The blueprint for a circular gazebo has a scale of 2 inches=5 feet. The blueprint shows that the gazebo has a diameter of 5.1 inches. What is the actual diameter of the​ gazebo? What is its​ area? Use 3.14 for π.

The expression (X+1)(2x-8) in the form of trinomial is 2x²-6x-8

An expression is combination of variables, numbers and operators.

The given expression is (X+1)(2x-8)

Apply distributive property

(X+1)(2x-8)

x(2x-8)+1(2x-8)

2x²-8x+2x-8

Trinomial is an expression which has three terms.

2x²-6x-8

Hence, the expression (X+1)(2x-8) in the form of trinomial is 2x²-6x-8

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expression : 75+90m

the 75 is the base payment, plus 90 per month, and the variable m symbolizes the amount of months.

Hope this helped =)

-YinAhara

The bedroom's area in meters squared is 55.1693 m².

finding the area of the basement:

The length of the basement is 2 * 10.5 m = 21 m

The width of the basement is 8 m / 4 = 2 m

The area of the basement is 21 m * 2 m = 42 m²

Next, let's find the equivalent area of the 10 square feet tile in meters:

1 square foot = 0.092903 m²

10 square feet = 10 * 0.092903 m^2 = 0.92903 m²

finding the area of the bedroom:

The length of the bedroom is 10.5 m - 6 m = 4.5 m

The width of the bedroom is 8 m * 34 = 2.72 m

The area of the bedroom is 4.5 m * 2.72 m = 12.24 m²

So the total area covered with carpet and tile is:

12.24 m² + 42 m² + 0.92903 m²

  = 55.1693 m²

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Answer:

Each bucket will be [tex]\dfrac{1}{2}[/tex] full

Step-by-step explanation:

First add up all the different fractions to find out how many buckets of water are in all 3 buckets combined.

Adding up the fractions we get the expression:

[tex]\dfrac{5}{12} + \dfrac{3}{4} + \dfrac{1}{3}[/tex]

To add these fractions first find the LCM(least common multiple of the denominators, 12, 4 and 3

This is the smallest number divisible by all 3 numbers without a remainder

There are several strategies for finding the LCM but here we can see that 12 is evenly divisible by12, 4 and 3

We convert each of the fractions to have the same denominator as the LCM of 12 and adjust the numerator accordingly

Multiply each of the fractions by the LCM

12 x 5/12 = 5

12 x 3/4 = 9

12 x 1/3 = 4

These will become the numerators in the addition with the common denominator of 12

[tex]\dfrac{5}{12} + \dfrac{3}{4} + \dfrac{1}{3}\\\\= \dfrac{5 + 9 + 4}{12}\\\\= \dfrac{18}{12}\\\\[/tex]

This is how many buckets it will take to hold the water from all three buckets

Divide numerator and denominator by 6 to reduce to lowest fraction

[tex]\dfrac{18 \div 6}{12\div6} = \dfrac{3}{2}[/tex]

This is 1 1/2 buckets. If this amount of water is to be evenly divided among 3 buckets then the amount of water in each bucket

[tex]\dfrac{3}{2} \div 3\\\\= \dfrac{3}{2} \times \dfrac{1}{3}\\\\= \dfrac{1}{2}[/tex]

So each bucket will be half full

Answer:

A ≈ 5568.2 cm²

Step-by-step explanation:

the area (A) of a circle is calculated as

A = πr² ( r is the radius )

here the diameter = 84.2 , then r = 84.2 ÷ 2 = 42.1 , then

A = π × 42.1² = π × 1772.41 ≈ 5568.2 cm² ( to 1 decimal place )

In order to buy four bananas, then the number of apples that he bought will be 8.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Assume that a consumer has a given budget or income of $10 and that she can buy only two goods, apples or bananas. The price of an apple is $1.00 and the price of a banana is $0.50.

Let 'x' be the number of apples and 'y' be the number of bananas. Then the equation is given as,

1x + 0.50y = 10

x + 0.50y = 10

In order to buy four bananas, then the number of apples that he bought is given as,

x + 0.50 (4) = 10

x + 2 = 10

x = 8

In order to buy four bananas, then the number of apples that he bought will be 8.

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Answer:

Option D) 10mi

Step-by-step explanation:

A rectangle has 90 degree angles. When a line cuts it diagonally, it makes a right angle.

When there is a right angle we think about the Pythagorean theorem.

a²± b² = c²

Plug the values:

8²+6²= c²

Simplify:

64+36 = c²

Combine like terms:

100 = c²

Rooting hypotenuse we get

10 = c

The length of the path is 10 miles.

Answer:

12 ft

Step-by-step explanation:

To find the height of a rectangular box with a base measuring 3 feet by 6 feet and a volume of 72 cubic feet, we need to use the formula for the volume of a rectangular prism:

Volume = Length x Width x Height

We are given the volume of the box and the length and width, so we can substitute the values and solve for the height:

72 = 3 x 6 x Height

72 / (3 x 6) = Height

12 = Height

So, the height of the box is 12 feet.

Answer:

The "one number" is equal to 4 and "another number" is equal to 6.

Step-by-step explanation:

1. We can write an equation for "one number": X = 2n - 8 (X is one number and another number is N)

2. Since their sums are 10 we can write it was X + N

3. Plug in the value of X to get: 2n - 8 + N = 10

4. Put 8 to the other side to get + 8 --> 2n + N = 10 + 8

5. Now you form the equation 3n = 18

6. N = 18 / 3 which is 6

7. To get X you do 10 - 6 which is equal to 4

8. To make sure the answer is correct plug in the values into the equation: 4 = 2(6) - 8 which simplifies to 4 = 12 - 8

Therefore, one number is equal to 4 and another number is equal to 6

The surface area of the prism is 166 square centimetres.

A three-dimensional object's surface area is the sum of all of its faces. Real-world applications of the concept of surface areas include wrapping, painting, and eventually building things to achieve the best possible design.

Given that the sides of the prism are 5 cm, 4 cm, and 7 cm. The surface area of the prism will be calculated as:-

Surface area = 2 [ ( 5x 4 ) + ( 4 x 7 ) + ( 7 x 5 ) ]

Surface area = 2 [ 20 + 28 + 35 ]

Surface area = 2 x [ 83 ]

Surface area = 166 square cm

Therefore, the surface area of the prism is 166 square cm.

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Answer:

The equation for the new graph is e^(x -6)

The discount is $278.59 and the proceeds for the following simple discount note,  using 360 days for a year is $9421.41

Discount refers to a reduction in the price of an item or service. It can be expressed as a percentage or an absolute value, and it is usually calculated as a difference between the original price and the reduced price. In finance, discount is often used to refer to the reduction in the face value of a financial instrument, such as a bond or a bill, before it matures. The amount of the discount is usually based on the interest rate and the time to maturity. The term "discount" is also used in various other contexts, such as in retail sales, where items are sold at a lower price than their regular price to encourage customers to buy.

(a) The discount is calculated by multiplying the face value of the note by the discount rate and then dividing by the number of days in a year (360).

Discount = $9700 * 9.5% * 135/360

Discount = $9700 * 0.095 * 3/10

Discount = $9700 * 0.285/10

Discount = $278.59

(b) The proceeds are calculated by subtracting the discount from the face value of the note.

Proceeds = Face Value - Discount

Proceeds = $9700 - $278.59

Proceeds = $9421.41

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Answer:

SA = 439.8 in²

Step-by-step explanation:

the surface area (SA) is the total area of the 6 triangular faces and the base

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

here b = 10 and h = 6 , then

A = [tex]\frac{1}{2}[/tex] × 10 × 6 = 5 × 6 = 30 in²

so area of 6 triangles = 6 × 30 = 180 in²

Then

SA = 180 + 259.8 = 439.8 in²

Answer: 4

Step-by-step explanation: i took the test

La ecuación de la circunferencia que pasa por los puntos (0, 0), (3, 4) y (6, 2) es x² + y² - (55 / 9) · x - (5 / 3) · y = 0.

Según la geometría analítica, la fórmula general de una circunferencia contiene tres coeficientes reales (D, E, F) en la siguiente expresión:

x² + y² + D · x + E · y + F = 0

En consecuencia, se requiere el conocimiento de tres puntos distintos para determinar las condiciones de la ecuación. Es preciso construir un sistema de ecuaciones lineales, cuya forma es:

D · x + E · y + F = - x² - y²

Si sabemos que (x₁, y₁) = (0, 0), (x₂, y₂) = (3, 4) y (x₃, y₃) = (6, 2), entonces tenemos el siguiente sistema de ecuaciones lineales:

F = 0

3 · D + 4 · E + F = - 25

6 · D + 2 · E + F = - 40

Cuya solución se obtiene mediante métodos numéricos:

(D, E, F) = (- 55 / 9, - 5 / 3,  0)

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A positive and a negative coterminal angle for each given angle is

A. 13π/4 and -3π/4.

B. 97π/36 and -47π/36.

What is the coterminal angle?

Coterminal angles are those with a common terminal side that are in standard position (angles with the starting side on the positive x-axis). Coterminal angles are the angles that have the same initial side and share the terminal sides.

Here, we have

A. 5π/4

We have to find the coterminal angle.

5π/4 + 2π = 13π/4

5π/4 -  2π = -3π/4

Hence, a positive and a negative coterminal angle for each given angle is 13π/4 and -3π/4.

B. 25π/36

We have to find the coterminal angle.

25π/36 + 2π = 97π/36

25π/36 -  2π = -47π/36

Hence, a positive and a negative coterminal angle for each given angle is 97π/36 and -47π/36.

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Answer:

a. In a class of 58 students, 35 students offer Biology, 28 students offer Economics and 15 students offer Physics.

Using the Principle of Inclusion-Exclusion, we can calculate the number of students who offer all three subjects as follows:

The total number of students who offer at least one subject is 35 + 28 + 15 = 78

The number of students who offer Biology and Economics is 12

The number of students who offer Biology and Physics is 7

The number of students who offer Economics and Physics is 5

So the number of students who offer all three subjects is given by:

35 + 28 + 15 - (12 + 7 + 5) = 58 - 24 = 34

Therefore, 34 students offer all three subjects.

b. A regular polygon with (2m + 1) sides has each interior angle equal to 1440.

Each interior angle of a regular polygon with n sides is given by:

angle = (n-2) * 180 / n

So for a regular polygon with (2m + 1) sides, we have:

1440 = (2m + 1 - 2) * 180 / (2m + 1)

Expanding and simplifying:

1440 = 360m / (2m + 1)

Multiplying both sides by (2m + 1):

1440 * (2m + 1) = 360m

Expanding the left side:

2880 + 1440 = 360m

4320 = 360m

Finally, dividing both sides by 360:

m = 12

Therefore, the value of m is 12.

Answer:

216.25

Step-by-step explanation:

First multiply 4 × 37 = 148

Then add 148 + 68.25 = 216.25

Answer:in the latest published financial statements,an amount of $42000 appears against accounts payable.During the year,goods worthy $150000 were purchased on credit .assuming 365 days in a year ,what is the approximate accounts payable payment period.

Step-by-step explanation:

The equation that represents the given graph is: D. y = 2/5x - 3.

The slope-intercept form of the equation of a line is given by y = mx + b, where m is the slope of the line and b is the y-intercept.

here, we have,

To find the equation of a line that passes through two points (x1, y1) and (x2, y2), we can use the following steps:

Find the slope (m) using the formula

m = (y2 - y1) / (x2 - x1).

Plug in the slope and one of the points into the equation

y = mx + b to find b.

So, for the line that passes through the points (0, -3) and (5, -1),

the slope is (-1 - (-3)) / (5 - 0)

                 = 2/5,

and the y-intercept can be found by plugging in the slope and the point (0, -3) into the equation y = mx + b:

-3 = (2/5) * 0 + b

-3 = b

Therefore, the equation of the line that passes through (0, -3) and (5, -1) is:  y = (2/5)x - 3

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The two numbers that when multiplied equal 5/9 and when added together equal -2 will be - 1/3 and - 5/3.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Let the two numbers be 'x' and 'y'. Then the equations are given as,

xy = 5/9                  ...1

x + y = - 2               ...2

From equations 1 and 2, then we have

x + 5 / (9x) = -2

9x² + 5 = - 18x

9x² + 18x + 5 = 0

9x² + 15x + 3x + 5 = 0

3x(3x + 5) + 1(3x + 5) = 0

(3x + 1)(3x + 5) = 0

x = -1/3, -5/3

At x = - 1/3, the value of y is given as,

- 1/3 + y = -2

y = - 5/3

At x = - 5/3, the value of y is given as,

- 5/3 + y = -2

y = - 1/3

The two numbers that when multiplied equal 5/9 and when added together equal -2 will be - 1/3 and - 5/3.

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The solution is, a) Negative linear; b) about 48

In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

here, we have,

a) Type of correlation

The graph shows a negative linear correlation.

b) Prediction

It looks like a student who makes 60 in Science would make about 48 in English.

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The pendulum will swing at the velocity of 3.06 m/s at the bottom of the swing.

Velocity is the rate of change of position of an object, usually measured in meters per second (m/s). It is a vector quantity, which means it has both magnitude and direction. Velocity is an essential notion in physics since it is used to describe motion and is one of the fundamental principles of classical mechanics. It is connected to other notions such as acceleration, momentum, and force. Velocity is a measure of how rapidly an item moves in a specific direction, and it is computed by dividing the distance travelled by the time it takes for the object to traverse that distance.

The speed of the pendulum at the bottom of its swing can be calculated using the formula:

v = √(2gh)

where v = velocity, g = gravitational acceleration (9.8m/s2), h = height (1.22m)

Therefore, the speed of the pendulum at the bottom of its swing is:

v = √(2*9.8*1.22)

v = 3.06 m/s

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225 pounds of the Earl Grey tea and 375 pounds of Orange Pekoe tea are​ required to get 600 pounds of a new blend costing $3.50

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

Let x represent the amount of Earl Grey tea and y represent the amount of Orange Pekoe tea.

Earl Grey tea sells for $6 per pound while Orange Pekoe tea sells for $2 per pound. Both teas were mixed to get 600 pounds of a new blend selling at $3.50. Hence:

x + y = 600    (1)

Also:

6x + 2y = 3.5(600)    (2)

From both equations:

x = 225, y = 375

225 pounds of the Earl Grey tea and 375 pounds of Orange Pekoe tea are​ required

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The probability that Deborah's first flight was delayed can be found to be 0. 85.

To find the probability that Deborah's first flight from Boston to Denver was delayed, use the following formula :

= 1 - probability that the flight takes off on time

Probability that the flight takes off on time = 0. 15 .

The probability that Deborah's first flight from Boston to Denver was delayed is therefore :

= 1 - 0. 15

= 0. 85

In conclusion, there is an 85 % probability that the first flight was delayed.

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The graph of the equation can be seen on the image at the end, and when she uses 17 cups of flour, she will use 76.5 cups of honey.

We assume that the relation is linear.

Remember that a general linear equation is:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the linear equation passes through the points (x₁, y₁) and (x₂, y₂) then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Here we have the two pairs:

(27, 6)

(45, 10)

First, you can graph these two points and connect them with a line, that will be the graph of our equation.

The slope is:

a = (10 - 6)/(45 - 27)

a = 4/18

a = 2/9

y = (2/9)*x + b

To find the value of b we can replace the values of the point (27, 6)

6 = (2/9)*27 + b

6 = 2*3 + b

6 = 6 + b

0 = b

So the equation is just:

y = (2/9)*x

And for 17 cups of flour, she will use:

17 = (2/9)*x

(9/2)*17 = x

76.5 = x

She needs to use 76.5 cups of honey.

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Kevin has $3840 invested in stocks in total.

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

Given that Annual interest in first investment - 11%

Annual interest in other investment - 14%

Total interest annually - $480

Let us assume, x is the investment in each stock

or, total investment = 2x

then, making an equation for the total interest

0.11x+.14x=480

Multiplying everything by 100

11x+14x=48000

25x=48000

Divide both sides by 25

x=1920

then, by total investment = 2x

2×(1920) = 3840

Hence, Kevin has $3840 invested in stocks in total.

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32/12 is the distance walked by the four friends.

A fraction represents a part of a whole.

3/4, 1/2,2/3,3/4 is the distance travelled by the four students.

We have to find the distance they walked all together.

We have to add the all the fractions.

3/4+1/2+2/3+3/4

The LCM of 4, 2 3, and 4 is 12

9+6+8+9/12

32/12

Hence, 32/12 is the distance walked by the four friends.

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The equation formed will be a linear equation, and it will be y=5t/2.

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

Given Samantha runs on the Lakeside Trail. She runs 2½ times around the loop and then walks the remainder of the way.

Let t=length of loop

then,  total running distance(y)=5t/2

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