Simplify the following polynomial expression.


(5x^4 - 9x^3 + 7x -1) + (-8^4 - 3x + 2) - (-4x^3 + 5x - 1) (2x - 7)

An intuitive definition: a function ݂f is said to be convex at an interval I if, for all pairs of points on the ݂f(x) graph, the line segment that connects these two points passes above the ݂f(x) curve.

A function ݂ is said to be concave at an interval I if, for all pairs of points on the graph f(x), the line segment that joins these two points passes below the ݂f(x) curve.

A convex function has a regularly increasing first derivative, making it appear to bend upwards.

Contrarily, a concave function has a regular decreasing first derivative making it bend downwards. It is very important to know the distinction between the first derivative, that tells us of the slope of the tangent of a function, and the second derivative, which shows us how it is curved.

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Answer:

no its incorrect

Step-by-step explanation:

-2(8m+8)=-16 is worng its m=0

The problem is incorrect.

The correct solution for the given equation is:

-2(8m +8) = -2(8m) -2(8) = -16m -16

You cannot simplify it to -16 as the equation is not a true equation.

Please let me know if there is something more I can assist you with.

Answer:

88.50

Step-by-step explanation:

0.12x400=48 dollars +the 40.50 dollars answer 88.50

Answer:

2.964

Step-by-step explanation:

4-1.036=2.964

Answer:

2.964

Step-by-step explanation:

4 - 1.036 = 2.964

The radius of the circle created by the ice skater is 1 yard.

What is circle ?

A circle is a two-dimensional geometric shape that is defined by a set of points that are all the same distance from a central point called the center. The distance from the center to any point on the circle is called the radius. The distance across the circle, passing through the center, is called the diameter.

The radius of a circle is half of its diameter, so the radius of a circle with a diameter of 2 yards is 1 yard.

Radius = Diameter/2

Radius = 2/2 = 1 yard

So, the radius of the circle created by the ice skater is 1 yard.

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The radius of a circle is half of its diameter, so the radius of a circle with a diameter of 2 yards is 1 yard.

Radius = Diameter/2

Radius = 2/2 = 1 yard

So, the radius of the circle created by the ice skater is 1 yard.

In the given arithmetic sequence, the First term is -74, 2nd term is -81 3rd term is -88 and 4th term is -95.

There are two ways to define an arithmetic sequence. It is a "sequence where the differences between every two successive terms are the same" (or) In an arithmetic sequence, "each term is obtained by adding a fixed number (positive or negative or zero) to its preceding term." The following is an arithmetic sequence where each term is obtained by adding 4 to the term before it.

We know that arithmetic sequence is:

[tex]a_{n}=a_{1}+(n-1)d[/tex]

Given

a = -74, d = -7

[tex]a_{1} = -74 + (1 - 1)(-7)[/tex]

[tex]a_{1} = -74 + (0)(-7)[/tex]

[tex]a_{1} = -74[/tex]  (First term)

[tex]a_{2} = -74 + (2 - 1)(-7)[/tex]

[tex]a_{2} = -74 + (1)(-7)[/tex]

[tex]a_{2} = -81[/tex] (2nd term)

[tex]a_{3} = -74 + (3- 1)(-7)[/tex]

[tex]a_{3} = -74 + (2)(-7)[/tex]

[tex]a_3 = -88[/tex] (3rd term)

[tex]a_{4} = -74 + (4- 1)(-7)[/tex]

[tex]a_{4} = -74 + (3)(-7)[/tex]

[tex]a_3 =-95[/tex] (4th term)

Thus, In the given arithmetic sequence, the  First term is -74, 2nd term is -81 3rd term is -88 and 4th term is -95.

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Answer:

n = 28

Step-by-step explanation:

2^2 is equal to 4, so we can plug in 2^2 as 4. Then, 4 * 7 = 28, so n = 28.

The value of x as shown in the straight line is 32

An equation is an expression showing the relationship between numbers and variables.

An angle is formed when two lines intersect at a point. The sum of angles in a straight line is 180 degrees.

From the diagram:

(3x - 4) + (3x - 8) = 180° (sum of angle in a straight line)

3x + 3x - 4 - 8 = 180

6x - 12 = 180

6x = 192

x = 32

The value of x is 32

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The range of the data with the outlier is 7 and without is 2

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

0, 3; 1, 3; 2, 2; 3, 1; 8, 1.

The range without the outlier

The range is calculated as

Range = Highest - Least

Without the outlier, we have

Range = 3 - 1

Range = 2

The range with the outlier

The range is calculated as

Range = Highest - Least

With the outlier, we have

Range = 8 - 1

Range = 7

Hence, the range are 2 and 7

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The transformed equation is y = -1/(x + 2) - 3

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

y = -1/x

We have the transformation to be

(2, -3)

This implies that we transform the function be (x + 2, y - 3)

using the above as a guide, we have the following:

y = -1/(x + 2) - 3

The above represents the new equation when the previous is transformed

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The complete table would look like this:

Number of loaves    Number of Bananas

1                                    2 1/2

2                                   5                            

4                                    10

What is a number line?

A number line is a visual representation of a continuous range of numbers, usually represented as a straight line. Numbers are represented by points along the line, and the distance between two numbers corresponds to the difference between their numerical values. The numbers are usually represented by evenly spaced marks or tick marks on the line, and they can be positive or negative numbers, integers or fractions, or real numbers. The number line is used to represent various mathematical concepts such as inequalities, absolute values, and intervals. It is also used to help students understand concepts such as addition, subtraction, and ordering of numbers.

So the first one was easy because it already said it in the number line.

For the second one you simply multiply 2x 2 1/2

For the third one, you multiply 4x 2 1/2.

Hence, The complete table would look like this:

Number of loaves    Number of Bananas

1                                    2 1/2

2                                   5                            

4                                    10

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If the historical data says that the number of road bikes sold is 9 and the number of stationary bikes sold is 3, out of a total of 60 bikes, then  the probability that the next customer purchase a stationary bike is 1/20.

A probability based on historical data is referred to as empirical probability or experimental probability. In other words, empirical probability depicts the probability of an occurrence occurring based on past data.

Empirical probability is also known as the relative frequency.

Formula for the empirical probability is:

Empirical probability = times of event A occurs / total number of trials

In the problem, there are two kinds of bike: road bike and stationary bike.

The historical data:

sales of road bike = 9

sales of stationary bike = 3

total bikes = 60

Hence, the probability that the next customer will buy a stationary bike is:

P(stationary) = sales of stationary bike / total bikes

P(stationary) = 3/ 60 = 1/20

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Since b and g are the numbers of boys and girls in class b + 3g is equal to [tex]b^3 - 3b^2 + 5g^2 - 3g + 2b[/tex]

We can use the concept of combination to determine the value of b + 3g.

The number of ways to choose 3 boys from b boys and 2 girls from g girls is:

(b choose 3) x (g choose 2) = (b! / (3!(b-3)!) ) x (g! / (2!(g-2)!) ) = (b x (b-1)(b-2))/(321) x (g(g-1))/(2 x 1)

We know that this is equal to 168, so we can set up the equation:

(b x (b-1)(b-2))/(321) x (g(g-1))/(2 x 1) = 168

We can solve this equation to find the value of b + 3g. Since b and g are the numbers of boys and girls in the class, we know that b + g is the total number of students in the class.

So we can simplify the equation as:

(b x (b-1)(b-2)) x (g(g-1)) = 32121 x 168

and rearrange it to:

[tex](b^3 - 3b^2 + 2b) * (g^2 - g) = 1008[/tex]

[tex]= b^3 - 3b^2 + 2b = 1008 / (g^2 - g)b + 3g \\= (b^3 - 3b^2 + 2b) + 3(g^2 - g) \\= b^3 - 3b^2 + 2b + 3g^2 - 3g \\= b^3 - 3b^2 + 5g^2 - 3g + 2b[/tex]

So we can see that b + 3g is equal to b^3 - 3b^2 + 5g^2 - 3g + 2b. However, the exact value cannot be determined without the specific values of b and g.

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The numerator and denominator of a complicated rational expression must first be written as a single algebraic fraction in order to simplify the expression.

[tex]\frac{P(x)}{Q(x)}. Q(x)P(x)[/tex]

After that, simplify the result by multiplying the numerator by the reciprocal of the divisor. A rational expression with a fraction in the numerator, denominator, or both is referred to as a complex fraction. In other words, the overall fraction contains at least one small fraction.

There are two methods for reducing the complexity of fractions. For the numerator and denominator, identify common denominators. Make the numerators simpler. Add to the denominator and subtract the rational expressions from the numerator. Simplify.

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Answer:

x = 5

Step-by-step explanation:

Angles on a straight line add up to 180, so add up the angles and equate to 180:

9x + 85 + 10x = 180

Now we can solve for x by simplifying further:

19x + 85 = 180

Subtract 85 on both sides:

19x + 85 - 85 = 180 - 85

19x = 95

Divide 19 on both sides which cancels out the 19 on the left:

x = 95/19 = 5

The system has no solution when h is not equal to ( 18x+7 )/( -6x)

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

− 6(hx + 2) = 3(x − 3) + 2(x + 2) +13x

-6hx-12=3x-9+2x+4+13x

=>  -6hx-12= 18x-5

=> -6hx = 18x-5 +12

=>  -6hx = 18x+7

=> h = ( 18x+7 )/( -6x)

The system has no solution when h is not equal to ( 18x+7 )/( -6x)

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Answer:

-2+4=2

Step-by-step explanation:

All you need to do is count 4 spaces from -2 on the number line. See in image.

-Hope this helped

The evaluation of the simultaneous equation is as follows;

a) The simultaneous equations, indicates by plugging in the value of the variable x in the first equation, that the first equation is; 7·x² + 5·y + 3 = 0

b) The equation has no real solutions

Simultaneous equations are set two or more equations that have common solution.

The simultaneous equations are;

y² + x·y + 3 = 0...(1)

x = 6·y + 5...(1)

Plugging in x = 6·y + 5, in equation (1) we get;

y² + x·y + 3 = y² + y × (6·y + 5) + 3 = 0

y² + 6·y² + 5·y + 3 = 0

b) The number of solutions the simultaneous equation has can be obtained by solving the equation, obtained in part (a), 7·y² + 5·y + 3 = 0, as follows;

7·y² + 5·y + 3 = 0

The quadratic formula for finding the solution of the equation; a·x² + b·x  + c = 0, is; -b±√(b² - 4·a·c)/(2·a)

Where the discriminant is; b² - 4·a·c

Comparing the equations, we get;

a = 7, b = 5, and c = 3

b² - 4·a·c is therefore; 5² - 4 × 7 × 3 = -59

The discriminant is less than 0, therefore, there are no real solutions to the equation, but there are to imaginary solutions

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The process of dividing the two digit numbers without a calculator is solved by using the dividend, divisor, quotient and remainder.

Division in math is defined as the process to distribute the whole thing to a group in equal parts or make equal parts.

Here we need to find he way to divide two digit numbers without a calculator.

As per the definition of division, here we have to divide the first number of the dividend or the two first numbers if the previous step took another digit by the first digit of the divisor.

And then we have to write the result of this division in the space of the quotient.

Finally we have to multiply the digit of the quotient by the divisor, then write the result beneath the dividend and subtract it.

This process is repeated until we get zero as remainder.

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The area of the rectangle is 20. The length of the base and the height are 2√10 and √10.

From the case, we know that each point's locations are:

A = (-7, 4)

B = (-1, 6)

C = (0, 3)

D = (-6, 1)

Since the graph is a rectangle then it has 2 kind of sides, the height and the weight. Based on the given graph, we can categorize each side as:

Height = BC = DA

Base = AB = CD

We can find the length of each sides by using the coordinates of each point.

Length of a side = √[(x2 - x1)² + (y2 - y1)²]

Lenght of AB = √[(xB - xA)² + (yB - yA)²]

Length of AB = √[(-1 - (-7))² + (6 - 4)²]

Length of AB = √[6² + 2²]

Length of AB = √(36 + 4)

Length of AB = √40

Length of AB = 2√10 --> Length of the base

Length of BC = √[(xC - xB)² + (yC- - yB)²]

Length of BC = √[(0 - (-1))² + (3 - 6)²]

Length of BC = √(1² + (-3)²)

Length of BC = √(1 + 9)

Length of BC = √10 --> Length of the height

The area of the rectagle would be:

Area = base x height

Area = 2√10 × √10

Area = 20

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The roots of the quadratic equation 6x²-2x=8 are x=4/3 and x=-1.

Given that,

The equation is 6x²-2x=8

To find : The roots of the quadratic equation 6x²-2x=8

Any equation that can be rearranged in standard form as where x represents an unknown value, and a, b, and c represent known values, where a 0, is referred to as a quadratic equation in algebra (from Latin quadratus, "square"). The equation is linear, not quadratic, if a = 0 and b 0. The coefficients of the equation are the numbers a, b, and c, which can be separated by naming them, respectively, the quadratic coefficient, the linear coefficient, and the constant coefficient or free term.

We know that,

The solutions are x1 and x2  = -b±√b²-4ac/2a

Here b = -2 ,a = 6 and c= -8

No substitute those values in the formula,

= -b±√b²-4ac/2a

= -(-2) ± √(-2²)-4(6)(-8) / 2(6)

x = 4/3 and x =-1

So, The roots of the quadratic equation 6x²-2x=8 are 4/3 and -1

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The slope of a line is determined by the formula:

(y2 - y1) / (x2 - x1)

So for the points (9, 5) and (21, -5), the slope would be:

(-5 - 5) / (21 - 9) = -10 / 12 = -5/6

So the slope of the line that passes through the points (9, 5) and (21, -5) is -5/6 in simplest form.

y = (1/3)x - 2 is an equation of a line where the slope of the line is 1/3 and the y-intercept of the line is -2.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

y = (1/3)x - 2

This is in the form of y = m + c

So,

This is an equation of a line.

The slope of the line = 1/3

The y-intercept of the line is -2.

Thus,

y = (1/3)x - 2 is an equation of a line.

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The square root of negative number can be negative imaginary number (complex number)

As we know the square root of a number is nothing but the factor/value that we can multiply by itself to get that number.

Finding a square root of number is an inverse method of squaring a number.

A radical symbol '√' used to represent the square root of number.

If m is the square root of n, then it is represented as m = [tex]\sqrt{n}[/tex],

We can write above relation as, m² = n

We know that square of any real number is positive.

For example, 3² = (3 × 3) = 9

(-3)² = (-3) × (-3) = 9

i.e., the square root of 9 is 3 and -3

Thus the square root of a negative number is undefined among the set of Real Numbers.

As we know the set of real numbers is subset of complex numbers.

In complex numbers, the imaginary number 'i' is the square root of negative 1.

When an imaginary number is squared, the result is negative number.

Consider example,

[tex]\sqrt{-16}\\\\ =\sqrt{16} \times \sqrt{-1}\\\\ =(\pm 4)\times i\\\\=\pm4i[/tex]

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The range is the spread of the values of the output of a function.

To Find : The Range of a Function ,Consider a function y = f(x)

The spread of all the y values from minimum to maximum is the range of the function. In the given expression of y, substitute all the values of x to check whether it is positive, negative or equal to other values. Find the minimum and maximum values for y. Then draw a graph for the same.

The range of a function is a set of all its possible outputs.

Example: Let’s consider a function ƒ: A⇢A, where A = {1,2,3,4}.

The elements of the set Domain, are called pre-images, and elements of the set Co-Domain which are mapped to pre-images are called images. The range of a function is a set of all the images of elements in the domain. In this example, the range of the function is {2,3}.

The range is the spread of the values of the output of a function. If we are able to calculate the maximum and the minimum values of the function, we can get an idea of the range of the function.

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Answer: It's the same process to get the variable by itself. But once found depending on how you are required to represent the solution, the final answer may vary. You need to also keep in mind that with negatives when multiplying and dividing you have to flip the inequality sign.

Step-by-step explanation:

Ex. 2x>4

x>2

but if

-2x>4

x<-2