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An ant is standing at the centers of a perfectly circular plate. If the ant crawled in a straight line, he would have to crawl 6 inches to reach the edge of the plate. How many inches would he crawl if he crawled a full circle around the edge of the plate?

Based on the knowledge of trigonometric expressions and properties of trigonometric functions, the value of the sine function is equal to - √731 / 30.

Herein we must make use of trigonometric expressions and properties of trigonometric functions to find the right value. According to trigonometry, both cosine and sine are negative in the third quadrant. Thus, by using the fundamental trigonometric expression (sin² α + cos² α = 1) and substituting all known terms we find that:

[tex]\sin \theta = -\sqrt{1 - \cos^{2}\theta}[/tex]

[tex]\sin \theta = - \sqrt{1 - \left(-\frac{13}{30} \right)^{2}}[/tex]

sin θ ≈ - √731 / 30

Based on the knowledge of trigonometric expressions and properties of trigonometric functions, the value of the sine function is equal to - √731 / 30.

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The total amount of Chandra's investments after 8 years is $110.03

The formula for calculating the compound interest is expressed as;

A = P(1+r/n)^nt

where

P is the amount invested = $75

r is the rate. = 0.048

t is the time =8years

n = 12 (monthly)

Substitute

A = 75(1+0.048/12)^96
A = 75(1.467)
A = 110.03

Hence the total amount of Chandra's investments after 8 years is $110.03

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The graph above could be a graph of this exponential function: A. F(x) = 3.(1.2)^x.

Mathematically, the standard form of an exponential function is given by:

F(x) = ab^x

Where:

As a general rule, f(x) is an increasing function when b is greater than 1 (b > 1) and f(x) is a decreasing function when b is less than 1 (b < 1)

By critically observing the given graph, we can deduce that the initial value (a) is 3 and it's an increasing function (b > 1).

F(x) = 3.(1.2)^x

Thus, the graph above could be a graph of this exponential function F(x) = 3.(1.2)^x.

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Answer:

5/9

Step-by-step explanation:

4+5=9 and there are 5 boys

20 years is the answer.

A= R(1+r)^ t

A-415    

R=230

r=3%

415=230 (1+3%)^ t

t=log1.03  315/230

t=19.89 (use calculator)

David will invest at least 20 years.

An investment is a dedication of an asset to achieve an increase in value over a period of time. Investing requires the sacrifice of current assets such as time, money and effort. In finance, the purpose of an investment is to generate a profit on the invested asset

The most common example of an investment type. Investment is generally what you want to use in the future with the aim of generating regular cash flow or increasing the value of something over time so that you can sell it at a higher price than you purchased.

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Percentage for lakeside is 38%

Percentage for Jungle is 26%

Percentage for Desert is 18%

Percentage for Coast is 12%

Percentage for Prairie is 6%

To determine the percentage, divide the given value by the total number and multiply by 100

Total  = 24000

Percentage for lakeside = [tex]\frac{9120}{24000}[/tex] × 100

% of lakeside = [tex]0. 38[/tex] × 100 = 38%

Percentage for Jungle = [tex]\frac{6240}{24000}[/tex] × 100

% of Jungle = [tex]0. 26[/tex] × 100 = 26%

Percentage for Desert = [tex]\frac{4320}{24000}[/tex] × 100

% of Desert = [tex]0. 18[/tex] × 100 = 18%

Percentage for Coast = [tex]\frac{2880}{24000}[/tex] × 100

% of coast = [tex]0. 12[/tex] × 100 = 12%

Percentage for Prairie = [tex]\frac{1440}{24000}[/tex] × 100

% of Prairie = [tex]0. 06[/tex] × 100 = 6%

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Combining the like terms, the simplified polynomials are given as follows:

a) 4x² - 14x + 17

b) -5x² - 20x + 8

Polynomials are simplified combining the like terms, that is, adding these numbers with the same variable.

Item a:

4(x - 2)(x + 1) - 5(2x - 5)

Applying the distributive property:

4(x² - x - 2) - 10x + 25

4x² - 4x - 8 - 10x + 25

Combining the like terms:

4x² - 4x - 10x - 8 + 25

4x² - 14x + 17

Item b:

-5(x + 2)² + 28

-5(x² + 4x + 4) + 28

-5x² - 20x - 20 + 28

-5x² - 20x + 8

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The factorization that could represent the number of water bottles and weight of each water bottle is 12(5x^2 + 4x + 2). Option B

The term factorization has to do with the process of obtaining common factors in an expression. It involves dividing each term in the expression with a factor that is common to all the terms in the expression.

The factorization that could represent the number of water bottles and weight of each water bottle is 12(5x^2 + 4x + 2).

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Missing parts;

Mara carried water bottles to the field to share with her team at halftime. The water bottles weighed a total of 60x2 + 48x + 24 ounces. Which factorization could represent the number of water bottles and weight of each water bottle? 6(10x2 + 8x + 2) 12(5x2 + 4x + 2) 6x(10x2 + 8x + 2) 12x(5x2 + 4x + 2)

Answer:

  (c)  25/4

Step-by-step explanation:

A perfect square trinomial is obtained by "completing the square." The constant in a perfect square trinomial is the square of half the x-coefficient.

A "perfect square trinomial" is the square of a binomial.

  (x +a)² = x² +2ax +a²

Of note here is that the constant (a²) is the square of half of the x-term coefficient:

  ((2a)/2)² = a²

The given expression (x² +5x) has an x-term coefficient of 5. The square of half that is ...

  (5/2)² = 25/4

The constant that must be added to make x² +5x into a perfect square trinomial is 25/4.

  (x² +5x) +25/4 = x² +5x +25/4 = (x +5/2)²

The NBA league exhibits more competitive balance.

The chance that each team in a league has of winning the title is referred to as competitive balance. The championship would be won by each team on a regular basis in an ideal competitive environment. In contrast, if there was no balance between the two types of competition, the same team would consistently prevail.

Competitive balance is often regarded as a desirable trait because too much predictability makes fans of the lesser franchises angry and fans of the defending champions complacent, which lowers interest in the sport as a whole.

The "Noll-Scully" measure is the competitive balancing metric that is most frequently used in sports. The winning percentage of each league team's standard deviation (SD) is used to compute it. The SD is then divided by what it would be if all teams had equal talent and the outcomes were entirely random.

For NBA team, competitive balance = 0.134/32*82 = 0.343

For EPL team, competitive balance = 0.158/20*38 = 0.30

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The inverse function of [tex]A(b) = 12 \cdot \frac{b + 9}2[/tex] is b(a) = a/6 - 9

The function is given as:

[tex]A(b) = 12 \cdot \frac{b + 9}2[/tex]

Divide 12 by 2

[tex]A(b) = 6 \cdot (b + 9)[/tex]

Rewrite the function as

[tex]a = 6 \cdot (b + 9)[/tex]

Divide both sides by 6

a/6 = b + 9

Subtract 9 from both sides

b = a/6 - 9

Express as a function

b(a) = a/6 - 9

Hence, the inverse function of [tex]A(b) = 12 \cdot \frac{b + 9}2[/tex] is b(a) = a/6 - 9

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Answer:

Step-by-step explanation:

The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Rigid transformation is a transformation that preserves the shape and size of a figure such as translation, reflection and rotation. Dilation preserves only the shape.

Polygon ABCD has vertex at A(1, 1), B(2, 3), C(5, 4), and D(4, 2).

Slope of CD = (2 - 4) / (4 - 5) = 2

Polygon ABCD is dilated by a scale factor of 8 with the origin resulting in the image A′B′C′D′.

Slope of C'D' = slope of CD (because preserves shape) = 2

The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2

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The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2

What is transformation?

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Rigid transformation is a transformation that preserves the shape and size of a figure such as translation, reflection and rotation. Dilation preserves only the shape.

Polygon ABCD has vertex at A(1, 1), B(2, 3), C(5, 4), and D(4, 2).

Slope of CD = (2 - 4) / (4 - 5) = 2

Polygon ABCD is dilated by a scale factor of 8 with the origin resulting in the image A′B′C′D′.

Slope of C'D' = slope of CD (because preserves shape) = 2

The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2

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Answer:

The triangles are Congruent for the same reason as the answer above

Step-by-step explanation:

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here's the explanation ~

Zeros or roots of a function is the value of independent variable (usually x - coordinate or absicca) where the value of dependent variable (y - coordinate or ordinate) is 0.

That is :

The point where it cuts the x - axis, it has an x - coordinate = -6

Therefore, we can conclude that The zero of given function is -6

Answer:

x = -6.

Step-by-step explanation:

It is where the graph cuts the x-axis  (where the function is zero).

That is -6.

Answer:

Step-by-step explanation:

hello here is an solution

The domain and range are  (-∞,1/6)∪ (1/6, -∞), {x/x≠1/6} and  (-∞,-7/6)∪ (-7/6, ∞), {y/y≠-7/6} respectively.

A relation is a function if it has only One y-value for each x-value.

The given function is f(x)=(x+1)/6x+7

Let f(x)=y

(x+1)/6x+7=y

x+1=y(6x+7)

x+1=6xy+7y

6xy-x=7y-1

x(6y-1)=7y-1

Divide both sides by 6y-1

x=7y-1/6y-1

So f⁻¹(x)=1-7x/6x-1

The domain is (-∞,1/6)∪ (1/6, -∞), {x/x≠1/6}

The range is (-∞,-7/6)∪ (-7/6, ∞), {y/y≠-7/6}

Hence, the domain and range are  (-∞,1/6)∪ (1/6, -∞), {x/x≠1/6} and  (-∞,-7/6)∪ (-7/6, ∞), {y/y≠-7/6} respectively.

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Answer:

B

Step-by-step explanation:

Let t and d be their ages now.

2 years ago, their ages were t - 2 and d  2.

Now, Tyler is 3 years older than David: t = d + 3

2 years ago, Tyler was 4 times as old as David: t - 2 = 4(d - 2)

The system of equations is:

t = d + 3

t - 2 = 4(d - 2)

Answer: B

Answer:

D

Step-by-step explanation:

The length of each part of a the line segment is 1.6 cm if a line segment of length 6.4 cm and divided it in to 4 equal parts

An equation is an expression that shows the relationship between two or more number and variables.

The line segment has a length of 6.4 cm. Hence:

Dividing into 4 equal parts = 6.4 / 4 = 1.6 cm

The length of each part of a the line segment is 1.6 cm if a line segment of length 6.4 cm and divided it in to 4 equal parts

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Answer:

the following 3 equations are equivalent :

• x + 1 = 4

• 2 + x = 5

• -5 + x = -2

Step-by-step explanation:

2 + x = 5

x + 1 = 4

9 + x = 6

x + (- 4) = 7

-5 + x = - 2

Let’s take this equation :

x + 1 = 4

=======

By Adding 1 to both sides of the equation we get :

x + 1 + 1 = 4 + 1

⇔ x + 2 = 5

⇔ 2 + x = 5

Then the equations x + 1 = 4  and 2 + x = 5 are equivalent.

…………………………………………………………………

On the other hand ,if we subtract 6 from both sides

of the equation x + 1 = 4  we get :

x + 1 - 6 = 4 - 6

⇔ x - 5 = -2

⇔ -5 + x = -2

Then the equations x + 1 = 4  and -5 + x = -2 are equivalent.

Answer:

A. 2 + x = 5

B. x + 1 = 4

E. -5 + x = -2

Step-by-step explanation:

right on edg, hope it helps ya'll.

The number of visitors to the homepage of an online magazine in the year 2005 is 3527

An equation is an expression that shows the relationship between two or more number and variables.

Let y represent the total number of visitors x years since 2000. Hence:

y = 1100.74x - 1976.47

In the year 2005 (x = 5):

y = 1100.74(5) - 1976.47 = 3527.23

The number of visitors to the homepage of an online magazine in the year 2005 is 3527

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Answer:

  (2)  A=4, B=0, C=9 . . . (4x = 9)

Step-by-step explanation:

A linear equation in standard form has mutually prime integer coefficients with a positive leading coefficient.

The values that would be the appropriate values for an equation to be in standard form (Ax + By = C) is A = 4, B = 0 and C = 9.

The linear equation is the equation which has the coefficient as the mutual prime numbers and the coefficient must be the positive leading coefficient.

From the choices,

Therefore, the values that would be the appropriate values for an equation to be in standard form as it lead to positive leading coefficient and mutual prime is A = 4, B = 0 and C = 9.

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If the radius of sector is 12 centimeters and angle of 65 degrees then the arc's length is 13.6 cm.

Given a sector has a radius of 12 cm and an angle 65 degrees.

We have to calculate arc's length.

We know that arc's length is equal to Θr where Θ is in radians.

We have been given angle in degrees ,so we have to convert degrees in radians.

Angle=65*π/180=13π/36

length of arc =Θr

Putting the values in the formula above :

length =13π/36*12

=13*3.14/3

=40.82/3

=13.6

Hence if the radius of sphere is 12 cm and angle 65 degrees then the length of arc of sphere is 13.6 cm.

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Answer:

626.7 [tex]cm^{2}[/tex]

Step-by-step explanation:

Consider the figure as a circle with radius 7.5 and a rectangle with width 30 and length 15.

CIRCLE

A = pi*r*r = pi*7.5*7.5 = 56.25pi =176.7

RECTANGLE

A = l*w = 15*30 = 450

176.7 + 450 = 626.7 [tex]cm^{2}[/tex]

Answer: 626.7cm^2

Step-by-step explanation:

30 * 15 = 450

area of circle = πr^2

r = 15/2 = 7.5

[tex]7.5^2=56.25*pi=176.7[/tex]

450+176.7 = 626.7

Answer:

[tex]\sf Tan \ D = \dfrac{4}{3}[/tex]

Step-by-step explanation:

Trigonometry ratios:

       [tex]\sf \boxed{\bf \tan \ D =\dfrac{opposite \ side \ of \ \angle \ D}{adjacent \ side \ of \ \angle D}}[/tex]

                   [tex]\sf =\dfrac{BC}{DC}\\\\ =\dfrac{32}{24}\\\\=\dfrac{4}{3}[/tex]

One can easily convert the temperature using temperature conversion formula given below

K = [tex]\frac{5(F - 32)}{9} + 273.15[/tex]

where F = degrees in Fahrenheit

K = degrees in Kelvin

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The required equation is 135 + 9x > 250.

The number of lawns Ed must mow is assumed to be x.

The amount Ed charges for each lawn he mows is $9.

Thus, the total amount Ed earns by mowing x lawns = $9x.

The savings which Ed has is $135.

Thus, the total amount Ed will have to spend can be written as the expression, $(135 + 9x).

The cost of the video game is given to be $250.

We are asked to write an equation, that can be used to find the number of lawns Ed mow, that is x so that the amount Ed has will be more than the amount he needs to buy the video game.

This can be shown as the equation:

Total amount Ed has > Cost of the video game,

or, 135 + 9x > 250.

Thus, the required equation is 135 + 9x > 250.

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Answer:

70

Step-by-step explanation:

the 30/100 of 100 is 30

So 100-30=70

Answer:

70kg

Step-by-step explanation:

30% of 100kg is

--> 100 x 30/100 which is 30kg.

If you want to decrease 100kg by 30%, you can take away 30kg from 100kg.

--> 100 - 30 = 70

So 70kg is the remainder.

A $2.00 base fare charge, and per-mile, and per-minute rates related as follows; 3•x + 7•y = 6.5 and 7•x + 14•y = 14, give the distance traveled in the third ride as 4.5 miles

The base fare = $2.00

Let x represent the per-mile rate, and let y represent the per-minute rate, we have;

The cost of Ryan's first taxi ride = $8.50

Distance traveled in the first ride = 3.0 miles

Time taken during the first ride = 7 minutes

Therefore;

2 + 3•x + 7•y = 8.5

Which gives;

3•x + 7•y = 8.5 - 2 = 6.5

Distance traveled in the second ride = 7.0 miles

Duration of the second ride = 14 minutes

The second ride cost = $16.00

Therefore;

2 + 7•x + 14•y = 16

Which gives;

7•x + 14•y = 16 - 2 = 14

Solving the above simultaneous equations by multiplying equation (1) by 2 then subtracting the result from equation (2) gives;

(7•x + 14•y) - 2 × (3•x + 7•y) = 14 - 2×6.5 = 1

x = 1

3•x + 7•y = 6.5

7•y = 6.5 - 3•x

7•y = 6.5 - 3×1 = 3.5

y = 3.5/7 = 1/2 = 0.5

Duration of the third taxi ride = 10 minutes

Cost of the third ride = $13.50

Therefore;

2 + 1×a + 10×y = $13.50

Where a is the distance traveled during the third ride, we have;

2 + 1×a + 10×0.5 = $13.50

2 + a + 5 = 13.5

a = 13.5 - 2 - 7 = 4.5

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