-2/3 + y = -2 1/6
....................

To find the zeros of a polynomial algebraically, you can use the following steps:

Write the polynomial in standard form, with the terms arranged in descending order of the degree of the term. For example, if the polynomial is 3x^2 - 2x + 5, it is already in standard form.

Set the polynomial equal to zero. For example, if the polynomial is 3x^2 - 2x + 5, you would set the equation equal to zero like this:

3x^2 - 2x + 5 = 0

Use the quadratic formula to find the solutions (i.e., the zeros) of the equation if the polynomial is a quadratic (degree 2). The quadratic formula is:

x = (-b +/- sqrt(b^2 - 4ac)) / (2a)

where a, b, and c are the coefficients of the polynomial, and sqrt represents the square root.

For example, if the polynomial is 3x^2 - 2x + 5, the solutions would be:

x = (-(-2) +/- sqrt((-2)^2 - 4 * 3 * 5)) / (2 * 3)

x = (2 +/- sqrt(4 - 60)) / 6

x = (2 +/- sqrt(-56)) / 6

Since the square root of a negative number is not a real number, there are no real solutions (zeros) for this polynomial.

Use the Rational Root Theorem to find the solutions of the equation if the polynomial is not a quadratic. The Rational Root Theorem states that if a polynomial of degree n has a rational root p/q (where p and q are integers and q is not equal to zero), then p must be a divisor of the constant term and q must be a divisor of the coefficient of the term of highest degree.

For example, if the polynomial is x^3 - 2x^2 + x - 6, the constant term is -6 and the coefficient of the term of highest degree is 1. The divisors of -6 are -6, -3, -2, -1, 1, 2, 3, and 6. The divisors of 1 are 1 and -1. Therefore, the possible rational roots of this polynomial are -6, -3, -2, -1, 1, 2, 3, and 6.

To find the actual roots, you can try each of these numbers as a root and see if it works. For example, if you try -6 as a root, you would get:

(-6)^3 - 2(-6)^2 + (-6) - 6 = 0

(-216) - (-72) + (-6) - 6 = 0

-144 - 6 - 6 = 0

-156 = 0

This equation is not true, so -6 is not a root of the polynomial. You can repeat this process for each of the other possible rational roots until you find all of the roots of the polynomial.

the value of log2 base 2 is 1 because if base and logrithm value is same then it is always one

How do you find the value of log base 2?

Properties of Log Base 2

Multiply two numbers with base 2, then add the exponents. Divide two numbers with the base 2, subtract the exponents. Power Rule: Raise an exponential expression to power and multiply the exponents.

Use the change-of-base formula:

since we know that natural log and log with base 10 are different

So, if we want to write log3(6) as a logarithm of base 2, in these example a = 3, x = 6, b = 2:

Hence ,  the value of log2 base 2 is 1 because if base and logrithm value is same then it is always one

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The factors of given quadratic expression are (4a+3) and (a+6).

The factors are the polynomials which are multiplied to produce the original polynomial.

The given quadratic expression is 4a²+27a+18.

By splitting middle term method, we get

4a²+3a+24a+18

= a(4a+3)+6(4a+3)

= (4a+3)(a+6)

Therefore, the factors of given quadratic expression are (4a+3) and (a+6).

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The steps to solve two polynomial equations are given below.

What is polynomial?

A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

x^2 + 4x + 7 is an illustration of a polynomial with a single indeterminate x.

Apply the Zero Factor Property to an Equation Solving.

ZERO. FACTOR, write the equation with one side equal to zero. the expression by a factor.

PROPERTY. Solve the equation by setting each factor to zero.

Check by adding substitutes to the initial equation.

Write a polynomial equation in standard form before attempting to solve it. Factor it, then set each variable factor to zero once it has reached zero. The original equations' solutions are the solutions to the resulting equations. Factoring cannot always be used to solve polynomial equations.

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If six different colors of paint are available, 360 ways can the knobs be painted.

A coat hanger has four knobs, and each knob can be painted any color. If six different colors of paint are available,

When examining permutations and combinations, we use factorials. Permutations tell us how many different ways we can arrange things if their order matters. Combinations tells us how many ways we can choose k item from n items if their order does not matter.

coat hanger has four knobs

6!  / 4! ( 4!)

6 * 5 * 4* 3 / 4 * 3 * 2* 1 (4 * 3 * 2 * 1)

= 30 * 1 2

=360

360 ways can the knobs be painted.

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The percentage error is 16%

We know that the formula for the percentage error.

E = (absolute error / actual value) × 100

The formula for the absolute error is:

A = |actual value - experimental value|

A = |V1 - V2|

where V1 is the actual value

V2 is the experimental value

E is the percentage error

A is the absolute error

In this question, the experimental calculation of the specific heat of aluminum = 156 cal/g °C

And the actual specific heat of aluminum = 185 cal/g °C

Using above formula of absolute error,

A = |185 - 156|

A = 29 cal/g °C

And the percent error would be,

E = (absolute error / actual value) × 100

E = (29 / 185) × 100

E = 0.16 × 100

E = 16%

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Answer:

Step-by-step explanation:

The perimeter of a rectangle is the sum of all its sides. Since the perimeter is given as 84 cm, we can set up the following equation to represent the problem:

2l + 2b = 84

Where l is the length of the rectangle and b is the breadth.

We are also told that the length is 6 cm longer than the breadth. We can represent this relationship with the equation:

l = b + 6

Substituting the second equation into the first equation, we get:

2(b + 6) + 2b = 84

Expanding the left side of the equation gives:

2b + 12 + 2b = 84

Combining as terms gives:

4b + 12 = 84

Subtracting 12 from both sides gives:

4b = 72

Dividing both sides by 4 gives:

b = 18

Substituting this value back into the equation l = b + 6 gives us:

l = 18 + 6

l = 24

Therefore, the length of the rectangle is 24 cm and the breadth is 18 cm.

A high school statistics class wants to conduct a survey to determine what percentage of students in the school would be willing to pay a fee for participating in after-school activities. Twenty students are randomly selected from each of the freshman. sophomore. junior, and senior classes to complete the survey.  This plan is an example of Stratified random  type of sampling .

What does "stratified random sampling" mean?

A population is divided into smaller subgroups known as strata as part of a sampling technique called stratified random sampling.

           During stratified random sampling, also known as stratification, groups of people are divided into groups based on shared traits or characteristics, such as level of education or income.

What is a good illustration of a stratified sampling technique?

A stratified sample is one that guarantees that the various strata (subgroups) of a given population are fairly represented in the sample population as a whole.

                                   One could, for instance, divide a sample of persons into age-related subgroups, such as 18–29, 30-39, 40–49, 50–59, and 60 and above.

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By using the area of circle formula, the solution of the given problem of circle comes out to be 6 + π cm

Every location in the plane of a circle is equally separated from the center and is a closed, as double object. Each line tracing the circle contributes to the formation of a line of reflection symmetry. Additionally, each angle has axis of symmetry around the center.

Here,

A 9 Pi square centimeter circle's sector has a 60 degree center angle. The sector's exterior border is

Circle area is equal to. πR² = 9π

Circumference =2πR

=> 2π*3 = 6π cm

Arc length equals (60/360)*6 to cm

Arc's perimeter is calculated as follows: Radius + Length of Arc + Radius = π +3 + 3 = 6 +  π cm

Therefore , the solution of the given problem of circle comes out to be

6 + π cm.

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By using the area of circle formula and circumference of a circle formula, the solution of the given problem of circle comes out to be 12π cm

Every location in the plane of a circle is equally separated from the center and is a closed, as double object. Each line tracing the circle contributes to the formation of a line of reflection symmetry. Additionally, each angle has axis of symmetry around the center.

Here,

sector area of circle = 9π

arc measure = 90°

Area of sector  = (arc/360°)*πr²

⇒ 9π = (90°/360°)πr²

⇒ 9π = (1/4)πr²

⇒ 4*9π = πr²

⇒ 36 = r²

⇒ 6² = r²

r = 6

and Circumference of circle = 2πr

=> 2π*6 = 12π cm

Therefore , the solution of the given problem of circle comes out to be

12π cm.

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Answer: The odds in favor of an event happening are the ratio of the probability of the event happening to the probability of the event not happening. To find the odds in favor of an event, you can use the formula:

Odds in favor = probability of event occurring / (1 - probability of event occurring)

In this case, the event is that Adam will see a meteor in the next 10 minutes. The probability that this event will occur is 0.56. Therefore, the odds in favor of this event occurring are:

Odds in favor = 0.56 / (1 - 0.56)

= 0.56 / 0.44

= 1.27

So, the odds in favor of Adam seeing a meteor in the next 10 minutes are 1.27 to 1.

It means that Adam is 1.27 times more likely to see a meteor in the next 10 minutes than not seeing one.

Step-by-step explanation:

The odds in favor of Adam seeing a meteor in the next 10 minutes are 14 : 11

The number of chairs that should be removed, for there to be as few empty seats as possible but for all rows of chairs to be complete, is 33 chairs.

The number of chairs that make up a row is 11 chairs and there are to be 70 students in attendance. The number of rows that would take the students is therefore:

= Number of students / Number of rows

= 70 / 11

= 6. 36

= 7 rows rounded up

The number of rows needed is 7 rows which means the number of chairs would be:

= 7 rows x 11 chairs per row

= 77 chairs

The number of chairs to be removed is:

= Total chairs - Chairs needed

= 110 - 77

= 33 chairs

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The value of c will be 0.

The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

m = y2 - y1 / x2 - x1

where m = 0

y2 = c

y1 = 0

x1 = -2

x2 = -8

0 = c - 0 / -8 - -(2)

0 = c - 0 / -8 + 2

0 = c - 0 / -6

c - 0 = -6(0)

c - 0 = 0

c = 0

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Answer:

Below

Step-by-step explanation:

How many times will the colony double ?    124 / 31 = 4 times

2^4   * 100 000 = 1 600 000

Therefore , the solution of the given problem of tractable problem comes out to be Undecidable troubles are those for which there will never be a computer solution.

a technique that completes a manageable task in a polynomial period of time. Utilizing the polynomial upper bound is advantageous. A problem is said to be intractable if it cannot be solved in a polynomial amount of time. The bound has a minimum that is exponential.

Here,

Intractable problems would be those in which there is significant proof that, while they can be solved by a desktop, they cannot be solved quickly enough to be actually useful in practice.

Undecidable troubles are those for which there will never be a computer solution, whereas undecidable difficulties are those for which there will never be a computer solution.

Therefore , the solution of the given problem of tractable problem comes out to be Undecidable troubles are those for which there will never be a computer solution.

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The gradient of f(x, y, z) = log(x2 + y2 + z2) at (1, 0, 1) is (2/1, 0, 2/1)

This gradient is a vector that points in the direction of the greatest rate of increase of the function f(x, y, z) = log(x2 + y2 + z2). To evaluate this gradient, the partial derivatives of the function with respect to x, y, and z must be calculated.

The partial derivative of the function with respect to x is (2x / (x2 + y2 + z2)). When x is 1, this simplifies to 2/1. Similarly, the partial derivative with respect to y is 0, and the partial derivative with respect to z is (2z / (x2 + y2 + z2)), which simplifies to 2/1 when z is 1. Therefore, the gradient of f(x, y, z) = log(x2 + y2 + z2) at (1, 0, 1) is (2/1, 0, 2/1).

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Answer:

f(6) = - 50

Step-by-step explanation:

substitute x = 6 into f(x) , that is

f(6) = - 6² - 14 = - 36 - 14 = - 50

Answer:

-50

Step-by-step explanation:

f ( x ) = - x² - 14

Accordingly, to find the value of f ( 6 ) you have to replace x with ( 6 ).

f ( 6 ) = - (6)² - 14

f ( 6 ) = - 36 - 14

f ( 6 ) = -50

Answer:

4 ^ -8

Step-by-step explanation:

To graph the equation y = 1x / 2 + (-5), you will need to plot several points that satisfy the equation and then connect them with a line.

To do this, you can pick a few values of x, substitute them into the equation to find the corresponding values of y, and then plot these points on the coordinate plane.

For example, if you choose x = -2, the corresponding value of y is (-2) * (1 / 2) + (-5) = -5.5. If you choose x = 0, the corresponding value of y is (0) * (1 / 2) + (-5) = -5. And if you choose x = 2, the corresponding value of y is (2) * (1 / 2) + (-5) = -4.

You can then plot these points on the coordinate plane and connect them with a line to graph the equation.

Im really sorry that I was unable to provide a picture.  I hope this helped!

Answer:

Graph the line using the slope and y-intercept, or two points.

Slope:

1/2

y-intercept: (0,−5)

x   y

0 −5

2 −4

Step-by-step explanation:

Answer:

The answer is 48

Step-by-step explanation:

Answer:

48 students

4*12=48

Answer:Bilquis finds some nickels and quarters in her piggy bank. How much money (in

cents) does she have if she has 7 nickels and 5 quarters? How much money

does she have if she has n nickels and q quarters?

Step-by-step explanation:

Answer: 157 cents ($1.57)

Step-by-step explanation: Nickels are worth 5 cents each, so 5 cents times 7 nickels equals a total of 35 cents. After that, we have 5 quarters which cost 25 cents each, so 25 cents times 5 quarters equals a total of 125 cents. Combine these two products, and you get 157 cents. Or, if you want it in dollars, you can divide 157 by 100 cents (there are 100 cents in a dollar) and end up with $1,57.

A linear graph will have a straight line, whereas a logarithmic graph will have a curved line.

1. Look at the graph and identify the shape of the line.

2. If the line is straight, then the graph is linear.

3. If the line is curved, then the graph is logarithmic.

When looking at a graph, you can tell if it is linear or logarithmic by examining the shape of the line. A linear graph will have a straight line, whereas a logarithmic graph will have a curved line. This is due to the fact that a linear graph is plotted by plotting the points of a linear equation, whereas a logarithmic graph is plotted by plotting the points of a logarithmic equation. The linear equation is of the form y = mx + b, where m is the slope of the line and b is the y-intercept. The logarithmic equation is of the form y = logb(x), where b is the base of the logarithm. Thus, the shape of the line will depend on the form of the equation used to plot the graph. If the line is straight, then it is a linear graph, and if it is curved, then it is a logarithmic graph.

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For an expression containing two variables, a and b, the expression with the largest value is a+b, the expression with the smallest value is a-b, and the expression closest to zero is either a+b or a-b, depending on the values of a and b.

For a=-1/2 and b=6, the expression with the largest value is a+b, which is equal to 5.5. The expression with the smallest value is a-b, which is equal to -7.5. The expression closest to zero is a+b, which is equal to 5.5.

For a=12 and b=-6, the expression with the largest value is a+b, which is equal to 6. The expression with the smallest value is a-b, which is equal to 18. The expression closest to zero is a-b, which is equal to 18.

For a=-6 and b=-12, the expression with the largest value is a+b, which is equal to -18. The expression with the smallest value is a-b, which is equal to 6. The expression closest to zero is a+b, which is equal to -18.

For an expression containing two variables, a and b, the expression with the largest value is a+b, the expression with the smallest value is a-b, and the expression closest to zero is either a+b or a-b, depending on the values of a and b.

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Answer:

15

Step-by-step explanation:

the nickels ratio is 4. I then divided 60 : 4 = 15. I then timesed 15 with 3 and then came out 45. I then subtracted 60 with 45 which gave me the answer of 15.

Answer:

Set1 = 1/12

Set2 = 1/12

Set3 = -12

Step-by-step explanation:

Substitute, use Keep-Change-Flip to handle division when there's fractions involved. See image.

Also to multiply fractions, multiply

top×top and bottom×bottom straight across. Also negative times a negative is a positive and negative is like opposite so -(-6) is 6 and -(-1/2) is 1/2.

see image.

y=0 is the linear equation to denote the x - axis, as all the points on the x- axis, have their y co-ordinate =0.

What is linear equation ?

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

Because the equation y=0 has a slope of 0, the resulting graph must be a straight horizontal line. This is true for all equations with a slope of 0.

Hence , y=0 is the linear equation to denote the x - axis, as all the points on the x- axis, have their y co-ordinate =0.

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Equation of ellipse is x²/400 + (y-52) ²/256 =1

An ellipse is an oval shaped close geometrical figure. Ellipse has two radius, one is horizontal, and the other is vertical. An ellipse can be stretched either horizontal direction or vertical direction.

given, width of elliptical mirror = 16 inches

height of elliptical mirror = 20 inches

the center of ellipse = (0, 52)

as the width of elliptical mirror is less than height so the ellipse has vertical major axis.

vertical radius is denoted by b.

and horizontal radius is denoted by a.

as per the question, a = 16 inches and b = 20 inches.

we know the equation of ellipse whose major axis is vertical and center at the origin is shown by

x² / b² + y²/ a² = 1

we are given information about an ellipse having center (0, 52) and vertical radius 20 and horizontal radius 16.

the equation of this ellipse is.

x² / (20) ² + (y -52) ²/ (16)² = 1

x²/400 + (y - 52) ² /256 = 1

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Answer:

354acres

Step-by-step explanation:

Total acre = 59000

Percentage of old oak acre trees is 0.6%

Therefore, the acres of old trees are calculated:

59000 * (0.6÷100) = 354acres

On solving the provided question, we can say that - sequence (0.67,3-√4,√8,0.14) are the  rational, real, integer, irrational, irrational.

A sequence is a collection of numerals (referred to as "terms"), for example, 2, 5, 8. A specific pattern that some sequences follow may be leveraged to make them infinitely long. To continue the series, add 3 and use the example of 2,5,8. Formulas that show where to look for words inside a sequence can be found there. Informally, a sequence in mathematics is a collection of items that are in some order (or events). It has components, much like a set (also called elements or terms). The length of the sequence refers to the total, potentially unlimited number of ordered items. arranging two or more objects in a logical sequence. Chronological.

here,

the given sequence is (0.67,3-√4,√8,0.14)

as we can see that in the sequence we have a rational number, integer, real number and a irrational so,

the answer is  rational, real, integer, irrational, irrational.

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Answer:

To graph the quadratic function f(x) = -5x^2 - 2, we can use the parabola tool.

First, let's plot the vertex of the parabola. The vertex is the highest or lowest point on the graph of a parabola, and it is located at the point (h, k), where h is the value of the x-coordinate and k is the value of the y-coordinate.

For the quadratic function f(x) = -5x^2 - 2, the vertex is located at the point (0, -2).

Next, we can use the parabola tool to draw the graph of the quadratic function. To do this, we need to set the value of a, b, and c in the equation y = a(x - h)^2 + k. For the quadratic function f(x) = -5x^2 - 2, the values of a, b, and c are -5, 0, and -2, respectively.

Therefore, the equation of the graph of the quadratic function f(x) = -5x^2 - 2 is y = -5(x - 0)^2 - 2.

Using the parabola tool, we can draw the graph of the quadratic function by plotting several points on the graph and connecting them with a smooth curve.

The graph of the quadratic function f(x) = -5x^2 - 2 is a downward-facing parabola with its vertex at the point (0, -2). The graph opens downward because the value of a is negative. The parabola is symmetrical about the y-axis because the value of h is 0. The graph passes through the y-intercept (0, -2) because the value of k is -2.

Step-by-step explanation:

Answer:

d

Step-by-step explanation: