Let a,b,c be the three side lengths of a triangle. Prove that 4(ab+ac+bc)>(a+b+c)
2

Answer:

She will have 12 sections per fabric and 36 sections in all

Step-by-step explanation:

Betty buy 3 fabrics of 30 ft²

If she cut each to 2/5 of 1 ft²

Then she will have

30 × 2/5

= 6 × 2

= 12

She will have 12 for each fabric and for the 3 fabrics, she will have

12 × 3 = 36

Step-by-step explanation:

Answer:

225 sections

Step-by-step explanation:

Each fabric has an area of 30 sq ft.

All 3 fabrics have a total area of 3 * 30 sq ft = 90 sq ft.

Each sections has an area of 2/5 sq ft.

number of sections = total area of fabric / area of each section

90/(2/5) = 90 * 5/2 = 450/2 = 225

Answer: 225 sections

Answer:

B. No, Hannah should have used the ratio \( \frac{adjacent}{opposite} \)

Step-by-step explanation:

✍️The formula for calculating cotangent of an angle is given as:

\( cot = \frac{adjacent}{opposite} \).

The ratio, \( \frac{opposite}{adjacent} \), used by Hannah is the formula for calculating tangent of an angle.

Therefore, Hannah did not calculate the cotangent of the angle correctly.

She should have used, the ratio, \( \frac{adjacent}{opposite} \) instead.

The transformations for the indicated mapping are as follows:

Transformations in the graph of a function involve operations such as multiplication/division or sum/subtraction, either in the domain of the function, involving values of x, or the range, involving values of y.

Examples of transformations are as follows:

The original figure was in the second quadrant and was reflected to the fourth, hence, looking at equivalent vertices AM and BN the following rule was applied:

(x,y) -> (y - 2, -x).

One possible way to achieve this with two transformations is:

Vertice A is at (-4,4), hence:

Vertice M(equivalent to A) is at (2,-4).

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Answer:

2x^100000000000+ 5/2

Step-by-step explanation:

Answer:

400000000000

Step-by-step explanation:

The time the train takes to travel and the 45 miles distance from Ashford to Bromley indicates that the average speed and the difference between the average speeds are;

a) 30 mph

b) 3 mph

The speed is the rate at which the position of the train is changing with time.

The distance between Ashford and Bromley = 45 miles

The time it takes the train = 20:05 - 18:35 = 1 hour 30 minutes = 1.5 hours

a) The average speed = Total distance ÷ Time taken

Therefore;

Average speed of the train = 45 miles ÷ 1.5 hours = 30 miles per hour

b) The time the train leaves Ashford the following day = Normal time = 18:35

The time the train arrives Bromley = 10 minutes late = 10 + 20:05 = 20:15

The time it takes the train = 20:15 - 18:35 = 1 hours 40 minutes = 1 2/3 hours = 5/3 hours

The average speed of the train the following day is therefore;

Average speed = 45 miles ÷ 5/3 hours = 27 miles per hour

The difference between the average speed of the train on the two days is therefore; 30 mph - 27 mph = 3 mph

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Answer:

177

Step-by-step explanation:

Answer: a_10 = 177147/65536. Write the general term through the pattern:: a_n = 36 3/4 n - 1 Substitute and calculate:: a_10 = 177.

Answer:

i have no idea to big of a question byt why would your teacher give you that kind of math

Step-by-step explanation:

9514 1404 393

Answer:

  7.06

Step-by-step explanation:

This triangle can be solved a couple of ways. In the end, they amount to the same thing.

1) The area is ...

  A = 1/2bh = 1/2(8)(15) = 60 . . . using DG as the base

Using GE as the base, the height (DF) is ...

  A = (1/2)(17)(DF)

  2(60)/17 = DF = 120/17

  DF ≈ 7.06

__

2) Using similar triangles, we can find the ratio of the long side to the hypotenuse as ...

  (long side)/(hypotenuse) = DE/GE = DF/DG

  DF = DG(DE/GE) = 8(15/17) = 120/17

  DF ≈ 7.06

The given linear system, the eigenvalues and eigenvectors of the coefficient matrix are as follows: The eigenvalue is -3/5 + i/5 with the eigenvector (1, i). Thus, the real-valued solution to the initial value problem is y₁(t) = -10e^(-3t/5) + 15e^(it/5) and y₂(t) = 15e^(-3t/5) + 15ie^(it/5).

To find the real-valued solution to the initial value problem, we can use the eigenvalues and eigenvectors. The solution is y₁(t) = -10e^(-3t/5) + 15e^(it/5) and y₂(t) = 15e^(-3t/5) + 15ie^(it/5).

(a) To find the eigenvalues and eigenvectors, we start by solving the characteristic equation det(A - λI) = 0, where A is the coefficient matrix and λ is the eigenvalue. The coefficient matrix in this case is [[-3/5, -i/5], [5, 3]]. Solving the characteristic equation, we get (-3/5 - λ)(3 - λ) + 5i/5 = 0. Simplifying, we have λ² + (3/5 - 3/5i)λ + 14/5i = 0. Solving this quadratic equation gives us the eigenvalues λ = -3/5 + i/5 and λ = -3/5 - i/5.

Next, we find the eigenvectors corresponding to each eigenvalue. For the eigenvalue λ = -3/5 + i/5, we solve the equation (A - λI)v = 0, where v is the eigenvector. Substituting the eigenvalue and solving, we get (-3/5 + i/5)v₁ - (i/5)v₂ = 0. Simplifying, we find v₁ = i and v₂ = 1. Therefore, the eigenvector corresponding to λ = -3/5 + i/5 is (1, i).

(b) To find the real-valued solution to the initial value problem, we can express the solution in terms of the eigenvalues and eigenvectors. The general solution is given by y(t) = c₁e^(λ₁t)v₁ + c₂e^(λ₂t)v₂, where c₁ and c₂ are constants. Substituting the eigenvalues and eigenvectors, we have y₁(t) = c₁e^(-3t/5)(1) + c₂e^(it/5)(i) and y₂(t) = c₁e^(-3t/5)(i) + c₂e^(it/5)(1).

To find the real-valued solution, we use the initial conditions y₁(0) = -10 and y₂(0) = 15. Substituting t = 0 and solving, we get c₁ + c₂i = -10 and c₁i + c₂ = 15. Solving these equations simultaneously, we find c₁ = -10 and c₂ = 15i. Substituting these values back into the general solution, we obtain y₁(t) = -10e^(-3t/5) + 15e^(it/5) and y₂(t) = 15e^(-3t/5) + 15ie^(it/5). Thus, the real-valued solution to the initial value problem is y₁(t) = -10e^(-3t/5) + 15e^(it/5) and y₂(t) = 15e^(-3t/5) + 15ie^(it/5).

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Important notice:

/\2 = Power 2

Answer:

D. 1,047.2

Step-by-step explanation:

The volume of the grain silo can be found by adding the volumes of all the solids of which it is composed.

The silo is made up of a cylinder with the height of 10 feet and base radius of 5 feet and two cones, each having the height of 5 feet and base radius of 5 feet.

The formulas volume of cylinder πr /\2 h and volume of cone 1/3  πr/\2h can be used to determine the tatol volume of the silo.

Since the two cones have identical dimensions, the total volume, in cubic feet, of the silo is:

V = π(5)/\2 (10) + (2) ( 1/3) π(5) /\2 (5)

= ( 4/3 ) (250)π

= 1,047.2 cubic feet.

The area of the rectangle is 105 square centimeters.

The perimeter of a rectangle is equal to the sum of the lengths of all its sides. If the perimeter of a rectangle is 44 centimeters, and we call the length of the rectangle "l" and the width "w", we can write an equation to represent this:

2l + 2w = 44

Now we can solve for one of the dimensions if we have the other one. For example, if the length is 15 centimeters, then:

2 * 15 + 2w = 44

30 + 2w = 44

2w = 44 - 30

2w = 14

w = 14 / 2

w = 7

So the length is 15 centimeters and the width is 7 centimeters. To find the area of the rectangle, we can multiply the length by the width:

15 * 7 = 105 square centimeters

So the area of the rectangle is 105 square centimeters.

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The allowable is a term used in advertising and marketing to refer to the maximum cost per acquisition (CPA) that a business can afford to pay. So, the given statement is False.

"The allowable" is a term used in advertising and marketing to refer to the maximum cost per acquisition (CPA) that a business can afford to pay to acquire a customer while still remaining profitable. It is not directly related to the conversion rate needed to break even.

To determine the conversion rate needed to break even, you would need to consider the cost of acquiring a customer, the profit margin on the product or service being sold, and the total revenue generated by each customer. This calculation can help determine the minimum conversion rate needed to achieve profitability.

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Answer: you start at point (4,2) x= 4 and y=2

go up one that would be 4,3 but then u go down 2 which your answer should be (4,1)

Step-by-step explanation: you only go up and down here so you only move in Y

The first utility function, u(x,y) = min{x, 3y}, represents a utility function where the individual's utility is determined by the minimum value between x and 3y. The second utility function, u(x,y) = x + 2y, represents a utility function where the individual's utility is determined by the sum of x and 2y.

For the utility function u(x,y) = min{x, 3y}, we can graph it by plotting points on a two-dimensional plane. The graph will consist of two linear segments with a kink point. The first segment has a slope of 3, representing the portion where 3y is the smaller value. The second segment has a slope of 1, representing the portion where x is the smaller value. The kink point is where x and 3y are equal.
To estimate the marginal rate of substitution (MRS) for this utility function, we can take the partial derivatives with respect to x and y. The MRS is the ratio of these partial derivatives, which gives us the rate at which the individual is willing to trade one good for another while keeping utility constant. In this case, the MRS is 1 when x is the smaller value, and it is 3 when 3y is the smaller value.
For the utility function u(x,y) = x + 2y, the graph is a straight line with a slope of 1/2. This means that the individual values both x and y equally in terms of utility. The MRS for this utility function is a constant ratio of 1/2, indicating that the individual is willing to trade x for y at a constant rate of 1 unit of x for 2 units of y to maintain the same level of utility.

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Answer:

8

Step-by-step explanation:

AC=AB+BC

2X+26=1+x+16

2x-x=1+16-26

X= - 9

Now, AC=2X+26

=2*-9+26

= - 18+26

=8

Answer:

y=-3/2+1

Step-by-step explanation:

Answer:

The last choice (3,2), because both lines pass through this point.

Step-by-step explanation:

For a point to be a solution to a system of linear equations, both equation's lines have to pass through that same point.

Answer: (3, 2), because both lines pass through this point

Step-by-stepexplanation:

This can be solved by substitution. The graph will show the same result.

Answer:

Step-by-step explanation:

17

Answer: 8575/2

Step-by-step explanation:

Answer:

Well, 30% is equal to 0.3.

0.4 > 0.3

Step-by-step explanation:

Hope that this answers your question. If not please put any further questions below.

Have a great rest of your day/night!

The equivalent ratios of the given quantity of silver parts of paint to green which is 3:4 are: 6:8 and 9:12.

Equivalent ratios can be described as ratios that have the same values when compared to each other. For example, 8/16, 4/8 and 1/2 re equivalent ratios because:

8/16 = 1/2

4/8 = 1/2

Therefore, 8:16 = 4:8 = 1:2.

Given the table that shows the ratio of the number of parts silver to number of parts green as 3 parts silver to 4 parts green, the ratio is: 3:4.

This means that for 3 parts of silver paint, we would require 4 parts of green paint to give the shade of paint that is needed.

Therefore:

6/8 = 3/4

9/12 = 3/4

6/8 = 9/12 = 3/4

This implies that 6:8, 9:12 and 3:4 are all equivalent ratios.

Therefore, the ratios that are equivalent to 3 parts silver paint to 4 parts green paint are: 6:8 and 9:12.

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Answer:

T23=a+22d

d=T2-T1

d=8-10=-2

a(first term)=10

T23=10+22×-2

=10+(-44)

=10-44

=-34

therefore:T23=-34

Answer:

-34

Step-by-step explanation:

Set rule

T = -2(n) + 12

T23 = -2 × 23 + 12

= -34

Answer: 5.96

Step-by-step explanation: the bottom two are too much and the first is by far too less

Answer:

\((-infinity, +infinity)\)

Step-by-step explanation:

The range is all real numbers because y = x is a line. Lines continue upwards and downwards forever.

The balance of the account will be 1500 in a period of 8.31 years.

Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.

(a) The final amount in a compound interest is,

A = P(1 + \(\frac{r}{n}\) )^ (nt), where,

A : Final amount

P : Principal amount

r : Rate of interest

t : Time in years

n : number of times compounded in a year

Given A = $1500, P = $1000, r = 0.05, n = 1

The equation is,

1500 = 1000 (1 + 0.05)^t

(b) 1500 = 1000 (1 + 0.05)^t

1500 / 1000 = (1.05)^t

1.5 = (1.05)^t

Taking logarithm on both sides,

㏒ (1.5) = t ㏒ (1.05)         [since ㏒ (a)ᵇ = b ㏒ (a)]

t = ㏒ (1.5) / ㏒ (1.05)

t = 8.31 years

Hence the amount will be $1500 in 8.31 years.

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Answer:

(a)V=36πh

Explanation:

• Radius = 6 meters

Part A

An equation that represents the volume V as a function of the height h is:

Part B

Using 3.14 as an approximation for π

The graph of the function is attached below: (V is on the y-axis and h is on the x-axis).

Part C

The initial equation for volume is:

When h=1

If you double the height of a cylinder, h=2:

We observe that when the height is doubled, the volume of the cylinder is also doubled.

Part D

The initial equation for volume is:

If the height of the cylinder is multiplied by 1/3, we have:

The volume of the cylinder will be divided by 3.

Using the graph, we observe a horizontal stretch of the graph by 1/3.

Answer:

Step-by-step explanation:

Can you write it in lines instead of like that, I can answer if you do that.

Answer:

the answer is symmetry.