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A builder is using the scale drawing shown to build a house.


If the owner decides to increase the living room dimensions by 20%, what is the new length and width of the living room floor?


A: 14.4 feet × 9.6 feet

B: 12.8 feet × 8.4 feet

C: 13.2 feet × 8.8 feet

D: 15.2 feet × 9.8 feet

To find the height of an obtuse angle in a triangle, you can use the following steps:

It is important to note that the hypotenuse of the right triangle (the base) must be the side opposite to the obtuse angle, and the other two sides should be the legs of the triangle. Also, the altitude can fall inside or outside of the triangle, it does not affect the calculation of the height.

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Answer:

(f ⋅ g)(3) = 100, the distance in miles the bus traveled

Step-by-step explanation:

The product of (miles/hour) and (hours) is (miles), so only answers with units of distance are applicable. The numbers are ...

 f(3) = 2·3² +2 = 20 . . . . miles per hour

 g(3) = 3+2 = 5 . . . . hours

so (f·g)(3) = f(3)·g(3) = 20·5 = 100 . . . . miles

Answer:

(f ⋅ g)(3) = 100, the distance in miles the bus traveled.

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=2x^2+2\\g(x)=x+2\end{cases}[/tex]

To calculate the composite function (f ⋅ g)(3), multiply function f(3) by function g(3).

[tex]\begin{aligned}(f \cdot g)(3)&=f(3) \cdot g(3)\\&=(2(3)^2+2)(3+2)\\&=(2(9)+2)(3+2)\\&=(18+2)(3+2)\\&=(20)(5)\\&=100\end{aligned}[/tex]

If function f(x) represents the rate of a bus travelling in miles per hour,

and function g(x) represents the time the bus travelled in hours:

[tex]\implies f(x) \cdot g(x)=\rm miles/hour \cdot hour=\dfrac{miles}{hour} \cdot hours=miles=distance[/tex]

Therefore, (f ⋅ g)(3) = 100 represents the distance in miles the bus traveled.

The equation of the tangent line to the circle through the point (-6,8) has equation = Y = 0.75x + 3.5

For circles that have a center at (0,0), the equation is  [tex]x^{2} + y^{2} = r^{2}[/tex]

[tex]x^{2} + y^{2} = 10^{2}[/tex]

[tex]x^{2} + y^{2}[/tex] = 100

We check if the point (-6,8) is a circle

[tex]x^{2} + y^{2}[/tex] = 100

[tex]-6^{2} + 8^{2}[/tex] = 36 + 64 = 100

So the point is exactly at circle line, as picture below

We solve the gradient of a normal line (n)

Mn = [tex]\frac{y2 - y1}{x2 - x1}[/tex] = [tex]\frac{8 - 0}{-6 - 0}[/tex]  = [tex]- \frac{8}{6}[/tex]

For perpendicular lines the gradient is

Mp = [tex]- \frac{1}{Mn}[/tex]  = [tex]\frac{- 1 }{-\frac{8}{6} }[/tex] = [tex]\frac{6}{8} = \frac{3}{4}[/tex]

The standard equation of a linear line is

Y =  mx + c

We need to find constant (c). We substitute x and y with point (-6,8)

So, x = -6 and y = 8

C = y - mx

C = 8 - ¾(-6) = 8 – [tex]\frac{18}{4}[/tex] = 3.5

With m = Mp =  [tex]\frac{3}{4}[/tex] and c = 3,5    

So, Y =  mx + c

      Y =     [tex]\frac{3}{4}[/tex] x + 3.5

      Y = 0.75x + 3.5

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A conclusion or a hypothesis presented on an unproven foundation in mathematics is referred to as a conjecture, conjectures 6,it is divisible by 2,4,9,12.

Therefore the result is 6,it is divisible by 2,4,9,12.

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A 5 cm pentagon has a perimeter of 25 cm.

A perimeter is a closed route that covers, surrounds, or outlines a two-dimensional form or length. The circumference of a circle or an ellipse is its perimeter. There are various practical applications for calculating the perimeter. The perimeter of a thing is the distance surrounding it. Your house, for example, has a fenced-in yard. The perimeter of the barrier is its length. A perimeter is the length of a two-dimensional shape's border. It is sometimes defined as the total of the lengths of all the object's sides. The perimeter of such form is the algebraic sum of the lengths of each side. We have formulae for the various geometric forms.

Here,

side of pentagon=5 cm

perimeter of pentagon=5*side

=5*5

=25 cm

The perimeter of a 5 cm pentagon is 25 cm.

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A Riemann sum is a method used to approximate the definite integral of a function. A definite integral is a measure of the area between a function and the x-axis over a certain interval. The Riemann sum formula is used to approximate this area by breaking up the interval into a number of subintervals (or "rectangles") and summing the areas of each rectangle. The formula for a Riemann sum is given by:

∑ f(x_i) * Δx

where f(x) is the function being integrated, x_i is the right endpoint of the i-th subinterval, Δx is the width of the subinterval, and the sum is taken over all the subintervals.

The Riemann sum formula is defined with a limit, as the number of subintervals approaches infinity and the width of subintervals approaches zero, the Riemann sum formula becomes the definite integral.

There are different ways to calculate Riemann sum, such as Left Riemann Sum, Right Riemann Sum, Midpoint Riemann Sum, and Trapezoidal Riemann Sum, each one of them has different ways to calculate x_i, thus leading to different results, but all of them approach the definite integral as the number of subinterval increases.

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The algebraic formula to represent Giselle's profit is $b*1 - $18.72, or $b - $18.72, where $18.72 is spent on supplies.

A statement that contains at least two numbers or variables, along with at least one mathematical operation, is referred to as a mathematical expression. Any one of the following mathematical operations could be used: addition, subtraction, multiplication, or division. The following are an expression's fundamental parts: : (Number/Variable, Math Operator, Number/Variable). A statement that includes at least two numbers or variables, at least one mathematical operation, and the word "expression" is referred to as a mathematical expression. Let's review expressive writing. The alternative number, which is known as x, is 6 more than half of the given number. This sentence is denoted by the phrase x/2 + 6 in mathematics.

given

number of bracelets = b

profit = $b*1 - $18.72

The algebraic formula to represent Giselle's profit is $b*1 - $18.72, or $b - $18.72, where $18.72 is spent on supplies.

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Horizontal lines called latitudes are used to measure distances north or south of the equator. Vertical lines known as longitudes are used to determine the west or east of the meridian in Greenwich, England. Latitude and longitude work together to help cartographers, geographers, and others find specific locations on the globe.

Any location's distance from the equator may be determined using its latitude, which is based on its degree. We can locate any point on Earth using longitude and latitude. The GPS or Global Positioning System uses these coordinates.

The grid system that enables us to locate absolute or precise places on the surface of the Earth is made up of latitude and longitude. Latitude and longitude can be used to pinpoint certain locations. Landmark identification also benefits from knowledge of latitude and longitude.

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Correct option is D, To satisfy triangle inequality theorem, 4 < c < 42.

Triangle inequality is a theorem in Euclidean geometry that states any two triangle sides added together must be greater than or equal to the third side; it is represented by the symbols a + b c.

The basic tenet of the theorem is that a straight line connects any two places.

According to the triangle inequality theorem, any two sides' sums in a triangle must be bigger than the length of the third side.

If a, b, and c are the lengths of a triangle's sides, then the sum of a and b's lengths is greater than c's length. Similar to how a+ c > b, b + c > a.

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Answer:

Step-by-step explanation:

Answer:

7

2 meats + 5 cheeses

= 7 choices

Answer: i’m the biggest bird

Step-by-step explanation:

i’m the biggest bird

On solving the provided question we can say that by coordinates-  (4,-8)(4,−8) ; y - y1 = m(x-x1) => y - x 12 = 0

A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is represented by the second number. like in (12.5), when there are 12 units below and 5 above.

by coordinates-

(4,-8)(4,−8)

y - y1 = m(x-x1)

y +8 = x - 4

y - x 12 = 0

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The correct ratios are

sin(C) = [tex]\frac{\sqrt{3} }{2}[/tex] ,  tan(C) =[tex]\sqrt{3}[/tex] , sin(B) = [tex]\frac{1}{2}[/tex]

Consider the below figure attached to this question.

In triangle ABC, ∠A=90°, ∠B=30° and ∠C=60°, AC=9 and BC=18.

Using Pythagoras' theorem we get

hypotenuse² = perpendicular² + base²

BC² = AB² + AC²

⇒(18)² = AB² + 9²

⇒324 - 81 = AB²

Taking square root on both sides.

⇒√243 = AB

∴ √3 =AB

Trigonometric ratios are

[tex]sin(C) = \frac{opposite}{hypotenuse} = \frac{AB}{BC} = \frac{9\sqrt{3} }{18} =\frac{\sqrt{3} }{2}[/tex]

[tex]cos(B) = \frac{base}{hypotenuse} = \frac{AB}{BC} = \frac{9\sqrt{3} }{18} =\frac{\sqrt{3} }{2}[/tex]

[tex]tan(C) = \frac{opposite}{basee} = \frac{AB}{AC} = \frac{9\sqrt{3} }{9} =\sqrt{3}[/tex]

[tex]sin(B) = \frac{opposite}{hypotenuse} = \frac{AC}{BC} = \frac{9 }{18} =\frac{1}{2}[/tex]

[tex]tan(B) = \frac{opposite}{base} = \frac{AC}{AB} = \frac{9 }{9\sqrt{3} } =\frac{1 }{\sqrt{3} }[/tex]

Therefore, the correct ratios are

sin(C) = [tex]\frac{\sqrt{3} }{2}[/tex] , tan(C) = [tex]\sqrt{3}[/tex] , sin(B) =[tex]\frac{1}{2}[/tex]

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The complete question is:

Which trigonometric ratios are correct for triangle ABC? Select three options.

1. sin(C) = StartFraction StartRoot 3 EndRoot Over 2 EndFraction

2. cos(B) = StartFraction StartRoot 2 EndRoot Over 3 EndFraction

3. tan(C) = StartRoot 3 EndRoot sin(B) = One-half

4. tan(B) = StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction.

The baker can make 13 loafs of bread using 85 cups of flour using 6 1/4 c of flour for each loaf of bread.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

A baker has 85 cups (c) of flour to make bread she uses 6 1/4 c of flour for each loaf of bread.

Now, The fraction 6 1/4 can be written as 25/4.

Therefore, The number of bread loaf the baker can make is,

= (85/25/4).

= 85×(4/25).

= (17×4)/5.

= 68/5.

= 65/5 + 3/5.

= 13 + 3/5.

So, he can make 13 bread loafs.

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All the angles from the polygon path made by the students are;

∠1 = 96°

∠2 = 90°

∠3 = 162°

∠4 = 132°

∠5 = 60°

The images of the polygon are missing and so i have attached them. From the attached image, we can see we have;

Triangle (3-sided polygon)

Square (4-sided polygon)

Pentagon (5-sided polygon)

Hexagon (6 sided polygon)

Now, we know that formula for external angle of a polygon with n sides is 360/n.

Thus, for the 6-sided polygon, the ∠5 = 360/6

∠5 = 60°

Since ∠4 is shared by the pentagon and hexagon, then;

∠4 = (360/5) + 60

∠4 = 72° + 60°

∠4 = 132°

Since ∠3 is shared by the square and pentagon, then;

∠3 = 90 + 72

∠3 = 162°

∠2 = 90° because external angles of a square = 360/4 = 90°

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1 - √5x is not a polynomial.

Algebraic expressions called polynomials include constants and indeterminates.

Polynomials can be thought of as a type of mathematics.

Nearly all branches of mathematics employ them to express numbers, and calculus is one of those branches where they play a crucial role.

A specific kind of expression is a polynomial.

A mathematical statement without the equals symbol (=) is called an expression. Let's examine the definition and usage of polynomials as they are described below.

An algebraic expression known as a polynomial requires that all of its exponents be whole numbers.

Any polynomial must have variable exponents that are non-negative integers. Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.

Hence, 1 - √5x is not a polynomial.

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The perimeter of the polygon is 29.43

Polygon, in geometry, any closed curve consisting of a set of line segments (sides) connected such that no two segments cross. The simplest polygons are triangles (three sides), quadrilaterals (four sides), and pentagons (five sides).

Given here:  P(–4, 3), Q(1, 3), R(2, –3), S( 5, –3), and T(-7, -1).

PQ=[tex]\sqrt{(1+4)^{2} +(3-3)^{2} }[/tex]  =5

QR=[tex]\sqrt{1^{2} +9^{2} }[/tex] =9.055

similarly we can calculate the distance of the other edges and the perimeter of the polygon can be found out as PQ+QR+RS+ST+PT=29.43

Hence, The perimeter of the polygon is 29.43

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Answer:

Step-by-step explanation:

2

It take him to 7 minutes reach the ground. You can calculate the tangent  height of an object using the distance and angles

By multiplying "D * tan (theta)," where "tan" is the tangent of angle theta, you can determine the height of the object of interest. For instance, rounding up, the height is 40 tan 50 = 47.7 metres if theta is 50 degrees and D is 40 metres.

rate of descent=30 feet per minute

Height of climb=250 feet

Since he jumped 40 feet in no time,

hence,

new height=250-40=210

Time taken to reach ground=height/rate of descent

Time taken=210/30

Time taken=7 minutes

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Answer:

20 ducks

Step-by-step explanation:

4+5=9

4/9:x/45

9*5=45

4*5=20ducks

The length and width of the rectangle with 88 feet perimeter are 33 feet and 11 feet respectively

An equation is used to show the relationship between numbers and variables.

The perimeter of a shape is the sum of the distance along its sides. For a rectangle:

Perimeter = 2(length + width)

Let L represent the length and W represent the width of a rectangle with a perimeter of 88 feet

If the length of the rectangle is 3 times its width, hence:

L = 3W

Perimeter = 2(L + W)

88 = 2(L + W)

But L = 3W:

88 = 2(3W + W)

44 = 3W + W

4W = 44

W = 11 feet

L = 3W = 3(11) = 33 feet

The length and width are 33 feet and 11 feet respectively

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Answer:

Step-by-step explanation:

The center of a hyperbola is located at the point where the two foci (focii) are located. In this case, the center of the hyperbola is located at point (3,-2), which is option D.

Answer:

x<3

Step-by-step explanation:

3x+5<14

Your first step is to simplify the inequality.

To do this, always look to see if you can subtract any numbers from both sides to isolate a variable.

You can subtract 5 from both sides to isolate the 3x on one side.

After that, you will get 3x<9

Next, you must divide both sides by 3 to try and get x by itself, completing the inequality.

9/3 = 3

Your are left with: x<3

Done!

Answer:

x < 3

Step-by-step explanation:

3x + 5 < 14  subtract 5 from both sides

3x + 5 - 5 < 14 - 5

3x < 9  Divide both sides by 3

[tex]\frac{3x}{3}[/tex] < [tex]\frac{9}{3}[/tex]

x < 3

Set-builder notation: {x | x ∈ D} (where D is the domain) and {y | y ∈ R} (where R is the range), Interval notation: (a, b) (where a and b are the minimum and maximum of the domain) and [c, d] (where c and d are the minimum and maximum of the range) , Graphical notation: The domain and range are represented by a graph.

Set-builder notation is a way of representing the domain and range of a function. It uses curly brackets surrounding the domain and range variables, separated by a vertical bar. The form is {x | x ∈ D} (where D is the domain) and {y | y ∈ R} (where R is the range). This notation is useful when the domain and range are not easily written as a set of numbers.

Interval notation is another way of representing the domain and range of a function. It uses parentheses to represent the domain and square brackets to represent the range. The form is (a, b) (where a and b are the minimum and maximum of the domain) and [c, d] (where c and d are the minimum and maximum of the range). This notation is useful when the domain and range are quickly written as a set of numbers.

Graphical notation is a third way of representing the domain and range of a function. In this case, the domain and range are represented by a graph, with the x-axis representing the domain and the y-axis representing the range. This notation is useful when visualizing the relationship between the domain and range of a function.

Set-builder, interval, and graphical notations are all ways of representing the domain and range of a function. Set-builder notation is useful when the domain and range are not easily written as a set of numbers, while interval notation is useful when the domain and range are quickly written as a set of numbers. Graphical notation is useful when visualizing the relationship between the domain and range of a function.

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The value of x in the angle  is -6

                  m ∠B = (x +53)°

                 m ∠C = (x +53)°

         2 (x + 53) + 86 = 180

          2x + 106 + 86 = 180

                 2 x + 192 = 180

                            2x = 180- 192

                            2x = -12

                             x = -6

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8 is not a perfect number as sum of its proper divisors is not equal to 8.

A perfect number is a positive integer that is equal to the sum of its proper divisors, which are the divisors of the number excluding the number itself. In other words, a perfect number is a number that can be written as the sum of its divisors, excluding itself.

For example, the number 6 is a perfect number because its divisors are 1, 2, and 3, and 1+2+3 = 6.

8 is not a perfect number because it is not equal to the sum of its proper divisors. The divisors of 8 are 1, 2, 4, and 8, and 1+2+4 = 7, which is less than 8.

Therefore, 8 is not a perfect number. To this date, only 49 known perfect numbers have been found, they are all even numbers and the largest known perfect number is 2^(74,207,281) − 1, it has over 22 million digits.

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Rationales that may be involved : [tex]$\pm 1, \pm \frac{1}{2}, \pm 3, \pm \frac{3}{2}, \pm 5, \pm \frac{5}{2}, \pm 15, \pm \frac{15}{2}$[/tex] and real roots in reason: [tex]$1,-1,-\frac{15}{2} \mathrm{~}$[/tex] .

We can use the theorem of rational zeros since all coefficients are integers.The constant term's coefficient, or trailing coefficient, is 15, and The plus and minus signs can be used to find its components. [tex]$\pm 1, \pm 3, \pm 5, \pm 15$[/tex]  . The options for p are as follows. The maximum degree of the term's coefficient, or the leading coefficient, is -2.

The plus and minus signs can be used to find its components. [tex]$\pm 1, \pm 2$[/tex] . The possible possibilities for q are as follows.

Discover each potential value for [tex]$\frac{p}{q}: \pm \frac{1}{1}, \pm \frac{1}{2}, \pm \frac{3}{1}, \pm \frac{3}{2}, \pm \frac{5}{1}, \pm \frac{5}{2}, \pm \frac{15}{1}, \pm \frac{15}{2}$[/tex]

These could be the rationale for the following: [tex]$\pm 1, \pm \frac{1}{2}, \pm 3, \pm \frac{3}{2}, \pm 5, \pm \frac{5}{2}, \pm 15, \pm \frac{15}{2}$[/tex]                                                      rationales that may be involved: [tex]$\pm 1, \pm \frac{1}{2}, \pm 3, \pm \frac{3}{2}, \pm 5, \pm \frac{5}{2}, \pm 15, \pm \frac{15}{2}$[/tex] .

real roots in reason: [tex]$1,-1,-\frac{15}{2} \mathrm{~}$[/tex].

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The perimeter of the triangle formed by ABC is 26.56

A coordinate system is a method for determining how to position points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more integers, or coordinates.In order to make it simple to identify the points, a cartesian plane divides the plane space into two dimensions.

Here,

The coordinate plane is another name for it. The horizontal x-axis and the vertical y-axis are the two axes of the coordinate plane. The origin is the place where these coordinate axes connect, and they split the plane into four quadrants (0, 0). Additionally, each point in the coordinate plane is denoted by the coordinates (x, y), where x represents the point's location in relation to the x-axis and y represents its position in relation to the y-axis.

The points on the plane are

A (1,-2) , B(8,-5) and C (5,5)

The length of AB is

=> (81)2+(-5+1)2 = √72 +42

= √65

The length of BC is

(8-5)2+(-5-5)2 -

= /32+102 =

✓109

And Length of AC is

√(1 − 5)2 + (−2 −5)2 = √42 +72 = √65

The perimeter of the triangle is √65+ √65+√109 = 26.56

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