Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of π (no approximations).

Answer: To find an equation for a parabola that passes through three specific points, we can use the method of algebraic manipulation.

Since the parabola is symmetric about the y-axis, the equation of the parabola will have the form y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.

Given three points (-2,7), (1, 10), and (2,27), we can use the vertex form of the equation and substitute the x, y values of the three points to find the values of a, h and k

y = a(x-h)^2 + k

Since it is passing through (-2,7), we can substitute the values of x and y in the equation and get

7 = a(-2 - h)^2 + k

It passing through (1, 10), we can substitute the values of x and y in the equation and get

10 = a(1 - h)^2 + k

It passing through (2,27), we can substitute the values of x and y in the equation and get

27 = a(2 - h)^2 + k

Now we have three equations with three variables, we can solve it using any of the techniques such as substitution, elimination or matrix. But the final equation will be in the form of y= a(x-h)^2 + k

Here, x= (-2, 1, 2) and y = (7, 10, 27) . Therefore it has a unique parabola passing through these points.

Step-by-step explanation:

The probabilities are given as follows:

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

The parameter values for this problem are given as follows:

Hence the probability of one senior having the birthday on the same day as the graduation is of:

P(X = 1) = 68 x 1/365 x (364/365)^67 = 0.1550.

The probability of more than one is given as follows:

P(X > 1) = 1 - P(X <= 1).

In which:

P(X <= 1) = P(X = 0) + P(X = 1)

Hence:

Finally:

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The angle of a turn clockwise from South East to North is Option B 135°.

When determining the angle of turn, it is important to consider the direction of rotation (in this case, clockwise) and the starting and ending points (in this case, South East to North).

If we imagine the compass as a clock, with North at the 12 o'clock position, South at the 6 o'clock position, East at the 3 o'clock position, and West at the 9 o'clock position. Then South East would be at the 4:30 position and the North would be at the 12 o'clock position. To rotate from 4:30 (South East) to 12 o'clock (North) in a clockwise direction, we would have to rotate 135 degrees. Thus, the angle of a turn clockwise from South East to North is 135 degrees.

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Saad's income tax will be N.I.L.

Here, saad's yearly income is Rs 2,36,000.

The rate of income tax on his income will be nil because,

    INCOME                                TAX RATE

0-2,50,000                                    NIL

2,50,000-5,00,000                       5%

5,00,001-10,00,000                       20%

More than 10,00,000                      30%

                          Computation of tax liability of Saad

Tax on 1st 2,36,000 = N.I.L

As his income is less than 2,50,000 no income tax shall be charged to saad's income.

Therefore, the tax liability of saad would be 0.

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When subtracted -2a+7b=-5 from the other equation so the b-terms become opposites, we get 2a -7b = 5 as the result.

In mathematics, an equation is an expression or a statement made up of two algebraic expressions with the same value that are separated by the equal sign. It is a mathematically quantified version of an otherwise expressed statement. Equations can take many different forms. Equations are used to compare two expressions.

To Subtract -2a+7b=-5 from the other equation so the b-terms become opposites, we need to make +7b to -7b

This is only possible when the other term has 14,

Lets solve

 2a + 7b = - 5

- 4a + 14b = -10

-2a -7b = 5

Thus, when subtracted -2a+7b=-5 from the other equation so the b-terms become opposites, we get 2a -7b = 5 as the result.

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Answer:

x = 16/9

Step-by-step explanation:

9x -16 = 0

9x = 16

x = 16/9

Let's check

9(16/9) -16 = 0

144/9 - 16 = 0

16 - 16 = 0

0 = 0

So, x = 16/9 is correct!

Answer:

Step-by-step explanation:

9x = 16

x = 16/9

Answer:

4382 contains 4 significant figures, 4382 round to 1 significant figure is 4000.

The changes to the slope and to the intercept of the linear function after the transformation g(x) = f(x) + k, in which k = 2, are given as follows:

The slope-intercept definition of a linear function is presented as follows:

y = mx + b.

In which the coefficients are given as follows:

The function f(x) in this problem is given as follows:

f(x) = -2x + 3.

Meaning that it has a slope of -2 and and intercept of 3.

The function g(x) is defined as follows:

g(x) = f(x) + k.

Since k = 2, we have that:

g(x) = f(x) + 2

g(x) = -2x + 3 + 2

g(x) = -2x + 5.

Hence the slope and the intercept are given as follows:

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Answer:

y = 2x + 10

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 5, 0) and (x₂, y₂ ) = (0, 10) ← 2 points on the line

m = [tex]\frac{10-0}{0-(-5)}[/tex] = [tex]\frac{10}{0+5}[/tex] = [tex]\frac{10}{5}[/tex] = 2

the line crosses the y- axis at (0, 10 ) ⇒ c = 10

y = 2x + 10 ← equation of line

As per the power rule of exponents, the solution of 3 to the power of 3 is 27.

The term exponent in math is defined as a number shows how many times the number is multiplied by itself.

Here we have to solve 3 to the power of 3.

Here according to the Power Rule of Exponents then we have the rule as

=> aⁿ = a × a × a... (n times)

Therefore, the given expression is written as

=> 3³

Now, based on the power of exponent rule it can be rewritten as,

=>  3 × 3 × 3

Then we have to multiply the values then we get

=> 27

Therefore, the value of 3 raised to 3rd power is 27.

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The given sequence is arithmetic because the difference between consecutive terms is constant. The common difference is 1, since the difference between each pair of consecutive terms is 1 (e.g., 5 - 4 = 6 - 5 = 1). The common difference can be expressed in simplest form as 1/1 = 1.

Answer:

it is arithmetic, 6-5=1, 5-4=1

After simplifying each expression, we get (2+5a - 10 b), (8a² - 15ca +2c),

(11- 2a+b) and (a+ b) respectively.

The word simplify means to write an expression, equation or problems

in the simplest form so as to easy to evaluate it. we simplify an expression by removing the parenthesis and collecting like terms.

exercise 1.

given, A = 7 - 4a + 7a - 3b -5 -7b +2a

We collect the like term and get

A= 7 - 5 -4a +7a +2a -3b- 7b

A = 2 + 5a -10b

next, given B = 4a × 2a -5c - c +8c -3c × 5a

             B = 8a² -6c +8c - 15ca

        B = 8a² -15ca +2c

exercise 2.

given, A = 7 + [(2- a) -( 2+a) +9] + (b-5)

at first, we remove the parenthesis and get

A= 7 + [2-a - 2 -a+ 9] +b- 5

A = 7 + 9- 2a +b- 5

after collecting the like term

A = 11- 2a + b

given, B = 15 - [(7-b) - 9- (a-17)]

  B = 15 - [7- b- 9 - a+17]

 B = 15 - [15 - b -a]

after removing the parenthesis

B = b +a

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Answer:

The least common denominator is 8, you need to multiply the 3 by 2.

Answer:

8

Step-by-step explanation:

The factors of 2[tex]x^{2}[/tex] + 7x + 3 are ( x + 3) and (2x + 1)

Now, According to the question:

The given function is :

f(x) = [tex]2x^2+7x+3[/tex]

To find the factors of  [tex]2x^2+7x+3[/tex] we need to split the middle term, that is, 7x.

7x = 6x + x

Therefore, 2[tex]x^{2}[/tex] + 7x+ 3 can be written as 2[tex]x^{2}[/tex] + 6x + x + 3 .

On taking '2x' common from first two terms and +1 from next two terms we get

2x (x + 3) +1 (x + 3)

(x + 3) (2x + 1)

Thus, the factors of 2x2 + 7x + 3 are (x+3) and (2x+1)

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The complete question is this:

What are the factors of 2x^2+7x +3?

2x2+4x5=0 is a quadratic equation that can be solved. 2 x 2 + 4 x - 5 = 0. To find the answers, start with the quadratic formula.

Using the quadratic formula, determine the roots of the quadratic equations 2x2-3x-5= 0. The equation's roots must be located. As a result, the equation's roots are 5/2 and -1. Which equation with 2 as a root must be identified. As a result, 2 is not a root of x2-4x + 5= 0.

Since 2 is not a root, x2 + 3x-12= 0 cannot be solved. Thus, 2 is the root of the equation 2x2-7x + 6= 0. The roots of the quadratic equation ax2 + bx + c= 0 are real and equivalent if the discriminant is equal to zero (b2-4ac=0), a, b, and c are real values, and a0. The roots in this situation arex= -b/2a.

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Answer:

2[tex]x^{4}[/tex] + 8[tex]x^{2}[/tex]

Step-by-step explanation:

[tex]x^{2}[/tex](2[tex]x^{2}[/tex] + 8)  When you are multiplying powers that have the same bases, you add the exponents.

Negative Slope can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created.

In the given question, we have to find what phrases can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created.

As we know that,

(1) Negative Slope: A line with a negative slope is one that is moving from left to right in a downward direction. The rise to run ratio of the line, in other words, is negative.

(2) Decreasing Function: For a given function, y = F(x), the function is known as an increasing function if the value of y increases as the value of x increases, and the function is known as a decreasing function if the value of y decreases as the value of x increases.

(3) Constant Slope: Small slopes correspond to low speeds, negative slopes to high speeds, and constant slopes (straight lines) to steady speeds.

Hence, Negative Slope can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created.

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The 5th interval is called perfect

Interval notation is a method to represent an interval on a number line.

The 5th interval is called perfect

Interval notation is a method to represent an interval on a number line. In other words, it is a way of writing subsets of the real number line. An interval comprises the numbers lying between two specific given numbers. For example, the set of numbers x satisfying 0 ≤ x ≤ 5 is an interval that contains 0, 5, and all numbers between 0 and 5.

Interval Notation is a way of expressing a subset of real numbers by the numbers that bound them. We can use this notation to represent inequalities. We know an interval expressed as 1 < x < 5 denotes a set of numbers lying between 1 and 5.

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The expression 14x⁴y³ - 42x³y⁴ is rewritten to 14x³y³(x - y)

An algebraic expression can be described as a mathematical expression that is made up of terms, coefficients, variables, factors and constants.

They are also made up of some arithmetic operations, such as;

From the information given, we have the algebraic expression;

14x⁴y³ - 42x³y⁴

Now, factor the common numbers, we have;

14(x⁴y³ - 3x³y⁴)

Factor the common variables, we get;

14x³y³(x - y)

Hence, the expression is 14x³y³(x - y)

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The speed of the Bike is 5 meters per second

Speed is a scalar quantity that describes how fast an object is moving . It is defined as the distance an object travels divided by the time it takes to travel that distance. The units of speed are typically meters per second (m/s) or kilometers per hour (km/h).

To find out how fast you are traveling on your bike, you can use the formula:

Speed = [tex]\frac{Distance}{Time}[/tex]

In this case, the distance is 340 meters and the time is 68 seconds. So, you can plug these values into the formula and get:

Speed = 340 meters / 68 seconds

Speed =  [tex]\frac{340 meters}{68 seconds}[/tex]  =   5 meters per second

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Answer:

-8 [tex]\leq[/tex] -8

Step-by-step explanation:

-8[tex]\leq[/tex]2-10

-8[tex]\leq[/tex]-8

Answer:

-8

Step-by-step explanation:

-8≤2-10
2-10 = -8
-8≤-8

If a line is drawn so that it passes through the point [tex](2,-1)[/tex] and [tex](0,5)[/tex] , then  slope of line is -3 .

What is Slope ?

The slope of a line is defined as measure of steepness and direction of  line. The slope of line in a plane help in predicting whether lines are parallel, perpendicular, or none without using a compass.

The slope of line passes through points [tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] is calculated by formula ⇒ [tex]Slope = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex] ;

the points are given as  [tex](2,-1)[/tex] and [tex](0,5)[/tex]  ;

So , on substituting the values in the slope formula ,

we get ;

[tex]Slope = \frac{5 -(-1) }{0 -2 }[/tex] ;

= [tex]\frac{6}{-2}[/tex]

= -3 .

Therefore , the required slope of the line is -3 .

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The length of the straw is 3.74 inches.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

In rectangular box,

Length (l) = 2 inches

Width (w) = 1 inches

Height (h) = 3 inches

Here, The straw is said to fit into the box diagonally from the bottom.

So, the length (s) of the straw is calculated as:

⇒ s = √ l² + w² + h²

⇒ s = √ 2² + 1² + 3²

⇒ s = √ 4 + 1 + 9

⇒ s = √ 14

⇒ s = 3.74 inches

Thus, The length of straw = 3.74 inches

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The length of the straw will be 3.7416  inches long in radical form.

If a cuboid has length = l units, breadth = b units, and height = h units, then we can evaluate the length of the diagonal of a cuboid using the formula : X²=l²+b²+h²

Here,

As per the question the length of the straw is equal to length of the diagonal of Rectangular box.

l= 3 inch , b= 2 inch , h= 1 inch

Let us consider the length of the straw be 'x'.

As, Diagonal of Cuboid is,

X²=14

X=√14

i.e. X=3.7416

We get, X= 3.7416 (in radical form)

Hence, the length of the straw will be  5.91607 inches.

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The sum of the measures of the four interior angles of a quadrilateral is always 360°

A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles.

Given is, A quadrilateral is a polygon with four sides. Consider the quadrilateral and the dashed segment

If we draw one diagonal to quadrilateral we will get two triangles i.e. △ABC and △ACD and we know that sum of the angles of a triangle is 180°

Sum of angles of quadrilateral ABCD = sum of angles of △ABC + sum of the angles △ACD

= 180° + 180°

= 360°

If we take examples of a square or a rectangle, we know that they are also a quadrilateral and also their each angle is right angle, i.e. 90°

Therefore, the sum of their interior angles will = 90×4 = 360°

Hence, we can say that the sum of the measures of the four interior angles of a quadrilateral is always 360°

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Answer:

Below

Step-by-step explanation:

Formula for sum of interior angles of a   n - gon

(n-2) * 180

for this 12 sided 'gon

  (12-2) * 180 = 1800°        

            ( and for a 'regular' dodecagon each would be 1800/12 = 150°

Answer:

Option C) 1,800°

Step-by-step explanation:

To Find : Interior Angles of a Decagon

In order to find interior angles of any polygon we usually use the formula

(n-2)x180

Over Here it is a 12 sided polygon

So,

(12-2)x180

10x180

1800

Hence the interior angles of a decagon is 1800°

%, a relative figure signifying hundredths of any amount. Before the raise, I was making $45,000.

A percentage that represents a tenth of a quantity. In essence, percentages are fractions with a denominator of 100. The percent symbol (%) is placed next to a number to indicate that it is a percentage. For instance, you would have received a 75% on the examination if you correctly answered 75 out of 100 questions (75/100).

Calculating a percentage involves dividing an item by its sum and multiplying the result by 100.

Considering the query

It was $52,200 after a 16% raise in my pay.

In light of the conditions stated, come up with

[tex]$=\frac{52200}{1+16 \%}$$=\frac{52200}{1+0.16}$$=\frac{52200}{1.16}$$=\frac{5220000}{116}$[/tex]

= $45000

Before the raise, I was making $45,000.

Therefore, the answer is $45,000.

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Answer:

x < -20

Step-by-step explanation:

To solve x/5 + 6 < 2,

First subtract 6 from both sides of the equation.

This makes x/5 < -4.

Then multiply both sides of the equation by 5.

This makes x < -20.

Therefore, the solution to the equation is x < -20.

The secret calculator app is used to protect confidential Photos, Videos, Documents, Passwords, Notes, Contacts and To Dos.

The term calculator is referred as a device that performs arithmetic operations on numbers and it does the basic calculators can do only addition, subtraction, multiplication and division mathematical calculations.

Here we need to find definition and the usage of secret calculator app.

As per the definition of calculator here we know that the app is used to acts like a photo vault to store all password protected files, and can only be viewed inside the app.

As the user who is unaware of this app you will never expect a simple calculator looking app is used to hide files.

Here if you want to access this you will need the password to open the photos from your child.

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The simplified form of the given fraction is, [tex]\frac{1}{x^2y}[/tex].

What is simplified form of the expression?

If a fraction's top and bottom have only the number one in common, then it is expressed in its simplest form. The top and bottom cannot be divided further and remain whole numbers, in other words. The phrase "lowest terms" is another term for the simplest form.

Consider, the given expression

[tex]\frac{(\frac{1}{x^2}-\frac{2}{y} )}{y-2x^2}[/tex]

We have to find the simplified form of the given expression.

Taking cross multiplication of numerator of the above fraction.

[tex]\frac{(\frac{y-2x^2}{x^2y} )}{y-2x^2}[/tex]

Using: [tex]\frac{(\frac{a}{b} )}{c} = \frac{a}{b}*\frac{1}{c}[/tex]

⇒  [tex]\frac{(\frac{y-2x^2}{x^2y} )}{y-2x^2} = \frac{y-2x^2}{x^2y} *\frac{1}{y-2x^2} = \frac{1}{x^2y}[/tex]

Hence, the simplified form of the given fraction is, [tex]\frac{1}{x^2y}[/tex].

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