Prove that the Union where x∈R of [3− x 2 ,5+ x 2 ] = [3,5]

Answer: x ≤ 5

Step-by-step explanation:

x - 9  -->   x + (-9)

-9 + 5 = -4

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

Explanation:

You are correct in thinking you'll set two things equal to one another. This type of thing happens often in algebra. The question you probably have is: what two things do I set equal?

The key term is "isosceles" which tells us we have two non-parallel sides equal in this trapezoid. In other words, we ignore the parallel sides.

The non-parallel sides of a trapezoid are known as the legs.

The legs in this case are

Set those expressions equal to one another and solve for the variable y.

AB = CD

7y-4 = 8y-18

-4+18 = 8y-7y

14 = y

y = 14 is the final answer

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

Check:

Both legs AB and CD are 94 units long to confirm this trapezoid is indeed isosceles. The answer is confirmed.

Side note: as mentioned earlier, we completely ignore BC = 4y-6. It was probably put in there as a distraction.

The required new average is 646-kilowatt hours per year,

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

here,
Last year, wind turbines along a hilly ridge had an average output of 340-kilowatt hours per year. The turbines were upgraded, and now their average annual output is 90% more.

So,
new average = 340 + 90% of 340
new average = 340 + 0.90 × 340
new average = 340 + 306 = 646 kilowatt hours per year,

Thus, the required new average is 646-kilowatt hours per year,

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Answer:

100 should be added as 8100 is square root of 90 ...

The equation which is used to determine number of balloons were originally in bag is 3(b-8)=21 and the number of balloons in each bag on?

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Based on the given conditions, formulate:  3×(b-8)=21

Reduce the greatest common factor on both sides of the equation:

b-8 =7

Rearrange unknown terms to the left side of the equation: b = 7+8

Calculate the sum or difference: b=15

The equation which is used to determine number of balloons were originally in bag is 3(b-8)=21 and the number of balloons in each bag is 15.

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The circumference of the jar is 56.57cm.

The radius of the jar is 9 cm.

A cylinder is a three-dimensional object. It is a prism with a circular base.

The curved surface area of a cylinder = 2πrh

Where:

1584 = 2 x 3.14 x 28 x r

r = 1584 / (2 x 3.14 x 28)

r = 9 cm

Circumference = 3.14 x diameter

diameter = 2 x radius

3.14 x 2 x 9 = 56.57cm

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On solving the provided question, we can say that the domain of the following data will be domains = [  (( 2.28 , 2.06) to ( 1.18 , 0.70) ] and  [  (( 9 , 11) to ( 11 , 17) ]

The domain of a function is the set of possible values that it can accept. The x-values of a function like f are represented by these integers (x). A function's domain is the set of possible values on which it can be used. This set is the value that the function returns after the insertion of the x value. Y = f is the definition of a function with x as the independent variable and y as the dependent variable (x). A value of x is said to be in a function's domain if it can be successfully utilised to produce a single value of y by using the value of x.

the domain of the following data will be

domains = [  (( 2.28 , 2.06) to ( 1.18 , 0.70) ]

domains = [  (( 9 , 11) to ( 11 , 17) ]

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According to the following interpretation, a correlation value of 0.7 between two variables denotes a significant and favorable association between them.

Correlation coefficients demonstrate how strongly two independent variables, x and y, are connected linearly.

A linear correlation coefficient greater than zero indicates a relationship that is favorable.

A value less than zero denotes a bad relationship. To summarize, when x and y have values of 0, there is no link between them.

A statistic that describes how closely two variables' movements are related to one another is the correlation coefficient (r2).

The most widely used correlation coefficient is the Pearson product-moment correlation, which is used to detect if two variables are linearly related.

This correlation value, however, might not always be an accurate predictor of reliance in a non-linear link.

Hence, According to the following interpretation, a correlation value of 0.7 between two variables denotes a significant and favorable association between them.

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Answer: 3 = 12 , 4 = 2 , 2 = 22
             

Step-by-step explanation: Since t represents the number of tickets purchased, we need to plug that into our equation.

d = -10t + 42

d = -10(3) + 42

We know that d is the balance of the bank account, so if we plug in the number of tickets purchased, we will solve to get the balance of the bank account.

d = -10(3) + 42

d = -30 + 42

d = 12

In this equation, If we purchase 3 tickets, the balance of the bank account would be 12 dollars.

Let's do the last 2 equations using d = -10t + 42.

d = -10(4) + 42

d = -40 + 42

d = 2

In this equation, If we purchase 4 tickets, the balance of the bank account would be 2 dollars.

d = -10(2) + 42

d = -20 + 42

d = 22

In this equation, If we purchase 2 tickets, the balance of the bank account would be 22 dollars.

Solving the provided question, we can say that the quadratic equation  2x³+4x2 + 7x + 5 is divided by (x+1) =  -2+4-7+5 = 0

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

the quadratic equation

2x³+4x2 + 7x + 5 is divided by (x+1)

which means X+1 is factor

so, x = -1

2x³+4x2 + 7x + 5  = -2+4-7+5 = 0

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Answer:

Skills Practice. Multiplying a Polynomial by a Monomial. Find each product. 1. a(4a + 3). 2. -c(11c + 4). 4a2 + 3a. -11c2 - 4c. 3. x(2x - 5). 4. 2y( y - 4).

Step-by-step explanation:

Answer:16

Step-by-step explanation:

Residual=actual y value−predicted y value,ri=yi−^yi. Residual = actual y value − predicted y value , r i = y i − y i ^ . Having a negative residual means that the predicted value is too high, similarly if you have a positive residual it means that the predicted value was too low..

What Exactly Is Residual Value?

The estimated value of an asset that is fixed at the end of its useful life or lease term is its residual value, which is often referred to as salvage value. In lease agreements, the residual value is one of the lessor's main methodologies for calculating the lessee's periodic lease payments.

A good residual value is what?

Check out the Car Lease Ratings section of our Lease Kit for a complete list of high-residual vehicle brands and models.

                A car is probably not a good lease deal if the lease-end residual value is less than 50% of the MSRP (for a 36-month lease). 55% to 65% of MSRP would be a nice residual.

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Double prime is called by different names as per the topics used in Mathematics :

Inches in length , second order derivative in differentiation, conjugate points, transformed coordinates etc.

As given in the question,

Therefore, the double prime is known by many names such as inches in length, second order derivative, conjugate points, transformed coordinates etc.

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A number's square root multiplied by another number's square root does not always equal the total of these two numbers' square roots.

A statistical method called the sum of squares (SS) is used in regression analysis to determine how well the data can fit the model and how dispersed the data are. Since it is determined by adding up the squared differences, the sum of squares is how it is calculated.

A sum's square is equal to the product of its summands' squares and its double products' sums of summands in twos.

So, it is not always true that the square root of a sum is equal to the sum of the square roots.

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A number's square root multiplied by another number's square root does not always equal the total of these two numbers' square roots.

In regression analysis, the sum of squares (SS), a statistical technique, is used to assess how well the data fit the model and how distributed they are. The sum of squares is used to compute it as it is obtained by combining together the squared differences.

The product of a sum's square and its double products' sums of its summands in twos is known as the summands' square. Hence, the square root of such a sum is not necessarily equal to the total of the square roots.

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12 m length rope of 10 pieces and 17 m rope of 5 pieces.

The equation that has two variable terms and another equation is needed to solve both equations simultaneously is called equation with two variables.

Given, total length of rope = 205 m.

The rope is cut into 10+5 = 15 pieces, in where 10 pieces rope are the same size, and the remaining 5 pieces are different size.

assume, length of first 10 piece = X m

length of last 5 piece = Y m

As per the first condition, total length of three of the first 10 length exceeds that of two the second length by 2 m.

hence, 3X - 2Y = 2

again, we know the total length = 205 m

10X + 5Y = 205

from the first equation, 3X = 2 +2Y

                                X = (2+2Y) / 3

putting the X value to the 2nd equation and we get

10(2+2Y)/3 + 5Y = 205

20+ 20Y+15Y = 615

35Y = 595

Y = 17 m

X = (2+2×17) /3 = 12 m

10 pieces of X length = 10 pieces of 12 m length

5 pieces of Y length = 5 pieces of 17 m length

10×12 = 120m

5×17 = 85m

120m + 85m = 205m

hence, verified.

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Breanna was biking at a constant rate of 14 miles per hour.

A rate can be defined as the speed at which something happens or changes or the amount or number of times it happens or changes in a particular period.

The formula that describes the relationship between distance (d), rate (r), and time (t) is d = rt.

Now, we will solve for r. From d = rt. Our r will equals to:

= d/t.

Now we compute the rate at which Breanna was biking.

= 84 miles/6 hours

= 14.

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The quadrant of the given point (2,3) is given A I ( that is first quadrant ).

As given in the question,

Given point is equal to :

Point ( 2, 3 )

Conditions of the quadrant in the coordinate plane is given by :

Let ( x ,y ) be the coordinates in the coordinate plane.

In the first quadrant :  ( x , y ) both x and y are positive.

In the second quadrant :  ( -x , y )  x is negative and y is positive.

In the third quadrant :  ( -x , -y ) x is negative and y is negative.

In the fourth quadrant :  ( x , -y )  x is positive and y is negative.

Here in the given point ( 2,3 ) both x and y are positive.

Given point lies in the first quadrant.

Therefore, the quadrant of the given point (2,3) is equal to A I ( that is first quadrant ).

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A line of best fit can be described by the equation y=mx+b, where m denotes the slope and b the y-intercept. For a better understanding of the idea of approximating the equation of a line of best fit and making predictions, we will look at two examples that show a scatter plot with a line of best fit.

What is a line, exactly?

Having only length and no width, a line is a one-dimensional figure. A line is created from a collection of points that are endlessly stretched in the opposing directions.

                  A two-dimensional plane's two points serve as its determining factors. Collinear points are two points that are located on the same line.

What is the equation for a straight line?

. A straight line has the equation y=mx+c, where c is the height at which the line crosses the y-axis, also known as the y-intercept, and m is the gradient.

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The percent of the dresses that are for films set in the 1700s or during the civil war era is; 75%

Percentage is normally calculated by dividing the value by the total value, and then multiplying the result by 100. It is given by the expression; Percentage = (value / total value) * 100%

Now, we are told that;

Number of movie dresses kept = 240 dresses

Fraction used for  movies that take place in the 1700s = 3/5

Percentage used for movies in the civil war era = 15%

Thus;

Number of dresses in the 1700 = 3/5 * 240 = 144

Number of dresses for the civil era = 15% * 240 = 36

Thus;

Total for civil era and in the 1700s = 144 + 36 = 180

Thus;

Percentage for either period = 180/240 * 100% = 75%

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Perimeter of a semi circle = ñr + d(2r),ñ=22/7,r=?, d=2r

54=22/7 × r +2r

54=3.142r +2r

54=5.142r

r=54/5.142

r=10.5

d=2r

d=2×10.5017

d=21.00cm

The domain of f(x) = x is all real numbers. This is because the input (x) is the same as the output (f(x)).

This means that any value that is inputted into the function will result in the same value as the output, regardless of the value. The domain of the function can be expressed mathematically as:

Domain of f(x) = x = {x ∈ R}

This means that the domain of f(x) is all real numbers, as any real number put into the function will result in that same real number being outputted. For example, if x = 5, then f(x) = 5. This illustrates that the domain of f(x) = x is all real numbers.

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The solution using laws of exponents are;

A) 10⁻⁵

B) 10³

C) 10⁻²

D) 10⁻²⁰

E) 10⁻¹

F) 10⁻¹⁴

Some of the laws of exponents are;

1) Product of powers rule:

When multiplying two bases with the same value, keep the bases the same and then add the exponents together to get the solution

2) Quotient of powers rule; When trying to divide two bases of the same value, keep the base the same, and then subtract the exponent values.

3) Power of a power rule; This rule tells how to solve equations where a power is being raised by another power.

4) Power of a product rule; Whenever any base is being multiplied by an exponent, then we distribute the exponent to each part of the base.

A) 10⁻³ × 10⁻²

= 10⁻³⁻²

= 10⁻⁵

B) 10⁴ × 10⁻¹

= 10⁴⁻¹

= 10³

C) 10⁵/10⁷

= 10⁵⁻⁷

= 10⁻²

D) (10⁻⁴)⁵

= 10⁻⁴*⁵

= 10⁻²⁰

E) 10⁻³ × 10²

= 10⁻³⁺²

= 10⁻¹

F) 10⁻⁹/10⁵

= 10⁻⁹⁻⁵

= 10⁻¹⁴

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Therefore , the solution of pythgoras theorem is the value of is dx/dt = 0.95, when x = 12 and y =5.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.

Here,

It is given that -

dz/dt = 1,

dx/dt = 3(dy/dt)

⇒dy/dt = 1/3 (dx/dt)

As shown in the diagram x = base, y = perpendicular and z = hypotenuse.

According to the Pythagoras theorem -

z² = x² + y²

Differentiating both sides -

d/dt (z²) = d/dt (x² + y²)

2z dz/dt = 2x dx/dt + 2y dy/dt

z dz/dt = x dx/dt + y dy/dt

Substituting the value of  dy/dt -

z dz/dt = x dx/dt + y/3 (dx/dt)

z dz/dt = dx/dt (x + y/3)

dx/dt = (z dz/dt)/(x + y/3)....equation 1

So, when x = 12 and y = 5, the value of z -

z = √[(12)² + (5)²]

z = √(144+25)

z = √169

z = 13

Substituting the value of x, y, z and dz/dt in equation 1 -

dx/dt = (13 × 1)/(12 + 5/3)

dx/dt = 13 / 41/3

dx/dt = (13 × 3)/41

dx/dt = 39/41

dx/dt = 0.95

Therefore, the value of dx/dt = 0.95.

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Therefore , the solution of pythgoras theorem is the value of is dx/dt = 0.95, when x = 12 and y =5.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.

Here,

It is given that -

dz/dt = 1,

dx/dt = 3(dy/dt)

⇒dy/dt = 1/3 (dx/dt)

As shown in the diagram x = base, y = perpendicular and z = hypotenuse.

According to the Pythagoras theorem -

z² = x² + y²

Differentiating both sides -

d/dt (z²) = d/dt (x² + y²)

2z dz/dt = 2x dx/dt + 2y dy/dt

z dz/dt = x dx/dt + y dy/dt

Substituting the value of  dy/dt -

z dz/dt = x dx/dt + y/3 (dx/dt)

z dz/dt = dx/dt (x + y/3)

dx/dt = (z dz/dt)/(x + y/3)....equation 1

So, when x = 12 and y = 5, the value of z -

z = √[(12)² + (5)²]

z = √(144+25)

z = √169

z = 13

Substituting the value of x, y, z and dz/dt in equation 1 -

dx/dt = (13 × 1)/(12 + 5/3)

dx/dt = 13 / 41/3

dx/dt = (13 × 3)/41

dx/dt = 39/41

dx/dt = 0.95

Therefore, the value of dx/dt = 0.95.

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Answer:

an average weight of 10student was calculated to be 75. later it was discovered thatone weight wss insread as 35 instead of 50k.g. calculate the correct average weight

The mean of the given data set is 21.7 and the sample proportion of numbers less than the mean is 60%.

Consider the given data set (in the image attached to this answer). We have to find the mean of the data set is, and the sample proportion of numbers. We have been told that any non-integer answers should be entered as decimals, rounded to the tenth place. The means is the average of any data set.

Here, mean = (20.5 +24.2 +18.3 + 1.3 +27+25.5 +21+19.8+27.3+18·4 + 20.5+17-6 +25.5 +23.4 +20.2)/15

Mean = 325.5/15 =21.7

The sample proportion of numbers less than

Mean = 9/100 * 15 %

Answer: 21.7 60%

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The value of the function (g - f)(x) = 6 - 4 + x² at x = 3 will be 11.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The functions are given below.

f(x) = 4 - x² and g(x) = 6

The function (g - f)(x) will be given as,

(g - f)(x) = 6 - 4 + x²

(g - f)(x) = 2 + x²

The value of the function (g - f)(x) at x = 3 will be give as,

(g - f)(x) = 2 + (3)²

(g - f)(x) = 2 + 9

(g - f)(x) = 11

The value of the function (g - f)(x) = 6 - 4 + x² at x = 3 will be 11.

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Answer:

Step-by-step explanation:

divided by nine ;)

The histogram for the data-set in this problem is given by the image presented at the end of the answer.

The histogram of a data-set shows the number of times that each item was observed in the data-set.

For this problem, we have that:

Hence the histogram is given by the image at the end of the answer.

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