A rectangular garden must have a perimeter of 540 feet and and area of at least
12,000 square feet. Describe the possible lengths of the garden. round to the nearest
whole number

I need help please!

Step-by-step explanation:

so, we have

6x² + 8xy + 8y²

and

5x² + 3xy + 16y²

we can combine only terms of the same kind (defined by the type and exponent of the used variables).

this is like adding fruit.

e.g. when we have a mixture of 3 apples, 4 oranges and 5 plums, and we add a mixture of 6 apples, 2 oranges and 3 plums - what do we get ?

we get a new mixture of

3+6 = 9 apples

4+2 = 6 oranges

5+3 = 8 plums

and exactly the same thing happens with mixing terms when adding them up.

so, we get

6+5 = 11x²

8+3 = 11xy

8+16 = 24y²

so, the result is

11x² + 11xy + 24y²

it is really that simple.

Step-by-step explanation:

I don't see the options and how they are written, but I can tell you the right answer in numbers :

sin(F) = 3/5 = 0.6

cos(F) = 4/5 = 0.8

sin(G) = 4/5 = 0.8

cos(G) = 3/5 = 0.6

why ?

remember the norm circle (radius 1) with ask the trigonometric functions.

the sine of an angle is the vertical height from that point in the circle arc down to x-axis.

the cosine of an angle is the length on the x-axis from the center of the circle to the point, where the sine touches the x-axis.

in any case, sine and cosine enclose the right angle (90°).

each function is now defined for the norm circle with radius = 1.

for angles in larger circles we need to divide the find lengths by the actual radius (we formality do this in the norm circle too, but a division by 1 does not change anything).

for the angles at F and G the radius is the side with the length 5.

Looking at the triangles, the values of x in the figures are

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions

figure in 14)

The solution for x

8 / (x + 5) = (x - 9) / 21

21 * 8 = (x + 5)(x - 9)

168 = x^2 - 4x - 45

x^2 - 4x - 213

x = 16.73 or -12.73

using the positive value

x = 17

figure in 15)

The solution for x

(x + 3) / 15 = 4 / (3x + 1)

cross multiplying

(x + 3)(3x + 1) = 15 * 4

3x^2 + 10x + 3 = 60

3x^2 + 10x - 57 = 0

x = 3 OR -6.333

taking the positive value

x = 3

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Answer: 110°

Step-by-step explanation:

Looks like a bit more than 100°.

Based on the information provided, ETS is an abbreviation for these three terms (Error, Trend, and Season). Following that, Exponential Smoothing Methods for an ETS system can be described, with the details specified in a smoothing style.

=> As should be obvious, combining Error, Trend, and Season on any occasion in three distinct ways yields a plethora of combinations.

=> The trend depicts the overall layout of the time. It communicates with the data's drawn-out model — its tendency.

=> The seasonal section displays the types associated with anticipated events. Finally, the error component explains what the season and trend components do not. The error is due to the disparity between the first data and the combination of trend and seasonality. As a result, if we crystallize all three parts, we will have the first data back.

=> It has a counted substance conduct when the period of seasonal swings remains constant.

=> We can label our model as ETS (M,A,M).

-> Multiplicative Mistake

-> Added substance Trend

-> Multiplicative Seasonality.

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The measured interior angles of the triangle are 40°, 60°, and 80° in ascending order.

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.

The triangle has interior angles are:

(2x)°, (3x)° and (4x)°

As we know that the sum of interior angles is 180 degrees in the triangle.

According to the given figure,

(2x)° + (3x)° + (4x)° = 180°

Apply the addition operation in the above equation,

9x = 180

x = 180/9

x = 20°

Thus, The triangle has interior angles are:

(2x)° = 2 × 20° = 40°

(3x)° = 3 × 20° = 60°

(4x)° = 4 × 20° = 80°

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This comes to $141, indicating that Ms. Patel spent that money on four sets of pliers, two wrench sets, and a chisel set.

The given condition states that;

Make a ratio first.

This ratio might be expressed as 4:2:1 (in pliers, wrenches, and chisels).

Then, multiply every one of these sums by their respective prices before adding them all up.

Pliers : 4 times 17.50 equals $70

Wrenches : $2 x $21.5 = $43

Chisels : 1 x 28 equals $28

Thus,

Sum = $70 + $43 + $28

Sum = $141

This amounts to $141, proving that she purchased a chisel set, two wrench sets, and four pairs of pliers.

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Answer:

a) 2.0 x 10^5

b) 8.0 x 10^4

c) 9 x 10^9

d) 1 x 10^10

Equation of the given data y = 1750x -20,000 and graph of the equation is attached.

As given in the question,

Data of the table :

Year :               1                 2                   3              4                5

Investment : $20,000      $21,750      $23,500    $25,250      $27,000

(x₁, y₁) = ( 1, 20,000)

(x₂, y₂) = ( 2, 21,750)

Equation of the given graph is :

( y - 20,000)/ (x -1) = (21,750 - 20,000)/ (2 -1)

⇒ ( y - 20,000)/ (x -1) = 1750

⇒ y = 1,750x -18,250

Graph of the equation  y = 1,750x -18,250 s represented by the graph.

Graph is attached.

Therefore, equation of the given data y = 1750x -20,000 and graph of the equation is attached.

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Answer:

4:1

Step-by-step explanation:

12÷3=4

3÷3=1

white to blue

12 : 1

The amount of money that Amelia would spend on five bags of cat food is $22.5.

Amelia needs to buy some cat food. At the nearest store, three bags of cat food cost $13.50. We need to find out the amount of money that Amelia would spend on five bags of cat food.

Let the amount of money that Amelia would spend on 5 bags of cat food be represented by the variable M. We will use the unitary method. First of all, we will calculate the cost of one bag of cat food.

C = $13.50/3

C = $4.5

Now we need to find out the cost of five bags of cat food.

M = $4.5×5

M = $22.5

Hence, the amount of money that Amelia would spend on five bags of cat food is $22.5.

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The strategy which would eliminate a variable in the system of equations is to multiply the top equation by 6 ,multiply the bottom equation by -5 then add the equation and is denoted as option B.

This is a mathematical term which is made up of two expressions and is connected by an equal sign.

In the example given below:

8x + 5y = -7

-7x + 6y = -4

We can multiply the top by 6 and the bottom by -5 which will result in:

48x + 30y = -42

35x - 30y = 20

They are then added to each other to give:

48x + 35x + 30y - 30y = -42 + 20

83x = - 22

x = -22/83

From this we can notice that the variable y was eliminated which is why option B is the correct choice.

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Answer:

It's correct

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation. Point Form: (-2, 4)  Equation Form : X= -2, Y = 4.

7 i do not feel like explaining tbh

Vertex form

f(x)= 3(x+2)^2+4

For given expression  (7^3) * (7^x) equivalent expressions are:

343 * 7^x and 7^(3+x)

The correct options are option (C) and option (D)

In this question, we have been given an expression (7^3) * (7^x)

We need to find expressions that are equivalent to given expression.

Consider given expression (7^3) * (7^x)

We know that 7^3 = 343

So given expression becomes, (7^3) * (7^x) = 343 * (7^x)

For given expression, the bases of the exponents are equal.

so, by the properties of exponents

(7^3) * (7^x) =  7^(3 + x)

Therefore, for given expression  (7^3) * (7^x) equivalent expressions are:

343 * 7^x and 7^(3+x)

The correct options are option (C) and option (D)

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AB has endpoints A (1, 7) and B (5, 4) and DE has endpoints D (-6, -2) and E (-2,-5). The translation is by the rule (x - 7, y - 9), is used to transform AB to DE

Translation is a type of transformation that involve a linear movement.

The translation rule is gotten by comparing the points as below

preimage point A (1, 7) and B (5, 4)

image points D(-6, -2) and E(-2,-5)

x coordinate

using point A and D = -6 - 1 = -7

using point B and E = -2 - 5 = -7

y coordinate

using point A and D = -2 - 7 = -9

using point B and E = -5 -  = -9

Therefore the translation rule is (x - 7, y - 9) that got the image, point D and E from the preimage , point A and B

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Answer:

-2 ; -1 ; 0 ; 1

Step-by-step explanation:

the inequality is satisfied in this interval [-2.5,1].

We are searching the integers: -2 ; -1 ; 0 ; 1

All the values of x that satisfy the inequality will be;

⇒ x = - 2, - 1, 0, 1

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is given.

Now,

The solution of the inequality are given as;

⇒ x ∈ [- 2.5, 1]

But we can find the integers which satisfy the inequality.

Hence, All the values of x that satisfy the inequality will be;

⇒ x = - 2, - 1, 0, 1

Thus, All the values of x that satisfy the inequality will be;

⇒ x = - 2, - 1, 0, 1

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Answer:

y=-3/32

Step-by-step explanation:

2-18y=11+78y

-18y-78y=11-2

-96y=9

y=-3/32

Answer: Positive

Step-by-step explanation: It would be positive because the question is asking how much money they lost. The lost a positive amount of money.

Answer:

b = 10.06 in

Step-by-step explanation:

Formula we use,

→ (AC)² = (BC)² + (AB)²

Now the value of a will be,

→ (10.5)² = b² + (3)²

→ 110.25 = b² + 9

→ b² = 110.25 - 9

→ b = √101.25

→ [ b = 10.06 in ]

Hence, value of b is 10.06 in.

The number of grams of salt in the tank at time t is given by the differential equation [tex]A(t)=200-170e^{-\frac{1}{50}t}[/tex].

The rate is basically a measurement of something's number, amount, or degree in relation to another item. Its the ratio of some quantity to some other quantity.

An equation with a function and one or more of its derivatives is referred to as a differential equation:

At the start, the tank contains A(0) = 30 g of salt.

Salt flows in at a rate of

(1 g/L) * (4 L/min) = 4 g/min

and flows out at a rate of

(A(t)/200 g/L) * (6 L/min) = 3A(t)/100 g/min

so that the amount of salt in the tank at time t changes according to

A'(t) = 4 - A(t)/50

So,

[tex]A'(t) = 4 - \frac{A(t)}{50}[/tex]

The solution of linear differential equation y' + ay = g(x) is in the form,

[tex]e^{ax}y=\int {e^{ax}g(x)} \, dx +c[/tex]

Now, putting the values,

[tex]a=\frac{1}{50} \\g(x)=4[/tex]

[tex]e^{\frac{1}{50}t}A(t)=\int {e^{\frac{1}{50}t}4} \, dt +c\\=4\int {e^{\frac{1}{50}t}} \, dt +c\\=4\times50e^{\frac{1}{50}t}+c\\=200e^{\frac{1}{50}t}+c\\[/tex]

Now,

[tex]A(t)=200+Ce^{-\frac{1}{50}t}\\[/tex]

Putting the initial value,

[tex]30=200+Ce^{-\frac{1}{50}(0)}\\\\200+C=30\\C=-170[/tex]

So, the function will be [tex]A(t)=200-170e^{-\frac{1}{50}t}[/tex].

Therefore, the number of grams of salt in tank at time t is given by differential equation [tex]A(t)=200-170e^{-\frac{1}{50}t}[/tex].

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The largest sample size required is 2886.4.

Here we have to calculate how large of a sample size is required.

The formula:

(Z ∝I2/ E)² × P( 1- P)

The given data:

Margin error (E) = 1.5%

=0.015

As it is given that 90% confident that your estimate is within 1.5% of the true population proportion, therefore we have:

The level of significance(∝) = 1 - 0.90

= 0.10

The z value for the 90% confidence is 1.645

Therefore the largest of a sample size is required = ( 1.645/ 0.015)²× ( 0.4)(1- 0.4)

= 2886.4

The largest a sample size required is 2886.4

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Answer:

The factory makes 12,000 (12k) hats each day

Step-by-step explanation:

4000

× 3

--------

12,000

The students and courses have one to many relationship.

A one to many relationship is such kind of relation which exist when a particular function is linked to many other functions. It means that many elements of the set A is related to a single element of the set B.

In this case, the course is only one but the students studying the course are more in number. The same course is studied by many student but in different manner but the course is same. This is why we conclude that the relationship between the students and the course is one to many.

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The function has a maximum value of 30 at x = 3.

Given Function:

f(x) = -3+18x+3

here a = -3 , b = 18 , c = 3

a is negative so it has maximum value

x = -b/2a

= -18/2*(-3)

= -18/-6

= 18/6

= 3

f(x) = -3* + 18*3 + 3

= -3*9+54+3

= -27+54+3

= 27+3

= 30

Therefore the function has a maximum value of 30 at x = 3.

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Step-by-step explanation:

the triangle above is an isosceles triangle,

two sides and angles are equal

AC=AD

triangle ACB=triangle ABD(because it is an isosceles triangle )