Solving quadratic equations is one of the main topics of this unit. Some quadratic equations can be solved with only one method, some can be solved with multiple methods, and some can’t be solved at all. Think about a task in your daily life that can be accomplished in a variety of ways. How do you decide the best course of action for accomplishing that task? How is this process like choosing a method for solving a quadratic equation that can be solved in multiple ways?

The slope of the new road is zero.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Take points from the Graph (5, 0) and (5, 4).

Slope of a line = m = tanθ

where θ is the angle made by the line with the x−axis.

For a line parallel to y−axis ,θ= π/2.

​

∴m = tan π/2 = undefined

The new road will therefore have 0° of inclination if it is perpendicular to D street because if they are perpendicular and D street is vertical, the new road is level and has 0° of inclination.

An horizontal line now has zero slope.

The new road has a zero slope as a result.

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Answer:

Option 3

Step-by-step explanation:

The slope is \(\frac{-2-6}{5-1}=-2\).

The equation of the line through \((x_1, y_1)\) with slope \(m\) is \(y-y_1=m(x-x_1)\).

y-6=-2(x-1) is the equation is a point slope form equation for line AB

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

point A, with coordinates (1, 6), and point B, with coordinates (5, -2)

m=-2-6/5-1

m=-8/4

=-2

So slope is -2.

The point slope intercept of line is

y-y₁=m(x-x₁)

y-6=-2(x-1)

Hence y-6=-2(x-1) is the equation is a point slope form equation for line AB

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Answer:

They are equivalent

Step-by-step explanation:

If you divide 36 and 45 by 9, you get 4 and 5

Answer:

a) 12d + 9

c) 30d + 12

d) 207

Explanation:

First, we need to write an expression for each accessory.

Since d is the number of boxes, we get:

Turbo Jet Pack. Six times the number of boxes plus seven

6d + 7

X-Ray Vision Glasses. Five less than two times the number of boxes

2d - 5

Invisible Shield. One more than ten times the number of boxes

10d + 1

Part A.

Then, the Laser Saber has sales equal to 1.5 times the difference of the number of Invisible Shields and X-Ray Vision Glasses.

1.5((10d + 1) - (2d - 5))

Because 10d + 1 is the number of invisible shields and 2d - 5 is the number of X-Ray Vision Glasses.

Now, we can simplify the expression as

1.5(10d + 1 - 2d + 5)

1.5(8d + 6)

1.5(8d) + 1.5(6)

12d + 9

Part C.

Then, we need to add all the expressions before to get:

(6d + 7) + (2d - 5) + (10d + 1) + (12d + 9)

(6d + 2d + 10d + 12d) + (7 - 5 + 1 + 9)

30d + 12

Therefore, the total number of all four accessories is 30d + 12

Part D.

To know how many accessories did it sell, first, we need to find how many dozens are 78 action figures, so

78/12 = 6.5

Therefore, they sold 6.5 boxes of the action figure. Now we can find the number of accessories sold, replacing d with 6.5 in the expression of part C, so

30d + 12

30(6.5) + 12

195 + 12

207

Then, they sold 207 accessories.

It cannot be determined. At least one other point on the line is needed to determine if x is proportional to y

Given data ,

A point on a straight line has an x-coordinate of 3 and a y-coordinate of 6

Now , A single point on a straight line does not define the connection between x and y. We must evaluate the connection between x and y for several places on the line in order to establish if x is proportional to y.

As a result, the relationship between x and y cannot be inferred only from the supplied location (3, 6). To establish the proportionality between x and y, at least one more point on the line is required

Hence , the equation of line is solved

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Equation employing the slope-intercept method for two points

The slope-intercept version of the equation may be used to calculate the two-point Y-intercept.

The shape of a point-slope is\(\mathbf{Y-Y_{1} = m(X-X_{1})}.\)

Steps to find the y-intercept with two ordered pairs?

Determine the slope using two points.

\(Slope = \frac{Y_{2}-Y_{1}}{X_{2}-X_{1}} = \frac{Rise}{Run} = \frac{\bigtriangleup Y}{\bigtriangleup X}\)

As an illustration, two points are (3, 5) and (6, 11)

Slope = \(\frac{Y_{2}-Y_{1}}{X_{2}-X_{1}} = \frac{11 - 5}{6 - 3} = \frac{6}{3} = 2\)

In the slope-intercept form of the equation, substitute the slope(m).

\(\\y = mx+b \\y = 2x+b\)

Either point may be substituted in the equation. You may either use (3,5) or (6,11).

\(\\y = 2x+b \\5 = 2(3)+b\)

Find the answer to the equation for b, the line's y-intercept.

\(\\5 \ \ \ = 2(3) + b \\5 \ \ \ = 6 + b \\\underline{-6\ = -6 \ \ \ \ \ \ \ } \\-1 = b\)

Substitute b,  into the equation.

\(\\y = 2x + b \\y = 2x - 1\)

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Option D has a non-zero component function in the y-direction and a zero component function in the x-direction.

The vector field →F is normal to the line x=2, so it must be tangent to the line y-axis at every point. This means that the component function of →F in the x-direction should be 0 and the component function of →F in the y-direction should be non-zero.

Option D has a non-zero component function in the y-direction and a zero component function in the x-direction, so it satisfies the given property. Therefore, the answer is: D. →F=(0,y)

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Answer:

creo que es 4cm y la otra B no se por que esta en ingles ok

Answer:

x = 9

Step-by-step explanation:

Unfortunately you didn’t provide the figure however we can use the picture below to work on:

from a property of the parallelogram (opposit angles) we know that angle 2 and 4 are equal in measure

then

5x - 28 = 3x - 10

then

5x - 3x = 28 - 10

then

2x = 18

then

x = 18/2

  = 9

Answer:

y=6x-8

Step-by-step explanation:

3x-2y=-4

3x^2-2y^2=-4^2

6x-y=8

y=6x-8

The two unit vectors orthogonal to vec(u) and vec(v) are ⟨4/sqrt(17), -3/(5sqrt(17)), 4/(5sqrt(17))⟩ and ⟨2/sqrt(21), -44/(5sqrt(21)), -83/(5sqrt(21))⟩.

The step-by-step process of finding the orthogonal unit vectors. First, we find the cross product of vec(u) and vec(v) by taking the determinant of the matrix formed by the components of the two vectors:

vec(u) x vec(v) = ⟨(4)(3) - (-2)(4), (-2)(0) - (1)(3), (1)(4) - (4)(0)⟩

              = ⟨12 + 8, 0 - 3, 4 - 0⟩

              = ⟨20, -3, 4⟩

Next, to obtain a unit vector, we divide the resulting vector by its magnitude:

Magnitude of vec(u) x vec(v) = sqrt((20)^2 + (-3)^2 + (4)^2)

                           = sqrt(400 + 9 + 16)

                           = sqrt(425)

                           = 5sqrt(17)

Unit vector orthogonal to vec(u) and vec(v) = (1/(5sqrt(17))) * ⟨20, -3, 4⟩

                                           = ⟨20/(5sqrt(17)), -3/(5sqrt(17)), 4/(5sqrt(17))⟩

                                           = ⟨4/sqrt(17), -3/(5sqrt(17)), 4/(5sqrt(17))⟩

To find another unit vector orthogonal to vec(u) and vec(v), we can take the cross product of vec(u) x vec(v) with one of the vectors, such as vec(u):

vec(u) x (vec(u) x vec(v)) = ⟨1,4,-2⟩ x ⟨20, -3, 4⟩

                          = ⟨4(4) - (-2)(-3), (-2)(20) - (1)(4), (1)(-3) - (4)(20)⟩

                          = ⟨16 - 6, -40 - 4, -3 - 80⟩

                          = ⟨10, -44, -83⟩

Again, we normalize this resulting vector to obtain a unit vector:

Magnitude of vec(u) x (vec(u) x vec(v)) = sqrt((10)^2 + (-44)^2 + (-83)^2)

                                       = sqrt(100 + 1936 + 6889)

                                       = sqrt(8925)

                                       = sqrt(9 * 25 * 105 / 9)

                                       = 5sqrt(21)

Unit vector orthogonal to vec(u) and vec(v) = (1/(5sqrt(21))) * ⟨10, -44, -83⟩

                                           = ⟨10/(5sqrt(21)), -44/(5sqrt(21)), -83/(5sqrt(21))⟩

                                           = ⟨2/sqrt(21), -44/(5sqrt(21)), -83/(5sqrt(21))⟩

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The two unit vectors orthogonal to vec(u) and vec(v) are ⟨4/sqrt(17), -3/(5sqrt(17)), 4/(5sqrt(17))⟩ and ⟨2/sqrt(21), -44/(5sqrt(21)), -83/(5sqrt(21))⟩.

The step-by-step process of finding the orthogonal unit vectors. First, we find the cross product of vec(u) and vec(v) by taking the determinant of the matrix formed by the components of the two vectors:

vec(u) x vec(v) = ⟨(4)(3) - (-2)(4), (-2)(0) - (1)(3), (1)(4) - (4)(0)⟩

             = ⟨12 + 8, 0 - 3, 4 - 0⟩

             = ⟨20, -3, 4⟩

Next, to obtain a unit vector, we divide the resulting vector by its magnitude:

Magnitude of vec(u) x vec(v) = sqrt((20)^2 + (-3)^2 + (4)^2)

                          = sqrt(400 + 9 + 16)

                          = sqrt(425)

                          = 5sqrt(17)

Unit vector orthogonal to vec(u) and vec(v) = (1/(5sqrt(17))) * ⟨20, -3, 4⟩

                                          = ⟨20/(5sqrt(17)), -3/(5sqrt(17)), 4/(5sqrt(17))⟩

                                          = ⟨4/sqrt(17), -3/(5sqrt(17)), 4/(5sqrt(17))⟩

To find another unit vector orthogonal to vec(u) and vec(v), we can take the cross product of vec(u) x vec(v) with one of the vectors, such as vec(u):

vec(u) x (vec(u) x vec(v)) = ⟨1,4,-2⟩ x ⟨20, -3, 4⟩

                         = ⟨4(4) - (-2)(-3), (-2)(20) - (1)(4), (1)(-3) - (4)(20)⟩

                         = ⟨16 - 6, -40 - 4, -3 - 80⟩

                         = ⟨10, -44, -83⟩

Again, we normalize this resulting vector to obtain a unit vector:

Magnitude of vec(u) x (vec(u) x vec(v)) = sqrt((10)^2 + (-44)^2 + (-83)^2)

                                      = sqrt(100 + 1936 + 6889)

                                      = sqrt(8925)

                                      = sqrt(9 * 25 * 105 / 9)

                                      = 5sqrt(21)

Unit vector orthogonal to vec(u) and vec(v) = (1/(5sqrt(21))) * ⟨10, -44, -83⟩

                                          = ⟨10/(5sqrt(21)), -44/(5sqrt(21)), -83/(5sqrt(21))⟩

                                          = ⟨2/sqrt(21), -44/(5sqrt(21)), -83/(5sqrt(21))⟩

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Answer:18/35

Step-by-step explanation: 6*3 = 18

7*5 = 35

18 /35

Answer: 18/35

Step-by-step explanation:

6*3=18

7*5=35

18/35

Answer:

9:11

Step-by-step explanation:

subtract the amount of girls to get the amount of boys then put it in ratio form in the order it is asked so it is 9:11

The exact distance between the planes after 2 hours, using the law of cosines:

d = sqrt((2 * 425)^2 + (2 * 530)^2 - 2 * 2 * 425 * 530 * cos(67° - 355°))

where d is the distance between the planes in miles.

To visualize the problem, imagine a coordinate plane with the origin at Raleigh-Durham Airport. Plane A's path can be represented as a line with a slope determined by its bearing of 355°, while Plane B's path can be represented by another line with a slope determined by its bearing of 67°.

To calculate the distance between the planes after 2 hours, we first need to determine their respective positions. Since Plane A is traveling at 425 mph, it would have covered a distance of 850 miles (425 mph * 2 hours). Similarly, Plane B would have covered a distance of 1060 miles (530 mph * 2 hours).

Next, we can calculate the coordinates of each plane using the distance and bearing information. Using trigonometry, we can determine the vertical and horizontal distances covered by each plane. Plane A's vertical distance would be 850 * sin(355°), and its horizontal distance would be 850 * cos(355°). Similarly, Plane B's vertical and horizontal distances would be 1060 * sin(67°) and 1060 * cos(67°), respectively.

Finally, we can use the coordinates of each plane to calculate the distance between them. This can be done using the distance formula: distance = sqrt((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of Plane A and Plane B, respectively.

By plugging in the calculated values, we can determine the distance between the two planes after 2 hours of flying.

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Answer:

27 = n - 3

Step-by-step explanation:

27 equals 3 less than a number n as an equation is:

27 = n - 3

Answer:

The correct option is -

Yes, because the Expected value is 1 and not negative which would imply that there is a chance of winning.

Step-by-step explanation:

Given - A bag contains 10 blue marbles, 3 yellow marbles, and 12 orange marbles. If a blue marble is drawn you win $10. If a yellow marble is drawn you win $15. if an orange marble is drawn you lose $10. it cost $1 to play.

To find - Should you play the game?

Formula used -

Expected value , E[x] = ∑x p(x)

where p(x) is the probability.

Proof -

Given that,

Total blue marbles in a bag = 10

Total yellow marbles in a bag = 3

Total orange marbles in a bag = 12

So,

Total number of marbles in a bag = 10 + 3 + 12 = 25

Now,

Probability of getting blue marble = \(\frac{10}{25}\)

Probability of getting yellow marble = \(\frac{3}{25}\)

Probability of getting orange marble = \(\frac{12}{25}\)

So,

Expected value , E[x] = ∑x p(x)

                                   = (10)( \(\frac{10}{25}\)) + (15)(\(\frac{3}{25}\)) + (-10)(\(\frac{12}{25}\))

                                   = \(\frac{100}{25} + \frac{45}{25} - \frac{120}{25}\)

                                   = \(\frac{100 + 45 - 120}{25}\)

                                   = \(\frac{25}{25}\)

                                   = 1

So,

Expected value = 1

So,

The correct option is -

Yes, because the Expected value is 1 and not negative which would imply that there is a chance of winning.

A confidence interval of 0.111 is not specific enough to interpret without more information about the context of the problem and the parameter being estimated.

A confidence interval is a range of values that is estimated to include an unknown parameter. The parameter is usually a mean or proportion and the range of values is estimated by using data from a sample.

A confidence interval of 0.111 expresses that the point estimate of the parameter (mean or proportion) falls within a range of values from 0.111 units below to 0.111 units above the point estimate.

The interpretation of the confidence interval depends on the context of the problem. For example, if the parameter is a mean of heights of all adult men in a population and the confidence interval is (175, 185), we would interpret this interval as follows:

we are 95% confident that the true mean height of all adult men in the population is between 175 and 185 centimeters long.

Another example: if the parameter is a proportion of registered voters who support a certain candidate and the confidence interval is (0.46, 0.54), we would interpret this interval as follows:

we are 95% confident that the true proportion of registered voters who support the candidate is between 46% and 54%.

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Answer:

Step-by-step explanation:

\(\sqrt{x-3} +5=x\\\sqrt{x-3} =x-5\\squaring ~both~sides\\x-3=x^2-10x+25\\x^2-10x-x+25+3=0\\x^2-11x+28=0\\x^2-7x-4x+28=0\\x(x-7)-4(x-7)=0\\(x-7)(x-4)=0\\x=7,4\)

put x=7 in the given equation

\(\sqrt{7-3} +5=7\\\sqrt{4} +5=7\\2+5=7\\7=7\)

which is true .

∴ x=7 is a solution of the given eq.

now put x=4 in the given eq.

\(\sqrt{4-3} +5=7\\1+5=7\\6=7\\\)

which is not true.

∴x=4 is an extraneous solution.

Answer:

None of them 180% would be written as 9/5

Step-by-step explanation:

14/5=280%

8/5=160%

1 1/8=112.5%

18/100=18%

The relative minimum of h(x) occurs at x = 2. Integrals can be used to solve a wide range of problems in mathematics and physics, such as finding the area under a curve

An integral is a mathematical concept that involves the concept of integration, which is a way to find the area under a curve or the volume of a solid of revolution. Integrals can be classified into two types: indefinite integrals and definite integrals.

To find the relative minimum of the function h(x), we need to find the value of x that minimizes the value of h(x).

First, let's find the derivative of h(x). We can do this by applying the chain rule to the function inside the integral:

\(h'(x) = (-4 * (t - 2)^2 + 8)' = (-4 * (t - 2)^2 + 8)' = -8 * (t - 2)\)

Next, we need to find the points where h'(x) = 0 or is undefined. Setting h'(x) = 0 and solving for t, we find that t = 2. Substituting this value back into the original expression for h(x), we get:

\(h(x) = -4 * (2 - 2)^2 + 8 = 8\)

Since h'(x) is undefined at t = 2, we need to check whether the function is increasing or decreasing at that point. To do this, we can take the second derivative of h(x):

\(h''(x) = (-8 * (t - 2))' = -8\)

Since the second derivative is negative at t = 2, this means that the function is decreasing at that point.

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Given set of subspaces are:

U = {(x − 2y, x+y, 3x − y) | x, y ≤ R} = 2V = {(x, y², x + y) | x, y ≤ R}

W = {(x, y, z) | −3x+y=0}X = {(x, z, -z) |

x, z = R}

Checking if U is a subspace of R³ for all x,y,z, k1, k2≤

RU = {(x − 2y, x+y, 3x − y) | x, y ≤ R} = 2

Let's take two vectors from set U say

(x1-2y1, x1+y1, 3x1-y1) and (x2-2y2, x2+y2, 3x2-y2)u1 = (x1-2y1, x1+y1, 3x1-y1) and

u2 = (x2-2y2, x2+y2, 3x2-y2)u1+u2 = (x1-2y1, x1+y1, 3x1-y1) + (x2-2y2, x2+y2, 3x2-y2)

u1+u2 = (x1+x2-2y1-2y2, x1+x2+y1+y2, 3x1+3x2-y1-y2)

Since x,y are less than equal to R u1+u2 will be less than equal to

Ru = (k1(x-2y), k1(x+y), k1(3x-y))u = k1(x-2y, x+y, 3x-y)

Since x,y are less than equal to R u will be less than equal to RSince u and v both satisfies all the conditions of being a subspace of R³ it is a subspace of R³.

\Checking if V is a subspace of R³ for all x,y,z, k1, k2≤ RV = {(x, y², x + y) | x, y ≤ R}

Let's take two vectors from set V say

(x1,y1², x1+y1) and (x2,y2², x2+y2)u1 = (x1,y1², x1+y1) and

u2 = (x2,y2², x2+y2)u1+u2 = (x1+y1²+x2+y2², x1+x2+y1+y2, )

Since x,y are less than equal to R u1+u2 will be less than equal to

RV = (k1(x, y², x + y))v = k1(x, y², x + y)

Since x,y are less than equal to R v will be less than equal to RSince v and u both satisfies all the conditions of being a subspace of R³ it is a subspace of R³.

W = {(x, y, z) | −3x+y=0}W = {(x, y, z) | y=3x}

Let's take two vectors from set W say

(x1,3x1, z1) and (x2,3x2, z2)u1 = (x1,3x1, z1)

and

u2 = (x2,3x2, z2)u1+u2 = (x1+x2,3x1+3x2, z1+z2)

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Answer:

The answer to your question is in the file.

The answer to subtracting the two polynomials is 2x2 - 10x - 7.  The process of subtracting polynomials is like that of subtracting any other type of numerical expression.

Polynomials are mathematical expressions consisting of variables, coefficients, and exponents. They are used to represent a variety of functions, such as polynomial equations, rational equations, and trigonometric functions.

In this case, our like terms are 2x2 and 4x2, and -6x and -4x, and -4 and +3. We begin by subtracting the coefficients of the like terms. We subtract the coefficient of the term with the highest power first. In this case, that is 2x2 and 4x2, we subtract 2 from 4 to get 2. Next, we subtract the coefficients of the terms with the second highest power. This is -6x and -4x, so we subtract -6 from -4 to get -2. Thus, our answer now reads 2x2 -2x.

Finally, we subtract the coefficients of the terms with the lowest power. This is -4 and +3, so we subtract -4 from 3 to get -7. Thus, our answer now reads 2x2 -2x -7.

This answer can then be placed in the proper position on the grid.

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Answer:

\( \rm\displaystyle 4\cos( \theta) \cos \left( {2\theta} \right) \cos \left( {4 \theta } \right) \)

Step-by-step explanation:

I assume the question want us to rewrite cosθ+cos3θ+cos5θ+cos7θ by using Sum-to-Product Formula and note that it's not an equation therefore θ can never be specified

===========================

so we want to rewrite cosθ+cos3θ+cos5θ+cos7θ by using Sum-to-Product Formula the good news is that the number of the function of the given expression is even so there's a way to do so, rewrite the expression in parentheses notation:

\( \rm\displaystyle \left( \cos( \theta) + \cos(3 \theta) \right) + \left(\cos(5 \theta) + \cos(7 \theta) \right)\)

recall that,Sum-to-Product Formula of cos function:

\( \rm \boxed{\displaystyle \cos( \alpha ) + \cos( \beta ) = 2 \cos \left( \frac{ \alpha + \beta }{2} \right) \cos \left( \frac{ \alpha - \beta }{2} \right) }\)

notice that we have two pair of function with which we can apply the formula thus do so,

\( \rm\displaystyle \left( 2\cos \left( \frac{ \theta + 3 \theta}{2} \right)\cos \left( \frac{ \theta - 3 \theta}{2} \right) \right) + \left(2\cos \left( \frac{5 \theta + 7 \theta}{2} \right) \cos \left( \frac{5 \theta - 7 \theta}{2} \right) \right)\)

simplify addition:

\( \rm\displaystyle \left( 2\cos \left( \frac{4 \theta}{2} \right)\cos \left( \frac{ - 2\theta }{2} \right) \right) + \left(2\cos \left( \frac{12 \theta }{2} \right) \cos \left( \frac{ - 2 \theta}{2} \right) \right)\)

simplify division:

\( \rm\displaystyle \left( 2\cos \left( {2 \theta} \right)\cos \left( { - \theta } \right) \right) + \left(2\cos \left( {6 \theta } \right) \cos \left( { - \theta} \right) \right)\)

By Opposite Angle Identities we acquire:

\( \rm\displaystyle \left( 2\cos \left( {2 \theta} \right)\cos \left( { \theta } \right) \right) + \left(2\cos \left( {6 \theta } \right) \cos \left( { \theta} \right) \right)\)

factor out 2cosθ:

\( \rm\displaystyle 2 \cos( \theta) (\cos \left( {2 \theta} \right) + \cos \left( {6 \theta } \right) )\)

once again apply Sum-to-Product Formula which yields:

\( \rm\displaystyle 2 \cos( \theta) (2\cos \left( {4\theta} \right) \cos \left( {2 \theta } \right) )\)

distribute:

\( \rm\displaystyle 4\cos( \theta) \cos \left( {2\theta} \right) \cos \left( {4 \theta } \right) \)

and we're done!

There will be 0.84% chances that resulting sequence in cat to occur.

Total number of nucleotides floating around = 10

Let the event of picking cat be "A"

Number of cat in group = 3

Probability of picking cat is picked at first position = P(A1) = 3 / 10

= 0.3

Probability of picking cat is picked at second position = P(A2) =  2 / 9

= 0.223

Probability of picking cat is picked at third position = P(A3) = 1 / 8

= 0.125

so , probability of picking cat in first position and again in second position and again in third position will be = P(A1) . P(A2) . P(A3)

= 0.3 × 0.223 × 0.125

= 0.0084 required probability

There will be 0.84% chances that resulting sequence in cat

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The magnitude and direction of the resultant force are respectively; F = 44.954 N and θ = 36.47°.

We are given two forces as;

F₁ = 34 N

F₂ = 46 N

Angle between the two forces; θ =  42°

Now, the formula to find the resultant of the two forces is gotten by using the cosine rule as;

F = √[F₁² + F₂² + 2F₁F₂cos θ]

Where θ represents the angle between the two force vectors

Thus;

F = √[34² + 46² + 2(34 * 46 * cos 42]

F = 44.954 N

the direction will be;

θ = tan⁻¹(34/46)

θ = 36.47°

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The fractions to show the value of each 9 in the decima 0.999 are 9/10, 9/100, 9/1000.

To write the fraction that shows the value of each 9 in the decimal 0.999, we can use the following method

The digit 9 in the tenths place represents 9/10 or 0.9.

The digit 9 in the hundredths place represents 9/100 or 0.09.

The digit 9 in the thousandths place represents 9/1000 or 0.009.

Thus, the fractions are

0.9 = 9/10

0.09 = 9/100

0.009 = 9/1000

The value of the 9 on the left is related to the value of the 9 in the middle by a factor of 10.

The value of the 9 on the right is related to the value of the 9 in the middle by a factor of 10, so the 9 on the right is one-tenth the value of the 9 in the middle.

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Answer:

1658.3

Step-by-step explanation:

the perimeter of a semi - circle is simply half the circumference of a circle.

that is ;

1 / 2 ( pi ( r² ) )

where;

pi = 3.14 ( this is a constant that should be known and also equals 22 / 7 )

r = radius ( or half a diameter )

in our question, we are given a diameter with no radius

this means that we will have to halve the diameter to give us our radius

that is;

d = 65cm

r = 65 / 2

r = 32.5

so, using our formula;

1 / 2 ( 3.14 ( 32.5² ) )

1 / 2 ( 3.14 ( 1056.26 ) )

1 / 2 ( 3316.65 )

1658.3125

rounded to 1 DP;

1658.3