average cost for 200 is  $699.

The price to manufacture a second unit of output is known as the marginal cost. Since marginal cost aids in determining the level of production that is the most effective for a manufacturing process, it is a crucial topic in cost accounting. It is estimated by estimating the costs incurred even if just one more unit is produced.

Given The total cost​ (in dollars) of manufacturing x auto body frames is ​C(x)=40,000+500x.

Average cost = Cx / x

Average cost = (40,000 + 500x)/ x

For x = 200

Average cost = (40,000 + 500 * 200)/200

Average cost = 700$ per frame

Marginal average cost = d(Cx/x)/dx

d(Cx/x)/dx = -40,000/ x^2

at x = 200

Marginal average cost = -40,000/ 200^2  = -1

Marginal average cost = -1 tells us the average cost

decrease at the rate of -1 for every x

Average cost for 200 = 700$ per frame

Average cost for 200 = 700 + 1 (-1)

The average cost for 200 = 700 -1 = 699$

therefore, the Marginal average cost for 200 is $699.

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Answer:

n=15/4c

Step-by-step explanation:

y=mx+b

b=0 as it does not state any initial value

y=n

x=c

m=3 3/4 or 15/4

combining these together you get:

n=15/4c+0

The equation representing the number of number of cups of flower Darien uses, c, to bake n loaves of bread is [tex]n = 3\frac{3}{4} c[/tex]

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, Darien uses [tex]3\frac{3}{4}[/tex] cups of flour to make one loaf of bread, we need to establish an equation, that will represent the number of cups of flower Darien uses, c, to bake n loaves of bread,

So,

Since, she uses [tex]3\frac{3}{4}[/tex] cups for one loaf of bread so for n loaf =

(We will multiply the amount used in one loaf to the number of loafs needed)

Therefore,

To make n number of loafs = [tex]3\frac{3}{4} c[/tex]

Hence, the equation representing the number of number of cups of flower Darien uses, c, to bake n loaves of bread is [tex]n = 3\frac{3}{4} c[/tex]

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9514 1404 393

Answer:

  72°

Step-by-step explanation:

The external angle E is half the difference of subtended arcs CG and DF.

  E = (CG -DF)/2

  2E = CG -DF . . . . . . multiply by 2

  DF = CG -2E = 160° -2(44°) . . . . . add DF-2E to both sides; substitute values

  arc DF = 72°

[tex] \sf \: 5(4x -1.5x) + 12 = 4x - 124 \\ \sf \: 5 \times 2.5x + 12 = 4x - 124 \\ \sf \: 12.5x + 12 = 4x - 124 \\ \sf \: 12.5x - 4x = - 124 - 12 \\ \sf \: 8.5x = - 136 \\ \sf \: x = - 16[/tex]

Answer: 4t

Step-by-step explanation:

You just do t times the amount of boxes you have, which is 4. So you have 4 times t, but in algebra, we don't write the multiplication sign. So the expression would be written as 4t. Yw!

Also please tell me if I was unhelpful/incorrect, thanks!

The unit rate for 4543.08 km in 52.4 hours is 86.7 km.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

4543.08 km = 52.4 hours

Divide 52.4 into both sides.

86.7 km = 1 hour

Thus,

The unit rate is 86.7 km.

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Answer:

its A

Step-by-step explanation:

just took the test

Answer:

The first graph on edge 2021

Answer:

12/30, if you reduce then it would be 2/5 because you divided by 6 hope this helps! :D

Step-by-step explanation:

The fraction that represents the eaten portion of the cake is [tex]\frac{2}{5}[/tex]

Given the following data:

To find the fraction that represents the eaten portion of the cake;

In this exercise, you're required to find what fraction represents the eaten portion of the wedding cake.

[tex]Fraction = \frac{E}{W}[/tex]

Substituting the values into the equation, we have;

[tex]Fraction = \frac{12}{30}[/tex]

Dividing both sides by 6, we have;

[tex]Fraction = \frac{2}{5}[/tex]

Therefore, the fraction that represents the eaten portion of the cake is [tex]\frac{2}{5}[/tex]

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Answer:

triangle

Step-by-step explanation:

It looks like a traingle

Answer:

it is 62 or 58 because they are show the most times

Answer:

The answer is 61.

Step-by-step explanation:

The function f(x) = -x-3.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.

Given function:

f(x)+3f(-x) = 2x+6.

Let the function is an even function.

So, f(-x) = f(x)

To solve for f(x):

Substituting the property of an even function,

f(x) - 3f(x) = 2x + 6

-2f(x) = 2x + 6

f(x) = -x-3

Therefore, f(x) = -x-3 is the function.

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Answer:

(1, 1)

Step-by-step explanation:

in the order pair you have (x, y) so if is ( 3, 0) it means is ( x=3, y=0)

substitute in the inequality those x, and y values and see if it checks

y ≥ 4x-5

for ( 3, 0) is 0 ≥ 4*3-5 false

for ( 3,4)  is 4 ≥ 4*3-5 false

for (1,1) is 1 ≥ 4*1-5 true because 1 ≥ -1

for (2, 1) is 1 ≥ 4*2-5 false

Answer:

A is linear

Step-by-step explanation:

check the delta y  (y2 - y1)  and or the delat x (x2 - x1)   and see if the differences are the same from each neighboring ordered pairs

answer A has a slope (m) of  (y2 - y1) / (x2 - x1) = 2/2 = 1

Answer: 6

Step-by-step explanation:

Yogurt production is affected by the production technological conditions.

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