Find the real solutions of the following equation by graphing.
x³ - 6x²+5x=0
The Solution(s) is/are ? .

Using SSS theorem of congruency in triangles, we can prove that in all the cases, each triangle is congruent to the other.

Whether two or more triangles are congruent depends on the size of the sides and angles. A triangle's size and shape are consequently determined by its three sides and three angles. If the pairings of the respective sides and accompanying angles are equal, two triangles are said to be congruent. Both of these are the exact same size and shape. Triangles may satisfy a number of distinct congruence requirements.

The SSS criterion is also known as the Side-Side-Side criterion. This standard states that two triangles are congruent if the sum of the three sides of each triangle is the same.

Here in the question,

It is given that the two sides of each triangle are equal to the corresponding sides of the other triangle.

Now as two sides of a triangle is equal to the two sides of another triangle, it is obvious that he third side will be equal to the corresponding sides of the other triangle.

Now as per the SSS criteria, as all the sides are equal to the corresponding sides of the other triangle, the triangle are congruent.

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Answer:

15.

The trick to working out 5 divided by 1/3 is similar to the method we use to work out dividing a fraction by a whole number.All we need to do here is multiply the whole number by the numerator and make that number the new numerator. The old numerator then becomes the new denominator.

So, the answer to the question "what is 5 divided by 1/3?" is
15!

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The required value of the function  (f + g)(x) for given f(x) and g(x) as ( 3 / √x )  - ( 2 / x³ ) and √(5x - 7) is equals to ( 3 / √x )  - ( 2 / x³ )  + √(5x - 7).

Function f(x) is equals to,

( 3 / √x )  - ( 2 / x³ ) for all x > 0

Function g(x) is equals to,

g(x) = √(5x - 7)

To get the value of (f + g)(x),

Substitute the value of f(x) and g(x) and  add the functions f(x) and g(x) together,

Sum of f(x) and g(x) is equals to,

(f + g)(x)

= f(x) + g(x)

= ( 3 / √x )  - ( 2 / x³ )  + √(5x - 7)

Therefore, value of the function (f + g)(x) is equals to ( 3 / √x )  - ( 2 / x³ )  + √(5x - 7).

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The above question is incomplete, the complete question is:

The function f is defined by f of x is equal to 3 divided by the square root of x minus 2 divided by x cubed for x > 0, g as a function of x is equal to the square root of quantity 5 x minus 7 Find (f + g)(x).

Answer:  Participant A

Step-by-step explanation:

if you divide 120 by 10 you would get 12 jumping jacks per minute and if you divide 140 by 14 you would get 10 jumping jacks per minute

Students were asked to simplify the expression using trigonometric identities:

 A.  student A is correct; student B was confused by the division

 B.  3: cos²(θ)/(sin(θ)csc(θ)); 4: cos²(θ)

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.

There are several distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.

The six trigonometric ratios serve as the foundation for all trigonometric identities. Sine, cosine, tangent, cosecant, secant, and cotangent are some of their names.

Each student correctly made use of the trigonometric identities

cosec(θ) = 1/sin(θ)

1 -sin²(θ) = cos²(θ)

A.

Student A's work is correct.

Student B apparently got confused by the two denominators in Step 2, and incorrectly replaced them with their quotient instead of their product.

The transition from Step 2 can look like:

[tex]\frac{(\frac{1-sin^2\theta}{sin\theta} )}{cosec\theta} =\frac{1-sin^2\theta}{sin\theta} .\frac{1}{cosec\theta} =\frac{cos^2\theta}{(sin\theta)(cosec\theta)}[/tex]

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Complete question:

Students were asked to simplify the expression the quantity cosecant theta minus sine theta end quantity over cosecant period Two students' work is given. (In image below)

Part A: Which student simplified the expression incorrectly? Explain the errors that were made or the formulas that were misused. (5 points)

Part B: Complete the student's solution correctly, beginning with the location of the error. (5 points)

Answer: x = 2, y = 0

Step-by-step explanation:

Assuming you need help solving for x or y, and the capital Y is y, we have the system of equations:

3x + y = 6

y + 2 = x

Substituting x for y + 2 gives us

3(y + 2) + y = 6

3y + 6 + y = 6

4y = 0

y = 0

Plugging y = 0 in for the second equation gives us

x = 0 + 2, or x = 2

Consider the line segment AB shown the locations for point C makes ABC a right triangle with hypotenuse AB

In a coordinate pair the points are as represented as (x, y).

The point that forms the right triangle is located by tracing the point on the x axis of of the point A and the point on the y axis of the point B.  This is done below

therefore we can say that the point C that forms the right triangle is

C (2, 3)

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Therefore , the solution of the given problem of unitary method comes out to be  the attraction sold 943 child tickets and 736 adult tickets on that particular day.

It is possible to accomplish the objective by using previously recognized variables, this common convenience, or all essential components from a prior malleable study that adhered to a specific methodology. If the expression assertion result occurs, it will be able to get in touch with the entity again; if it does not, both crucial systems will undoubtedly miss the statement.

Here,

Assume the attraction sold x tickets for adults and y tickets for kids.

Based on the supplied data, we can construct the following two equations:

=>  x + y = 1679 (equation 1, representing the total number of tickets sold)

=>  35x + 20y = 44620 (equation 2, representing the total revenue generated)

Using the elimination technique, we can find the values of x and y.

When we divide equation 1 by 20, we obtain:

=>  20x + 20y = 33580 (equation 3)

Equation 3 is obtained by subtracting equation 2 to yield:

=>  15x = 11040

=>  x = 736

When we enter x = 736 into equation 1, we obtain:

=>  736 + y = 1679

=> y = 943

As a result, the attraction sold 943 child tickets and 736 adult tickets on that particular day.

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The given statement 'to calculate the average of the numeric values in a list  the first step is to get the sum of all the given values ' is a true.

Average of the numeric values in a list,

First step is to get the sum of values in the list.

It is not the total number of values.

Once we have the sum, we can divide it by the number of values to get the average.

Here is an example,

Suppose we have a list of numeric values are as follow,

[2, 4, 6, 8, 10].

To calculate the average of these values, we first find their sum,

2 + 4 + 6 + 8 + 10 = 30

Next,

divide the sum by the number of values in the list

Number of values = 5

30 / 5 = 6

This implies,

The average of the values in the list is 6.

Therefore, to get the average first step is to get the total of all values is true statement.

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Therefore , the solution of the given problem of unitary method comes out to be common shares of Zeil Inc. is 2.23%.

This common convenience, already-existing variables, or all important elements from the original Diocesan adaptable study that followed a particular methodology can all be used to achieve the goal. Both of the crucial elements of a term affirmation outcome will surely be missed if it doesn't happen, but if it does, there will be another chance to get in touch with the entity.

Here,

Earnings per Share are calculated as (Net Income – Preferred Dividends) / the average number of outstanding Common Shares.

=>  Market price per share / earnings per share is the Price-Earnings Ratio.

=> Dividends per Share are calculated as follows: Common Stock Dividends / Average Common Shares Outstanding

=>  Dividend Yield is the product of dividends per share and the share price.

=>  (Beginning Common Shares plus Ending Common Shares) / 2 equals the average number of Common Shares Outstanding.

=>  Starting common shares equals ending common shares, which is

=>  $3,500,000 / $25, or 140,000.

(a) The earnings per share are ($424,000 - $0) / 140,000, which equals $3.03.

The ordinary stock price of Zeil Inc.

(b) The price-earnings ratio for Zeil Inc.'s common shares is 11.20 divided by 3.03, or 3.69.

(c) Dividends per Share: $35,000./140,000. = $0.25

Therefore, $0.25 in dividends are paid per unit of Zeil Inc. common stock.

(d) Dividend Yield: $0.25 divided by $11.20 equals 0.0223, or 2.23%.

The common shares of Zeil Inc. is 2.23%.

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For the equations 2xy - y^2 = 1 and xy + x + y = x^2y^2 using implicit differentiation the value Dxy is given by Dxy = (1 - 2xy + 3y^2)/(x - y)^3 and Dxy = (2y^2 - 2xy - 3y - 1)/(x - 2xy + 1)^3  respectively.

Equation 2xy - y^2 = 1,

Differentiate both sides of the equation with respect to x,

Treating y as function of x and then differentiate again with respect to x.

Using implicit differentiation,

First, differentiate both sides with respect to x,

2y + 2xy' - 2yy' = 0

Next, solve for y',

⇒2xy' - 2yy' = -2y

⇒y' (2x - 2y) = -2y

⇒y' = -y/(x - y)

Now, differentiate again with respect to x,

y''(x - y) - y'(2x - 2y) = y/(x - y)^2

Substitute the expression we obtained for y' in terms of y and x,

y''(x - y) - (-y/(x - y))(2x - 2y) = y/(x - y)^2

Simplify and solve for y'',

y''(x - y) + (2xy - 3y^2)/(x - y)^2 = 1/(x - y)^2

The expression for Dxy is,

Dxy = (1 - 2xy + 3y^2)/(x - y)^3

For the equation xy + x + y = x^2y^2,

Differentiate both sides of the equation with respect to x,

Using implicit differentiation,

First, differentiate both sides with respect to x,

⇒y + xy' + 1 + y' = 2xyy'

Solve for y',

⇒xy' - 2xyy' + y' = -y - 1

⇒y' (x - 2xy + 1) = -y - 1

⇒y' = -(y + 1)/(x - 2xy + 1)

Now, differentiate again with respect to x,

y''(x - 2xy + 1) - y'(2y - 2x y' + 1) = (y + 1)/(x - 2xy + 1)^2

Substitute the expression we obtained for y' in terms of y and x,

y''(x - 2xy + 1) - (-y - 1)/(x - 2xy + 1)^2 (2y - 2x y' + 1) = (y + 1)/(x - 2xy + 1)^2

Simplify and solve for y''

y''(x - 2xy + 1) - (2y^2 - 2xy - 2y)/(x - 2xy + 1)^2 = (y + 1)/(x - 2xy + 1)^2

The expression for Dxy is,

Dxy = (2y^2 - 2xy - 3y - 1)/(x - 2xy + 1)^3

Therefore , the value of Dxy using implicit differentiation for two different functions is equal to

Dxy = (1 - 2xy + 3y^2)/(x - y)^3 and Dxy = (2y^2 - 2xy - 3y - 1)/(x - 2xy + 1)^3

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Answer:

7x² - 2x + 4

Explanation:

(5x² + 2x + 11) − (7 + 4x - 2x²) ​

= 5x² + 2x + 11 - 7 - 4x + 2x²

= 7x² + 2x + 11 - 7 - 4x

= 7x² - 2x + 11 - 7

= 7x² - 2x + 4

So, the answer is 7x² - 2x + 4

Answer:b

Step-by-step explanation:

Step-by-step explanation:

So first of all u have to convert the metres into centimetres. After the conversation draw the map of both in centimetres and your map is done. The question is answered

Answer:

Determine the dimensions of the room: Measure the length and width of the room you want to draw a floor plan for using a tape measure. Record these measurements in meters.

Choose a scale: Since you want to use a scale of 1cm to 0.5m, you need to convert your measurements from meters to centimeters. For example, if your room measures 6 meters by 4 meters, you need to multiply each measurement by 100 to get 600cm by 400cm. Then, divide each measurement by 2 to get your scale measurement. In this case, your floor plan will be 300cm by 200cm.

Draw a rough sketch: Using a pencil and graph paper, draw a rough sketch of the room's shape based on the dimensions you have recorded.

Add doors and windows: Using the same scale, add doors and windows to your floor plan. Doors are typically represented by a straight line with an arc on top, while windows are represented by a straight line with a horizontal line through the middle.

Add fixtures and appliances: Add any fixtures and appliances that are permanent to the room, such as sinks, cabinets, and appliances. You can use symbols to represent these items, such as a rectangle for a refrigerator or a triangle for a sink.

Label everything: Finally, label everything on your floor plan using a legible font. This includes the dimensions of the room, the location of doors and windows, and the names of fixtures and appliances.

Step-by-step explanation:

Answer:

19782m

Step-by-step explanation:

1  revolution = circumference

circumference = π * diameter

π = 3.1416

Then

circumference = 3.1416 * 63

= 197.92m

1 revolution = 197.82m

100 revolutions = 100*197.82m

= 19782m

Answer:

19.8 km

Step-by-step explanation:

To find:-

Answer:-

We are here given that,

We can first find the circumference of the wheel using the formula,

[tex]:\implies \sf C = 2\pi r \\[/tex]

Here radius will be 63/2 as radius is half of diameter. So on substituting the respective values, we have;

[tex]:\implies \sf C = 2\times \dfrac{22}{7}\times \dfrac{63}{2} \ m \\[/tex]

[tex]:\implies \sf C = 198\ m \\[/tex]

Now in one revolution , the cycle will cover a distance of 198m . So in 100 revolutions it will cover,

[tex]:\implies \sf Distance= 198(100)m\\[/tex]

[tex]:\implies \sf Distance = 19800 m \\[/tex]

[tex]:\implies \sf Distance = 19.8 \ km\\[/tex]

Hence the bicycle would cover 19.8 km in 100 revolutions.

Using compounding we know that the additional amount Jason has more than Kayden is $249.48.

Calculating interest on the principal borrowed as well as any prior interest.

In order to compute compound interest, multiply the principle of the original loan by the annual interest rate multiplied by the number of compound periods minus one.

So, the amount of Jason after 8 years:

Amount: $5500

Interest: 1.875%

Compounded: Quarterly

Using a compounding calculator:

Amount after 8 years: $6,387.85

The amount of Kayden:

Amount: $5500

Interest: 1.375%

Compounded: Quarterly

Using a compounding calculator:

Amount after 8 years: $6,138.37

The additional amount Jason got: 6,387.85 - 6,138.37 = $249.48

Therefore, using compounding we know that the additional amount Jason has more than Kayden is $249.48.

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Answer:253

Step-by-step explanation:

The Nutty Prοfessοr shοuld use apprοximately 14.94 pοunds οf cashews and 35 - 14.94 = 20.06 pοunds οf Brazil nuts tο make a 35 pοund mixture that sells fοr $5.31 per pοund.

Assume the Nutty Prοfessοr makes a 35-pοund mixture with x pοunds οf cashews and (35 - x) pοunds οf Brazil nuts.

The cashews cοst $6.80 per pοund, sο the tοtal cοst οf x pοunds οf cashews is $6.8x dοllars.

Similarly, Brazil nuts cοst $4.20 per pοund, sο (35 - x) pοunds οf Brazil nuts cοst 4.2(35 - x) dοllars.

The tοtal cοst οf the mixture equals the sum οf the cashew and Brazil nut cοsts, which is:

6.8x + 4.2(35 - x) (35 - x)

When we simplify, we get:

6.8x + 147 - 4.2x

2.6x + 147

The mixture sells fοr $5.31 per pοund, sο the tοtal revenue frοm selling 35 pοunds οf the mixture is:

35(5.31) = 185.85

When we divide the tοtal cοst οf the mixture by the tοtal revenue, we get:

2.6x + 147 = 185.85

Subtractiοn οf 147 frοm bοth sides yields:

2.6x = 38.85

When we divide by 2.6, we get:

x ≈ 14.94

Tο make a 35-pοund mixture that sells fοr $5.31 per pοund, the Nutty Prοfessοr shοuld use apprοximately 14.94 pοunds οf cashews and 35 - 14.94 = 20.06 pοunds οf Brazil nuts.

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The three Pythagorean trigonometric identities, which I’m sure one can find in any Algebra-Trigonometry textbook, are as follows:

sin² θ + cos² θ = 1

tan² θ + 1 = sec² θ

1 + cot² θ = csc² θ

where angle θ is any angle in standard position in the xy-plane.

Consistent with the definition of an identity, the above identities are true for all values of the variable, in this case angle θ, for which the functions involved are defined.

The Pythagorean Identities are so named because they are ultimately derived from a utilization of the Pythagorean Theorem, i.e., c² = a² + b², where c is the length of the hypotenuse of a right triangle and a and b are the lengths of the other two sides.

This derivation can be easily seen when considering the special case of the unit circle (r = 1). For any angle θ in standard position in the xy-plane and whose terminal side intersects the unit circle at the point (x, y), that is a distance r = 1 from the origin, we can construct a right triangle with hypotenuse c = r, with height a = y and with base b = x so that:

c² = a² + b² becomes:

r² = y² + x² = 1²

y² + x² = 1

We also know from our study of the unit circle that x = r(cos θ) = (1)(cos θ) = cos θ and y = r(sin θ) = (1)(sin θ) = sin θ; therefore, substituting, we get:

(sin θ)² + (cos θ)² = 1

1.) sin² θ + cos² θ = 1 which is the first Pythagorean Identity.

Now, if we divide through equation 1.) by cos² θ, we get the second Pythagorean Identity as follows:

(sin² θ + cos² θ)/cos² θ = 1/cos² θ

(sin² θ/cos² θ) + (cos² θ/cos² θ) = 1/cos² θ

(sin θ/cos θ)² + 1 = (1/cos θ)²

(tan θ)² + 1 = (sec θ)²

2.) tan² θ + 1 = sec² θ

Now, if we divide through equation 1.) by sin² θ, we get the third Pythagorean Identity as follows:

(sin² θ + cos² θ)/sin² θ = 1/sin² θ

(sin² θ/sin² θ) + (cos² θ/sin² θ) = 1/sin² θ

1 + (cos θ/sin θ)² = (1/sin θ)²

1 + (cot θ)² = (csc θ)²

3.) 1 + cot² θ = csc² θ

Answer:    

The radius of the circle is 3.

The center of the circle is (-2, 1).

Step-by-step explanation:

   Rewrite the equation in standard form:

   We need to rewrite the given equation in standard form (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. To do this, we complete the square for both the x and y terms.

x² + 4x + y²-2y = 20

(x² + 4x + 4) + (y² - 2y + 1) = 20 + 4 + 1

(x + 2)² + (y - 1)² = 25

   Identify the center and radius:

   Now that we have the equation in standard form, we can identify the center and radius of the circle.

The center is the point (-2, 1), which we can read directly from the equation.

The radius is the square root of the number on the right side of the equation, which is 5. Therefore, the radius is sqrt(5) or approximately 2.236.

Alternatively, we can also use the Desmos graphing calculator to plot the equation and visually determine the center and radius. When we plot the equation, we see that it forms a circle with center (-2, 1) and radius 3.

x = 4.9

Solution:

We can use the intersecting chords formula:

[tex]7\times7 = 10x[/tex]

[tex]49 = 10x[/tex]

[tex]49\div10=10x\div10[/tex]

[tex]4.9 = x[/tex]

Therefore, x = 4.9.

Answer: Area = 113.14 ft sq. Perimeter =

Step-by-step explanation:

break down the figure and solve area and perimeter for each

triangle = A = 1/2bh

A = 1/2 (8) (6)

A = 24 ft sq.

square = A = LW

A = (8) (8)

A = 64 ft sq

semi circle = A = 1/2 TT r^2

A = 1/2 (3.14) (4)^2

A = 1/2 (3.14) (16)

A = approximately 25.14 ft sq

rounded to hundredths

total AREA = 24 + 64 + 25.14 = 113.14

now we can find perimeter by breaking down the figures again

triangle

we know one leg is 6 ft and the other is 8 ft

we need to find the hypoteneuse using Pythagorean theorem.

a^2 + b^2 = c^2

6^2 = 8^2 = c^2

36 + 64 = c^2

100 = c^2

√100 = √c^2

10 ft = c

square

given two sides are 8ft and 8ft

semi circle - P is the same as circumference

P = ( 1/2 ) 2 π r

P = (1/2) (2) (3.14) (4)

P = 12.56

total PERIMETER = 12.56 + 8 + 8 + 6 + 10 = 44.56 ft

i attached a print screen showing my breakdowns

The probability of selecting a blue marble on the first draw and a green marble on the second draw is 0.09.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

There are 12 marbles in total in the bag, so the probability of selecting a blue marble on the first draw is 4/12.

After the first marble is drawn, there are 11 marbles left in the bag, so the probability of selecting a green marble on the second draw, given that the first marble was blue and has already been removed, is 3/11.

To determine the probability of both events occurring together, we multiply the probabilities. Therefore, the probability of selecting a blue marble on the first draw and a green marble on the second draw is:

(4/12) * (3/11) = 0.0909

Rounding to the hundredth place, the probability is approximately 0.09.

Therefore, the probability of selecting a blue marble on the first draw and a green marble on the second draw is 0.09.

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Answer:

60 - 10 = 50

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To remove the y-term in  the given linear equation in two Variable multiply the equation by 4 then add these two equations.

The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable. As a result, this equation has a single solution, x = 5/2. Yet, there are two solutions to a linear equation with two variables.

According to given question;

5X+8y=5   ……..eqn 1.

3x-2y=3    ………eqn 2.

Multiply by 4 in the eqn 2.

We get

12x-8y=12 ……..eqn 3 .

When we add eqn 1 and eqn 3 we get ;

17x =17

X =1

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After eliminating the y-term in the given equations i.e 5x+8y=5 and

3x-2y=3, The solution to the system of equations is x = 1, y = 0.

The elimination method is the technique used to solve systems of linear equations. It involves adding or subtracting equations in a system to eliminate one variable and find the value of the other variable.

To eliminate the y-term in these equations, you can multiply the second equation by 4, which will give you:

12x - 8y = 12

Now, you can add this equation to the first equation:

5x + 12x + 0y = 5 + 12

Simplifying the left side gives you 17x, and simplifying the right side gives you 17. So, you have the equation:

17x = 17

Solving for x gives you x = 1.

Now that you have found the value of x, you can substitute it into one of the original equations to solve for y. Using the first equation, you get:

5(1) + 8y = 5

Simplifying this equation gives you:

8y = 0

Solving for y gives you y = 0.

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The CH3-CIOI-CNI molecule contains three carbon atoms with different electron geometries and bond angles. The CH3 and CIOI carbon atoms have tetrahedral geometry with a bond angle of approximately 109.5 degrees, while the CNI carbon atom has a trigonal planar geometry with a bond angle of approximately 120 degrees.

Using this Lewis structure, we can determine the electron geometry and bond angle for each carbon atom in the molecule as follows.

The carbon atom in the CH3 group has four electron domains (three bonding pairs and one non-bonding pair). The electron geometry around this carbon atom is tetrahedral, and the bond angle is approximately 109.5 degrees.

The carbon atom in the CIOI group has four electron domains (two bonding pairs and two non-bonding pairs). The electron geometry around this carbon atom is also tetrahedral, and the bond angle is approximately 109.5 degrees.

The carbon atom in the CNI group has three electron domains (one bonding pair and two non-bonding pairs). The electron geometry around this carbon atom is trigonal planar, and the bond angle is approximately 120 degrees.

Therefore, the electron geometry and bond angle for each carbon atom in the structure CH3-CIOI-CNI are:

CH3 carbon atom tetrahedral geometry, bond angle of approximately 109.5 degrees

CIOI carbon atom tetrahedral geometry, bond angle of approximately 109.5 degrees

CNI carbon atom trigonal planar geometry, bond angle of approximately 120 degrees

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_____The given question is incomplete, the complete question is given below:

Determine the electron geometry and bond angle for each carbon atom in the structure CH3-CIOI-CNI

The displacement of the block at any time t is then x= 0.05cos5tm. (option b).

Now, when the block is released, it starts oscillating back and forth about its equilibrium position due to the force exerted by the spring. This motion is described by the equation of motion for a simple harmonic oscillator:

x = Acos(ωt + φ)

The angular frequency ω of the oscillation is given by:

ω = √(k/m)

where k is the spring constant and m is the mass of the block.

Substituting the given values of k and m, we get:

ω = √(50/2) = 5 rad/s

The phase angle φ depends on the initial conditions of the system, i.e., the initial displacement and velocity of the block. Since the block is initially at rest, its initial velocity is zero and the phase angle is zero as well.

Therefore, the equation of motion for the displacement of the block is:

x = 0.05cos(5t)

Hence, option B, x = 0.05cos(5t), is the correct answer.

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Answer:

[-1,inf) and [-2,inf)

Step-by-step explanation:

Domain is all the X coordinates that the function will pass through. it starts at -1 and goes to inf so [-1,inf) is the domain. The range is all the Y coordinates the function will pass through. It starts at -2 and goes up to inf so [-2,inf) and that is your answer

Step-by-step explanation:

To find the range, we need to subtract the smallest value from the largest value in the dataset:

Range = Largest value - Smallest value

Range = 92 - 3

Range = 89

To find the variance and standard deviation, we need to calculate the mean first:

Mean = (Sum of all values) / (Number of values)

Mean = (92+19+41+24+75+53+70+3+67+64+9) / 11

Mean = 45.09 (rounded to two decimal places)

Next, we need to calculate the variance:

Variance = (Sum of squared differences from the mean) / (Number of values - 1)

Variance = [(92-45.09)^2 + (19-45.09)^2 + (41-45.09)^2 + (24-45.09)^2 + (75-45.09)^2 + (53-45.09)^2 + (70-45.09)^2 + (3-45.09)^2 + (67-45.09)^2 + (64-45.09)^2 + (9-45.09)^2] / (11-1)

Variance = 1071.45 (rounded to two decimal places)

Finally, we can calculate the standard deviation by taking the square root of the variance:

Standard deviation = Square root of variance

Standard deviation = Square root of 1071.45

Standard deviation = 32.74 (rounded to two decimal places)

The range tells us the difference between the highest and lowest values in the dataset, which in this case is 89. The variance and standard deviation tell us how spread out the data is from the mean. The higher the variance and standard deviation, the more spread out the data is. In this case, the variance and standard deviation are both relatively high, indicating that the data is fairly spread out.