In the diagram, there are 6 vertices and 15 different lines. A diagram like this is called a mystic rose.
Another mystic rose has 153 different lines. How many vertices does it have?

The factored form of the quadratic function is f(x) = a(bx + c) (dx + e)

The term quadratic function is defined as a polynomial function with one or more variables in which the highest exponent of the variable is two and the graph of the quadratic equation is always forms the parabola.

Here we have given that we have to find the  the factored form of a quadratic function

As we all know that the general form of the quadratic function is written as,

=>  f(x) = ax² + bx + c

While we factorize the general form then it can be expanded like the following,

=> f(x) = a(bx + c) (dx + e)

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Answer:

move 5 blocks to the west.

Step-by-step explanation:

A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. The location of Katha after she walked west is -5 on the number line.

[tex] \frac{6}{2k - 6} = 3 \\ \\ \longrightarrow \: 6 = 6k - 18 \\ \\\longrightarrow \: 6k = 18 + 6 \\ \\\longrightarrow \: 6k = 24 \\ \\ dividing \: both \: sides \: by \: 6 \: , \\ \\\longrightarrow \: \cancel \frac{6k}{6} = \cancel \frac{24}{6} \\ \\ \longrightarrow \: \boxed{k = 4}[/tex]

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The solution set of the inequality x 4 5x 2/3 7x 3 5 is x> 7.

To solve this inequality, we need to isolate the x term on one side and all the other terms on the other side. We can do this by subtracting 4 from both sides of the equation, which gives us 5x 2/3 7x 3 - 4 < 0.

Next, we can add 7x 3 to both sides of the equation, giving us 5x 2/3 - 4 + 7x 3 < 7x 3.

Now, since the denominator of the first term is 3, we can multiply both sides of the equation by 3/3. This gives us 5x 2 - 4 3 + 21x 3 < 21x 3.

Next, we can subtract 21x 3 from both sides of the equation, which gives us 5x 2 - 4 3 < 0.

Now, we can divide both sides of the equation by 5, which gives us x 2 - 4/5 < 0.

Finally, we can take the square root of both sides of the equation, which gives us x - 2/√5 < 0.

This means that x > 2/√5 + 2. Since 2/√5 + 2 > 7, the solution of the inequality is x > 7.

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If the radius of sphere is 7 units, the volume of the sphere is 1,437.33 units³

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Given that, the value of π = 22/7

The radius of sphere is 7 units

Volume of a sphere = 4/3πr³, where r is the radius of the sphere.

= 4/3 * 22/7 * 7³

= 4/3 * 22/7 * 7 * 7 * 7

= (4 * 22 * 7 * 7 * 7) / (3 * 7)

= 30,184/21

= 1437.3333333333 unit³

So that, the volume of a sphere = 1,437.33 unit³

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The centroid of the region enclosed by y = ex, y = 0, x = 0 and x = 5 is at the point ( (5e^5 - 5) / (e^5 - 1) , (e^10 - 1) / 2(e^5 - 1) ).

To find the centroid of a region, we need to first find the area of the region and the coordinates of the center of mass of the region.

The region enclosed by y = e^x, y = 0, x = 0 and x = 5 can be represented by the definite integral of the function y = ex between the limits of x = 0 and x = 5. The area of this region is given by the definite integral:

∫[0,5] e^x dx

The definite integral of ex is e^x, so the area of the region is e^5 - e^0 = e^5 - 1.

To find the x-coordinate of the centroid, we need to find the integral of

x e^x from 0 to 5, divided by the area.

= ∫[0,5] xe^x dx / (e^5 - 1)

The integral of xe^x is

= (xe^x - ∫e^x dx)

= (xe^x - e^x)

So the x-coordinate of the centroid is

= ∫[0,5] xe^x dx / (e^5 - 1)

= (4e^5 + 1) / (e^5 - 1)

To find the y-coordinate of the centroid we need to find the integral of

ye^x from 0 to 5, divided by the area.

∫[0,5] (e^x * e^x) dx / (e^5 - 1)

∫[0,5] (e^(2x)) dx / (e^5 - 1)

The integral of e^(2x) is (1/2)e^(2x)

So the y-coordinate of the centroid is

∫[0,5] e^(2x) dx / (e^5 - 1) = (1/2) * (e^10 - e^0) / (e^5 - 1)

= (1/2) * (e^10 - 1) / (e^5 - 1)

= (e^10 - 1) / 2(e^5 - 1)

So the centroid of the region enclosed by y = ex, y = 0, x = 0 and x = 5 is at the point ( (5e^5 - 5) / (e^5 - 1) , (e^10 - 1) / 2(e^5 - 1) ).

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The average speed of the trip will be 1.60 miles/mins and 96.64 miles/hrs.

What is an average?

An average of a list of data is a mathematical expression for the center value of a set of data. It is defined mathematically as the ratio of the total of all the data to the number of units in the list. In statistics, the average of a particular collection of numerical data is also known as the mean.

e.g.

The average of 2, 3, and 4 equals (2+3+4)/3 = 9/3 = 3. As a result, the central value of 2,3, and 4 is 3. Thus, the definition of average is to determine the mean value of a set of data.

Average speed:-

The formula for average speed is found by calculating the ratio of the total distance traveled by the body to the time taken to cover that distance.

average speed = total distance / total time

Now,

As given

Total distance covered = 16+185+145

                         =346 miles

Total time taken=20 + 120 + 75

                  =215 minute  (3.58 hours)

Average speed=346/215

                         =1.60 miles/mins

Average speed=346/3.58

                            =96.64 miles/hrs

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AX² is the standard form of a quadratic equation, where A is a coefficient and X is a variable.

In mathematics, a quadratic equation is a polynomial equation of the form ax2 + bx + c = 0, where a, b, and c are real numbers and a is not equal to zero. A quadratic equation can have either one, two, or no real solutions, depending on the value of the discriminant, b2 - 4ac. The discriminant determines the nature of the roots of the equation: if it is positive, the equation has two distinct real solutions; if it is zero, the equation has one repeated real solution; and if it is negative, the equation has two complex conjugate solutions.

The standard form of a quadratic equation is ax2 + bx + c = 0, where a is the coefficient of the x2 term, b is the coefficient of the x term, and c is the constant or free term. AX2 is the standard form of the equation, where A is the coefficient of the x2 term and X is the variable. If the coefficient A is not equal to 1, the equation can be simplified by dividing both sides of the equation by A. Solving a quadratic equation requires the use of the quadratic formula, which is used to find the roots of the equation. The quadratic formula states that the roots of the equation are x = [-b ± √(b2 - 4ac)]/2a.

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On solving the provided question, we can say that from provided graphs we say  [tex]x^2 = 4y + 7[/tex] =.> [tex]x^2 = 15 = > x = \sqrt{15}[/tex]

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle

here,

from provided graphs we say

[tex]x^2 = 4y + 7[/tex]

y = 2

[tex]x^2 = 15 \\x = \sqrt{15}[/tex]

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The remainder when 2x² - 5x - 1 divided by x - 3 is (2x + 1)

Let p(x) represents a polynomial  2x² − 5x − 1 and m(x) represents a polynomial x - 3

i.e., p(x) =  2x² − 5x − 1

and m(x) = x - 3

we need to find the remainder when 2x² − 5x − 1 divided by x − 3

If we divide a polynomial  p(x) =  2x² − 5x − 1  by m(x) = x - 3 using polynomial long division method, the result is:

p(x) / m(x)

= ( 2x² - 5x - 1 ) ÷ (x - 3)

= [ ( 2x² - 5x - 1 ) × ( 2x + 1)] + 2

This means, the quotient is  ( 2x + 1) and the remainder is 2

(see in attachment)

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Answer: The square root of 36 is expressed by √36, where '√' is the radical symbol and 36 is the radical form.

Step-by-step explanation: √36 is equal to 6, which is a rational number. Since 36 is a perfect square, therefore, it becomes easy for us to find its square root.

Hoped It Helped

The square root of 36 is expressed by √36, where '√' is the radical symbol and 36 is the radical form is 6 .

What is square root ?

Its like abundance (quantity ) of which is called amplitude (quantity) of the particular square .

Give : √36

Now,

Few examples of square root,

√4 = 2

√9 = 3

√16 = 4

√25  = 5

√36 = 6

√36 is equal to 6, which is a rational number. Since 36 is a perfect square, therefore, it becomes easy for us to find its square root.

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Answer:

The correct answer is A. A trapezoid has only 1 pair of parallel sides, but a parallelogram has 2.

A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. A trapezoid is a quadrilateral with one pair of opposite sides that are parallel, known as the bases. The other two sides are called legs.

Both a parallelogram and a trapezoid are quadrilaterals that have four sides, but parallelogram has opposite sides parallel to each other, while trapezoid has only one pair of parallel sides, the bases. Also a parallelogram has opposite angles are equal while a trapezoid doesn't have this property.

Option B and D is incorrect, A parallelogram doesn't need to have 4 right angles, and a trapezoid doesn't need to have 4 right angles as well.

Option C is incorrect as well, A parallelogram has two pairs of parallel sides.

Answer:

Simplify the following:

-5 g - 6 - (4 g - 1)

Factor -1 out of -5 g - 6 - (4 g - 1):

-(5 g + 4 g - 1 + 6)

Grouping like terms, 5 g + 6 - 1 + 4 g = (5 g + 4 g) + (6 - 1):

-((5 g + 4 g) + (6 - 1))

5 g + 4 g = 9 g:

-(9 g + (6 - 1))

6 - 1 = 5:

Answer: -(9 g + 5)

Step-by-step explanation:

Answer:

the absolute value of 0 is just 0

Step-by-step explanation:

Logarithm and Natural Log are abbreviated as Log and Ln, respectively. Natural logarithms are distinct from regular logarithms.

Ln essentially refers to a base-e logarithm. This is also referred to as a basic logarithm. A natural logarithm is another name for this.

Logarithm and Natural Log are abbreviated as Log and Ln, respectively. When an unknown variable appears in an equation as the exponent of another quantity, logarithms are crucial for solving the problem.

Different from ordinary logarithms are natural logarithms. A natural logarithm's base is the special number e, whereas a common logarithm's base is 10. This appears to be a variable, but it actually represents a fixed, irrational number roughly equivalent to 2.718281828459.

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Therefore , the solution of the given problem of expression comes out to be -2,4 and 1.

It is important to multiply, divide, add, or delete in mathematics. The following is how an expression is put together: Number, expression, and mathematical operator The components of a mathematical statement, such as additions, subtraction, multiplication, or division, etc., include numbers, variables, and functions. It is possible to contrast expressions and phrases.

Here,

Given  :x = -8.x = 16, and x = 4.

The expression is:

=> X/4

For x =-8

=> -8/4 =-2

For x =16

=> 16/4 =4

For x=4

=>4/4 =1

Therefore , the solution of the given problem of expression comes out to be -2,4 and 1.

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The solution to the equations are as follows:

x = 0

r = -4

b = -8

n = -3

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

The equation can be solved by find the values of the variables as follows:

Hence,

5.

1 - 3x = 3x + 1

-3x - 3x = 1 - 1

-6x = 0

x = 0

6.

4r + 8 + 5 = -15 - 3r

4r + 13 = -15 -3r

13 + 15 = -3r - 4r

28 = -7r

r = 28 / -7

r = -4

7.

-12 - 4b = 4 - 2b

-12 - 4  = -2b + 4b

-16 = 2b

b = -8

8.

3n - 15 = 7n + n

3n - 7n - n = 15

-5n = 15

n = -3

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Answer:

The theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.

Step-by-step explanation:

The length of the side [tex]\overline{BC}[/tex], and [tex]\overline{AB}[/tex], found using Pythagorean Theorem, and the measures of the angle ∠B in the right triangle ΔABC are;

The Pythagorean Theorem defines the relationship between the legs and the length of the hypotenuse side of a right triangle.

According to Pythagorean Theorem, the sum of the squares of the legs of a right triangle is the same magnitude as the square of the of the length of the hypotenuse side.

The parameters of the right triangle are;

∠A = 45°

[tex]\overline{AC}[/tex] = 14 km

∠C = 90°

The angle sum property can be used to find the measure of the angle ∠B as follows;

m∠A + m∠B + m∠C = 180° (Angle sum property of a triangle)

45° + m∠B + 90° = 180°

m∠B = 180° - (90° + 45°) = 45°

Two angles in the triangle ΔABC are congruent, therefore, the triangle is an isosceles right triangle and the legs, [tex]\overline{AC}[/tex] and [tex]\overline{BC}[/tex] are congruent.

[tex]\overline{AC}[/tex] = [tex]\overline{BC}[/tex] (definition of congruency)

[tex]\overline{BC}[/tex] = [tex]\overline{AC}[/tex] = 14 kilometers

The hypotenuse side of the right triangle = [tex]\overline{AB}[/tex]

The legs of the right triangle are; [tex]\overline{AC}[/tex] and [tex]\overline{BC}[/tex]

Pythagorean Theorem, states that we get;

Therefore;

[tex]\overline{AB}[/tex]² = 14² + 14² = 14² × (1 + 1) = 14² × 2

[tex]\overline{AB}[/tex] = √((14)²×2) = 14·√2

The correct option is option c.

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C. Obtuse Angle measures more than 90 degrees but less than 180 degrees.

An obtuse angle is an angle that measures more than 90 degrees but less than 180 degrees. It is greater than a right angle (which measures exactly 90 degrees) but less than a straight angle (which measures exactly 180 degrees). Obtuse angles are often referred to as "greater than a right angle."

A Right angle is an angle which measures exactly 90 degrees.

An Acute angle is an angle which measures less than 90 degrees.

A Reflex angle is an angle which measures greater than 180 degrees but less than 360 degrees.

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It can be concluded that the population of Italy is increasing.

        [tex]${\displaystyle G=\{(x,f(x))\mid x\in X\}.}[/tex]

Given is the population {P} (in millions) of Italy from 2003 through 2015 can be approximated by the model → {P} = 57.59[tex]$e^{0.0051t}[/tex], where {t} represents the year, with {t} = 3 corresponding to 2003.

We have the function -

{P} = 57.599[tex]$e^{0.0051t}[/tex]

For {t} = 1, we can find P(1) as -

P(1) = 57.79 x [tex]$e^{0.0051}[/tex]

P(1) = 57.79 x 1.00511302714

P(1) = 58.1

Now, P(3) > P(1), this means that the population of Italy is increasing.

Therefore, it can be concluded that the population of Italy is increasing.

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A collection of numbers, variables, and mathematical operations is referred to as an expression. When g = 10 and h = 6, the result of the expression (2/5)g + 3h - 6 is 16.

What is an Expression?

An expression in mathematics is a group of numbers, variables, and mathematical operations created in accordance with context-dependent rules.

The value of the equation with g = 10 and h = 6 is, given the expression (2/5)g + 3h - 6,

(2/5)g + 3h - 6

= (2/5)(10) + 3(6) - 6

= 4 + 18 - 6

= 16

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The full question:

Evaluate 2/5g + 3h - 6 when g = 10 and h = 6

The required number of ways the 6 medals can be distributed among boys and girls is 14400 ways.

In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.

Here,
10 boys and 11 girls are competing, Number different ways, the six medals possibly be given out is,
= 10C3 × 10C3
= 14400

The required number of ways the 6 medals can be distributed among boys and girls is 14400 ways.

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The way to convert the vertex form to factored form is explained below.

The term vertex is defined as  a special point of a mathematical object, and is usually a location where two or more lines or edges meet.

Here we have to write down the steps to convert the vertex form to factored form.

The very first steps is to expand the vertex form into standard quadratic form and then use the quadratic root formula to determine the roots.

Here as we all know that factored term is the product of a constant and two linear terms and they are the roots of the function.

So, now we have to use the quadratic formula to convert them into factor form.

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Using trigonometric function concepts, it is found that:

The angle is of 45 degrees, or  radians.

Since pi radians is 180º, this angle is of 180/4 = 45 degrees.

From the tangent: cot∅ =1

For the cosecant and secant: csc∅=√2 :sec∅=√2.

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To find the domain and range of a piecewise function, you will need to consider each piece separately and then combine the results. First Identify the domain of each piece, then Identify the range of each piece and Combine the domains and ranges

Note: Sometimes you may find that domain or range of a certain piece is not mentioned in the function, in that case, you can assume it to be the default domain or range of real numbers.

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a. The amount in the account at the end this year after the interest is paid will be 1.04x

b. The amount in the account at the end this year after the interest is paid will be 1.08x.

c. The expression for the amount in the account after N years will be x + 0.04xn

From the information, Mybankaccount pays 4% interest at the end of each year. The person had $x in the bank account at the start of this year. The amount in the account at the end this year after the interest is paid will be:

= x + (x × 0.04 × 1)

= x + 0.04x

= 1.04x

The amount in the account at the end of 2 years after the interest is paid will be:

= x + (x × 0.04 × 2)

= x + 0.08x

= 1.08x

The expression for the amount in the account after N years will be:

x + (x × 0.04 × n)

x + 0.04xn

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Answer:

Solve for X by simplifying both sides of the equation, then isolating the variable.

X = 4x − 2

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