Which type of polynomial is x² 9x 20?

The remainder is 2 when x⁴ + x³ - 2x² + x + 1 is divided by x - 1.

The given polynomial is x⁴ + x³ - 2x² + x + 1.

The given divisor is x - 1

First we choose a term to multiply with the first term of the divisor such that we get the first term of the polynomial.

(x)(x^3) = x^4

Thus, we multiply the divisor (x - 1) by x^3 which gives x^4 - x^2.

Now we subtract this from the polynomial which gives 2x^3 - 2x^2 + x + 1.

Next we multiply the divisor by 2x^2 which gives 2x^3 - 2x^2. Again we subtract the same from the remaining polynomial 2x^3 - 2x^2 + x + 1 and get x + 1.

Repeating the same we multiply the divisor by 1 which gives x - 1. Subtracting the same from the remaining polynomial x + 1 we get the remainder 2.

Thus, the quotient is x^3 + 2x^2 + 1.

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The monthly payment in the 5th year is $2,005.18

To calculate the monthly payment in the 5th year of the adjustable rate mortgage, you would need to know the remaining balance of the loan at the beginning of the 5th year, the interest rate for the 5th year, and the loan term (number of remaining payments) for the 5th year. With the given information, you can calculate the monthly payment using the following formula:

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]

Where:

M = monthly payment

P = remaining balance at the beginning of the 5th year

i = interest rate for the 5th year (expressed as a decimal)

n = loan term for the 5th year (number of remaining payments)

Given that the remaining balance at the end of the 4th year is $231,975.40, and the interest rate for the 5th year is 5.8%

i = 5.8% / 12 = 0.004833

n = (1512) - (412) = 108

M = 231975.40 [ 0.004833(1+ 0.004833)^108] / [(1 + 0.004833)^108 -1]

M = $2,005.18

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At the point of tangency, the tangent line (or segment, or ray) is perpendicular to the circle's radius.

In geometry, the straight line that "just touches" the curve at a particular position is known as the tangent line to a plane curve at that location. According to Leibniz, it is the path connecting two points on a curve that are infinitely close to one another. 

A tangent line is a simple straight line that only touches a function once. (See atop.) The instantaneous rate of change of the function at that specific position is shown by the tangent line. The derivative of the function at a location on the function is equal to the slope of the tangent line at that point (See below.)

Therefore, the correct answer is option a. The tangent line (or segment, or ray) is perpendicular to the radius of the circle at the point of tangency.

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The perimeter of the following kite is 32.

Perimeter is the total of the sides, whereas area is half the product of the diagonals. Remember that a kite is a quadrilateral with distinct adjacent congruent sides and that a rhombus is a quadrilateral with four congruent sides.

The sides of each pair can be added to determine the kite's perimeter. Kite is another name for a quadrilateral with two sides that are equally long on either side. Therefore, a kite's perimeter is equal to 2(a+b), or twice the length of its two sides.

parameter = 2(a+b)

P = 2[(3+3) + (6+4)]

P = 2(6 + 10)

P = 32.

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To find the solution to the equation 4(q + 56.5) = 30q - 112, we can start by isolating the variable on one side of the equation.

First, we'll distribute the 4 on the left side:

4q + 4(56.5) = 30q - 112

4q + 226 = 30q - 112

Now we'll subtract 4q from both sides:

226 = 26q - 112

Next, we'll add 112 to both sides:

338 = 26q

Finally, we'll divide both sides by 26 to find the value of q:

q = 13

So the solution to the equation 4(q + 56.5) = 30q - 112 is q = 13.

Answer:

q=13

Step-by-step explanation:

The triangle ABC is equal to DEF because they possess the same sides.

If all three sides and all three angles of two triangles are equal, then two triangles are said to be congruent.

The triangles are congruent if two sides and the included angle of one triangle match the corresponding sides and angle of another triangle.

Side-Side-Side, or SSS, is a type of triangle congruence rule that states that two triangles are congruent if their three sides are equal to their respective three sides of another triangle.

In this case, triangle ABC is equal to triangle DEF.

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The minimum distance from the starting point is 52.5 miles

First you travels 60 miles north as shown in the image, then 34 miles  west and 20 miles south. We can draw a straight line from the endpoint to the stating point.

We could construct a triangle as shown in the figure. From that we can see that AC is the minimum distance from the start.  AC is the hypotenuse of the triangle we have drawn..

To calculate the hypotenuse, we can use the Pythagoras theorem.

Hypotenuse² = base²+alt²

AC² = BC²+ AB²

        = 34²+40² = 2756

AC = √2756 = 52.497 = 52.5 miles

So the minimum distance is 52.5 miles.

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The percentage he run on Saturday is 150%

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation

Let the d represent the entire distance Raj run on Saturday.

If he ran an entire distance and then half of the way back to the starting point. We can write:

Percentage ran on Saturday = (d + 1/2(d))/(d) × 100%

Percentage ran on Saturday = 1.5d/d × 100%

Percentage ran on Saturday = 1.5 × 100%

Percentage ran on Saturday = 150%

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The value of x is 55 degrees.

If two lines are parallel and intersected by a transversal, then the consecutive interior angles formed are supplementary, meaning they add up to 180 degrees.

Since we know that m∠A + m∠B = 180 and we know that m∠A = x, we can use this information to find the value of x.

m∠A + m∠B = 180

x + (x+70) = 180

x + x + 70 = 180

2x = 110

x = 55

Therefore, the value of x is 55 degrees.

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There are 2 pounds of apples Hannah buy for the cost for her purchase to be the same from both stores.

Given that;

At Giant Eagle, a box of cereal costs $2.89 and apples cost $1.29 per pound.

And, At Shop & Save, the apples are $1.05 per pound and a box of

cereal is $3.37.

Now,

Let number of pounds of apples can Hannah buy for the cost for her purchase to be the same from both stores = x

So, We can formulate;

For, At Giant Eagle, a box of cereal costs $2.89 and apples cost $1.29 per pound.

The total cost is,

⇒ $2.89 + $1.29x

And, For Shop & Save, the apples are $1.05 per pound and a box of

cereal is $3.37.

Total cost is,

⇒ $3.37 + $1.05x

Now, We can equate both the equation to find the number of pounds of apple to buy.

⇒ $3.37 + $1.05x = $2.89 + $1.29x

⇒ 3.37 + 1.05x = 2.89 + 1.29x

⇒ 3.37 - 2.89 = 1.29x - 1.05x

⇒ 0.48 = 0.24x

⇒ x = 0.48 / 0.24

⇒ x = 2

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The complete solution to this problem is: x = 1.8, y = 3.

Equations can be used to represent relationships between variables and to solve problems. They are written using an equal sign (=) and can include numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

For example, the equation 2x + 3 = 7 is an equation that states that the expression on the left side (2x + 3) is equal to the expression on the right side (7). The goal is to find the value of the variable x that satisfies the equation. In this case, x = 2 is a solution to the equation.

To find the value of x for which the pair of numbers (x; 3) would be a solution to the equation 10x - y = 15, we need to substitute the value of y with 3 and solve for x. So, we have:

10x - 3 = 15

Next, we can add 3 to both sides to isolate x:

10x = 18

Finally, we can divide both sides by 10 to find x:

x = 1.8

So, for the pair of numbers (x; 3) to be a solution to the equation 10x - y = 15, x must be equal to 1.8.

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X = 68 is the possible values of r.

Based on the given conditions,

X÷2-16 18

Rearrange variables to the left side of the

Equation: x/2=18+16

Calculate the sum or difference:

X/2=34

Divide both sides of the equation by the

Coefficient of variable X=34 × 2

Calculate the product or quotient: x=68

An inequality can be represented in four ways: equation notation, set notation, interval notation, and solution graph. Many basic inequalities may be handled by adding, removing, multiplying, or dividing both sides until the variable is all that remains. However, these factors will alter the direction of the inequality: Using a negative number to multiply or divide both sides. Swapping the left and right sides.

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Yes.The equation y = -3 represents a line that is parallel to the x-axis.

In a two-dimensional coordinate system, the x-axis is the horizontal axis and the y-axis is the vertical axis. A line parallel to the x-axis will have a constant y-value, and a line parallel to the y-axis will have a constant x-value.

In this case, the equation y = -3 represents a line that has a constant y-value of -3. This means that for every point on the line, the y-coordinate will be -3 and the x-coordinate can take any value. This line is parallel to the x-axis as it does not change in its x-coordinate, so it does not have a slope and it's equation is a horizontal line.

Note, a line parallel to the x-axis is also called a horizontal line, and a line parallel to the y-axis is also called a vertical line.

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The formula that can be used to represent this function is N*L^2 = k

The number of animal species, N, is inversely proportional to the square of the body length, L. Therefore, the formula representing the function would be:

N = k/L^2

Where k is the proportionality constant. It represents the relationship between N and L^2, and it is a constant value.

The above formula can also be written as

N*L^2 = k

It means that the product of N and L^2 is constant.

It can be derived by assuming that there is some proportionality constant k such that N=k/L^2 and then testing this relationship against data on animal species and body lengths.

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Sunday is the week was November 16, 2014

We see that there is a 13-year span from November 16, 2001, to November 6, 2014. If each year were 365 days, the total number of days in this 13-year span would be 365 x 13 = 4,745 days.

However, since 3 of the years during this span, each has 1 extra day, the actual number of days in this span is 4,745 + 3 = 4,748 days.

Since 4,748/7 = 678 R2, we know that there were 678 weeks and 2 days from Friday, November 16, 2001, until November 16, 2014. The remainder of 2 tells us that November 16, 2014, was 2 days after Friday, so it was Sunday.

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A phrase, "the difference of c and 6 is greater than or equal to -26" as an expression, is c - 6 ≥ -26.

A term is a single mathematical phrase. It might consist of only one variable-a letter-one number-positive or negative-or several variables multiplied but never added or subtracted. A number is placed in front of some nouns that have variables. The number used before a sentence is called a coefficient.

Given:

A phrase: The difference of c and 6 is greater than or equal to -26.

The difference of c and 6 can be expressed as,

c - 6.

And c - 6 is greater than or equal to -26 can be expressed as,

c - 6 ≥ -26.

The expression is c - 6 ≥ -26.

Therefore, the phrase can be expressed as c - 6 ≥ -26.

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The degree of polynomial 3x^4-0x^3+0x^5 is 4

Degree of a polynomial is the highest power that its terms pertain (for multi-variables, the power of term is addition of power of variables in that term).

Therefore, inx^3+3x+5, the degree of the polynomial is 3 as the highest power in its terms is 3. (power and exponent are same thing);

Given in the question;

Polynomial= 3x^4-0x^3+0x^5

The highest degree from observation is of 3x that is equal to 4

Hence, the correct degree will be 4

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Answer:

When hot milk is poured into a cold ceramic bowl, heat moves from the milk to the bowl.

The 95% confidence intervals, along with their interpretations, are described by the following option:

The confidence interval from the first simulation is (0.560, 0.620), and the confidence interval from the second simulation is (0.610, 0.670). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.560 and 0.620. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.610 and 0.670.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

n is the sample size.

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

For the first simulation, the parameters are given as follows:

[tex]n = 1000, \pi = \frac{590}{1000} = 0.59[/tex]

Hence the lower bound of the interval is of:

[tex]0.59 - 1.96\sqrt{\frac{0.59(0.41)}{1000}} = 0.56[/tex]

The upper bound is of:

[tex]0.59 + 1.96\sqrt{\frac{0.59(0.41)}{1000}} = 62[/tex]

For the second simulation, the parameters are given as follows:

[tex]n = 1000, \pi = \frac{640}{1000} = 0.64[/tex]

Hence the lower bound of the interval is of:

[tex]0.64 - 1.96\sqrt{\frac{0.64(0.36)}{1000}} = 0.61[/tex]

The upper bound is of:

[tex]0.64 + 1.96\sqrt{\frac{0.64(0.36)}{1000}} = 0.67[/tex]

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The general steps to factor a composite number are dividing the composite number by the smallest prime number, if the division is exact, you have found one of the factors of the composite number.

After that then divide the quotient by the smallest prime number that is greater than the divisor used in step 1. Repeat this step with the quotient until the quotient is a prime number. The prime factors of the composite number are the divisors used in the previous steps and the quotient obtained in step 4.

Factoring is the process of finding the prime factors of a composite number.

For example, if you want to factor the composite number 60, you would begin by dividing 60 by 2. Since 60 is divisible by 2, we know that 2 is a factor of 60. The quotient is 30.

We will then divide 30 by 3 and got 10 as quotient.

Then we divide 10 by 2 and got 5 as quotient. 5 is a prime number, so we know that the prime factors of 60 are 2 x 3 x 5

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Yes, 3x^3 is a polynomial. It is a third-degree polynomial, which is a monomial.

A polynomial is a mathematical expression that can be written as the sum or difference of one or more terms, where each term is a constant multiplied by one or more variables raised to a non-negative integer power.

A monomial is a polynomial with only one term. It is of the form ax^n, where a is a constant and n is a non-negative integer. In this case, the constant is 3 and the variable is x raised to the power of 3.

The degree of a polynomial is the highest power of the variable in the polynomial.

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Answer: M=3

Step-by-step explanation: because for every 3 pencils there is 1 student.

The length of the third side in the right angled triangle is 12 units

An equation shows the relationship between numbers and variables in an expression.

Pythagoras theorem shows the relationship between the sides of a right angled triangle. It is given by:

hypotenuse² = opposite² + adjacent²

From the diagram, let x represent the missing side, hence:

15² = 9² + x²

x² = 144

x = 12 units

The missing side is 12 units

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The equation of parabola is f(x) = y= ax² + bx + c

Here we have to find the equation of the parabola.

In order to find the equation of parabola, here we need to know what is meant by parabola.

The term parabola in math is defined as a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone.

Through the definition, we have found the standard form of parabola equation is expressed as,

=> f(x) = y= ax² + bx + c

Here we have know that the orientation of the parabola graph is determined using the “a” value.

While the value of a is greater than 0 (a>0) then the parabola graph is oriented towards the upward direction.

Whereas the value of a is less than 0 (a<0) then the parabola graph opens downwards.

And the axis of symmetry from the standard form of the parabola equation is given as x= -b/2a.

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Answer:

area : lxb,..,.................

Answer:

Step-by-step explanation:

These are the statements I think is true:

The parallelogram and rectangle formulas are both the same.

In the trapezoid formula, the bases are added.

Explanation:

I’ll just give you the formulas..

Area for trapezoid:

(a + b) ÷ 2 x h

a & b are the bases, h is for height.

Area for rectangle:

Length x width

Area for parallelogram:

Base x height

(Choose the height that is perpendicular to the base)

Also, I would liek you to know I did not understand the other few choices because ai think they have wrong grammar. But I really tried my best for now.

HOPE THIS HELPS!

On the third day of the camp miles hiked by the tourist as per given data is equal to 41 miles .

As given in the question,

On the first day,

Miles hiked by tourist is 9 miles to the east from camp.

Let x miles be hiked by tourist on the second day to the north.

let h miles be hiked by tourist on third day

Total distance travelled = 90 miles

It represent the right angled triangle

'h' represents the hypotenuse.

By Pythagoras theorem,

h² = x² + 9² ___(1)

x + h + 9 = 90

h = 81 - x  __(2)

Substitute the value h from (2) in (1) we get,

( 81 - x )² = x² + 9²

⇒ 6561 - 162x + x² = x² + 9²

⇒ 162x = 6480

⇒ x = 40

⇒ h = 41 miles

Therefore, on the third day of the camp miles hiked by tourist is equal to 41 miles.

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Answer: A mapping diagram is a way to visualize a relation by plotting its ordered pairs on a coordinate plane.

For the relation {(2, 8), (-1, 5), (0, 8), (-1, 3), (-2, 3)}, the mapping diagram would look like this:

(x,y)

(-2,3) (-1,3)

(0,8)

(-1,5) (2,8)

In the above diagram, each point represents an ordered pair from the relation. You can see that the relation maps x-coordinates -2, -1, 0, 1 and 2 to y-coordinates 3,3,8,5 and 8 respectively.

Step-by-step explanation:

Cramer’s rule is the direct method for solving simultaneous algebraic equations.

Because polynomials are included on both sides of the equal sign, algebraic equations are sometimes referred to as polynomial equations. Variables, coefficients, constants, and algebraic operations like addition, subtraction, multiplication, division, and exponentiation are all components of an algebraic equation.

One of the key techniques for solving a system of equations is Cramer's rule. In this approach, determinants of matrices are used to compute the values of the system's variables. Cramer's rule is frequently referred to as the determinant technique as a result.

Which of the methods is a direct method for solving simultaneous algebraic equations?

a) Jacobi’s method

b) Relaxation method

c) Cramer’s rule

d) Gauss seidel method

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Deb had 2 3/4 pounds of blueberries. Deb let her friend clarence eat 1/4 of the blueberries. Clarence ate 0.6875 pounds of blueberries.

To find out how many pounds of blueberries Clarence ate, we need to first convert the 2 3/4 pounds to a decimal. We can do this by dividing the numerator (3) by the denominator (4) and adding the result to the whole number (2).

2 3/4 pounds = 2 + (3/4) = 2 + 0.75 = 2.75 pounds

Now we know that Deb had 2.75 pounds of blueberries. To find out how many pounds of blueberries Clarence ate, we need to multiply this amount by the fraction of blueberries he ate (1/4).

2.75 pounds x 1/4 = 0.6875 pounds

So Clarence ate 0.6875 pounds of blueberries.

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