Find the distance between
the two points rounding to the nearest tenth (if necessary).
(8, 7) and (1, -2)

The leading term, the degree of the polynomial is  −6x3 is 3rd degree and coefficient −6.

Option (C) is correct.

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables .It is  is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.

Given:

The given expression is

−6x3

We have to find the  polynomial by degree and tell the leading coefficient.

According to given question we have

The leading term of a polynomial is the term with the highest degree.

The leading coefficient of a polynomial is the coefficient of the leading term.

The degree of a polynomial is the highest degree of its terms.

Hence, the leading term, the degree of the polynomial is  −6x3 is 3rd degree and coefficient −6.

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You can make 106.67 L of 25% v/v acid solution by mixing 6.67 L of pure acid with 100 L of 20% v/v acid solution.

Acids are a type of chemical that can either absorb electrons or give off protons or hydrogen ions. An anion and a cation can form in water when a hydrogen atom that is bonded to an acid releases (dissociates). How acidic a substance is and how acidic its solution pH is depends on how many hydrogen ions it produces.

The word acid stems from the Latin words acidus or acere, which suggest "sour," because one of the characteristics of acids in water is a sour taste (e.g., vinegar or lemon juice).

How thoroughly an acid splits into its ions after being dissolved in water indicates whether it is strong or weak. A strong acid, like hydrochloric acid, completely dissociates into its ions in water.

100 liters * (20/100) = 20 liters acid

Let's assume that the number x represents the amount of pure acid you need to add to your initial solution. The volume of acid will increase by x because you are working with pure acid.

V(acid) = 20 +x

V(solution) = 100+ x

As a result, the percent concentration by volume of the target solution will be equal to

{V(acid)/V(solution)} * 100 = 25%

{(20+x)/(100+x)} * 100 = 25%

(20 +x) 100 = 25(100+x)

2000+100x = 2500 + 25x

75 x = 500

x = 6.67 liters

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The point (1,1) represents 1+i in the two dimensional complex plane. Absolute value of 1+i = [tex]\sqrt{2}[/tex].

Given the complex number, z = 1+i

The general form of a complex plane is x+iy, where x and y are real numbers.

We can place any complex number into a two-dimensional complex plane with two axes - X and Y.

For z = 1+i, x = 1 and y = 1. So the point (1,1) will represent z = 1+i in the two dimensional complex plane.

The absolute value of a complex number z = x+iy is given by ,

|z| = [tex]\sqrt{x^2+y^2}[/tex]

So for z = 1+i, |z| =  [tex]\sqrt{1^2+1^2}=\sqrt{2}[/tex]

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Using the distance between two points formula to calculate the side lengths, it is found that the figures are not congruent.

Congruent figures are figures that have the same outer side lengths.

We are given the vertices for this problem, hence we use the distance between two points formula to calculate the lengths.

Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the xy-plane, with the hypotenuse being the distance between them.

For Triangle LMK, the side lengths are given as follows:

For Triangle XYW, the side lengths are given as follows:

Due to different side lengths, the figures are not congruent, and nothing can be stated about the transformations that were used.

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Answer:

x = 3

Step-by-step explanation:

Hello!

Solve for x by isolating the variable

The value of x is 3.

Answer:

Domain: x > -4

Range: y > -1

Step-by-step explanation:

Domain is the points on the x axis that could be vaild for that line.

Range is the points on the y axis that could be valid for that line.

Answer:

I think that the answer is D.

Step-by-step explanation:

Step-by-step explanation:

To graph an equation using the slope and y-intercept, 1) Write the equation in the form y = mx + b to find the slope m and the y-intercept (0, b). 2) Next, plot the y-intercept. 3) From the y-intercept, move up or down and left or right, depending on whether the slope is positive or negative.

It would take 21 8/ 12 seconds to fill 2 tires

Proportion can be defined as the comparison between two numbers or elements

It is also an equation with two ratios draw equal to each other.

From the information given,

If 31/ 3 tires (10/ 3 ) tires is filled in 3 1/4 seconds ( 13/ 4)

Then 2 tires = x seconds

cross multiply

x = 13 / 4 × 2 ÷ 10/ 3

x = 26/ 4 × 3/ 10

x = 260/ 12

x = 21 8/ 12 seconds

Thus, it would take 21 8/ 12 seconds to fill

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Answer:

- 75

Step-by-step explanation:

- 5(15) means - 5 × 15 = - 75

The percentage of the company’s employees are both female and over 6 feet tall is 3.75%

Let the total number of employees in the given company be x. So, the number of female employees in the company are : 75% × x

Number of female employees in company = 0.75x

Now, calculating number of female employees that over 6 feet tall = 0.75x × 5%

The number of female employees that over 6 feet tall = 0.0375x

Percentage of the company’s employees are both female and over 6 feet tall = percentage of female and tall employees ÷ total number of employees × 100

Percentage of the company’s employees are both female and over 6 feet tall = (0.0375x÷x)×100

Percentage of the company’s employees are both female and over 6 feet tall = 3.75%

Therefore, the percentage of the company’s employees are both female and over 6 feet tall is 3.75%

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Answer:

2,7

Step-by-step explanation:

when y=x similary x= y

c

in an arithmetic expression

The answer is expressed in terms of unit vectors  x^ and y^ as B = B (cos θ  x ^ + sin θ  y ^)

For expressing the magnetic field B in terms of vectors we need to know the magnitude of the magnetic field and the angle between them.

the angle we have is with respect to the positive side of the x-axis, let's use trigonometry.

cos θ = Bₓ / B

sin θ =  / B

Bx = B cosθ

By = B sinθ

hence the resulting vector is

 B = Bₓ i ^ + [tex]B_{y}[/tex] j^

The unit vectors are

x ^ = i ^

y ^ = j ^

The answer is expressed in terms of unit vectors  x^ and y^ as B = B (cos θ  x ^ + sin θ  y ^)

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The equation of line passing through the point (4, 6) and parallel to x axis is y = 6.

According to the given question.

A line which is passes through the point (4, 6).

And also parallel to x-axis.

As we know that, the equation of line parallel to the x-axis, cuts the y-axis at the point (0, b) is y = b.

Since, the line is passing through the point (4, 6) and parallel to x-axis, cuts the y-axis at the point (0, 6).

As per the formula, the equation of line passing through the point (4, 6) and parallel to x axis is y = 6.

Hence, the equation of line passing through the point (4, 6) and parallel to x axis is y = 6.

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Answer:

This is also known as "Derivative"." in mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus."! hope this helps!

Answer:

y=2

Step-by-step explanation:

The measure of angle J is 116°

Linear pair of angles are angles formed when two lines intersect at a single point.

Angles are said to be linear if they are adjacent to each other with the intersection of the two lines.

Note that the sum of angles of a linear pair is equal to 180°.

From the information given, we have that;

But we have the expression as;

Angle R + Angle J = 180°

substitute the values into the equation

3x - 5 + 5x + 1 = 180°

collect like terms

8x - 4 = 180°

8x = 180 + 4

8x = 184

To determine the value of x, divide both sides by the 8

8x/8 = 184/8

Divide through

x = 23

But we have that;

Angle J = 5x + 1

Angle J = 5(23) + 1

Angle J = 115 + 1

Angle J = 116°

Thus, the measure of angle J is 116°

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The expression when s=$125 would be as s/2. the money she gave in charities is $62.50 each.

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; which can also be used to indicate the logical syntax's order of operations and other features.

WE have been given that Juilan divided his savings equally between two charities. then Julian's savings as 's' =$125

First, we will write the expression;

s/2

Second, substitute the value 125 in for the variable s.

Then simplify by dividing 125 and 2.

=$125 / 2

= $62.50

Hence the  expression when s=$125 would be as s/2. the money she gave in charities is $62.50 each.

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The plane can fly 384 miles in 3/5 hours.

An airplane can cruise at 570 miles per hour.

We have to find the distance travelled by airplane in 4/3 hours.

Distance = Speed x Time

Distance = 640 x 3/5

Distance = 128 x 3

Distance = 384 miles

Hence, The plane can fly 384 miles in 3/5 hours.

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The  measures are possible for the other two angles are 70 degrees respectively

An isosceles triangle is a triangle that has 2 of its sides and angles to be equal.

Let the measure of the other possible angles be x and y such that x = y

Since the sum of angle in a triangle is 180 degrees, hence;

x+y +40 = 180

x+x+40=180

2x+40=180

2x=180-40

2x = 140

x = 70

x = y = 70 degrees

Hence the  measures are possible for the other two angles are 70 degrees respectively

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$32 money will she have after five bets.

What  is a linear equation?

starting amount = $1

she doubles her money on her each bet.

So, when she makes her first bet , her money doubles and keep doubling

on every bet of the previous amount .

Money she makes on her first bet =  2 * 1 = $2

Money she makes on her second bet =  2 * 2 = $4

money on third bet = 2 * 4 = $8

money on fourth bet =  2 * 8 = $16

money on fifth bet =  2 * 16 = $32

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Answer:-12

Step-by-step explanation:  -4b=48      b=48/-4        b=-12

hope it helps

Answer:

the answer is A

The committee can be selected by combinatorial argument  in

[tex]\sum ^{n}_{k=1} k(^n_k).[/tex] ways.

A counting-based argument is known as a combinatorial argument or combinatorial proof. This line of reasoning has previously been used, for instance in the section on Stirling numbers of the second sort.

By initially selecting k individuals from our group of n, we can then choose one of those k individuals to serve as the committee's chairperson.

A number of methods for completing the first task, k methods for completing the second task, and so on. ways to create a k-member committee with a chairperson.

[tex]\sum ^{n}_{k=1} k(^n_k).[/tex] is the number of methods to construct a committee with a chairman of size less than or equal to n can be found by adding up over 1≤k≤n.

A committee of size less than or equal to n can also be formed with a chairperson by selecting the chairperson first, followed by the members of the committee. The chairperson can be chosen from among n options. The picker has two options for the remaining n-1 individuals: to include them or not. We therefore have n options for the chairperson, 2 options for the following, 2 options for the following, etc. These can be multiplied together to give us [tex]n2^{n-1}[/tex], which is a proof of the identity.

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Answer:

Below.

Step-by-step explanation:

3x² - 1 = 0

3x² = 1

x² = 1/3

x = ±√(1/3)

  = -1/√3, 1/√3.

So, -1/√3 is a zero of 3x² - 1 .

Yes, x = -1/√3 is a zero of the polynomial 3x² - 1 because substituting the value results in zero, confirming its solution to the equation.

To verify whether x = -1/√3 is a zero of the polynomial 3x² - 1, we need to substitute this value into the polynomial and check if it results in zero.

Given polynomial: 3x² - 1

Now, substitute x = -1/√3 into the polynomial:

3(-1/√3)² - 1

Now, simplify:

3(1/3) - 1

1 - 1

The result is zero. Since the expression evaluates to zero when x = -1/√3, this means that x = -1/√3 is indeed a zero of the polynomial 3x² - 1.

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