a hotel offers a reward program based on the number of nights stayed. the function f(x) represents the number of free nights earned as a function of x, the number of nights stayed. f(x)

The entire area bounded by any triangle's three sides is referred to as the triangle's area.

In essence, it is equivalent to 1/2 of base times height, or A = 1/2 b times h. A triangular polygon's base (b) and height (h) must be known in order to calculate its area.

Whether a triangle is scalene, isosceles, or equilateral, it can be used to solve any kind of triangle.

Be aware that the triangle's base and height are at right angles to one another. In square units, the area unit is measured (m2, cm2).

Example :

Consider this triangle with a base of 3 cm and a height of 4 cm. What is its area?

Employing the formula,

Triangle's area is equal to half of b times h.

= 1/2 × 4 (cm) × 3 (cm) (cm)

= 2 (cm) × 3 (cm) (cm)

= 6 cm2.

In addition to the method mentioned above, Heron's formula can be used to determine a triangle's area when we know the lengths of its three sides.

In addition, when two sides of a triangle are known as well as the angle that forms between them, the area can be calculated using trigonometric functions. For each of these circumstances, we shall calculate the area.

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Using the given equation, the number of miles the family has already driven would be = 268,258,248 and 234 miles.

The substitution method of solving equation is defined as the method whereby by a known number is substituted into an equation to solve for the unknown.

The values given to be substituted in order to find out the miles the family has already driven are as follows:

where m ;

= 111 = 255- 111 + 124 = 144+124 = 268

121 = 255 - 121 +124 = 134 + 124 = 258

131 = 255 - 131 +124 = 124 + 124 = 248

141 = 255 - 141 + 124 = 114 + 124 = 234

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Answer:

90°

Step-by-step explanation:

This question is so weird, they are literally telling you to guess. It might be 90° as the BC and (AC)' looks like they r perpendicular to each other.

Answer:

  3/14

Step-by-step explanation:

Given a 2 appeared 3 times in 14 rolls, you want the experimental probability of rolling a 2.

The experimental probability of a given outcome is the number of times that outcome occurs divided by the total number of trials. Here, a "2" appeared on 3 of the 14 rolls, so the experimental probability is ...

  P(2) = 3/14

Answer:

Step-by-step explanation:

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A right angle is an angle that is exactly equal to 90 degrees (or π/2) in measure.

We can see many real-life examples of the right angles in our daily life. For example, the corner of a book, edges of the cardboard, etc. Any shape that is a square or a rectangle, will have its corners equal to 90 degrees or right angle. A right angle is hence called a 90-degree angle.

If the measure of the angle between two rays is exactly equal to 90 degrees or π/2, then the angle is called a right angle

The formula used to determine whether the given triangle is the right triangle or not is the Pythagoras theorem. The theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

(Hypotenuse)2 = (Base)2 + (Perpendicular)2

A right angle is an angle that is exactly equal to 90 degrees (or π/2) in measure.

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The 45 45 90 triangle theorem states that 45 45 90 special right triangles have sides of which the lengths are in a special ratio of 1 : 1 : 2 and two 45° angles and one right angle of 90°.

When two rays intersect and form a 90˚ angle or are perpendicular to each other at the intersection, they are said to form a right angle. It is the most frequently encountered angle in our daily lives. It can be noticed in room corners, box edges, mobile phone screens, and so on.

A square's and a rectangle's sides always make a right angle with each other. It is represented in radians as /2.

The angle formed by two lines that are perpendicular to each other is called a right angle. A right angle is equal to 90° and is in the shape of the letter "L". In the following figure, ray AB and BC form a right angle ABC.

Thus, The 45 45 90 triangle theorem states that 45 45 90 special right triangles have sides of which the lengths are in a special ratio of 1 : 1 : 2 and two 45° angles and one right angle of 90°.

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The answer are,

x=14√2

y=9.90

z=17.15

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

from the given figure,

we get.

x=14√2

y=9.90

z=17.15

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According to the unitary method, the store that has the best deal is Store 1 and it cost $202.18

The term unitary method is known as a process of finding the value of a single unit, and based on this value.

Here we have the original prices of the rugs are as follows:

Store #1: $289

Store #2: $265

Store #3: $310

And the discount on each store is written as,

Store #1: 20% (decrease)

Store #2: 12%(decrease)

Store #3: 30%(increase)

And the tax details are given as,

Store #1: 8%

Store #2: 8%

Store #3: no tax.

Then the shipping and the handling charges is $5.9

Then the price for each of the store is calculated as,

=> Store 1 = 289 - [(289 x 0.20) + (289 x 0.08) + 5.9] = 202.18

=> Store 2 = 265 - [(265 x 0.12) + (265 x 0.08) + 5.9] = 206.1

=> Store 3 = 310 + (310 x 0.30) - 5.9 = 397.1

Therefore, the store 1 provides the best deal on the rug.

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Answer:

The lower quartile, or first quartile (Q1), is the value under which 25% of data points are found when they are arranged in increasing order. The upper quartile, or third quartile (Q3), is the value under which 75% of data points are found when arranged in increasing order.

Step-by-step explanation:

The number whose three times the reciprocal of a positive number equals 9 times the reciprocal of 6 is 2.

Let the positive number be x. The three times reciprocal of the positive number will be 1/x × 3. The reciprocal of 6 will be 1/6.

Equating the values that represent Left Hand Side and Right Hand Side of the equation -

3×1/x = 9×1/6

Performing multiplication on both sides of the equation

3/x = 9/6

Rewriting the equation according to x

x = 3×6/9

Performing multiplication and division on Right Hand Side of the equation

x = 2

Thus, the number is 2.

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Answer: 2^3

Step-by-step explanation:

8 = 2 x 2 x 2 = 2^3

Answer:

Line Plot

Step-by-step explanation:

Logic)

It will show the progress of the athlete's sleep in accordance to each other, making it easier to make conclusions based on evidence.

Answer:

In Euclidean geometry, two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other.

Step-by-step explanation:

The steps to plot the graph a quadratic function in vertex form and standard form is explained below.

The term quadratic function is known as a second-order polynomial equation in a single variable x is written as ax² + bx + c = 0 with a ≠ 0 .

Here we need to write down the steps to plot the graph a quadratic function in vertex form and standard form.

In order to plot the graph we have to do the following:

The first steps is to determine whether the parabola opens upward or downward.

And then we have to find the equation of the axis of symmetry and the vertex.

Then we need to find the the y-intercept and the point symmetric to the y-intercept across the axis of symmetry.

Then through this we have to find the x-intercepts.

Then plot graph the parabola

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Answer: 24

Step-by-step explanation:

The sum of the exterior angles of a regular polygon is 360∘ As each of the exterior angles are equal, Exterior angle = 360∘ 15 = 24∘

Answer:

Step-by-step explanation:

To do this we need to show that the midpoints of the diagonals PR and QS are the same point.

The midpoint of PR = (-1+4)/2, (4-1)/2 = (3/2, 3/2).

The midpoint of QS = (-2+5)/2, )/2, (1 + 2)/2 = (3/2. 3/2).

We see that the points are identical so the diagonals do bisect each other.

The salary of the annual management trainee is equal to $15000

The quantitative relation between two amounts shows the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"

Given here: The ratio of middle-management salaries to management trainee salaries by 7:5 and salary of middle management salaries as $21000

Thus if 7 parts of 12 is equivalent to 21000

Then 1 part of 12 is equivalent to $3000

Therefore the salary of the management trainees is

$3000×5=$15000

Hence, The salary of the annual management trainee is equal to $15000

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The methods used in factoring are Greatest Common Factor (GCF), Grouping Method, Using Identities, Factor Theorem, and Polynomial with Four Terms.

Greatest Common Factor (GCF): To factorise, We have to find out the greatest common factor, of the given polynomial.

a(b + c) = ab + ac

But in the matter of factorisation, it is just an inverse process;

ab + ac = a(b + c)

where p is the greatest common factor.

Grouping Method: This method is also stated to be factoring by pairs. In this method, the given polynomial is distributed in pairs to find the zeros. 

Factoring Using Identities: The factorisation can be accomplished also by using algebraic identities. The most typical identities used in terms of the factorisation are:

(α + β)² = α² + 2αβ + β²

(α – β)² = α² – 2αβ + β²

α² – β² = (α + β)(α – β)

Factor Theorem: For a polynomial g(x) of a degree greater than or equal to 1,

x - b is a factor of g(x), if g(b) = 0

If g(b) = 0, then x - b is a factor of g(x)

Where ‘b’ is a real number.

Factoring Polynomial with Four Terms:

For example, x³ + x² – x – 1 is the polynomial. 

Split the given polynomial into two parts.

(x³ + x²) + ( –x – 1)

We can see, from the first part, x² is the greatest common factor and from the second part, we can take out the minus sign. Thus,

x²(x + 1) - 1(x + 1)

Again, regrouping the terms as the factors.

(x² - 1) (x + 1)Therefore, the factorisation of x³+ x² – x – 1 gives (x² -1) (x+1).

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A circle's circumference as a form of "perimeter."

The radius is RB = 35.0 ft, rounded to the nearest tenth (or 35 feet).

By rounding to the nearest tenth, we may determine the radius to be RG = 20.1 feet.

1.The circumferences of the two circles are 220 feet and 126 feet, respectively. We may think of a circle's circumference as a form of "perimeter."

2. The following is the radius of the circle made by Ana's brother in the blue car:

We know that the following formula determines a circle's circumference:

[tex]C=2\Pi \ r[/tex]

Then, we must get r by solving this equation. We know that C is 220 feet and pi is 3.14. Next, we have

[tex]220=2 \cdot \pi \cdot r \\\Rightarrow r=\frac{220}{2 \pi} \\\Rightarrow r=\frac{220}{2 \cdot 3.14} \\\Rightarrow r=35.0318[/tex]

The radius, rounded to the closest tenth, is RB = 35.0 feet (or 35 feet).

3. Using the same method, we can determine the radius of the circle that Ana's sister drew in the green automobile (she travelled 126 feet).

[tex]126=2 \cdot \pi \cdot r \\\Rightarrow r=\frac{126}{2 \cdot 3.14} \\\Rightarrow r=20.0637[/tex]

We may calculate the radius as RG = 20.1 feet by rounding to the closest tenth.

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Therefore the correct options are ,6 with multiplicity 2 ,-2 with multiplicity 2

The equation (x-6)²(x+2)² can be factored by using the difference of squares factorization. This factorization states that for any two binomials a-b and a+b, their product can be written as (a-b)(a+b)= a²-b². In this case, we have (x-6)² and (x+2)², which can be factored as (x-6)² = (x-6)(x-6) = (x-6)², and (x+2)² = (x+2)(x+2) = (x+2)².

So, the equation (x-6)²(x+2)² can be factorized as (x-6)²(x+2)² = (x-6)² * (x+2).

The roots of the equation are the values of x that make the equation equal to zero. To find the roots of the equation, we set each of the factors to zero and solve for x.

(x-6)² = 0, x = 6 , 6

(x+2)² = 0, x = -2 ,-2

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Complete question:

Find the root(s) of f (x) = (x- 6)2(x + 2)2.

-6 with multiplicity 1

-6 with multiplicity 2

6 with multiplicity 1

6 with multiplicity 2

-2 with multiplicity 1

-2 with multiplicity 2

2 with multiplicity 1

2 with multiplicity 2

Answer:

Step-by-step explanation:

x = 4y - 3

2x +3y = 16

First, plug the equation x = 4y - 3 into the second equation so it looks like this:

2 (4y - 3) + 3y = 16    Now we only have one variable to solve for.

8y - 6 + 3y = 16    Simplify like variables

11y - 6 = 16     try to get y by itself

11y = 16 + 6

11y = 22     divide both sides by 11

y = 2

Now you can put Y back into the first equation

x = 4y - 3

x = 4(2) - 3

x = 8 - 3

x = 5

so the answer is x = 5 and y = 2

Answer: You would go 3 to the left because it is a negative sign. Then you would go 1 up because it is positive.

Step-by-step explanation: You´re welcome

Check the picture below.

The bird flies at an angle of 60° degrees from the water, and its height from the ground when it drops the fish is 86.6 yards.

The bird caught the fish at point, flew to which is 100 yds away, and dropped the fish at C, which is horizontally 50 yards from A.

Now,
let the angle be x,
cosx = 50 / 100
x = cos⁻¹(1/2)
x = 60°

height of the bird is given as,
sin60 = height / 100
√3 / 2 = height / 100
height = 50√3 = 86.6

Thus, the bird flies at an angle of 60 °degrees from the water, and its height from the ground when it drops the fish is 86.6 yards.

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The distance between the two given points (5, 5) and (1 ,5) on a coordinate plane is equal to 4 units.

As given in the question,

Let the coordinates of the two given points in the coordinate plane are represented by:

 (x₁ , y₁) = (5, 5)

(x₂ , y₂ ) = (1 ,5)

Distance between two points  = √ ( x₂ - x₁)² + ( y₂ - y₁)²

Substitute the value we get,

Required Distance

= √ ( 1 - 5 )² + ( 5 - 5 )²

= √ ( -4 )² + ( 0 )²

= √ 16

= 4 units as distance is always positive.

Therefore, the distance between the given points on a coordinate plane is equal to 4 units.

The above question is incomplete , the complete question is :

What is the distance between points (5, 5) and (1 ,5) on a coordinate plane?

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Answer:

The multiplicative inverse of -11/7 is "A. -7/11".

Step-by-step explanation:

The multiplicative inverse of a fraction is found by flipping the numerator and denominator. So, if a fraction a/b has a multiplicative inverse, then it must be true that:

a/b * (b/a) = 1

In this case, we want to find the multiplicative inverse of -11/7:

-11/7 * x = 1

So, we flip the numerator and denominator of -11/7 to find x:

x = -7/11

Therefore, the multiplicative inverse of -11/7 is -7/11, which is option A.

The required percent of the people surveyed were satisfied with the car is 50%.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

We have,

Total car owner = 2600

People who said to buy car again = 1300

Now

Percentage of satisfied people = [tex]\frac{1300}{2600}[/tex] × 100

Percentage of satisfied people = 50 %

Thus,required percentage is 50%.

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An absolute value equation is an equation that contains an absolute value expression. To solve an absolute value equation, you need to consider two cases: when the argument inside the absolute value is positive and when it is negative.

Here is an example of how to solve an absolute value equation:

|x - 3| = 5

To solve this equation, we need to consider two cases: x - 3 = 5 and x - 3 = -5.

Case 1: x - 3 = 5

In this case, we can add 3 to both sides of the equation to get x = 8.

Case 2: x - 3 = -5

In this case, we can add 3 to both sides of the equation to get x = -2.

So, the solutions to the equation are x = 8 and x = -2.

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0.4225 is the value of log 7 ÷ 2

Given,

We have to find the value of log 7 ÷ 2

Here,

Logarithm;

The power to which a number must be raised in order to obtain other values is referred to as a logarithm. To put it another way, it provides the response to the query, "How many times is a number multiplied to get the other number?" The expression for a number's logarithm is. x = logb y.

Then,

Log 7 ÷ 2

The log value of 7 is 0.8450

So,

0.8450 ÷ 2 = 0.4225

That is,

The value of log 7 ÷ 2 is 0.4225

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The solution set of the inequality g < 5 is all the values of g that are less than 5.

What exactly is a math graph?

The term "graph" has at least two separate meanings in mathematics. The word "graph" in elementary mathematics refers to a plot or a function graph. In mathematical terms, a graph is a collection of points and the relationships between a subset of those points (which may be empty).

To graph this solution set, we use a number line, and place an open dot at 5 to indicate that 5 is not included in the solution set. Then, we shade the portion of the number line to the left of 5, which represents all the values of g that are less than 5. The graph of the solution set would look like this:

(shaded area represents all the values of g that satisfy the inequality)

|-----5----- |

Note: The value 5 is not included in the solution set as the inequality is strict inequality.

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