Jody buys 20 yards of fencing to build a garden. The garden will have 5 sides. What is the area of the largest garden she can build?
The 5-sided figure with the largest area for a given perimeter is a *blank* pentagon. Since Jody has 20 yards of fencing, the sides of the figure must measure *blank*
The area of the garden will be
approximately *blank*
square yards.

The next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term. None of the option is correct.

To find the pattern in the sequence 1, 1, 3, 8, 19, 41, we can examine the differences between consecutive terms:

1 1 3 8 19 41

0 2 5 11 22

Looking at the differences, we can observe that each subsequent difference is obtained by adding consecutive odd numbers: 2, 3, 4, 5, etc. This suggests that the original sequence may be related to square numbers.

Let's check if the differences between consecutive terms are square numbers:

2 = 1²

5 = 2² + 1²

11 = 3² + 2²

22 = 4² + 3²

Based on this pattern, we can make a reasonable assumption that the next difference should be 5² + 4² = 41 + 16 = 57. Adding this difference to the last term of the sequence (41), we get the next term:

41 + 57 = 98

Therefore, the next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term.

Hence, none of the given options accurately continue the pattern of the sequence. It's important to note that patterns in sequences can sometimes have multiple possible interpretations, and it's always essential to consider alternative patterns or extend the sequence further to confirm the pattern.

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The percentage change of the population is P = 1.7 %

Given data ,

To calculate the percent increase from 2014 to 2015, we need to find the difference between the two population values, divide it by the initial value, and then multiply by 100 to get the percentage.

Population increase = 7,375 - 7,250 = 125

Percent increase = (Population increase / Initial population) * 100

Percent increase = (125 / 7,250) * 100 ≈ 1.7241

Rounding to the nearest tenth of a percent, the percent increase is approximately 1.7%.

Hence , the percentage change is P = 1.7 %

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The greatest common factor will be (x² – xy + y²).

This is a value or expression that can divide the given expressions without leaving a remainder.

Given the following expressions

x^3+^3 and x^2 - xy + y^2

Expand x^3+y^3

x^3+y^3 =(x + y)(x² – xy + y²).

Since (x² – xy + y²) is common to both expression, hence the greatest common factor will be (x² – xy + y²).

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Answer:

96.25%

Step-by-step explanation:

The empirical rule regarding mean and standard deviation is that

Therefore between mean and +2 standard deviation or between mean and -2 standard deviation you will find  approximately 95/2 = 47.5% of the values

Between mean and ± 3 standard deviations you will find approximately 97.5/2 = 48.75% of the values

Therefore between 2 standard deviations above and 3 standard deviations below you will find approximately 47.5 + 48.75 = 96.25% of values

Answer:

$8.28

Step-by-step explanation:

So, first we must find the price per ticket so we do

13.80/5 = 2.76

So the $2.76 per ticket

So now all we do to find the price of three tickets we times the price per ticket by 3

2.76 x 3 = $8.28

Answer:

Step-by-step explanation:

You want to identify the graphs that go with each of these functions, along with a particular point on the curve.

The equations are written here in standard form, factored form, and vertex form. (The "factored form" is sometimes called "intercept form.") Each of these forms can be analyzed for characteristics relevant to identifying the corresponding graph.

In general, we can readily identify the opening direction, based on the sign of the leading coefficient. Depending on the form, we can also identify zeros, the vertex, and the y-intercept.

The line of symmetry (x-coordinate of the vertex) of the equation in the form ax² +bx +c is x = -b/(2a). That is, it will be left of the y-axis when the coefficients 'a' and 'b' have the same sign.

The graph of equation A will be graph 4, the only one with its vertex left of the y-axis. The y-intercept is the constant: point S = (0, 9).

Equation B has a positive leading coefficient, so opens upward. The zeros of the factors are -3 and +9, so identify the places where the graph crosses the x-axis. Graph 3 is the only one that opens upward and has x-intercepts. Point R is (9, 0).

The vertex form of a quadratic is ...

  y = a(x -h)² +k . . . . . . . vertex (h, k); leading coefficient 'a'

Equation C has its vertex at (h, k) = (3, 9) and opens upward (a>0). Graph 1 is the only one matching those characteristics. Point P is the vertex, so point P is (3, 9).

Equation D is the same as equation B, but with a negative leading coefficient. That is, it opens downward and crosses the x-axis in two places, at x = -3 and x = 9. Graph 2 is matches this description. The left zero is point Q, (-3, 0).

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Answer:

1/5

Step-by-step explanation:

Answer:

9^1 has a power of 1.  it evaluates to 9

Step-by-step explanation:

4/5 is a real number.

A real number is a value in mathematics that expresses a quantity along a continuous line. Real numbers can be expressed as fractions or decimals and can be positive, negative, or zero.

4/5 is a rational number in this situation, which is a form of real number that may be written as a ratio of two integers. A real number can also be irrational, which means that it cannot be stated as a ratio of two integers and that its decimal representation goes on indefinitely without repeating.

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Answer:

there are for bears but there are less than 2 black bears so that means 1 black bear 3 brown bears

Answer:

I believe the answer is 70

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

Answer:

$200

Step-by-step explanation:

If she made 4 withdrawals for $50 EACH or in other words divided the total by 4. So in this probelm, we need to work backwards. The opposite of dividing would be multiplying.

The two values we need to multiply would be 50 and 4.

50 x 4 = 200

Flora withdrew a total of $200.

Hope that helps and have a great day!

Answer:

i think its 64.3

Answer:

uhh judy has $3.024 in her bank acc

She is buying tickets for 11 friends and including herself too that means 12

Two friends decided help to buy the tickets and offered $100 each i.e $200

So I'm guessing that the cost price of one ticket is $100

Now than since 2 people paid their ticket cost than that means only 10 people left

Than for buying tickets for 10 people would cost (10×100=1000)

So I guess buying the tickets cost 1000 or if we add other two people's cost than that makes 1200

So this is graphically the situation given in the problem, and they ask us to calculate how many feet above sea level was the bridge?​ it will be easy to find only by subtracting 7 from 20 like we see in the graph. So there are 13 ft between the bridge and the sea level.

in this example we see the importance of drawing the physical situation, to clarify the information in our minds.

These are just a few examples of how positive and negative numbers are used in everyday life. Understanding and using them correctly is essential for various fields, including mathematics, finance, science, and navigation.

Positive and negative numbers are commonly used in everyday life for a variety of purposes. Here are some examples:

Temperature: Positive and negative numbers are used to represent temperature. Positive numbers indicate higher temperatures, while negative numbers represent lower temperatures. For instance, if the temperature is 10 degrees Celsius, it is represented as +10°C, and if the temperature is -5 degrees Celsius, it is represented as -5°C.

Financial Transactions: Positive and negative numbers are used in financial transactions. Positive numbers represent income, gains, or credits, while negative numbers represent expenses, losses, or debits. When managing bank accounts or budgeting, positive and negative numbers are used to track inflows and outflows of money.

Direction and Coordinates: Positive and negative numbers are used to indicate direction and coordinates. In navigation, positive and negative numbers are used to represent east and west directions or north and south coordinates. For example, a latitude of +40 degrees represents a location north of the equator, while a longitude of -75 degrees represents a location west of the prime meridian.

Sports Scores: Positive and negative numbers are used to keep track of scores in sports. In games such as basketball, soccer, or football, positive numbers represent points scored by a team, while negative numbers represent points scored against the team.

Elevations: Positive and negative numbers are used to represent elevations or heights above or below sea level. Positive numbers indicate locations above sea level, while negative numbers represent locations below sea level. This is particularly relevant in geography, construction, and aviation.

Debt and Credit: Positive and negative numbers are used to represent debt and credit. Positive numbers indicate money owed or credit received, while negative numbers represent payments made or credit used. It is commonly used in accounting, loans, credit cards, and personal finance.

These are just a few examples of how positive and negative numbers are used in everyday life. Understanding and using them correctly is essential for various fields, including mathematics, finance, science, and navigation.

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9514 1404 393

Answer:

  (a) 21 over four, rational

Step-by-step explanation:

  \(\sqrt{144}\times\dfrac{7}{16}=12\times\dfrac{7}{16}=\dfrac{84}{16}=\boxed{\dfrac{21}{4}}\)

This is the ratio of two integers, so is rational.

The factors of the expression 3i² - 27 are 1, -1, 2, -2, 3, -3, 5, -5, 6, -6, 10, -10, 15, -15, 30, and -30.

This process of finding two or more expressions whose product is the given expression is known as the factorization of algebraic expressions.

We can start by simplifying the expression 3i² - 27.

Remember that i² is equal to -1, so:

3i² - 27 = 3(-1) - 27 = -3 - 27 = -30

So the simplified term is  -30.

Now, we can find the factors of -30 by listing all of the pairs of numbers that multiply together to give -30.

The factors of -30 are:

1, -30

2, -15

3, -10

5, -6

Therefore, the factors of 3i² - 27 are 1, -1, 2, -2, 3, -3, 5, -5, 6, -6, 10, -10, 15, -15, 30, and -30.

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Using an algebraic equation to represent the word problem, the smallest integer is 1

This is a way of representing mathematical problems with words. To solve this, we have to use algebraic equations or expressions.

Let the integers be represented as

We can write an equation from the word problem given as

7 × (x + 2) = 15 + [x + (x + 4)]

7x + 14 = 15 + x + x + 4

7x + 14 = 15 + 2x + 4

collect like terms

7x - 2x = 15 - 14 + 4

5x = 5

Divide both sides by coefficient of x

5x / 5  = 5 / 5

x = 1

The smallest integer is 1

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Translation:

Find the smallest of three consecutive odd integers such that 7 times the middle integer is 15 more than the sum of the first and third integers

We have that the formula of the volume of a Sphere is

a.

the radius of the sphere is r=2

the volume will be

b.

the radius of the sphere is r=4

the volume will be

c. as we can see the radius of the sphere b, is twice the radius of sphere a, but as we can see because we calculated the volume of spheres, the volume of the sphere b is much bigger than the twice of the volume of the sphere a. It is because we don't have a linear relationship because we have an exponent 3 in the radius in the formula of the volume

The thing that t best determines whether a borrowers interest rate on an adjustable rate loan goes up or down is: C. A market's condition.

Market conditions  help to show how the state of an economy or how good or bad the economy of a nation is.

Market condition help to  show the state of affairs of a nation economy as well as the  overall situation that a market is facing at a particular period of time.

Therefore we can conclude that market condition can tend to show if a  borrowers interest rate on an adjustable rate loan goes up or down.

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The complete question is:

What best determines whether a borrower's investment on an adjustable rate loan goes up or down?

a fixed interest rate

a bank's finances

a market's condition

a person's finances

Using the Pythagoras theorem, the longest leg has the length of 24 feet.

Given that,

A ladder of length (2x+6) feet is positioned x feet from a wall.

Height of the ladder = (2x + 6) feet

Distance of ladder from the wall = x feet

Height of the wall that the ladder is placed = (2x + 4) feet

These three lengths form s right triangle where (2x + 6) feet is the hypotenuse.

Longest leg is (2x + 4) feet

Using the Pythagoras theorem,

(2x + 6)² = (2x + 4)² + x²

4x² + 24x + 36 = 4x² + 16x + 16 + x²

4x² + 24x + 36 = 5x² + 16x + 16

x² - 8x - 20 = 0

(x - 10) (x + 2) = 0

x = 10 or x = -2

x = 2 is not possible.

So x = 10

Longest leg = 2x + 4 = 20 + 4 = 24 feet

Hence the length of the longest leg is 24 feet.

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The binomial factors of x³- 4x²+x+6​ are (x+2), (x+3), and (x-1).

Using the splitting and grouping the terms:

x³ + 4x² + x - 6

= x³ + 2x² + 2x² + x - 6  [Splitting 4x² = 2x² + 2x²]

= (x³ + 2x²) + (2x² + x - 6)

= x² (x + 2) + (2x² + 4x - 3x - 6)

= x² (x + 2) + [ 2x (x + 2) - 3 (x + 2)]

= x² (x + 2) + (x + 2) (2x - 3)

= (x + 2) ( x² + 2x - 3)

= (x + 2) ( x² + 3x - x - 3)

= (x + 2) [x (x + 3) - 1 (x + 3)]

= (x + 2) (x + 3) (x - 1)

Hence, the binomial factors are (x + 2), (x + 3) and (x - 1)

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Answer:

D. A pair of intersecting lines

Step-by-step explanation:

A conic section is a fancy name for a curve that you get when you slice a double cone with a plane. Imagine you have two ice cream cones stuck together at the tips, and you cut them with a knife. Depending on how you cut them, you can get different shapes. These shapes are called conic sections, and they include circles, ellipses, parabolas and hyperbolas. If you cut them right at the tip, you get a point. If you cut them slightly above the tip, you get a line. If you cut them at an angle, you get two lines that cross each other. That's what happened in your question. The plane cut the cone at an angle, so the curve is two intersecting lines. That means the correct answer is D. A pair of intersecting lines.

I hope this helps you ace your math question.

Answer

radius of the sphere = 5 m

Explanation

The volume of a sphere is given as

Volume = (4/3) × πr³

where

Volume = 523.33 m³

r = radius of the sphere = ?

π = pi = 3.14

Volume = (4/3) × πr³

523.33 = (4/3) × 3.14 × r³

r³ = 125

Take the cube root of both sides

∛(r³) = ∛(125)

r = 5 m

Hope this Helps!!!

Step-by-step explanation:

Hello. Can you repost the question and just for clarification is this Taylor, Maclaurin Series?