how does math connect to animation?

Answer:

0.075

Step-by-step explanation:

to convert a fraction to a decimal fraction

divide the numerator by the denominator, that is

[tex]\frac{3}{40}[/tex] = 3 ÷ 40 = 0.075

What is an algebraic expression?

An expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, etc.

What is the substitution method?

The substitution method is generally used to solve the system of equations. In this method, first, solve the equation for one variable, and substitute the value of the variable in the other equation

5th question :

⇒ x(2y-x)²+2x²(x-2y)

let (x-2y) = A

⇒we can also write (2y-x)² as (x-2y)² as both have the same value

x(x-2y)²+2x²(x-2y)

x(A)²+2x²(A)

By taking xA common

⇒ xA(A+2x)

On putting the value of A=(x-2y)

⇒ x(x-2y) (x-2y+2x)

⇒x(x-2y) (3x-2y)

6th question :

2(x-y)-(y-x)²

let (x-y) = B

⇒we can also write (y-x)² as (x-y)² as both have the same value

2(x-y)-(x-y)²

2B-(B)²

By taking B common

⇒ B(2-B)

On putting the value of B=(x-y)

⇒(x-y) (2-{x-y})

⇒(x-y) (2-x+y)

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The new mixture exists 56.5% peanuts.

The first batch of 9 lb of mixed nuts possesses 40% peanuts.

This means the quantity of peanuts exists:

9 [tex]*[/tex] 40/100 = 3.6 lb

The second batch of 9 lb of mixed nuts possesses 73% peanuts.

This means the quantity of peanuts exists:

9 [tex]*[/tex] 73/100 = 6.57 lb

The total quantity of peanuts in the mix exists

3.6 lb + 6.57 lb = 10.17 lb

There exist 9 lb + 9 lb = 18 lb of mix.

Therefore, the percent of peanuts in the mix exists:

10.17 / 18 [tex]*[/tex] 100 = 56.5%

The new mixture exists 56.5% peanuts.

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Answer:

Step-by-step explanation: This example is saying that adding a negative number is the same as subtracting a positive number. For example 2-3 = 2 + (-3).

The height of the flagpole is 12.4 meters and the altitude of the balloon is 29.1 meters

See attachment for the diagram, when redrawn

Start by calculating the length AB using the following tangent function

tan(22) = BC/AB

This gives

tan(22) = 9/AB

Make AB the subject

AB = 9/tan(22)

Evaluate the quotient

AB = 22.3

The length DB is then calculated using:

tan(9) = DB/AB

This gives

tan(9) = DB/22.3

Make DB the subject

DB = 22.3 * tan(9)

Evaluate

DB = 3.35

The height of the flagpole is then calculated as:

Height = DB + BC

This gives

Height = 3.35 + 9

Evaluate

Height = 12.35

Approximate

Height = 12.4

Hence, the height of the flagpole is 12.4 meters

The diagram that illustrates the scenario is added as an attachment

Calculate the value of y using the following tangent functions

tan(57) = x/y and tan(72) = (15 + x)/y

Make y the subject in tan(57) = x/y and tan(72) = (15 + x)/y

y = x/tan(57) and y = (15 + x)/tan(72)

Substitute y = x/tan(57) in y = (15 + x)/tan(72)

x/tan(57) = (15 + x)/tan(72)

Evaluate the tangent ratios

x/1.5 = (15 + x)/3.1

Cross multiply

3.1x = 22.5 + 1.5x

Evaluate the like terms

1.6x = 22.5

Divide by 1.6

x = 14.1

The altitude of the balloon is then calculated as:

Altitude = 14.1 + 15

Altitude = 29.1

Hence, the altitude of the balloon is 29.1 meters

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The perimeter of a given shape implies the sum of all its sides. While the area of a given shape is the total value of space it would cover on a 2-dimensional plane.

The perimeter of the shape is 104 cm.

The area of the shape is 640 [tex]cm^{2}[/tex].

The perimeter of a given shape implies the sum of all its length of sides., such that the value of each individual side is summed to a total value.

The area of a given shape is the total value of space it would cover on a 2-dimensional plane. The area of shapes depends on the type of shape.

In the given question, the given shape has 12 sides. Some of these sides can sum up to a given length as shown in the diagram.

So that;

perimeter = 2 + 32 + 10 + 10 + 2 + 32 + 8 + 8

                 = 104 cm

Thus, the perimeter of the shape is 104 cm

ii. The area of the shape = length x width

                                         = 32 x 20

                                         = 640 [tex]cm^{2}[/tex]

Therefore, the area of the given shape is 640 [tex]cm^{2}[/tex].

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Answer:

c = 15

Step-by-step explanation:

expand the left side and compare with like terms on the right side

2x(4x + 5) + 3(4x + 5) ← distribute parenthesis

= 8x² + 10x + 12x + 15 ← collect like terms

= 8x² + 22x + 15

compare to ax² + bx + c

then c = 15

Triangles DEF and JKL can be proven to be congruent triangles based on:

C. ASA

E. AAS

F. LA

The ASA congruence theorem states that if two triangles that are have two pairs of corresponding congruent angles and a pair of corresponding included congruent sides, then both triangles are congruent to each other.

The LA congruence theorem states that two right triangles are congruent if they have a pair of congruent legs and a pair of congruent angles that are corresponding to each other.

The AAS congruence theorem states that two triangles with two pairs of congruent angles and a pair of congruent non-included sides are congruent.

From the image given, triangles DEF and JKL can be proven to be congruent triangles using the LA, AAS, and ASA congruence theorems.

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Multiply 9 with 9, and we get:

9 × 9 = 81

Multiply 10 with 10, and we get:

10 × 10 = 100

We get the final result as:

Hope this helps :)

The value of [tex](102)^3[/tex] exists 1061208.

Let us rewrite [tex](102)^3[/tex] as [tex](100+2)^3[/tex]

Now utilizing the identity [tex](a+b)^3=a^3+b^3+3ab(a+b)[/tex], we get

a = 100 and b = 2 then substitute the values of a and b then

[tex](100+2)^3=100^3+2^3+[(3\times100\times2)(100+2)][/tex]

= 1000000 + 8 + (600 × 102)

= 1000000 + 8 + 61200

= 1061208

Hence, [tex](102)^3=1061208[/tex]

Therefore, the value of [tex](102)^3[/tex] exists 1061208.

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Considering the graph of the velocity of the car, it is found that the interval in which it was stopped at a traffic light was:

Between 3 and 4 minutes.

When a car is stopped at a traffic light, the car is not moving, that is, it's velocity is of zero.

In this problem, the graph gives the velocity as a function of time, and it is at zero between 3 and 4 minutes, hence the interval in which it was stopped at a traffic light was:

Between 3 and 4 minutes.

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Answer:

First answer lol

Step-by-step explanation:

is the domain by any chance x ≥-2?

6) For the inverse to be a function, f(x) needs to be one to one. To accomplish this, restrict the domain to one side of the axis of symmetry

7) The y-intercept of the inverse is when x=0. This means we want to find when f(x)=0.

[tex]4(1/3)^x = 16 \\ \\ (1/3)^x= 4 \\ \\ x=\log_{1/3}(4) \approx -1.26[/tex]

The number which is express in each of the models as given in the image attached to the task content are as follows;

a). 1.37

b). 1.37

c). 1.37.

It follows from the task content that the models describe that One flat represents 1 whole, One rod represents 1 tenth and one unit represents 1 hundredth.

It therefore follows from the task content that in each of the models, the algebraic sum of flat(s), rods and units as the case may be results in the value; 1.37 as the utmost number represented by the models.

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Answer:

Below in bold.

Step-by-step explanation:

9t^2 - u^2     (the difference of 2 squares)

= (3t - u) (3t + u).

2c - 4d - pc + 2pd

= 2(c - 2d) - p(c - 2d)

c -2d is common to both parts so the factors are:

(2 - p)(c - 2d)

If the vertices of parallelogram ABCD is A(-6,-4),B(0,-4),C(3,4),D(-3,4) ,then the area of parallelogram ABCD will be 48 square units.

Given that the vertices of parallelogram ABCD is A(-6,-4),B(0,-4)

,C(3,4),D(-3,4).

We are required to find the area of parallelogram ABCD.

Let the point of intersection of height of parallelogram from point A is point E.

When we see the graph on which the parallelogram then we will be able to know that point E has coordinates of (-3,-4).

Area of parallelogram=Base*Height

=AB*DE

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

=[tex]\sqrt{64}[/tex]

=8 units

AB=[tex]\sqrt{(-4+4)^{2} +(0+6)^{2} }[/tex]

=[tex]\sqrt{36}[/tex]

=6 units

Area=6*8

=48 square units.

Hence if the vertices of parallelogram ABCD is A(-6,-4),B(0,-4),C(3,4),D(-3,4) ,then the area of parallelogram ABCD will be 48 square units.

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Answer:

x=1

Step-by-step explanation:

2/3(9x-6) = 1/4(12-4x)

We want to solve for x

Distribute

6x-4=3-x

Add x to each side

6x-4+x = 3-x+x

7x-4 = 3

Add 4 to each side

7x-4+4 = 3+4

7x=7

Divide by 7

7x/7 = 7/7

x=1

Answer:

x = 1

Step-by-step explanation:

[tex]\frac{2}{3}[/tex] (9x - 6) = [tex]\frac{1}{4}[/tex] (12 - 4x) ← distribute parenthesis on both sides

6x - 4 = 3 - x ( add x to both sides )

7x - 4 = 3 ( add 4 to both sides )

7x = 7 ( divide both sides by 7 )

x = 1

Answer:

Exact form: 78√2 - 17√3 / 54

Decimal form: 1.49747766

Step-by-step explanation:

Rationalize and simplify the expression.

Answer:

Assunming that the equation is y = -16x² +85x, I suggest Dario find a new profession.  He kicks the ball 133 feet high, but it only travels 2.7 feet downfield at that point.  It will have travelled 2*2.7 feet or 5.4 feet horizontal when it returns to ground.

Step-by-step explanation:

We can answer the question of how hiogh and far the ball travels (in feet) by either of two methods.  The first is to differentiate the equation and set it equal to 0, and the second is the graph it and look for the vertex and x intercept.

Differentiate

y = -16x² +85x

The first derivative produces an equation that gives us the slope of the line at any point x.  At the ball's top height, it stops and reverses direction, a point at which the slope is zero.

y = -16x² +85x

d(y)/d(x) = -32x + 85

0 = -32x + 85

32x = 85

x = 2.66 feet horizontal distance when the ball reaches its peak.

At x = 2.66, y is 112.9 feet high

When the ball returns, it adds amnother 2.66 feet to the horizontal distance, for a total of 5.4 feet.

Graph:

See attached plot of the function.

Horizontal distance is 2.66 feet and height is 133 feet. The x-intercept is at 5.4 feet.

After all that, the ball only travelled downfield (we hope downfield) a total of 5.4 feet.

The volume of the cone is  84.9 km³

Volume of a cone = 1 / 3 πr²h

where

Therefore,

radius = 3 km

height = √9.5² - 3²

height = √81.25

height = 9.01387818866

height = 9.014 km

Volume of a cone = 1 / 3 × 3.14 × 3² × 9.014

volume of the cone = 254.732197612 / 3

volume of the cone = 84.9107325372

volume of the cone = 84.9 km³

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Answer:

4

Step-by-step explanation:

h(x) = -1/3x+2 where we need to find -4h(9)

h(9): x = 9

h(x) = -1/3(9) + 2

h(x) = -3 + 2

h(x) = -1

-4h(9) is -4h(x):

-4(-1) = 4

The first five terms of the sequence are 1/5, 2/5, 3/5,4/5, 1

Recursive functions are functions that is used to determine the next term of a given sequence giving the common difference.

Given the recursive function shown below;

f(1) = 1/5

f(n) = f(n-1) + 1/5

For the second term;

f(2) = f(1) + 1/5

f(2) = 1/5 + 1/5

f(2) = 2/5

For the third term;

f(3) = f(2) + 1/5

f(3) = 2/5 + 1/5

f(3) = 3/5

For the fourth term;

f(4) = f(3) + 1/5

f(4) = 3/5 + 1/5

f(4) = 4/5

For the fifth term;

f(5) = f(4) + 1/5

f(5) = 4/5 + 1/5

f(5) = 5/5 = 1

Hence the first five terms of the sequence are 1/5, 2/5, 3/5,4/5, 1

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a. log₈8 = 1

b. log₇6/5

c. log₉3¹

1. log₈ 2 * 4 would produce an integer

= log₈8 = 1

The output is an integer

2. log₇6/5 would give us an irrational number

= log₇1.2

This would give us an irrational number

3. log₉3¹ would give us a rational number

= log₉9^[tex]^\frac{1}{2}[/tex] = 1/2 log⁹9

= 1/2

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The value of the solution is 3π/2.

What is a trigonometric equation?

An equation involving one or more trigonometric ratios of unknown angles is called a trigonometric equation.

tan x/2 = -1

tanx/2 = tan(-π/4)

tanx=tanФ

⇒ The general equation of tanx=tanФ is

⇒ x=nπ+Ф

x/2=nπ+(-π/4)

at n=0

x/2=-π/4

x=-π/2

at n=1

x/2=π-π/4

x/2=3π/4

x=3π/2

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Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Questions: Which value is a solution for the equation tan x/2 = -1?

A. 5pi/4

B. 7pi/4

C. 3pi/4

D. 3pi/2

Answer:

9/41

Step-by-step explanation:

Cosine represents adjacent / hypotenuse.

When A is the reference angle, AB is the adjacent side (9) and AC is the hypotenuse (41).

9/41 is already simplified.

Answer:43.289

Step-by-step explana

The term "altitude" is the same as "height of a triangle". It is perpendicular to the base. Since we can rotate the triangle to have any side be horizontal, there are effectively 3 possible bases. Hence, there are 3 heights. It all depends how you look at it.

Let h1, h2, and h3 be the three altitudes or heights.

Without loss of generality, we'll focus on the first two heights h1 and h2. Their respective bases are b1 and b2.

If we use b1 as the base, then the area is...

area = 0.5*base*height = 0.5*b1*h1

Similarly, the other base gives the area of:

area = 0.5*b2*h2

------------------------

Since both formulas refer to the same area (because we're working with the same triangle), we can set the expressions equal to one another

0.5*b1*h1 = 0.5*b2*h2

b1*h1 = b2*h2

Let's see what happens when b1 = b2, so,

b1*h1 = b2*h2

b1*h1 = b1*h2

b1h1 - b1h2 = 0

b1(h1 - h2) = 0

b1 = 0 or h1 - h2 = 0

b1 = 0 or h1 = h2

If the bases b1 and b2 were equal, then either those bases must be 0 which isn't possible, or the altitudes must be equal. However, the initial premise is that the heights must be different from one another.

Therefore, the bases b1 and b2 can't be the same length.

We could follow the same steps and logic to conclude that if the altitudes h1 and h3 were different, then the bases b1 and b3 can't be the same. Similarly, we would conclude that b2 and b3 can't be the same. This is where the "without loss of generality" kicks in.

In other words, we only need to focus on one subcase to extend the logic to the other cases, without having to actually do every single step. That would be a bit tedious busywork.

In conclusion, we've shown that if the heights are different, then their respective bases must be different. This leads to wrapping up the proof that we have a scalene triangle.

Side note: I used an indirect proof or proof by contradiction. I assumed that a non-scalene triangle was possible and it led to a contradiction of h1 = h2.

Answer:

= – 5 – 7

Step-by-step explanation:

= –5 – 7

Answer:

See below.

Step-by-step explanation:

Converse

The converse of a statement is formed by switching the hypothesis and the conclusion.

Given statement:  If n is an even integer, then 2n + 1 is an odd integer.

Converse:  If 2n + 1 is an odd integer, then n is an even integer.

Given statement:  If a transversal intersects two parallel lines, then each pair of corresponding angles is equal.

Converse:  If a transversal intersects two lines such that each pair of corresponding angles is equal, then the two lines are parallel to each other.

Given statement:  If each pair of opposite sides of a quadrilateral is equal, then the quadrilateral is a parallelogram.

Converse:  If a quadrilateral is a parallelogram, then each pair of opposite sides of the quadrilateral is equal.

Given statement:  If the decimal expansion of a real number is terminating, then the number is rational.

Converse:  If a real number is rational, then the decimal expansion of the number is terminating.

A sky wheel is a mechanical device that has a shape of a circle divided into a given number of equal sectors. Thus, the measure of each central angle required in the question is [tex]8.6^{o}[/tex].

A sky wheel is a mechanical device that has a shape of a circle divided into a given number of equal sectors. Thus each sector has an equal central angle. Since the sum of the internal angles of a circle is [tex]360^{o}[/tex].

From the given question, it has been stated that the sky wheel has 42 glass-enclosed gondolas. This implies that the sky wheel has been divided into 42 equal sectors.

Therefore,

the measure of each central angle = [tex]\frac{360^{o} }{n}[/tex]

where n represents the number of gondolas (42).

Thus,

the measure of each central angle between gondolas cars= [tex]\frac{360}{42}[/tex]

                                        = 8.5714

The measure of each central angle between gondolas cars is approximate [tex]8.6^{o}[/tex].

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