left model : 1 cm = 6 in
right model : 1 cm = 2 in
Above are two different models of the same triangular handkerchief. If the area of the model on the right is 36 sq cm, what is the area
of the model on the left?

The dimensions of the rectangular garden to maximize the area is length = width = 75 meters.

Let l be the length and w be the width of the rectangular garden.

We need to find the dimensions of the rectangular garden of greatest area that can be fenced off (all four sides) with 300 meters of fencing.

The perimeter of the  rectangular garden = 300 meters

We know that the perimeter of the rectangle =2(length + width)

300 = 2(l + w)

l + w = 150               .......(1)

Now, the maximum area of a  rectangular garden is when Length  = width

So, for equation 1

l + l = 150

l = 75 meters

So, w = 75 meters

And the area of the rectangular garden = length * width

                                                               = 75 * 75

                                                               = 5625 m²

So the maximum area of the  rectangular garden is 5625 m²

Therefore, the dimensions of the garden to maximize the area is length = width = 75 meters and maximum area is  5625 m²

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Answer:

hii

Step-by-step explanation:

3(x-2)-2x+3=-12

3 times x = 3x

3 times -2 = -6

3x-6-2x+3=-12

3x + 2x = 5x

-6 + 3 =-3

i don't know the rest I'm sorry

Answer:

i think d

Step-by-step explanation:

Answer:

What is this table above?....is there anything related to this that u can show

Step-by-step explanation:

Answer:

4.140393356

Step-by-step explanation:

Mean = (3+4+5+7+10+12+15) / 7 = 8

Count = 7 numbers

Sum of the numbers = 56

Each number minus the mean =

(3-8=-5)(4-8=-4)(5-8=-3)(7-8=-1)(10-8=2)(12-8=4)(15-8=7)

Now square of each of these numbers:

25+16+9+1+4+16+49 = 120

Variance = 120/7 = 17.14285714

Standard deviation = square root of the variance

Sqrt 17.14285714 = 4.140393356

The linear equation which relates p and c is c = 600 + 30p

c = total cost

c = total cost p = number of parts

Cost per part = $30

Monthly fixed cost = $600

Total cost = Fixed cost + variable cost

Varibale cost = number of parts × cost per part = 30p

Hence. Total cost :

Total cost = $600 + 30p

Therefore,

c = 600 + 30p

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Answer:

-5°F I'm sure. hope this helps :)

Step-by-step explanation:

The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.

The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.

The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.

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Answer:

Step-by-step explanation:

Answer:

g(x) = -f(x) +5

Step-by-step explanation:

The sign on the 'x' changes, this implies a reflection.

g(x) = -f(x) = -(x+1) = -x -1

Now apply a vertical translation 'up 5' to f(x)

g(x) = -f(x) + 5 = (-x-1) +5 = -x +4

The volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis will be V = 149.2.

From the question.

x = 5 + y2,

x = 0,

y = 2,

y = 3

The equation for the volume is mathematically given as

\(V = \int\limits^3_2 (2\pi y)(5+y^2) \, dy \\\\\\V = 2\pi \int\limits^3_2(5y+y^3) \, dy \\\\\\V = 2\pi \frac{5y^2}{2} + \frac{y^4}{4} |^3_2\\\\\\V = 149.2\)

Therefore

The volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis will be V = 149.2.

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Answer:

7 m

Step-by-step explanation:

To find the length of the apothem of a regular pentagon, we can use the formula:

apothem = (side length) / (2 * tan(180/n))

where n is the number of sides of the regular polygon.

In this case, the side length of the pentagon is 7.1 meters and n is 5. Plugging in these values, we get:

apothem = (7.1) / (2 * tan(180/5))

apothem = 7 meters (rounded to the nearest meter)

Therefore, the length of the apothem of the pentagon is 7 meters.

Answer:

Step-by-step explanation:

Step-by-step explanation:

Odds against = failures / successes

Probability = successes / (successes + failures)

0.21 = cats / (cats + no cats)

1 / 0.21 = (cats + no cats) / cats

4.76 = 1 + (no cats / cats)

3.76 = no cats / cats

So the odds against are 3.76 to 1.  

Answer:

1 1/5

Step-by-step explanation:

i took the k12 test

Answer:

400 students increased after 2 years in the school

Step-by-step explanation:

(1000÷5)1×2

=)200×1×2

=)200×2

=)400 students

Answer:

15 yards.

Step-by-step explanation:

This is because there are 3 feet in one yard, and 5x3= 15.

Answer:

1.66667

Step-by-step explanation:

Answer:

x = 1/5 - first box

Step-by-step explanation:

Let's interpret this by using what I call the "isolated-x method."

First, we can simplify whatever's being affected in the parentheses.

#1: 3 times (2x) is equal to 6x

#2: 3 times (- 1 | equal to -1) results in -3, or + -3

So now we're working with 6x - 3 = -9x.

Now, we'll add a positive 9x to the -9x, since it can be hugely helpful to have one side result in 0.

Now we're working with 15x (6x + our new 9x) - 3 = 0

Since we have "whole like terms" we can now easily add 3 to each side.

Now we're working with 15x = 3 (0 + our new 3)

We can finish by dividing each side by 3.

15x = 3 now turns into 5x = 1.

To get from 5 to 1 you can multiply 5 by its "multiplicative inverse," also known as 1/5.

Therefore, x = 1/5

Hopefully this helped a bunch! Tell me if you need any further assistance...

( :

Answer:

X=5

Step-by-step explanation:

X=5

15x+25>100

-25 -25

15x>75

—- —-

15x 15x

X>5

Act like there is a line under the >sign

Answer: $400

Step-by-step explanation:

Discount = 15%

The original price/value of an item is always 100%

So selling price (%) = original price - discount = 100%-15% = 85%

We got selling price as 85%

This implies that 85% = 340

Let's find 1% first, then 100%

1% = 340÷85 = 4

100% = 4 × 100 = $400

The usual (normal/original) price is $400

Juan sold a bicycle at a discount of 15% if the selling price was $340 then the usual price of the bicycle was $400.

percentage, a relative value indicating hundredth parts of any quantity.

Let's represent the usual price of the bicycle by P.

Since Juan sold the bicycle at a discount of 15%, the selling price (S) would be 85% of the usual price (P).

We can express this relationship as an equation:

S = 0.85P

We also know that the selling price of the bicycle was $340.

Substituting S = $340 into the equation above, we get:

$340 = 0.85P

To find P, we can solve for it:

P = $340 / 0.85

P = $400

Therefore, the usual price of the bicycle was $400.

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Answer:

First know the formula for the area of a circle;

Where 'π' represents pi(3.14 or 22/7), and 'r' stands for the radius being squared.

For the first problem, we can see that 12 is our diameter.

And to find the radius, we need to find 1/2 of the diameter (half of the diameter), so;

D/2 = R

Replace with actual values;

12/2 = 6, 6 is our radius.

Now we plug this into our formula:

A = π\(r^{2}\)

A = 3.14(6^2)

A = 3.14(36)

A = 113.04 centimetres is the area of the circle.

For the second problem, we can see that 18 is our diameter.

And to convert the diameter into the radius, we do what we did to the past problem, find 1/2 of the diameter.

So;

D/2 = R

18/2 = 9, 9 is our radius.

Now we plug this into our formula:

A = π\(r^{2}\)

A = 3.14(9^2)

A = 3.14(81)

A = 254.34 inches is the area for this circle.

For the third problem, we can see that our radius is already given, 5.

So now we just simply and easily plug this into our formula;

A = π\(r^{2}\)

A = 3.14(5^2)

A = 3.14(25)

A = 78.5 meters is the area for this circle.

Answer:

a). y = 0.25x + 15

b). x = 480 cups

Step-by-step explanation:

(a). Let the equation of the linear function passing through a point (x', y') is,

y - y' = m(x - x')

'm' = slope of the line

b = y-intercept

Two points lying on the linear function will be (200, 65) and (250, 77.5).

Slope of the line 'm' = \(\frac{y_2-y_1}{x_2-x_1}\)

m = \(\frac{77.5-65}{250-200}\)

   = \(\frac{12.5}{50}\)

   = 0.25

Therefore, equation of the line passing through (200, 65) and slope 0.25 will be,

y - 65 = 0.25(x - 200)

y - 65 = 0.25x - 50

y = 0.25x + 15

(b). For y = $135 we have to calculate the number of cups of coffee produced.

135 = 0.25x + 15

0.25x = 135 - 15

0.25x = 120

x = 480 cups

Therefore, 480 cups of coffee will be produced.

Answer:

4444444

Step-by-step explanation:

sorry not that smart ok

The company can build 5 child bikes and 15 adult bikes in a week.

The answer is "Yes because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100".

Linear Equations are mathematical statements, which can be used to find an unknown quantity or any value in a given problem. Here we use variables like x, y .. etc. to represent unknown values.

Here we will use Linear Equations to solve the equations.

Here we have

One child bike requires 4 hours to build and 4 hours to test  

Number of hours to build 'c' number of child bikes = 4c

Number of hours to test 'c' number of child bikes = 4c

One adult bike requires 6 hours to build and 4 hours to test.

Number of hours to build 'a' number of adult bikes = 6a

Number of hours to test 'a' number of adult bikes = 4a  

Number of hours taken to build bikes in one week = 120

=> 4c + 6a ≤ 120  --- (1)

Number of hours taken to test the bikes in one week = 100  

=> 4c + 4a ≤ 100 --- (2)  

Assume that

The company can build 5 child bikes and 15 adult bikes in a week

Substitute c = 5 and a = 15 in (1) and (2)

(1) => 4(5) + 6(15) ≤ 120

=> 110 ≤ 120   [ which can be true ]

(2) => 4(5) + 4(15) ≤ 100

=> 80 ≤ 100  [ which can be true ]  

From the above calculations,

Both (1) and (2) are satisfied

Therefore,

The company can build 5 child bikes and 15 adult bikes in a week.

The answer is "Yes because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100".

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Given that the average score of freshmen students' on the college entrance exam last year was 1160, it can be deduced that

Last year some of their freshman students had a score of less than 1320 on the exam.

Last year at least one of their freshman students had a score of at least 1160 on the exam.

The first and fifth options are the correct answers.

Answers:

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

Explanation:

Answer:

It has only 1 pair of parallel sides.

Step-by-step explanation:

Answer:

It has only 1 pair of parallel sides

Step-by-step explanation:

Answer:

Y=KX so its 10=K2

Step-by-step explanation:

Plug in the Number OR K=y/x

Answer:

13 Hours

Step-by-step explanation:

subtract 14 from 79. That leaves you with 65 dollars. Divide 65 by 5 and you get 13.

The two composite functions have their values to be (w o s)(x) = 7x² - 49x + 33 and (s o w)(x) = (7x - 2)² - 7(7x - 2) + 5

Composite function 1

The given parameters are

w(x) = 7x - 2

s(x) = x² - 7x + 5

To calculate (w o s)(x), we make use of

(w o s)(x) = w(s(x))

So, we have

(w o s)(x) = 7s(x) - 2

Substitute s(x) = x² - 7x + 5

(w o s)(x) = 7(x² - 7x + 5) - 2

Expand

(w o s)(x) = 7x² - 49x + 35 - 2

Simplify

(w o s)(x) = 7x² - 49x + 33

Composite function 2

Here, we have

w(x) = 7x - 2

s(x) = x² - 7x + 5

To calculate (s o w)(x), we make use of

(s o w)(x) = s(w(x))

So, we have:

(s o w)(x) = w(x)² - 7w(x) + 5

Substitute w(x) = 7x - 2

(s o w)(x) = (7x - 2)² - 7(7x - 2) + 5

So, the composite functions are (w o s)(x) = 7x² - 49x + 33 and (s o w)(x) = (7x - 2)² - 7(7x - 2) + 5

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