john is making a poster for safety awareness week. His poster has 2 sides of equal length. Which math words and numbers are important in this problem

The right triangle in marked question number 3 have the value of u = 2 and v = √2 using the trigonometric ratio of sine and cosine of the angle 45°.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

Considering the angle 45° for the right triangle, recall that sin 45° and cos 45° are generally both equal to √2/2

sin 45° = √2/u {opposite/hypotenuse}

√2/2 = √2/u

u = √2/√2 × 2 {cross multiplication}

u = 2

cos 45° = v/u {adjacent/hypotenuse}

√2/2 = v/2

v = 2/2 × √2

v = √2

Therefore, the value of u = 2 and that of n = 10, using the trigonometric ratio of sine and cosine of the angle 45° for the right triangle.

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The only true statement among the options given is C, The total cost of your books depends on how many books you buy.

What is the direct proportion?

Direct proportion, also known as direct variation, is a relationship between two variables in which the ratio of the variables is always constant. This means that if one variable increases, the other variable will also increase, and if one variable decreases, the other variable will also decrease.

According to the information given, all books are $1.50 each, so the price does not depend on what kind of book you buy. The statement A is false.

Also, the kind of book you buy does not depend on the price, so statement B is false.

The number of books you buy does depend on the total cost, so statement C is true.

Therefore, the only true statement among the options given is C, The total cost of your books depends on how many books you buy.

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The measurement of angle BCD is 30°

A cyclic quadrilateral is a four sided shape that can be inscribed into a circle. Each vertex of the quadrilateral lies on the circumference of the circle and is connected by four chords. The opposite angles of a cyclic quadrilateral have a total of 180°.

Given that, ABDE is a cyclic quadrilateral. ABC and EDC are straight lines. Angle DBC = 60°

According to the figure, BD║ AE

Therefore,

∠ DBC ≅ ∠ EAB (definition of corresponding angles)

∠ EAB = 60°

Since, ∠ EAB : ∠ BCD = 2:1

Therefore, ∠ BCD = 60 × 1/2 = 30°

Hence, the measurement of angle BCD is 30°

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The shifted coordinates for each of the following are (20,-11) and (6,2).

Coordinates are a pair of integers (Cartesian coordinates), or sporadically a letter and a number, that identify a certain place on a grid, also referred to as a coordinate plane. The x axis (horizontal) and y axis are the two axes that make up a coordinate plane (vertical).

Given, (x,y) → (x + 10, y - 6)

a)  when the input is (10,-5) -

10 + 10 = 20

- 5 - 6 = - 11

(20,-11)

b) when the input is (-4,8) -

-4 + 10 = 6

8 - 6 = 2

(6,2)

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Answer:

Please provide more information. Since you don't provide the original amount of walnuts used, we can't solve the problem.

The linear equation to represent the value of the car in terms of the year will be c = 64000 - 5000y

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

In this situation, the upfront cost of a Porsche is 64K and at the end of 12 Years, the car is worth only $4000.

The difference in amount will be:

= $64000 - $4000

= $60000

Number of years = 12

Amount in depreciation per year = $60000 / 12

= $5000 per year

The linear equation to represent the value of the car in terms of the year will be:

c = 64000 - 5000y

where c = value

y = number of years

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By solving these equations, Cole is currently 27 years old, and Anya is 30 years old.

A person's date of birth is compared to the date on which their age needs to be calculated as part of the age calculation process. The person's age is determined by deducting the person's birthdate from the given date. Age equals Given Date - Birthdate

Let x stand in for Anya's current age and y for Cole's present age.

Cole's older brother, Anya, is three years older. Hence:

x = y + 3

x - y = 3 (1) (1)

The total of their ages will be 79 in 11 years. Hence:

(x + 11) + (y + 11) = 79

x + y = 57 (2) (2)

Equations 1 and 2 are simultaneously solved to produce:

x = 30, y = 27

Cole is currently 27 years old, and Anya is 30 years old.

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1. MO = NP (Given)

2. MO = MN + NO (Segment Add)

  NP = NO + OP (Segment Add)

3. MN + NO = NO + OP (Transitive / Substitution)

4. MN = OP (Subtraction POE)

The cost price of large pizza is $12 and that of toppings is 0.75.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. For example, 3x + 5 = 15. There are different types of equations like linear, quadratic, cubic, etc.

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Let the cost of large pizza be x and that of toppings be y.

x + 2y = 13.50

x = 13.50 - 2y    - (1)

x + 5y = 15.75   - (2)

substitute equation (1) in equation (2),

13.50 - 2y + 5y = 15.75

3y = 15.75 - 13.50

3y = 2.25

y = 2.25 / 3

y = 0.75

now, put the value of y = 0.75 in equation (1),

x = 13.50 - 2 × 0.75

x = 13.50 - 1.5

x = 12

Therefore, the cost price of large pizza is $12 and that of toppings is 0.75.

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We have plotted the point (2/3) on a number line and attached and explained it below.

A number line is one of the methods of visually representing any point that is a real number on a graduated straight line. This is made by marking graduations on a simple normal line and then marking whatever point we need on it.

The point (2/3) has been given in the problem which we need o plot on the number line. Since this point is a fraction, we need to divide/solve it first and then see where it will fit. On dividing the fraction, we find that the point is 0.66. Now, we find the graduations 0 and 1 since it lies between them. The image for this has been attached below.

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Every coordinate point of the original triangle has its scale factor doubled by one-half if the scale factor is one. multiply by half after dilation with a scale factor of two.

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Every coordinate point of the original triangle has its scale factor doubled by one-half if the scale factor is one. multiply by half after dilation with a scale factor of two.

We locate the dilation's center point and measure the distances between it and other points on the preimage and the image in order to get the scale factor for the dilation. As correctly stated by Math Bits Notebook, the scale factor is determined by the ratio of these distances.

Keep in mind that each coordinate must be multiplied by the scale factor in order to enlarge an object in the coordinate plane. The mapping will be (x, y) (1.5 x, 1.5 y) with this dilation. The original is represented by the blue quadrilateral in the graph above, while the dilatation is shown by the red picture. Connect the image's vertices to the center of dilation by drawing straight lines.

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A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, which satisfies the equation i2 = -1.

What is complex number?
The number a is the real part of the complex number and b is the imaginary part. A complex number is said to be a sum of a real number and an imaginary number. Complex numbers are used in many branches of mathematics, including calculus, linear algebra, quantum mechanics, and electrical engineering.

They are also used in engineering, physics, chemistry, and other scientific fields. Complex numbers are useful in many real-world applications, such as finding the roots of a polynomial equation or solving systems of linear equations. Complex numbers can also be used to represent points in the plane and can be used to model phenomena in the physical world, such as electrical circuits and waveforms.

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Answer:

A- NQ,

B- 24,

C- 14+10=24

Applying the triangle sum theorem, the value of x in the triangle is: C. 36.

The Triangle Sum Theorem states that the sum of the measures of the interior angles of a triangle is 180 degrees. This theorem applies to all triangles, regardless of their shape or size.

The theorem can be proven using the fact that the sum of the measures of the interior angles of any polygon with n sides is (n-2)x180. Since a triangle has three sides, the sum of its interior angles is 180 degrees.

Therefore:

2x + 2x + x = 180

Combine like terms

5x = 180

Divide both sides by 5

5x/5 = 180/5

x = 36

The value of x is: C. 36.

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The average cost per passenger - mile of driving is $0.503 per mile.

Average cost is calculated by dividing the total cost by the total output quantity.

There are two options for Daniel and Elizabeth, either by driving car or by plane.

We have to calculate the average cost per passenger - mile of driving in car.

Cost of gas = $60

Food bill for a day for two of them = $25

Food bill for a day for one = 25 / 2 = $12.5

Food bill for one passenger for 4 days = $12.5 × 4 = $50

Cost of room for 1 night = $48

Cost of room for 4 nights = $192

Total cost for 1 passenger = $60 + $50 + $192 = $302

Average cost per passenger - mile of driving = 302 / 600 = $0.503 per mile.

Hence the average cost per mile per passenger is $0.503 per mile.

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The first step in solving the quadratic equation is subtracting 8 from both sides.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

5x² + 8 = 133

Subtract 8 into both sides.

5x² = 133 - 8

5x² = 125

Divide both sides by 5.

x² = 125/5

x² = 25

x = √25

x = 5

Thus,

The root of the equation is 5.

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The median would be the best representation of the typical value or behavior of the data set for "Ages of college students".

The median is the value in the center of a data collection, which means that 50% of the data points have a value less than or equal to the median, and 50% of the data points have a value greater than or equal to the median. The statistical median is the number in the midpoint of a series of numbers. To get the median, sort the numbers by size; the number in the center is the median. The term median is derived from the Latin word medius, which also meaning middle. A number in the center of a list is known as the median in mathematics.

Here,

The median would be the best depiction of the data set's usual value or behavior for "Ages of college students".

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Answer:

36

Step-by-step explanation:

4 x 4 = 16

2 x 10 = 20

You would have to separate the square and the rectangle.

The way you do this is by cut of the number and subtracting them, like 6 and 2 to get the square.

Answer:x=35/2 or 17.5

Step-by-step explanation:

x + .2x = 21

1.2x = 21

1.2x/1.2 = 21/1.2

x = 17.5

answer a i just did it

Step-by-step explanation:

The base of the triangle 7 can be divided in half by a line of symmetry of the isosceles triangle, which will bisect the vertex angle. This creates two right triangles: Each with a base of 3.5 and a hypotenuse of 5.

What is meant by isosceles triangle?

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The base of triangle 7 can be bisected by the line of symmetry of the isosceles triangle that bisects the apex angle. This creates two right triangles.

Each has a base of 3.5 and a hypotenuse of 5.

A triangle with two equal sides is called an isosceles triangle in geometry.

Both exactly 2 equal sides and at least 2 equal sides are permissible specifications, with the exception of equilateral triangles in the latter version. The bipyramid, the golden triangle, the isosceles right triangle, and the face of the Catalan solid are examples of isosceles triangles.

Isosceles triangles have been studied mathematically since Babylonian and Egyptian times.

Used as an ornament since the dawn of time, isosceles triangles are widely used in architecture and design, including in the construction of pediments and pediments.

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The difference between the y coordinates  and the difference between the x coordinates then divide them

Gradient is a differential operator used in mathematics to transform a three-dimensional vector-valued function into a vector whose three elements are the partial derivatives of the function with respect to its three variables. The gradient sign is  ∇

As a result, f = ifx + jfy + kfz, where fx, fy, and fz are the first partial derivatives of f and I j, and k are the unit vectors of the vector space, is the gradient of a function, also known as grad f or f. f is the direction of the heat-flow vector in a temperature field, where f is a temperature field in physics that indicates the temperature at every point in a space.

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Answer:

79%

Step-by-step explanation:

imma human calculator and no one can stop me

Yes, the mentioned sides of triangle will be right angles triangle because they follow Pythagoras theorem.

A right angled triangle is characterized by presence of hypotenuse, perpendicular and base. The sides of right angled triangle are related through Pythagoras theorem, which is -

Perpendicular² = Base² + Hypotenuse²

As we know that hypotenuse is the longest side of triangle, hence, will be the 13 cm.

So, keeping the values in formula -

13² = 5² + 12²

Taking square on both the sides of equation

169 = 25 + 144

Performing addition on Right Hand Side of the equation

169 = 169

Since, LHS is equal to RHS, hence, it is right angled triangle.

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Factor of scale (Dilation) Factor of scale (Dilation) How much larger or smaller the image will be depends on the scale factor in the dilation of a mathematical entity (compared to the original object).

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Answer:

Step-by-step explanation:

Isosceles triangle (Same angle) means both sides are the same length, triangle is also right meaning you can plug values into Pythagorean theorem ([tex]a^2 + b^2 = c^2[/tex])

[tex]x^2+x^2 = 1^2\\2x^2=1\\x = \sqrt{\frac{1}{2} }\\x = 0.707...\\x=0.7[/tex]

Assuming all my math is right, this is your answer

The value of expression 9x for x= 2 is 18.

what are expressions?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

Now,

Given expression = 9x

For x=2

Value of expression=9*2

=18

Hence,

          After evaluating 9x for x=2 value will be 18.

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So, on solving the question we can say that  equation p= 126-6m ; p = 2 = -124 = -6m => m = 20.6666666667

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

the equation is p= 126-6m

p = 2

-124 = -6m

m = 20.6666666667

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The math word problems with the given words is A has 52 marbles, B has 105 marbles, find the difference between the number of marbles between A and B.

A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world."

1. A has 52 marbles, B has 105 marbles, find the difference between the number of marbles between A and B.

2. The temperature of city A is 35 degrees, on the second day the temperature decreased to 15 degrees. How much did the dropped (temp)?

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Answer:

12.5%

Step-by-step explanation:

0.125 * 2 = .25

2+.25 =2.25