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Resultant polynomial is  [tex]-2x^2 -2x +3[/tex].

(4x^2 - 2x )+ ( -6x^2 + 3)

[tex]4x^2 - 2x + 0[/tex]             +

[tex]-6x^2 + 0x + 3[/tex]

[tex]-2x^2 -2x +3[/tex]

Resultant polynomial is  [tex]-2x^2 -2x +3[/tex].

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Square Bases:  A = s².

Rectangle-shaped bases: A = l x w.

Circular bases: A = pi x r².

In geometry, a three-dimensional object's bottom is referred to as its base; if the solid's top is parallel to its bottom, it is also referred to as a base.

The bases of cubes as well as square pyramids are square. The length of one of a square's sides multiplied on its own, or squared, determines the area of a square: It goes like this: A = s².

Pyramids and several rectangular solids have rectangular bases. A rectangle's area is determined by multiplying its length, l, by it's own width, w: A = l x w.

Cones and cylinders have round bases. The radius of a circle, r, squared, plus the number pi, is equal to a area of the circle:

A = pi x r².

Pi is  approximately 3.14.

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Answer:

$6000

Step-by-step explanation:

So, we know that

$1500 = 25%

We find 1% by taking

1500 divided by 25% = $60

We have to find the 75% off by taking

60 times 75 = $4500

Then we have to find the original price by taking

4500 + 1500 = $6000

So, the original price is $6000

Answer:

$6000

Step-by-step explanation:

The total cost is 100%

The discount was 75%

then:

100% - 75% = 25%

The percentage paid was:

25%

then:

$1500 ⇒ 25%

$A ⇒ 100%

A = 1500*100/25 = 6000

A = $6000

The equation 4x²+8xy+ky²-9 = 0 will have a pair of straight lines when k = 0.

An equation obtained from the standard form of a linear differential equation by replacing the right member by zero.

Given that, an equation having a pair of straight line 4x²+8xy+ky²-9 = 0

The auxiliary equation of a line is given by, ax²+2hxy+by²+2gx+2fy+c = 0

or, abc-2fgh-af²-bg²-ch²= 0

Comparing with the given equation,

a = 4, h = 4, b = k, g = 0, f = 0 and c = -9

4k(-9)+0-0-0+9(4)² = 0

36k = 144

k = 4

Hence, The equation 4x²+8xy+ky²-9 = 0 will have a pair of straight lines when k = 0.

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Answer:

( D ) x must be a number divisible by 3

Step-by-step explanation:

Rational numbers cannot be whole numbers.

( A ) x must be an odd number

if x is an odd number, Let's take x as 1 then the answer will be in rational number. So, Option A is wrong.

( B ) x must be an even number

If x is an even number, Let's take x as 2 then the answer will be in Rational number. So, Option B is wrong.

( C ) x must be a number greater than 3

Let's take x as 4, then the answer will be in Rational number. So, Option C is wrong.

( D ) x must be a number divisible by 3

Let's take x as 6 as 6 is divisible by 3, then

[tex] \frac{2}{3}x+ 1[/tex]

[tex] \frac{2}{3}(6)+ 1[/tex]

[tex]2(2) + 1[/tex]

[tex]4 + 1[/tex]

[tex]5[/tex]

The repeated sampling of a population is known as distribution of sample in R.

The probability distribution of a statistic acquired from a bigger sample size taken from a certain population is known as the sampling distribution. The frequency distribution of a variety of possible outcomes for a population statistic makes up the sampling distribution of a specific population.

The relationship between observations of various heights is described by the distribution, a mathematical function. Simply said, a distribution is a grouping of data, or scores, on a variable. These scores are typically listed from smallest to largest, after which they might be displayed graphically.

The probability distribution of a statistic that is acquired by repeated sampling of a particular population is called the sampling distribution. It outlines a variety of potential possibilities for a statistic, such as the mean or mode of a population's mean or mode of some variable.

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Yes, the UNIQUE function is an array function. The results of this function just need to be written once, and the full array will be filled with the results (range of cells).

A formula with numerous computations capabilities on one or more elements in an array is known as an array formula. An array can be thought of as a row, column, or mix of rows and columns of values. Array formulae may provide a single result or a number of outputs.

Array formulae may provide a single result or a number of outputs. Any formula that can provide several outcomes will automatically spill them either down, starting with the Microsoft 365 September 2018 upgrade.

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The cost of 1 oz in dollars if 10 oz cost $0.95 is $0.095

Based on the given concept; we can solve by using ratio

Cost of 10 oz = $0.95

Cost of 1 oz = x

Equate the ratio of number of oz to cost in dollars

10 : 0.95 = 1 : x

10/0.95 = 1/x

cross product

10 × x = 0.95 × 1

10x = 0.95

divide both sides by 10

x = 0.95/10

x = $0.095

In conclusion, 1 oz cost $0.095

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The coordinate of the image point A (-1, 4).

In mathematics, a translation is an up, down, left, or right movement of shapes. Because the translated shapes appear to be identically similar in size to the original ones, they are congruent with one another.

The Rule of Translation of points is given by (x, y) → (x ± h, y ± k)

where the horizontal and vertical shiftings are h units and k units, respectively.

Given that

The image point of A after a translation right 4 units and up 4 units is the point B

Let A(x, y) be the point that translated to right 4 units and up 4 units

According to the given formula

(x, y) → (x ± h, y ± k)

Since the point is translated to right and up

=> (x, y) → (x + h, y + k)  

=> (x, y) → (x + 4, y + 4)

From the given data the final point is B(3, 8)

=> (x + 4, y + 4) = (3, 8)  

=> x + 4 = 3  and  y + 4 = 8

=> x + 4 = 3      

=> x = 3 - 4 = -1

=> x = -`1          

=> y + 4 = 8  

=> y = 8 - 4

=> y = 4  

Therefore,

The coordinate of the image point A (-1, 4).

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Answer:

⭐ There are 3 ways you can write a linear function (⭐ = most common):

Answer: see below

Step-by-step explanation:

x=-1 is a vertical line at x=-1

A t-statistic rather than a z-score is used when (C) the population's variance and standard deviation are unknown.

The t-statistic, which is used in statistics, measures how far a parameter's estimated value deviates from its hypothesized value relative to its standard error.

Through the Student's t-test, it is utilized in hypothesis testing.

In a t-test, the t-statistic is used to decide whether to accept or reject the null hypothesis.

When the variance and standard deviation of the population are unknown, a t-statistic is employed rather than a z-score.

The p-value is the likelihood that, if the null hypothesis is correct, each test will result in a t-value with an absolute value at least as great as the one we actually observed in the sample data.

The t-value is a way to measure the difference between population means.

Therefore, a t-statistic rather than a z-score is used when (C) the population's variance and standard deviation are unknown.

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Correct question;
In what circumstances is the t-statistic used instead of a z-score for a hypothesis test?

(A) the t-statistic is used when the population variance (or standard deviation) is known

(B) you use the z-test when the sample size is less than 30

(C) the t-statistic is used when the population variance (or standard deviation) is unknown

The value of x° and y° are 48.5° and  38.6°.

What is the cosine law?

The square of the length of any one side of a triangle is equal, by the cosine rule, to the total of the squares of the lengths of the other two sides, multiplied by the cosine of the angle they are a part of.

The length of sides of the triangle are 10, 12, and 16.

Assume that AB = c = 10, BC = a = 16, and AC = b = 12

m∠B = x° and m∠C = y°.

Cosine law:

c² = a² + b² - 2ab cos C  ....(i)

b² = a² + c² - 2ac cos B  ....(ii)

a² = b² + c² - 2bc cos A  ....(iii)

Putting a = 16, b = 12, c = 10, and C = y° in law (i)

10² = 16² + 12² - 2×16×12 cos y

100 = 256 + 144 - 384 cos y

384 cos y = 300

cos y = 300/384

y = 38.6°

Putting a = 16, b = 12, c = 10, and B = x° in law (ii)

12² = 16² + 10² - 2×16×10 cos x

144 = 256 + 100 - 320 cos x

320 cos x = 212

cos x = 212/320

x =48.5°

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The mean of following numbers is 4.

To find: mean of given numbers .

Given data : 1, 2, 3, 4, 5, 6, 7

Mean: Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Here, sum of observations =1+2+3+4+5+6+7=28

sum of observations=28

Arithmetic mean refers to the average amount in a given group of data. It is defined as the summation of all the observation is the data which is divided by the number of observations in the data

Total number of observations =7

The number of observations provides information on the total number of values that are contained in the Dataset. This property is intended to provide an indication of the size of a Dataset.

Substituting values in above formula,

=[tex]\frac{28}{7}[/tex]=4

Therefore, the mean is 4.

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5 is the required mean of the given values 4 and 6.

The mean is a specific type of average.

A list of values, such as measurements or numbers, is used to calculate it by dividing the total number of values in the list by the total number of values in the list.

To find the mean, add up each value in the set.

Now, we got the values which are:

4 and 6

Mean formula: Sum of terms / Number of terms

Now, we will use the above-given formula and calculate the mean of 4 and 6 as follows:

Mean: Sum of terms / Number of terms

Mean: 10/ 2

Mean: 5

Therefore, 5 is the required mean of the given values 4 and 6.

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Complete question:

How do you find the mean of 4 and 6?

The book  'Terrible Weather' was written by WAYNE DROPS

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Solving the equations,

1) 5x-7 = 4x+3

x = 10 (N)

2) 6+2x = 7x-9

5x = 15

x = 3 (O)

3) 8x+1 = -8-x

-9x = 9

x = -1 (A)

4) -5+12x = 18x+7

6x = -12

x = -2 (S)

5) -4x+3 = 5x-13-x

8x = 16

x = 2 (R)

6) -10-11x+24 = 3x

14x = 14

x = 1 (E)

7) 8+3x = x+11+2x

3x-3x = 11-8

3 = 0

No solution (Y)

8) 5+17x+9 = 2x+21x+14

6x = 0

x = 0 (D)

9) 6x+8-13x+10 = 4-6x-11+4x

-7x+18 = -7-2x

5x = 25

x = 5 (W)

10) -14+5-x-3 = x+6+x+3x

-18 = 6x

x = -3 (P)

Now, the answer is coded as 93716 852104

Decoding with the help of the solutions of the given equations

WAYNE DROPS

Hence, the answer is WAYNE DROPS

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The Multiplication table that comes in the number 64 is 1, 2, 4, 8, 16, 32, and 64.

Multiples are numbers that are multiplied by another number to get a particular number.

In mathematics, multiples are the results of multiplying an integer by a given number.

Multiples of 5 include, for instance, 10, 15, 20, 25, 30, etc.

Numerous 7s include 14, 21, 28, 35, 42, 49, etc.

A multiple in mathematics refers to the outcome of multiplying two numbers together.

Here, the number 7 is multiple by 56.

Because the result of multiplying 0 by any number is 0, 0 is a multiple of all numbers.

So, in order to know what tables come in 64, we need to check that what numbers multiples ae 64:

64/1 = 64

64/2 = 32

64/4 = 16

64/8 = 8

64/16 = 4

64/32 = 2

64/64 = 1

Therefore, the Multiplication table that comes in the number 64 is 1, 2, 4, 8, 16, 32, and 64.

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Answer:

Step-by-step explanation:

The perimeter of a rectangle is the sum of its 2 widths and 2 lengths.

Lets call the width ‘W’ and the length ‘L’. The perimeter (P) is equal to 2W + 2L. So 28 = 2W + 2L which simplifies to 14 = W + L.

28/2=14

The area of a rectangle is the width multiplied by the length so the formula is A = W x L. We want to get rid of the length. So, if we rearrange the first equation 14 = W + L to make L the subject we get L = 14 - W. We can now substitute this into the area equation so we get → A = W x (14 - W). That’s your answer!

Your answers are correct! Well done!

Answer:

49

Step-by-step explanation:

Vertical angles are congruent.

8x-23=6x-5

8x-6x=23-5

2x=18

divide

x=9

8(9)-23

=49

The vertex of a parabola is the point at which the parabola changes direction, the vertex of y =-x² + 4 is (0, 4).

The equation for a parabola in standard form is y = ax² + bx + c. To find the vertex of y = -x² + 4, we need to use the formula x = -b/2a. In this equation, a is -1, and b is 0, so x = 0. Therefore, the vertex of y = -x² + 4 is (0, 4).

To find the vertex of a parabola, we can use the formula x = -b/2a. In this formula, a is the coefficient of x², and b is the coefficient of x. Therefore, to find the vertex of a parabola, we need to find the coefficients of x² and x and then plug them into the formula. This formula will give us the x-coordinate of the vertex, and we can then use the equation of the parabola to find the y-coordinate of the vertex. In the case of y = -x² + 4, the coefficient of x² is -1 and the coefficient of x is 0. Plugging these values into the formula, we get x = 0. We can then use the equation of the parabola to find the y-coordinate of the vertex, which is 4. Therefore, the vertex of y =-x² + 4 is (0, 4).

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On solving the provided question we can say that, - the roots of the given equations  are - x = -5/2 and x = 1

When referring to the values of a variable for which the supplied polynomial equals zero, we use the term "roots of a polynomial." The polynomial p(x) has zero roots if and only if an is its root. By setting each component to 0, you may solve for x to determine the roots, or solutions, of the polynomial equation P(x) = 0. Factoring is used to solve the polynomial equation. Set each component to a value of 0 (2x4), (x-6) or (x+1). Calculate x using the solution.

here,

[tex]2x^2 + 3x - 5[/tex]

(2x + 5)(x-1)

x = -5/2 and x = 1

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Answer:

x² -9x + 20

Step-by-step explanation:

x²-4x -5x + 20

x² - 9x + 20

(i), (ii), (iv) and (vii) are the given expressions that represents polynomial.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

Monomial, binomial and trinomial are the three types of polynomials.

A polynomial may contain exponents, constants, and variables, but it never divides by a variable.

There cannot be a negative exponent in a polynomial.

No variable at all, one variable, two variables, or more are all possible for polynomials.

Exponents can only be multiples of 0, 1, or 2, not fractions.

Based on above definitions (i), (ii), (iv) and (vii) are the given expressions that represents polynomial.

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Julie has spent 40.25 + 10.56 = <<40.25+10.56=50.81>>50.81 seconds on wall climbing and the ropes.

She needs to complete the course in 74.6 - 50.81 = <<74.6-50.81=23.79>>23.79 seconds to match Lisa's record. Answer: \boxed{23.79}.

To graph linear inequalities with two variables separation of variables and plotting are two basic steps.

Mathematical expressions known as linear inequalities compare two expressions using the inequality symbol. The expression may be either a numerical or an algebraic expression, or it may be both.

3x-2y>1 is an illustration of a linear inequality. The inequality equation's LHS is in this case clearly greater than the RHS.

Step 1:Always begin by separating the variable y from the inequality's left side.

Step 2: Replace the inequality symbol with the equality symbol.

Step 3: In the X, Y, XY, XY plane, graph the boundary line from step 2.

Step 4:The final step is to shade a portion or one side of the border line.

If your boundary line contains the inequality symbols >> or \ge≥., shade the upper side of the boundary line.

If the inequality symbols << or \le≤ are present, shade the boundary line's bottom side.

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The median of 1 - 50 is 25.5.

The midway value in a given set of figures or data is referred to as the median. To get the average value for a given group of integers, three distinct metrics are employed in mathematics.

The first fifty numbers are 1,2,3,4,5................50

The number of terms in the data, n=50.

As the number of terms is even thus the median will be (n/2 th term + n/2 +1 th term) / 2

Median = (50/2 +50/2+1)/2

The 25th term of the sequence is 25.

The 26th term of the sequence is 26.

Median = 25+26/2 = 25.5.

Thus, the median of 1-50 is 25.5.

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The first fifty numbers are 1,2,3,4,5................50

The number of terms in the data, n=50.

Median = (50/2 +50/2+1)/2

The 25th term of the sequence is 25.

The 26th term of the sequence is 26.

Median = 25+26/2 = 25.5.

Thus, the median of 1-50 is 25.5.

Step-by-step explanation:

If a = b^2 c^3 and c = j^2 k^5, then we can substitute c = j^2 k^5 into the expression for a to get:

a = b^2 (j^2 k^5)^3

= b^2 j^6 k^15

This is a correct expression for a in terms of b, j, and k.

The correct expression for a in terms of b, j, and k is [tex]a = b^2 j^6 k^{15}[/tex].

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol be used to indicate the logical syntax's order of operations and other features.

We are given the terms as a = b^2 c^3 and c = j^2 k^5, then

we can substitute c = j^2 k^5 into the expression for a to get:

[tex]a = b^2 (j^2 k^5)^3\\= b^2 j^6 k^{15}[/tex]

Which is a correct expression for a in terms of b, j, and k.

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Bring the variable to the left side and bring all the remaining values to the right side.

Now, According to the question:

Let's know:

What is an algebraic value?

An algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example, the golden ratio, , is an algebraic number, because it is a root of the polynomial x2 − x − 1.

An algebraic formula is an equation or a rule written using mathematical and algebraic symbols and terms. It is an equation that involves algebraic expressions on both sides. The algebraic formula is a short quick formula to solve complex algebraic calculations.

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Answer:

0.002827 m^2

Step-by-step explanation:

A = pi * r^2

d = 2r

r = 3 cm = 0.03 m

A = pi * (0.03) ^ 2

A = 0.002827 m^2

The area of the circle is - 0.028 [tex]m^{2}[/tex]

The diameter (D) of a circle - 6cm

                          D=[tex]\frac{r}{2}[/tex]

The radius of a circle is = [tex]\frac{6}{2}[/tex] cm

                                      = 3 cm  = 0.03 meter

Now,  

       The formula of the area of a circle  = π[tex]r^{2}[/tex]

                    (the value of π = [tex]\frac{22}{7}[/tex] )

        Area of a circle = [tex]\frac{22}{7}[/tex] * [tex](0.03)^{2}[/tex]   [tex]m^{2}[/tex]

                                  =[tex]\frac{22}{7}[/tex] * 0.0009 [tex]m^{2}[/tex]

                                  = 0.028 [tex]m^{2}[/tex]

∴ The area of the circle is - 0.028 [tex]m^{2}[/tex]

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