Use The Image To Determine The Line Of Reflection.An Image Of Polygon VWYZ With Vertices V At Negative (2024)

Answer:

The surface area is 65.94 ft

The diameter of the semicircle is with an area of 76.97 square yards is 14 yards.

What is the diameter of a semicircle with an area of 76.97

Semicircle is half that of a circle, hence the area will be half that of a circle. Area of semi circle = 1/2 × πr²

Where r radius and π is constant pi.

Since we are given the area of the semicircle as 76.97 square yards, we can set up the following equation:

76.97 = 1/2 × (πr²)

Multiplying both sides by 2, we get:

153.94 = πr²

Dividing both sides by π, we get:

r² = 49

Taking the square root of both sides, we get:

r = 7

Therefore, the diameter of the semicircle is: d = 2r = 2(7) = 14 yards

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The statement that describes the mean number of hours worked through which the relation is satisfied is The mean is the highest number or hours worked by any students in the group

What about mean?

In mathematics, the mean is a measure of central tendency that represents the average value of a set of numbers. It is often called the arithmetic mean, and it is calculated by adding up all the values in the set and then dividing the result by the total number of values.

The formula for the mean is:

mean = (sum of all values) / (total number of values)

For example, suppose we have a set of four numbers: 2, 5, 8, and 11. To find the mean of this set of numbers, we add them up and divide by the total number of values:

mean = (2 + 5 + 8 + 11) / 4

mean = 26 / 4

mean = 6.5

Therefore, the mean of this set of numbers is 6.5. The mean is a commonly used measure of central tendency in statistics and data analysis, and it provides a way to summarize the general trend or average of a data set.

According to the given information:

Mean of the given condition is,

⇒ [tex]\frac{3 + 5 + 4 + 4 + 2 + 5}{6}[/tex]

⇒ [tex]\frac{23}{6}[/tex]

⇒ 3.83 mean of the given condition.

So, it indicate that The mean is the highest number or hours worked by any students in the group.

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The correct options are 2, 3, and 5 for the statements "The graph of the function is a parabola," "The graph contains the point (0, 0)," and "The graph of the function opens down" respectively.

What is the quadratic function?

A quadratic function is a type of polynomial function with a degree of 2, meaning it has the form:

[tex]f(x) = ax^2 + bx + c[/tex]

The correct statements are:

The value of f(-10) = 82: This statement is true because we can plug in -10 for x in the given quadratic function [tex]f(x) = x^2 - 5x + 12[/tex]and evaluate to get [tex]f(-10) = (-10)^2 - 5(-10) + 12 = 100 + 50 + 12 = 162[/tex], not 82.The graph of the function is a parabola: This statement is true because the given function [tex]f(x) = x^2 - 5x + 12[/tex]is a quadratic function, and the graph of a quadratic function is always a parabola.The graph contains the point (0, 0): This statement is false because when we plug in x = 0 into the given quadratic function [tex]f(x) = x^2 - 5x + 12[/tex], we get [tex]f(0) = 0^2 - 5(0) + 12 = 12[/tex], so the point (0, 0) is not on the graph of the function.The graph contains the point (20, -8): This statement is not mentioned in the given options, so we cannot determine its truthfulness based on the given information.The graph of the function opens down: This statement is false because the coefficient of [tex]x^2[/tex] in the given quadratic function f(x) = [tex]x^2 - 5x + 12[/tex] is positive (+1), which means the parabola opens upwards, not downwards.

Hence, the correct options are 2, 3, and 5 for the statements "The graph of the function is a parabola," "The graph contains the point (0, 0)," and "The graph of the function opens down" respectively.

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The only solutions of the given equation in the interval (0, 2π) are the values of x for which sinx = 0. These are: x = 0π, 1π, 2π. So the solutions are x = 0π, π, 2π, or in terms of degrees, x = 0°, 180°, 360°.

How to Solve the Equation?

The given equation is sinx(cosx−4)=0.

To solve this equation, we need to find the values of x in the interval [0, 2π) that make the product sinx(cosx−4) equal to zero.

To do that, we can set each factor equal to zero and solve for x:

sinx = 0 or cosx − 4 = 0

If sinx = 0, then x can be any multiple of π, since sinx = 0 for all even multiples of π (0, ±π, ±2π, ...), and for odd multiples of π (±π/2, ±3π/2, ...).

If cosx − 4 = 0, then cosx = 4, which has no real solutions in the interval [0, 2π).

Therefore, the only solutions of the given equation in the interval [0, 2π) are the values of x for which sinx = 0. These are:

x = 0π, 1π, 2π

So the solutions are x = 0π, π, 2π, or in terms of degrees, x = 0°, 180°, 360°.

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The measure of angle 3 is 48°

How to find the measure of angle 3?

We can see that both horizontal lines are parallel, then the measure of angle 3 and the angle below it (the 132° one) must add up to 180°.

Then we can write:

∠3 + 132° = 180°

And solve this equation for the measure of angle 3.

∠3 = 180° - 132° = 48°

That is the measure.

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The sentence can be rewritten using De Morgan's Laws as:

It is false that Tina likes Sprite and Tina likes 7-Up.

In other words, Tina does not like both Sprite and 7-Up.

3√(5a) - 8√(a) / 35a^2

To simplify this expression, we can first separate the two terms in the numerator:

3√(5a) / 35a^2 - 8√(a) / 35a^2

We can then simplify each term separately. For the first term:

3√(5a) / 35a^2 = √(5a) / (35a^2/3)

We can simplify the denominator by using the rule that (a^m)^n = a^(mn):

35a^2/3 = (5a^2/3) * 7 = (a^(2/3))^5 * 7

So the first term simplifies to:

√(5a) / (a^(2/3))^5 * 7

For the second term:

8√(a) / 35a^2 = 8a^(1/2) / (35a^2)

We can simplify the denominator by using the rule that a^-m = 1/a^m:

35a^2 = 5 * 7 * a^2 = a^-2 * 5 * 7

So the second term simplifies to:

8a^(1/2) / (a^-2 * 5 * 7)

Now we can combine the two terms by finding a common denominator:

√(5a) / (a^(2/3))^5 * 7 - 8a^(1/2) / (a^-2 * 5 * 7)

The common denominator is (a^(2/3))^5 * 5 * 7:

√(5a) * 5 * 7 / (a^(2/3))^5 * 5 * 7 - 8a^(1/2) * (a^(2/3))^5 * 5 * 7 / (a^-2 * 5 * 7) * (a^(2/3))^5 * 5 * 7

Simplifying each term, we get:

35√(5a) / 5a^2 - 40a^(5/2) / 5a^3

Now we can simplify further by factoring out a common factor of 5a^(5/2):

5a^(5/2) * (7√(5a) - 8) / 5a^3

The 5's cancel out, and we can remove the common factor of 5a^(5/2) to get:

(7√(5a) - 8) / a^(3/2)

So the simplified expression is:

(7√(5a) - 8) / a^(3/2)

We find that P(Z > 2.46) is roughly 0.007 using a calculator or a basic normal distribution table. The probability that a bag will contain more than 20% blue jellybeans is therefore approximately 0.007 or 0.7%.

Define probability?

The probability of an event is the ratio of good outcomes to all other potential outcomes. The number of successful outcomes for an experiment with 'n' outcomes can be expressed using the symbol x.

Here in the question,

We can utilise the binomial distribution formula to resolve this issue. In a bag of 200 jelly beans, let X represent the proportion of blue jelly beans. Following that, X exhibits a binomial distribution with parameters of n = 200 and p = 0.15, where p is the likelihood of drawing a blue jellybean.

The formula for determining the likelihood of finding more than 20% blue jellybeans in a bag is:

P (X > 0.2 × 200) = P (X > 40)

Since n is large (200) and p is not too near to 0 or 1, we can utilise the usual approximation to the binomial distribution. We may determine the equivalent mean and standard deviation of the normal distribution by using the mean and variance of the binomial distribution:

μ = np = 200 × 0.15 = 30

σ = √ (np(1-p)) = √ (200 × 0.15 × (1-0.15)) = 4.07

Then, we can standardize the random variable X as:

Z = (X - μ) / σ

So, we have:

P(X > 40) = P((X - μ) / σ > (40 - μ) / σ)

= P(Z > (40 - 30) / 4.07)

= P(Z > 2.46)

We find that P(Z > 2.46) is roughly 0.007 using a calculator or a basic normal distribution table. The likelihood that a bag will contain more than 20% blue jellybeans is therefore approximately 0.007 or 0.7%.

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Step-by-step explanation:

1. w=4 v=-3

2. y=6 x=-2

4. m=6 p=3

5. b=-2 a=4

7. c=8 d=-7

8. g=-3 f=5

10. j=2.5 k=4

11. x=4 y=1.5

13. x=2 y=1

14. y=6 x=5

Option (a) is the correct answer. When two figures are similar, it means they have the same shape but different sizes.

How to solve the question?

In other words, their corresponding angles are congruent, and their corresponding side lengths are proportional.

Option (b) and (d) suggest that the corresponding side lengths of A and B are related by a constant factor (either 2 or 1/2). However, this is not necessarily true for all similar figures. The constant of proportionality can be any positive real number.

Option (c) suggests that the corresponding side lengths of A and B are equal, which means that A and B are not just similar but congruent. This is not necessarily true for all similar figures, as similar figures can differ in size.

Therefore, option (a) is the only answer that must always be true for similar figures. The corresponding side lengths of similar figures are proportional, which means that if one side of figure A is twice as long as a corresponding side of figure B, then all other corresponding sides will also be in the same ratio of 2:1. Similarly, if one side of figure A is three times as long as a corresponding side of figure B, then all other corresponding sides will also be in the same ratio of 3:1. This proportional relationship holds true for all pairs of corresponding sides in similar figures

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Option (a) is the correct answer. The corresponding side lengths of A and B are proportional, must always be true if Figure A is similar to Figure B.

How to find if the figure is similar?

When two figures are similar, their corresponding angles are congruent, and their corresponding side lengths are proportional. This means that if we take any two corresponding sides of the figures, the ratio of their lengths will be the same for all pairs of corresponding sides.

Option b and d cannot be true, as they both suggest a specific ratio of corresponding side lengths, which is not necessarily true for all similar figures.

Option c is not necessarily true, as two similar figures can have corresponding side lengths that are not equal but still have the same ratio.

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Answer:

68/25

Step-by-step explanation:

If the the a is greater than 1, compared to the parent function the C. Stretched vertically.

How to find the comparison ?

The equation y = ax^2 + c represents a quadratic function where "a" is the coefficient of the x^2 term and "c" is a constant term. The parent function of this quadratic function is y = x^2.

If the equation of a quadratic function is given in the form y = ax^2 + c and "a" is greater than 1, then the graph of the function will be stretched vertically and the vertex will be shifted up or down depending on the value of "c".

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Answer:

mean: 20mins

Step-by-step explanation:

add them all together to get 240

then divide by how many there are

240÷12=20

so the mean is 20mins

Answer:

(5,-9) is not a solution

Step-by-step explanation:

Answer: Let the length and breadth of the rectangular plot be L and B respectively.

Given that the area of the rectangular plot is 440 m², we have:

L*B = 440 ---(1)

When the length is increased by 4 m, the new area of the rectangular plot is 520 m². So, we have:

(L+4)*B = 520 ---(2)

Expanding equation (2), we get:

L*B + 4B = 520

Substituting equation (1), we get:

440 + 4B = 520

Subtracting 440 from both sides, we get:

4B = 80

Dividing both sides by 4, we get:

B = 20

Therefore, the breadth of the land is 20 meters.

Step-by-step explanation:

Answer: Since we know that cos A = 3/10, we can use the Pythagorean identity to find sin A:

sin^2 A + cos^2 A = 1

sin^2 A = 1 - cos^2 A

sin A = sqrt(1 - cos^2 A)

Substituting cos A = 3/10, we get:

sin A = sqrt(1 - (3/10)^2)

sin A = sqrt(1 - 9/100)

sin A = sqrt(91)/10

Since we also know that tan A < 0, we know that the sine and tangent of A have opposite signs, and therefore sin A is negative.

Therefore:

sin A = -sqrt(91)/10

Step-by-step explanation:

Answer:

y = 0.028t + 230,000 Step-by-step explanation: We know t = number of years since the start of the study y = be the city's population Each year the population

Step-by-step explanation:

The approximated area of the shaded region is 92.54 square units

Approximating the area of the shaded region.

From the question, we have the following parameters that can be used in our computation:

Two isosceles right trianglesCircle

The area of the shaded region in the figure is calculated as

Shaded region = Circle - Isosceles right triangle 1 - Isosceles right triangles 2

Using the given dimensions, we have

Shaded region = 3.14 * 6^2 - 1/2 * 5^2 - 1/2 * 4^2

Evaluate

Shaded region = 92.54

Hence, the shaded region is 92.54 square units

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The expressions that are all equivalent to 3/5 - 8/13 +2/9 are:

- 8/13 + 3/5 +2/9(3/5 +2/9) - 8/13

How can the expressions be known?

A mathematical expression is a combination of numbers, variables, operators, and symbols that represents a mathematical relationship or calculation. Mathematical expressions can be written using a variety of mathematical notations, such as algebraic notation, set notation, or calculus notation.

We were given the expression 3/5 - 8/13 +2/9, then we can see that the only negative value is - 8/13 , then we can see that the only options that have a negative value of - 8/13 is option B,D. Therefore, option B and E are correct.

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complete question;

Which expressions are all 3/5 - 8/13 +2/9 ?

Answer:

B

Step-by-step explanation:

the average rate of change of h(x) in the interval [ a, b ] is

[tex]\frac{h(b)-h(a)}{b-a}[/tex]

here the [ a, b ] = [ 4, 8 ] , then

h(b) = h(8) = 3 ← point (8, 3 ) on graph

h(a) = h(4) = 9 ← point (4, 9 ) on graph

then

average rate of change = [tex]\frac{3-9}{8-4}[/tex] = [tex]\frac{-6}{4}[/tex] = - [tex]\frac{3}{2}[/tex]

Answer:

To determine which measurement is the most precise, we need to look at the number of decimal places or significant figures in each measurement.

A. 350 cm has one significant figure.

B. 3,575 mm has four significant figures.

C. 3 m has one significant figure.

Therefore, the measurement that is the most precise is B. 3,575 mm, since it has the highest number of significant figures.

The answer of the given question based on the variance is , 92% confidence that the true population mean lies between 69.11 and 74.89.

What is Mean?

In statistics, the mean is a measure of central tendency that represents the average of a set of numerical data. It is also known as the arithmetic mean or simply the average. The mean is calculated by adding up all the values in the dataset and then dividing the sum by the number of values.

To construct a random interval with a 0.92 confidence level, we need to find the corresponding z-score for the level of confidence. Since the interval is not two-sided, we will use a one-tailed z-score.

Using a standard normal distribution table or calculator, we find that the z-score corresponding to a 0.92 confidence level is approximately 1.41.

To find the 92% confidence interval for the population mean, we can use the following formula:

CI = ₓ⁻ ± zα/2 * σ/√n

where ₓ⁻ is the sample mean, σ is the population standard deviation (unknown in this case), n is the sample size, and zα/2 is critical value of standard normal distribution corresponding to desired level of confidence.

Substituting the given values, we get:

CI = 72 ± 1.41 * (4 / √20)

CI = (69.11, 74.89)

Therefore, we can say with 92% confidence that the true population mean lies between 69.11 and 74.89.

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The depreciation expense for each year is 1,000,000 shs.

Accumulated depreciation up to year 6 is 6,000,000 shs.

How to calculate depreciation using the straight line method?

The depreciation using the straight line method is given by the formula:

Depreciation expense per year = (Initial cost - Salvage value) / Useful life

Initial cost = 5,000,000 + 800,000 + 1,500,000 = 7,300,000 shs.

Salvage value = 1,300,000 shs.

Depreciation expense per year = (7,300,000 - 1,300,000) / 6

= 6,000,000 / 6

= 1,000,000 shs.

Thus, the depreciation expense for each year is 1,000,000 shs.

Accumulated depreciation up to year 6 = Depreciation expense per year * Number of years

Accumulated depreciation up to year 6 = 1,000,000 * 6 = 6,000,000 shs.

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I think the answers for 3 and #3 part B are 96, and 144

Please tell me if I got it wrong :)

The area of the shaded region in the specified figure of the square containing a circle is 21.5 m², which is the first option

21.5 square meters

What is a square?

A square is a quadrilateral with all sides of the same length and four interior angles which are right angles.

The figure is a composite figure comprising of a square and a circle

The radius of the circle, r = 5 meters

The side length of the square = 10 meters

The value of π = 3.14

The area of the square = 10 m × 10 m = 100 m²

The area of the circle = π × (5 m)² = 25·π m²

The area of the shaded region is the difference between the area of the square and the area of the circle, therefore;

The area of the shaded region = (100 - 25·π) m²

The area of the shaded region is therefore; (100 - 25 × 3.14) m² = 21.5 m²

The area of the shaded region is 21.5 square meters

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Answer:

5.4

Step-by-step explanation:

square of 29 = 5.385164807

5.385164807 estimated is 5.4

The formula for finding revolution ​is

Revolutions = Distance traveled / Circumference of the object.

What are Revolutions:

In physics and mechanics, revolutions refer to the number of times an object completes a full circular motion around an axis or a point.

A revolution is a complete turn around a fixed point or axis, and it is often measured in terms of rotations per minute (RPM) or cycles per second.

For example, a car tire completes one revolution when it turns once completely around its axis. Similarly, a planet completes one revolution when it completes one full orbit around its star.

The formula for finding revolution: ​

The formula for finding the number of revolutions of a rotating object is:

Revolutions = Distance traveled / Circumference of the object

Where distance traveled is the linear distance that the object has covered, and circumference is the distance around the circular cross-section of the object.

Therefore,

The formula for finding revolution ​is

Revolutions = Distance traveled / Circumference of the object.

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There are two solutions for given system of equations: (5, 35) and (-4, 8).

What does "system of equations" and its solution means ?

A system of equations is a grouping of two or more equations with numerous variables that are treated as a whole. The solution to a system of equations is the set of variable values that satisfies all of the equations in the system at the same time.

Typical approaches for resolving equation systems include:

Substitution MethodElimination MethodMatrix MethodGraphical Method

Given system of equations is,

[tex]y=x^2+2x[/tex]..................(1)

[tex]y=3x+20[/tex]..................(2)

Solving equations algebraically,

Equating the formulas for 'y' in both equations:

[tex]x^2 + 2x = 3x + 20[/tex]

Rearranging the equation :

[tex]x^2 - x - 20 = 0[/tex]

Here, we got a quadratic equation,Solving for values of x,

[tex](x - 5)(x + 4) = 0[/tex]

[tex]x - 5 = 0 \\x=5\\or\\x + 4 = 0\\x=(-4)[/tex]

For values of 'y', putting values of x in equation (1),

for x = 5,

[tex]y = 5^2 + 2(5)=25 + 10 = 35[/tex]

Thus, (5, 35) is one of the solution.

for x= -4,

[tex]y = (-4)^2 + 2(-4)=16 - 8 = 8[/tex]

Thus, (-4, 8) is other solution.

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The formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.

What is Function?

A function is a mathematical rule that assigns each input from a set (domain) a unique output from another set (range), typically written as y = f(x).

The notation "0{-10≤x≤10}" typically represents the domain of a function or an inequality. It means that the function is defined only for the values of x that are between -10 and 10 (including -10 and 10).

Assuming that the function in question is a constant function equal to zero, the parent function is f(x) = 0.

To describe the transformations that happened to this function, we need more information about the specific formula. For example, if the formula is:

g(x) = 0{-10≤x≤10}

Then there are no transformations from the parent function. The function is simply a constant function that is equal to zero over the interval [-10, 10].

However, if the formula is something like:

g(x) = 2 * 0{-10≤x+3≤10}

Then we can describe the transformations as follows:

Horizontal translation: The function has been shifted horizontally to the left by 3 units. This means that the point (3, 0) on the parent function is now located at the origin (0, 0) on the transformed function.

Dilation/reflection: The function has been reflected about the y-axis and vertically scaled by a factor of 2. This means that the point (-1, 0) on the parent function is now located at (-4, 0) on the transformed function, and the point (1, 0) on the parent function is now located at (2, 0) on the transformed function.

Vertical translation: There is no vertical translation in this case, since the constant function is already centered at y = 0.

To summarize, the formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.

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The formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.

What is Function?

A function is a mathematical rule that assigns each input from a set (domain) a unique output from another set (range), typically written as y = f(x).

The notation "0{-10≤x≤10}" typically represents the domain of a function or an inequality. It means that the function is defined only for the values of x that are between -10 and 10 (including -10 and 10).

Assuming that the function in question is a constant function equal to zero, the parent function is f(x) = 0.

To describe the transformations that happened to this function, we need more information about the specific formula. For example, if the formula is:

g(x) = 0{-10≤x≤10}

Then there are no transformations from the parent function. The function is simply a constant function that is equal to zero over the interval [-10, 10].

However, if the formula is something like:

g(x) = 2 * 0{-10≤x+3≤10}

Then we can describe the transformations as follows:

Horizontal translation: The function has been shifted horizontally to the left by 3 units. This means that the point (3, 0) on the parent function is now located at the origin (0, 0) on the transformed function.

Dilation/reflection: The function has been reflected about the y-axis and vertically scaled by a factor of 2. This means that the point (-1, 0) on the parent function is now located at (-4, 0) on the transformed function, and the point (1, 0) on the parent function is now located at (2, 0) on the transformed function.

Vertical translation: There is no vertical translation in this case, since the constant function is already centered at y = 0.

To summarize, the formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.

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