Find the area of the right triangle below.
9m
4m

Answer: To find the ratio of the dimensions of the actual room to that of the scale model, we can divide the dimensions of the actual room by the dimensions of the scale model.

The dimensions of the actual room are 15m by 9m by 12m, and the dimensions of the scale model are 5m by 3m by 4m.

Therefore, the ratio of the dimensions of the actual room to that of the scale model is:

length: 15m / 5m = 3 : 1

width: 9m / 3m = 3 : 1

height: 12m / 4m = 3 : 1

So, the ratio of the dimensions of the actual room to that of the scale model is 3:1 for all dimensions (length, width, and height)

The ratio of the dimensions of the scale model to that of the actual object is 1:16

so to find the length and width of the actual object, you can use this relation

length = scale model length * 16 = 2.416 = 38.4m

width = scale model width * 16 = 1.816 = 28.8m

So the length and width of the actual object are 38.4m and 28.8m respectively.

Step-by-step explanation:

The == operator determines if two operands are equivalent in terms of value. The === operator determines if two operands are equivalent in terms of value and datatype.

The assignment operator = is straightforward. The left side operand receives values from the right side operands.

On the other hand, == determines whether or not the values of two operands are equal.

The Python is operator determines if two variables point to the same memory item as opposed to the == operator, which compares the value or equality of two objects. This implies that you should almost always employ the equality operators == and != Difference between == and = in Python.

A single equal sign is used to assign a value to a variable in Python and many other programming languages, whereas two successive equal signs are used to determine if two expressions provide the same result.

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On solving the provided question, we can say that - the function value will be [tex]g(x) = -3 + 12x + 15[/tex] and

The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.

Here,

[tex]y =a(x-x1)(x-x2),[/tex] y equals a(x-5)(x+1)

g(x) = -3(x-5)(x+1)

[tex]g(x) = -3(x-5)(x+1)[/tex]

g(x) = -3 + 12x + 15

y-intercept of g(x) is (0,15)

Therefore , the solution to the given problem of the equation comes out be  y-intercept of g(x) is (0,15).

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Answer:

Don't join the points with lines

Make the numbers on the vertical axis larger

Label the axes

Step-by-step explanation:

Make all the points different colours → I don't think that would be useful. Unless the teacher asked you to in class, it's probably not a good answer.

Put the title on the bottom → Same. Unless the teacher asked you to in class, it's not really useful and probably not a good answer.

Don't join the points with lines → Teachers ask indeed not to do this, so I think it's a good answer. Most of the time they prefer students to use curves (hope it's the good translation).

Make the numbers on the vertical axis larger → Since both axes represent notes, it would be easier to compare with the same scale. If that's what the teacher meant, then I think it's correct.

Label the axes → This one is interesting, because right now we don't what they represent at all.

Hope it helps, good luck for your exercices :)

The station of PT is 12305.58 ft

The station of PT can be determined using the formula:

PT = PI + R * (central angle in radians)

To use this formula, we first need to convert the central angle from degrees to radians. We can do this by multiplying the central angle by (π/180)

Next, we need to determine the radius (R) of the curve. We can use the formula:

R = L / (central angle in radians)

Where L is the tangent length.

Finally, we can substitute the values into the formula for PT:

PT = 105 00 + (1200 / (29.86 * (π/180)))

PT = 105 00 + (1200 / (0.5236))

PT = 105 00 + 2295.58

PT = 12305.58

It's important to note that this calculation assumes that the degree of curvature is a circular curve and that the PI is at the tangent point of the curve.

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Answer:

To drain the tank to the right level, you need to remove 859 - 635 = <<859-635=224>>224 gallons.

So you need to work for 224 / 56 = <<224/56=4>>4 minutes.

Step-by-step explanation:

Answer:

It appears that you are trying to find a quadratic function in standard form that models the number of guests at the large resort as a function of the number of months since the beginning of the year.

To do this, you can use the given data points to solve for the constants a, b, and c in the standard form of the quadratic function f(x) = ax^2 + bx + c.

To find the values of a, b, and c, you will need to have at least three data points. You can then use these data points to solve a system of three equations with three variables.

For example, using the data points (0, 10), (2, 15), and (4, 18), you can set up the following system of equations:

f(0) = 10 = a(0)^2 + b(0) + c

f(2) = 15 = a(2)^2 + b(2) + c

f(4) = 18 = a(4)^2 + b(4) + c

Solving this system of equations will give you the values of a, b, and c that you can use to write the standard form of the quadratic function that models the data.

I hope this helps! Let me know if you have any questions or need further assistance.

Step-by-step explanation:

The cumulative total in Vietnam j(n) is 23(n-1),cumulative takes into account all data up to the present. In month four, j(n) will be worth more than v(n).

The distinction between total and cumulative is that total refers to the entirety of something, whereas cumulative takes into account all data up to the present.

When a new number is added to a series of numbers, the running total is updated by adding the new number's value to the previous running total. Partially sum is another name for it. Running totals serve two distinct objectives.

We take it for granted that you mean that vehicles delivered to Vietnam should be modeled by v(n) = 5 + 11 and those sent to Japan by j(n) = 23(n-1).

In month four, j(n) will be worth more than v(n).      

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When Jim's model car ownership is compared to Terrence's model car ownership, the ratio is 8:6, Jim possesses 48 model vehicles.

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, according to the definition given by the term in its most basic form.  When two terms are placed on each side of an equal sign, a simple equation is used to show their relationship. The four mathematical operations of addition, subtraction, multiplication, and division may be used singly or in combination in simple equations.

given

You are aware that Jim and Terrence both own four model automobiles in comparison to three owned by Jim.

Let's assume that Jim owns Jim has the following number of model cars, then you can answer the task as follows:

4/3 = x/36

x = (4* 36)/ 3

x = 48

Therefore, Jims owns 48 model cars.

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Using the Pythagoras Theorem the value of c=11.40 and the number that goes beneath the radical is 130.

What is Pythagoras Theorem?

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.

The rectangle is divided into two triangles which have exactly same sides.

So take any one triangle.

Apply the Pythagoras theorem since it is a right-angled triangle with base = 9 and perpendicular = 7.

So, according to Pythagoras theorem -

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

Plugging in the values in the equation -

c^2=(9)^2+(7)^2

c^2=81+49

c^2=130

c=[tex]\sqrt{130}[/tex]

c=11.40

Therefore, the value of c is obtained as 11.40.

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Answer:

Step-by-step explanation:

from the figure we kown the speed is 9/3=15/5=21/7=3 km per minute

the distance in 8 minute is 3 ×8=24 km

The corresponding equation of the proportional relationship will be;

⇒ y = - 1/4x

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

The graph of a proportional relationship contains the point (-12, 3).

Now,

Let the equation of the proportion is,

⇒ y = kx

Where, 'k' is constant of proportion.

Since, The graph of a proportional relationship contains the point (-12, 3).

Hence, Substitute x = 0 12 and y = 3 in above equation we get;

⇒ 3 = k × - 12

⇒ 3 / (-12) = k

⇒ k = - 1/4

Thus, The equation of the proportion is,

⇒ y = - 1/4x

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Scale factor required to map the first line segment onto second line segment is 3/9=0.33

The scale factor is the ratio of the length of the image to the length of the pre-image.

In this case, we're looking for the  that would map the first line segment (length 9cm) onto the second line segment (length 3cm).

To find the scale factor, we can divide the length of the image by the length of the pre-image:

scale factor = length of image / length of pre-image

In this case:

[tex]ScaleFactor=\frac{Length Of Image}{Length Of Pre-image}[/tex]

[tex]scale factor = 3cm / 9cm = 1/3=0.033[/tex]

So the scale factor to map the first line segment onto the second line segment is 1/3.

It means the 1st line is 3 times longer than the second one.

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Answer:

SSS

Step-by-step explanation:

We have three pairs of corresponding, congruent sides. Therefore, the SSS Postulate can be used to prove the two triangles congruent.

The value of a is zero.

Now, According to the question:

The given equation is:

a + 5 = -5a + 5

To solve the above equation:

Subtract 5 on both sides

a + 5 - 5 = -5a + 5 - 5

a = -5a

Add 5a on both sides:

6a = 0

Divide both sides by 6

a = 0

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The complete question is this:

How do you solve a + 5 = -5a + 5

When a calcium atom forms an ion, it loses two electrons. The electrical charge of the calcium ion is +2

Calcium ions are net positive two charges. In calcium, when it has assumed its most stable state, the relationship between the quantity of protons (20) and the quantity of electrons (18) is represented by the +2 charge.

In the event that calcium (Z = 20) picks up two electrons, the resultant ion will have 18 electrons and 20 protons, giving it a charge of +2. (two more positive protons than negative electrons). It's a cation, this ion. Using the Ca2+ symbol, we can identify a calcium ion.

Atoms that lose electrons acquire a positive charge as there are fewer electrons left with negative charges to balance the positive charges of the protons in the nucleus. Positively charged ions are known as cations.

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Answer:

Step-by-step explanation:

Here is how to solve the given problem above.

Given that the calculator costs $32 and has a tax of 6%, what we are going to do is to find how much is 6% of 32. So 32 times 0.06 is 1.92. So, we add this amount to 32 dollars, and the total price would be 33.92 dollars. Hope this answer helps.

Answer:

33.92

Step-by-step explanation:

32 times 6 divided by 100 gives you 1.92, the sales tax,

add it to 32 and then you get 33.92

The population of the city grew from 2010 to 2020 by 13.37%.

A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.

We have to given that;

In 2010, the population of a city was 237,000.

And, From 2010 to 2015, the population grew by 7.6%. From 2015 to 2020, it fell by 4.7%.

We know that;

Where, A = P (1+r)ⁿ

A = final population.

P = Initial population.

r = rate

n = time

Hence, The population in 2015 is, =

A = 237,000(1 + 0.076)⁵

A = 341829.629

And, The population in 2020 =

A = P (1 - r)ⁿ

A = 341829.629 (1 - 0.047)⁵

A = 268704.047

So, Percent grow = (268704.047 - 237,000) / 237,000 × 100

                           = 31704.047 / 237,000 × 100

                            = 13.37 %

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The numeric value for each trigonometric expression is given as follows:

3. [tex]\sin{\left(-\frac{5\pi}{6}\right)}\cos{\left(\frac{2\pi}{3}\right)} - \cos{(-\pi)} = \frac{5}{4}[/tex]

4. [tex]\frac{\sin{\left(\frac{\pi}{4}\right)}}{\cos^2{\left(\frac{\pi}{3}\right)}} = 2\sqrt{2}[/tex]

The first trigonometric expression for this problem is defined as follows:

[tex]\sin{\left(-\frac{5\pi}{6}\right)}\cos{\left(\frac{2\pi}{3}\right)} - \cos{(-\pi)}[/tex]

The numeric value of each term of the expression is given as follows, using equivalent angles on the trigonometric circle:

Hence:

[tex]\sin{\left(-\frac{5\pi}{6}\right)}\cos{\left(\frac{2\pi}{3}\right)} - \cos{(-\pi)} = \left(-\frac{1}{2}\right)^2 + 1 = \frac{1}[4} + 1 = \frac{5}{4}[/tex]

For item 4, the angles are on the first quadrant, hence:

Hence the numeric value of the expression is given as follows:

[tex]\frac{\frac{\sqrt{2}}{2}}{\left(\frac{1}{2}\right)^2} = 4 \times \frac{\sqrt{2}}{2} = 2\sqrt{2}[/tex]

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The answer of Coin word problem is Sarah has 425 quarters.

There are often two different equation types in coin word problems. The total number of coins is described by one equation, while the total amount of money is described by the other equation. However, let's choose some variables that will represent the problem's unknown values before we begin creating our equations.

Word Problems, also known as story problems, can be found in both daily life and the Common Core State Standards for every school level,  

Let q  be the number of quarters and d  be the number  of dimes

Then we are doing as :

q  +  d    =  600  →   d = 600  - q    (1)

0.25q + 0.10d  = 123.75      (2)

Sub (1)  into (2)  for d

0.25q + 0.10 ( 600 - q)   = 123.75    

simplify,

0.25q + 60  -0.10q  =  123.75

0.15q + 60 = 123.75    (subtract 60 from both sides)

0.15q  =  63.75     ( divide both sides by  0.15)

q = 425

Therefore, she has  425 quarters

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The domain of the given function would be x > 0.

What is a function?

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

The given function is f(x) = logb(x)

The domain of the logarithmic function [tex]f(x) = log_b(x)[/tex] is the set of all positive real numbers x such that x > 0. This is because the logarithm of a non-positive number is undefined.

Hence, the domain of the given function would be x > 0.

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The domain of the given function would be x > 0.

What is a function?

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

The given function is f(x) = logb(x)

The domain of the logarithmic function [tex]f(x)=log_b(x)[/tex] is the set of all positive real numbers x such that x > 0. This is because the logarithm of a non-positive number is undefined.

Hence, the domain of the given function would be x > 0.

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Lia gave away 3/5 of the trail mix, which is equal to 2 2/5 pounds.

Lia bought 4 3/5 pounds of trail mix. She gave 3/5 of it to her iter.Since Lia bought 4 3/5 pounds of trail mix, we can express this as 4 + 3/5 pounds, or 9/5 pounds.

To find out how much trail mix Lia gave away, we can multiply 9/5 by 3/5.

3. 3/5 multiplied by 9/5 is equal to 27/25.

To simplify this fraction, we can divide both the numerator and denominator by 3.

27/25 can be simplified to 9/5 or 2 2/5 pounds.

Therefore, Lia gave away 2 2/5 pounds of the trail mix.

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The inequality representing p, the number of people who can go to the amusement park, is given as follows:

10.5p + 16.5 ≤ 90.

The inequality for this problem is build considering the linear cost function, defined in slope-intercept format as follows:

C(p) = mp + b.

In which the parameters are given as follows:

Parking is $16.50, and tickets cost $10.50 per person, hence the numeric values of the slope and the intercept are given as follows:

m = 10.50, b = 16.50.

Thus the cost function is given as follows:

C(p) = 10.5p + 16.5.

They have no more than $90 to spend on parking and admission, hence the inequality is defined as follows:

C(p) ≤ 90.

10.5p + 16.5 ≤ 90.

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Answer: The statement "if sin 0 < 0 and cos 0 > 0" is not true, as both the sine and cosine of an angle of 0 degrees are equal to 0. Therefore, the statement is not meaningful and the question cannot be answered.

It is important to note that sine, cosine, and all the trigonometric functions are defined in radians and not degrees and the value of sin(0) and cos(0) is not zero but 1

Please provide more context or specify what you are asking about in order to give a more accurate answer.

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

To find f(-3), substitute x with (-3)

f(x) = -x² - 8x

f(-3) = - (-3)² - 8*(-3)

      = - (9) + 24

       = - 9 + 24

       = 15

Answer:

15

Step-by-step explanation:

f ( x ) = - x² - 8x

Accordingly, to find the value of f ( -3 ) you have to replace x with ( - 3 ).

f ( -3 ) = - (-3)² - 8 × -3

f ( -3 ) = - 9 + 24

f ( -3 ) = 15

Answer:

2A/h - b2= b1

Step-by-step explanation:

Answer:

30 in.²

Step-by-step explanation:

Real:

length 30 ft

width 36 ft

Scale:

length 5 in.

width ?

30/36 = 5/x

30x = 5 × 36

x = 6

The scale width is 6 inches.

Scale area:

area = length × width

area = 5 in. × 6 in.

area = 30 in.²

The area, of the floor in the scale drawing is 30 in.²

The area is the total amount of space that an object's shape or a flat (2-D) surface occupies.

Given that  rectangular floor of a classroom is 30 feet in length and 36 feet in width. A scale drawing of the floor has a length of 5 inches.

length 30 ft

width 36 ft

Scale: length 5 in.

Then we have

30/36 = 5/x

30x = 5 × 36

x = 6

The scale width is 6 inches.

Scale area:

The area = length × width

area = 5 in. × 6 in.

area = 30 in.²

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In class 7, adjacent angles are defined as two angles that share a common vertex and a common side but do not have any common interior points. They are angles that are next to each other.

Adjacent angles are often used in geometry to describe the angles formed by intersecting lines or figures. The adjacent angles can be classified into two types, namely:

Interior adjacent angles: They are formed by two lines that intersect inside a closed figure, such as in a parallelogram.

Exterior adjacent angles: They are formed by two lines that intersect outside a closed figure, such as in a straight line.

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According to the given algebra Darla is 17 years old and Maria is 30 years old.

Numbers, parameters, constants, expressions, equations, linear equations, and quadratic equations are all part of the fundamentals of algebra. Additionally, the algebraic expressions contain the fundamental arithmetic operations of addition, subtraction, multiplication, as well as division.

Maria is 4 years younger than Don,

thus if Don is x years old, then Maria is x years younger. (2x-4)

If their ages added together equal 47,

then x + (2x-4) = 47

Solving for x, then determining Maria's age (2x-4)

3x=47+4

3x=51

x=51/3

x=17 years

Maria's age=2*17-4=30 years

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