Solving in equality

The minimum value of the function g(x) = (x-3)² occurs at the vertex of the parabola, which is located at x = 3. At this point, the value of the function is g(3) = (3-3)² = 0.

To see why this is the case, we can use the fact that the vertex of a parabola in the form f(x) = a(x-h)² + k is located at (h,k). In the case of g(x) = (x-3)², we have a = 1, h = 3, and k = 0, so the vertex is located at (3,0).

Since the parabola opens upwards (the coefficient a is positive), the value of the function is minimized at the vertex.

Therefore, the minimum value of g(x) is 0, which occurs at x = 3.

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Answer:  b and c

Step-by-step explanation:

just trust the sources

1/2πx2

The area of a circle is defined by πr2, and given the diameter, we must also multiply it to pi and square the value only after getting half of the value x.

Answer: 7/48

Step-by-step explanation:

The word of is interchangeable with multiplication.

1/6 times 7/8 = 7/48

Answer/Step-by-step explanation:

Since you know that the answer is x = 36, Then you can substitute it in the equation.

3/4(36) - 11 = 16          → Multiply 3/4 by 36

27 - 11 = 16                  → Subtract 11 from 27

16 = 16                        → They are equal

Hence as you can see, x = 36.

RevyBreeze

The equation "Y^2/9 - x^2/4=1" will produce the given graph. Therefore option B would be the correct answer.

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”. For example, 2x – 5 = 13.

An equation combines two expressions connected by an equal sign (“=”). These two expressions on either side of the equals sign are called the “left-hand side” and “right-hand side” of the equation. We generally assume the right-hand side of an equation is zero. This will not reduce the generality since we can balance this by subtracting the right-hand side expression from both sides’ expressions.

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The correct answer to the given question about possibility of the license plate is 7, 894, 720.

This problem involves counting the number of possible license plates that can be created with certain restrictions. The first two digits must be odd and repetition is not permitted. The remaining five characters can be any uppercase letter, also without repetition. By using the multiplication principle of counting, we can calculate the total number of possible license plates by multiplying the number of choices for each character position. In this case, we obtain a total of 7,894,720 possible license plates. For the first digit, there are 5 odd digits to choose from (1, 3, 5, 7, 9). After choosing the first odd digit, there are only 4 odd digits left to choose from for the second digit since repetition is not permitted.

For the third, fourth, and fifth characters, there are 26 uppercase letters to choose from for each character, with repetition not permitted. Therefore, the total number of possible license plates is:

5 × 4 × 26 × 26 × 26 × 26 × 26 = 7,894,720

So the correct answer is 7,894,720.

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Answer: x= 137 degrees and y= 43 degrees

Step-by-step explanation: The opposite angles of a parallelogram are congruent (equal). ∠A = ∠C and∠D = ∠B.

x is 137 because the opposite angle is congruent.
y is 43 because a parallelogram is equal to 360 degrees, so we would subtract the angles we already know (137+137) from the 360 which leaves you with 86. Since opposite angle are the same you’d have to divide 86 to make it equal for both opposite sides. So 43 on y and its opposite angle.

Answer

x=47°, y=43°

please mark as brainliest answer

To solve for n, we need to isolate the variable on one side of the equation.

Starting with:

-4.2 = -2.1n

We can divide both sides by -2.1:

-4.2 / (-2.1) = n

n = 2

To check, we can substitute 2 back into the original equation:

-4.2 = -2.1(2)

-4.2 = -4.2

Since both sides are equal, our solution of n = 2 is correct.

Therefore, the answer is a. 2.

Answer:

a. 2

negative times a positive equals a negative

n=2

the sum of the numbers in the sequence 3, −4, 5, −6, . . . , 101 is 51.

Company revenue quadratic function.

Angel

The revenue, in billions of dollars, for a company in the year 2002 was $2.7 billion. One year later, in 2003, the revenue had risen to $3.4 billion. In 2005, the revenue climbed to $3.9 billion, before falling to $2.7 billion in 2008. The revenue, r, in billions of dollars, for the company, is a quadratic function of the number of years since 2002, x. what is the vertex of the function?

To find the quadratic function that represents the revenue of the company as a function of the number of years since 2002, we can use the vertex form of a quadratic function:

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

where a is the coefficient of the quadratic term, h is the x-coordinate of the vertex, and k is the y-coordinate of the vertex.

We can use the given revenue values to set up a system of three equations:

2.7 = a(0 - h)^2 + k

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

2.7 = a(6 - h)^2 + k

Subtracting the first equation from the second, and the first equation from the third, we get:

0.7 = a(1 - h)^2

0 = a(6 - h)^2

Since a cannot be zero (otherwise we wouldn't have a quadratic function), we can divide the second equation by the first to get:

6 - h = 10

which gives us h = -4.

Substituting h = -4 into the first equation, we get:

2.7 = a(0 - (-4))^2 + k

2.7 = 16a + k

Substituting the revenue value for 2005, we get:

3.9 = a(3 - (-4))^2 + k

3.9 = 49a + k

Solving for a and k, we get:

a = -0.1

k = 4.3

Therefore, the quadratic function that represents the revenue of the company as a function of the number of years since 2002 is:

r(x) = -0.1(x + 4)^2 + 4.3

The vertex of this function is at (-4, 4.3).

Angel

What is the sum of the numbers in the sequence 3, −4, 5, −6, . . . , 101?

We can notice that the sequence alternates between adding an odd number and subtracting an even number. The first term is 3, which is odd, so the sequence starts by adding an odd number. The second term is -4, which is even, so the sequence then subtracts an even number. This pattern continues, so the sum of the sequence can be written as:

3 - 4 + 5 - 6 + ... + 101

We can group the terms into pairs:

(3 - 4) + (5 - 6) + ... + (99 - 100) + 101

Each pair of terms adds up to -1, so we can simplify the expression to:

-1 -1 -1 ... -1 + 101

where there are 50 pairs of -1's. The sum of 50 -1's is -50, so the sum of the sequence is:

-50 + 101 = 51

Therefore, the sum of the numbers in the sequence 3, −4, 5, −6, . . . , 101 is 51.

Step-by-step explanation:

[tex]f(-x)=-x^3+\frac{7}{x}[/tex]

[tex]-f(x)=-x^3+\frac{7}{x}[/tex]

To find [tex]f(-x)[/tex], you have to plug [tex]-x[/tex] into the function for [tex]x[/tex].

To find [tex]-f(x)[/tex], you have to multiply the entire function by [tex]-1[/tex].

Since both functions are the same, by the property of odd functions ([tex]f(-x)=-f(x)[/tex]), the function is odd.

Ball A reaches a greater height than Ball B.

To determine which ball reaches a greater height, we need to compare the maximum height each ball reaches.

For Ball A, we can use the formula for the vertex of a parabola, which is given by [tex]x = - \frac{b}{2a} [/tex], where a and b are the coefficients of the quadratic equation in standard form (ax² + bx + c = 0). In this case, a = -4.9 and b = 14.7, so the vertex of Ball A's path is at [tex]x = \frac{ - 14.7}{2 \times 4.9} = 1.5 [/tex] seconds.

To find the maximum height of Ball A, we can plug this value into the original equation:

[tex]f(1.5) = -4.9 \times {1.5}^{2} + 14.7(1.5) + 0.975 = 9.9 \: \: meters.[/tex]

For Ball B, we can look at the table and see that it reaches a maximum height of 8 meters.

Therefore, Ball A reaches a greater height than Ball B by 1.9 meters (9.9 - 8 = 1.9)

We can answer this question without graphing either function by using the properties of quadratic functions. The maximum height of a quadratic function occurs at the vertex, which can be found using the formula x = -b/2a. We can then plug this value into the function to find the maximum height. By comparing the maximum heights of the two balls, we can determine which ball reaches a greater height.

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The radius of the sphere when the volume and the radius are increasing at the same numerical rate is √(1/2π) cm.

The numerical rate of increase in the volume of a sphere with respect to the increase in the radius is given by numerical rate,

dn/dt=4πr² * dr/dt.

Here, dn/dt is the rate of increase of volume with time, dr/dt is the rate of increase of radius with time, and r is the radius of the sphere.

The rate of increase of radius is given as dr/dt=18 cm/s. We need to find the radius of the sphere when the volume and the radius are increasing at the same numerical rate.

Let dn/dt=18 cm³/s, which means the volume and radius are increasing at the same numerical rate. Then

18=4πr² * 18So, r²=1/2π => r = √(1/2π) cm

Therefore, In a sphere whose volume and radius increase at the same numerical rate, the radius is √(1/2π) cm.

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First five terms of the sequence are 4, 5, 9, 14, and 23.

For the given sequence an = an-1 + an-2, with a1 = 4 and a2 = 5:

1. Its first term is a1 = 4.
2. Its second term is a2 = 5.
3. To find the third term, use the formula: a3 = a2 + a1 = 5 + 4 = 9.
4. For the fourth term, apply the formula again: a4 = a3 + a2 = 9 + 5 = 14.
5. Finally, for the fifth term: a5 = a4 + a3 = 14 + 9 = 23.

So, the first five terms of the sequence are 4, 5, 9, 14, and 23.

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We can see here that the problem that can be solved using synthetic division is: A. [tex]\frac{2y^{2} + 4y - 6}{y-1}[/tex]

Synthetic division is a simplified method of polynomial division, used to divide a polynomial by a linear factor of the form (x - a). This method can be used to quickly evaluate a polynomial for a particular value of x, or to find the roots of a polynomial equation.

In order to solve with synthetic division, we have:

Step 1: Make the denominator to equal zero. The numerator is written in descending order.

Step 2: Bring the first number or the leading coefficient straight down.

Step 3: Put the result in the next column by multiplying the number in the division box with the number you brought down.

Step 4: Write the result at the bottom of the row by adding the two numbers together

Step 5: Until you reach the end of the problem, repeat steps 3 and 4.

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The number of ways car 2 or more tires can be selected out of 8 tires is 247 ways

To select 2 or more tires out of 8 tires, we can use the concept of combinations.

The total number of ways to select r items out of n items is given by the formula:

nCr = n! / (r! * (n-r)!)

where n is the total number of items, and r is the number of items to be selected.

For selecting 2 or more tires out of 8 tires, we can find the total number of ways to select 2 tires, 3 tires, 4 tires, 5 tires, 6 tires, 7 tires, and 8 tires, and then add them together.

Adding all the above results, we get:

28 + 56 + 70 + 56 + 28 + 8 + 1 = 247

Therefore, there are 247 ways to select 2 or more tires out of 8 tires.

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the correct answer to the given question about car loan is option D: $2,315.38; $383.22.

To determine the interest and monthly payment for the car loan, we can use the add-on interest formula:

Total Interest = Principal x Rate x Time

where:

Principal = $16,079 (the amount of the loan)

Rate = 3.6% (the add-on interest rate)

Time = 4 years

Total Interest = $16,079 x 0.036 x 4

Total Interest = $2,315.38

So the total amount of interest on the loan is $2,315.38.

To calculate the monthly payment, we can use the following formula:

Monthly Payment = (Principal + Total Interest) / (Number of Payments)

where:

Principal = $16,079 (the amount of the loan)

Total Interest = $2,315.38 (the total interest on the loan)

Number of Payments = 4 x 12 = 48 (since the loan is for 4 years, and there are 12 months in a year)

Monthly Payment = ($16,079 + $2,315.38) / 48

Monthly Payment = $383.22

Therefore, the amount of interest on the loan is $2,315.38 and the monthly payment for the car loan is $383.22.  

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Please provide the dot plots so we can analyze the data.

A mathematical expression is a sentence that combines variables, numbers, and mathematical operations to represent a single value or a range of values. It can be straightforward or intricate, and algebraic problems and mathematical relationships are frequently solved with it.

A mathematical expression is made up of a mixture of numbers, variables, and operations like addition, subtraction, multiplication, and division.

To determine which of the two girls has the more consistent swing, we need to look at the spread of the data in the dot plots. If the data is tightly clustered, then the swings are more consistent. If the data is more spread out, then the swings are less consistent.

Without seeing the dot plots, we cannot make a determination. Please provide the dot plots so we can analyze the data.

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Without viewing the dot maps, we are unable to draw any conclusions. To enable us to analyse the data, kindly provide the dot maps.

A sentence that combines variables, numbers, and mathematical operations to describe a single value or a range of values is known as a mathematical expression. Algebraic issues and mathematical connections are frequently resolved with it, and it can be simple or complex.

Adding, subtracting, multiplying, and dividing are just a few of the processes that make up a mathematical expression.

We must examine the distribution of the data in the dot plots to ascertain which of the two females has a more steady swing. The fluctuations are more predictable if the data is densely clustered. The fluctuations are less predictable when the data is more dispersed.

Without viewing the dot maps, we are unable to draw any conclusions. To enable us to analyse the data, kindly provide the dot maps.

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The complete question is,

At the driving range, Danae and Sabrina each shot 25 golf balls. The dot maps below show the overall distance that each ball is estimated to have travelled. Which of the two females has the more reliable swing, according to the data?

The solutions to the equation are approximately x = 0.89 and x = -0.89.

Squares as well as square root both ideas are diametrically opposed to one another. Squares are the numbers that are produced when a value is multiplied by itself. In contrast, a number's square root is a value that, when multiplied by itself, returns the original value. Both are hence vice-versa approaches. For instance, 2 is squared to provide 4, and 2 is the square root of 4, giving 2.

When n is a number, its square is denoted by n raised to the power 2, or n2, and its square root is denoted by the symbol "n," where "n" is referred to as a radical. The term "radicand" refers to the value under the root symbol.

The given equation is 5x² + 2 = 6.

5x² = 4

x² = 4/5

x = ±√(4/5)

x ≈ ±0.89

Hence, the solutions to the equation are approximately x = 0.89 and x = -0.89.

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9 is the centre of enlargement in triangle .

What is a triangle, exactly?

A triangle, a three-sided polygon, is made up of three vertices. When the triangle's three sides are joined end to end at a single point, the angles are created. Three angles in a triangle add up to 180 degrees in total. A triangle is a closed, two-dimensional geometry with three sides, three angles, and three vertices. Triangles are also a type of polygon.

First draw lines from point O through A, B and C, as shown in the diagram

Measure the length O A and multiply it by 1.5 to get the distance from O of the image point A'.

      O A' = 1.5 × O A

       OA' = 1.5 * √(4 - 0)² + (4 - 0)²

              = 1.5*4√2

       OA' = 6

Mark the point A' on the diagram

The images B' and C' can then be marked in a similar way and the enlarged triangle A' B' C' can then be drawn.

OB' = 1.5OB

OB' = 1.5 √(4 - (-2))² + ( 4 -0 )²

OB' = 1.5*2√13

 OB' = 3√13

 OC' = √1.5 * √(4 - (-2))² + 4 - 4

 OC' = 1.5*6

   OC' = 9

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To find the number that is 1/5 as big as the given number, you need to divide the given number by 5.

A fraction is a numerical quantity that represents a part of a whole. Fractions are typically written in the form of two numbers separated by a horizontal line, with the number on top called the numerator and the number on the bottom called the denominator. Fractions can be used to represent numbers that are less than one, as well as numbers that are greater than one. They can be added, subtracted, multiplied, and divided like any other numbers, and they can be converted into decimals or percentages for easier comparison and computation. Fractions are commonly used in everyday life, for example, when dividing a pizza into equal slices or calculating a discount on a sale item. They are also used extensively in mathematics, science, and engineering to represent ratios, proportions, and other relationships between quantities.

Here,

For example, if the given number is 20, to find the number that is 1/5 as big, you would divide 20 by 5, which gives you 4. So, the answer to your question depends on the specific number that you have been given. If you provide me with the number, I can help you find the number that is 1/5 as big.

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Complete question:

You are given a number. Do you know the number that is 1/5 as big as the given number?

The graph of the function are attached

f(x) = 3x^2 - 4 (opens upward)

f(c) = -3x^2 + 1 (shifts 5 units upward)

f(c) = -3(x + 5)^2 - 4 (shifts 5 units to the left)

The quadratic equation required is f(x) = - 3x^2 - 4

For the graph to open upward change the sign opposite 3x^2 hence we have

f(x) = 3x^2 - 4 (graph attached)

The quadratic function f(c) = -3x^2 - 4 to shift up add some a number say 5 to it or down (subtract a number from it)

f(c) = -3x^2 - 4 + 5

f(c) = -3x^2 + 1 (graph attached)

to shift the graph left or right add or subtract a number say  to the x as below

f(c) = -3(x + 5)^2 - 4 (shifts to the left 5 units graph attached)

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The estimated answer of 40 is close to Keira's answer of 38.6. This suggests that her answer is reasonable.

One way Keira can check if her answer is reasonable is to use estimation.

She can round the numbers in the original division problem to the nearest multiples of 10, which makes the calculation easier, and check if the estimated answer is close to her actual answer. That is:

123.52 is approximately 120, and 3.2 is approximately 3. So the division problem becomes:

120 / 3 = 40

This estimated answer of 40 is close to Keira's answer of 38.6, which suggests that her answer is reasonable.

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Answer:

  ∠Z = 52°

  b = 59°

Step-by-step explanation:

You want to know the measures of an angle and a variable in the given quadrilaterals with angles marked.

Segment WY divides the figure into two congruent triangles, so you know angles X and Z have the same measure. The sum of angles in a quadrilateral is 360°, so ...

  ∠W +∠X +∠Y +∠Z = 360°

  134° +∠Z +122° +∠Z = 360° . . . . . . use ∠Z for ∠X

  2·∠Z = 104° . . . . . . simplify, subtract 256°

  ∠Z = 52°

Opposite angles of a rhombus are congruent, so ...

  2b = b +59°

  b = 59° . . . . . . . . . subtract b

Answer:

Step-by-step explanation:

[tex]3.25x - 1.5y = 1.25 \quad (a)[/tex]  

     [tex]13x - 6y = 10\quad\quad(b)[/tex]

Make [tex]y[/tex] the subject in [tex](b):[/tex]

   [tex]13x - 6y = 10[/tex]

             [tex]6y=13x-10[/tex]

               [tex]y=\frac{13}{6} x-\frac{5}{3} \quad(c)[/tex]

Substitute [tex](c)[/tex] into [tex](a):[/tex]

     [tex]3.25x - 1.5(\frac{13}{6} x-\frac{5}{3}) = 1.25 \quad \text{(I will change decimals to fractions)}[/tex]

            [tex]\frac{13x}{4} -\frac{3}{2} (\frac{13x}{6} -\frac{5}{3} )=\frac{5}{4} \quad\quad \text{(I will remove brackets)}[/tex]

                 [tex]\frac{13x}{4} - \frac{13x}{4} +\frac{5}{2} =\frac{5}{4}[/tex]

                                     [tex]\frac{5}{2} =\frac{5}{4}[/tex]

This is ambiguous meaning the system does not have a solution.

(I confirmed this on Wolfram Alpha)

What is meant by cyclic quadrilateral?

A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. It is also sometimes called inscribed quadrilateral. The circle which consists of all the vertices of any polygon on its circumference is known as the circumcircle or circumscribed circle.

A cyclic quadrilateral means a quadrilateral that is inscribed in a circle. That means there is a circle that passes through all four vertices of the quadrilateral. The vertices are said to be concyclic. The center of the circle is known as the circumcenter and the radius of the circle is known as the circumradius. In the figure given below, ABCD is a cyclic quadrilateral with a, b, c, and d as the side-lengths and p and q as the diagonals.

[tex](tanA+secA-1)/(tanA-secA+1)=(1+sinA)/cos A[/tex]

multiply LHS by cosA /cosA to get  

[tex](sinA+1-cosA) / (sinA-1+cosA)[/tex]

multiply again by cosA/cosA to get  

[tex](sinA.cosA+cosA-cos^2A) / cosA(sinA-1+cosA)[/tex]  

[tex]= ( cosA(1+sinA) - (1-sin^2A) ) / cosA(sinA-1+cosA)[/tex]  

[tex]= ( cosA(1+sinA) - (1+sinA)(1-sinA) ) / cosA(sinA-1+cosA)[/tex]  

[tex]= ( (1+sinA)(cosA-1+sinA) ) / cosA(sinA-1+cosA)[/tex]  

[tex]= \bold{(1+sinA)/cosA}[/tex]

Answer: We can simplify the expression using trigonometric identities:

tan a + sec a - 1 - (tan a - sec a + 1) / (1 + sin a cos a)

= tan a + sec a - 1 - (tan a - sec a + 1) / cos^2 a

= (sin a / cos a + 1 / cos a - cos a / cos a) - [(sin a / cos a - 1 / cos a - cos a / cos a) / cos^2 a]

= (sin a + 1 - cos a) / cos a - [(sin a - 1 - cos^2 a) / cos^3 a]

= [(sin a + 1 - cos a) cos^2 a - (sin a - 1 - cos^2 a)] / cos^4 a

= [sin a cos^2 a + cos^2 a - cos a cos^2 a - sin a + 1 + cos^2 a] / cos^4 a

= (2 cos^2 a - sin a + 1) / cos^4 a

Now, we can simplify the expression further using the identity:

1 + tan^2 a = sec^2 a

tan^2 a = sec^2 a - 1

tan a + sec a - 1 = (tan^2 a + 1) / (sec a + tan a - 1)

= (sec^2 a - 1 + 1) / (sec a + tan a - 1)

= sec a / (sec a + tan a - 1)

tan a - sec a + 1 = -(sec a - tan a - 1)

= -(1 / (sec a - tan a + 1))

Substituting these values in the original expression, we get:

(sec a / (sec a + tan a - 1)) - (-1 / (sec a - tan a + 1)) / (1 + sin a cos a)

= (sec a (sec a - tan a + 1) + (tan a - 1)) / ((sec a + tan a - 1)(sec a - tan a + 1)(1 + sin a cos a))

= [(sec^2 a - sin a + 1) + (tan a - 1)] / (cos^2 a (1 + sin a cos a))

= [(2 cos^2 a - sin a + 1)] / (cos^4 a (1 + sin a cos a))

Thus, we have simplified the given expression to (2 cos^2 a - sin a + 1) / (cos^4 a (1 + sin a cos a)).

Step-by-step explanation:

£45.84

Assuming that's 7.5%