-4(x + 3) = -12 - 4x

The complete factorization of the polynomial x³ + 2x² -x - 2 is equal to (x + 2)(x + 1)(x - 1)

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

A polynomial is an expression consisting of coefficients and variables forming an equation.

Given the polynomial:

x³ + 2x² -x - 2

Factorizing:

= (x + 2)(x² - 1)

= (x + 2)(x + 1)(x - 1)

The polynomial x³ + 2x² -x - 2 is equal to (x + 2)(x + 1)(x - 1)

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\(\frac{324-7.9}{\sqrt{46-5.832}}\)

= 49.87517031

Answer:

567.06 in.²

Step-by-step explanation:

The mat is a semicircle.

The straight side is a diameter.

d = 38 in.

r = d/2 = 19 in.

Area of circle = πr²

Area of semicircle = πr²/2

A = 3.14159 × (19 in.)² / 2

A = 567.06 in.²

The number of different spanning trees for each graph is: a) K3: 1, b) K4: 4, c) K2,2: 2 and d) C5: 5.

a) The complete graph K3 consists of 3 vertices, and in a spanning tree, we need to have exactly 3 vertices connected without forming any cycles. Therefore, K3 has only one possible spanning tree.

b) The complete graph K4 has 4 vertices. To form a spanning tree, we need to connect all 4 vertices without creating any cycles. K4 can be thought of as a tree with 4 branches extending from a central vertex. Each branch can be connected to any of the other vertices. Hence, there are 4 possible spanning trees for K4.

c) The complete bipartite graph K2,2 consists of 4 vertices divided into two sets, each containing 2 vertices. To form a spanning tree, we need to connect all 4 vertices without creating any cycles. Since there are only two possible edges between the two sets, there are only two possible spanning trees for K2,2.

d) The cycle graph C5 consists of 5 vertices arranged in a circular shape. To form a spanning tree, we need to connect all 5 vertices without creating any cycles. Removing any one of the edges from the cycle will result in a tree. Therefore, C5 has 5 different spanning trees.

Therefore, the number of different spanning trees for each graph is:

a) K3: 1

b) K4: 4

c) K2,2: 2

d) C5: 5  

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Answer:

(x + 6)(x + 7)

Step-by-step explanation:

To factor the trinomial x^2 + 13x + 42, we need to find two numbers that multiply to 42 and add up to 13.

One way to do this is to list all the pairs of factors of 42 and see which pair adds up to 13:

1, 42 -> 1 + 42 = 43

2, 21 -> 2 + 21 = 23

3, 14 -> 3 + 14 = 17

6, 7 -> 6 + 7 = 13

So the pair of factors that we want is 6 and 7. We can use these numbers to rewrite the middle term of the trinomial:

x^2 + 13x + 42 = x^2 + 6x + 7x + 42

Next, we can group the first two terms and the last two terms:

x^2 + 6x + 7x + 42 = (x^2 + 6x) + (7x + 42)

Now, we can factor out the greatest common factor from each group:

x(x + 6) + 7(x + 6)

Notice that we have a common factor of (x + 6) in both terms. We can factor this out:

(x + 6)(x + 7)

The area of the polygon with the given vertices is

Area=9

This is further explained below.

Generally, A regular polygon is a polygon that is straight equiangular, and equilateral, according to the Euclidean geometry definition. Convex, star, or skew profiles may be assigned to regular polygons.

In conclusion, The specified vertices are used to calculate the area of the polygon.

A=9

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Answer:

3/2 or 1 1/2 or 1.5

Step-by-step explanation:

first do the equations in each parentheses:

(-5+2) = -3

(-1/2) = -1/2

then multiply both sides:

-3 • -1/2 (which is the same as -3 • -1 over 2)

= 3/2 or 1 1/2 or 1.5

The crude oil is likely to be paraffinic. Paraffinic crude oils are characterized by having a high API°, low Watson characterization factor, and low refractive index. They also tend to have a high surface tension.

Specific gravity at 60 °F: 0.88

API° at 60 °F: 28

Watson characterization factor: 1.014

Refractive index: 1.44

Surface tension: 20 dyne/cm

Paraffinic, naphthenic, or aromatic: Paraffinic

Specific gravity at 60 °F the specific gravity of a liquid is its density relative to the density of water. The specific gravity of crude oil is typically between 0.8 and 1.0. A specific gravity of 0.88 means that the crude oil is 88% as dense as water.

API° at 60 °F: The API°, or American Petroleum Institute gravity, is a measure of the lightness or darkness of crude oil. A higher API° indicates a lighter crude oil. A crude oil with an API° of 28 is considered to be a medium-heavy crude oil.

Watson characterization factor the Watson characterization factor is a measure of the aromaticity of crude oil. A higher Watson characterization factor indicates a more aromatic crude oil. A crude oil with a Watson characterization factor of 1.014 is considered to be a paraffinic crude oil.

Refractive index the refractive index of a liquid is a measure of how much light is bent when it passes through the liquid. The refractive index of crude oil is typically between 1.4 and 1.5. A refractive index of 1.44 indicates that the crude oil is slightly more refractive than water.

Surface tension the surface tension of a liquid is a measure of the force that acts at the surface of the liquid, tending to minimize the surface area. The surface tension of crude oil is typically between 20 and 30 dyne/cm. A surface tension of 20 dyne/cm indicates that the crude oil has a relatively high surface tension.

Based on the estimated values, the crude oil is likely to be paraffinic. Paraffinic crude oils are characterized by having a high API°, low Watson characterization factor, and low refractive index. They also tend to have a high surface tension.

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Answer:

x=-11

Step-by-step explanation:

-2(x+3)+5x=-39

Remove parenthesis

-2x-6+5x=-39

Collect like terms

3x-6=-39

Move the constant to the right

3x=-39+6

Calculate

3x=-33

Divide both sides by 3

x=-11

Answer:

The number is 24

Step-by-step explanation:

1/6x + 3/8x = 13

4/24x + 9/24x =13

13/24x = 13

13x=312

x=24

Step-by-step explanation:

In order to rotate a coordinate point by 90° in the counterclockwise direction, follow the following transformation rule:

(x, y) ---> (-y, x)

Here is the list of the coordinates of the points on the fan blade and next to it is a list of points that are rotated by 90° in the counterclockwise direction:

Normal. Rotated

(x, y) (-y, x)

(3, 1) (-1, 3)

(5, 2) (-2, 5)

(8, 4) (-4, 8)

(9, 6) (-6, 9)

(8, 8) (-8, 8)

(6, 9) (-9, 6)

(4, 8) (-8, 4)

(2, 5) (-5, 2)

(1, 3) (-3, 1)

Simply repeat the pattern for the other two blades.

Answer:  radius = 5.83 cm     height = 8.12 cm

Step-by-step explanation:

First, let's find the circumference of the 210° section of the circle.

\(C=2\pi r\bigg(\dfrac{\theta}{360^o}\bigg)\\\\\\C=2\pi(10)\bigg(\dfrac{210^o}{360^o}\bigg)\\\\\\C=\dfrac{35}{3}\pi\)

The circumference of the the cone is \(\dfrac{35}{3}\pi\) .  We can use this to find the radius .

\(C=2\pi r\\\\\dfrac{35}{3}\pi=2\pi r\\\\\\\dfrac{35\pi}{3\cdot 2\pi}=r\\\\\\\dfrac{35}{6}=r\\\\\\5.83=r\)

When you fold the 210° section into a cone, the slant height is the original radius of 10.  We can use the radius and slant height of the cone to form a right triangle with the height.  Use the Pythagorean Theorem to find the height.

radius² + height² = slant height²

\(\dfrac{35}{6}^2\ +\ h^2=10^2\\\\\\.\qquad \quad h^2=10^2-\bigg(\dfrac{35}{6}\bigg)^2\\\\.\qquad \quad h=\sqrt{\dfrac{6^2(10)^2-35^2}{6^2}}\\\\\\.\qquad \quad h=\sqrt{\dfrac{2375}{36}}\\\\\\.\qquad \quad h=8.12\)

Answer: Here, m angle KEF = 80 Degrees

The Laplace transform of the periodic function f(t), with a period of 6, is given by: \(\(\mathscr{L}\{f(t)\} = \frac{15}{s}\)\).

To determine the Laplace transform of the periodic function f(t), we need to break it down into its individual periods and calculate the Laplace transform for each period separately.

The function f(t) is defined as follows:

For 0 < t < 3:

f(t) = 5t

For 3 < t < 6:

\(\[ f(t) = 15 - 5t \]\)

Since the period of the function is 6, we can consider the interval \(\( 0 < t < 6 \)\) as one complete period.

Now let's calculate the Laplace transform for each period:

For 0 < t < 3:

\(\[ \mathscr{L}\{f(t)\} = \mathscr{L}\{5t\} = \frac{5}{s^2} \]\)

For 3 < t < 6:

\(\[ \mathscr{L}\{f(t)\} = \mathscr{L}\{15-5t\} = \frac{15}{s} - \frac{5}{s^2} \]\)

To obtain the Laplace transform of the periodic function, we can use the linearity property of the Laplace transform. Since the Laplace transform is a linear operator, we can add the Laplace transforms of the individual periods:

\(\[ \mathscr{L}\{f(t)\} = \mathscr{L}\{5t\} + \mathscr{L}\{15-5t\} = \frac{5}{s^2} + \left(\frac{15}{s} - \frac{5}{s^2}\right) = \frac{15}{s} \]\)

Therefore, the Laplace transform of the given periodic function is \(\( \mathscr{L}\{f(t)\} = \frac{15}{s} \)\).

Now, let's graph the function f(t).

Since f(t) has a period of 6, we can graph it over one complete period from 0 < t < 6. Within this interval, f(t) consists of two linear segments: 5t for 0 < t < 3 and 15 - 5t for 3 < t < 6.

The graph starts at the point (0, 0), rises linearly to (3, 15), and then decreases linearly back to (6, 0). This pattern repeats for each period of the function.

Complete Question:

Determine L{f}, where f(t) is periodic with the given period. Also graph f(t).

\(f(t) = \left \{ {{5t,\ \ \ \ 0 < t < 3} \atop {15 - 5t,\ \ 3 < t < 6}} \right.\)

and f(t) has period 6 Determine L{f}.

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To solve this, all you need to do is compare the ratio to the amount of SUVS there are.

5/9 (SUVs to sedans)

140/? (SUVs to sedans)

140 ÷ 5 = 28

9 x 28 = 252

140/252

There are 252 sedans in the car dealership! :D

Answer:

252 Sedans

Step-by-step explanation:

your welcome ;)

There are 345,600 possible seating arrangements with the given restrictions.

To find the number of possible seating arrangements, we need to consider the restrictions given in the question.
1. The chairs are numbered clockwise from 11 through 1010.
2. Five married couples are sitting in the chairs.
3. Men and women are to alternate.
4. No one can sit next to or across from their spouse.

Let's break down the steps to find the number of possible arrangements:

Step 1: Fix the position of the first person.
The first person can sit in any of the ten chairs, so there are ten options.

Step 2: Arrange the remaining four married couples.
Since men and women need to alternate, the second person can sit in any of the four remaining chairs of the opposite gender, giving us four options. The third person can sit in one of the three remaining chairs of the opposite gender, and so on. Therefore, the number of options for arranging the remaining four couples is 4! (4 factorial).

Step 3: Consider the number of ways to arrange the couples within each gender.
Within each gender, there are 5! (5 factorial) ways to arrange the couples.

Step 4: Multiply the number of options from each step.
To find the total number of seating arrangements, we multiply the number of options from each step:
Total arrangements = 10 * 4! * 5! * 5!

Step 5: Simplify the expression.
We can simplify 4! as 4 * 3 * 2 * 1 = 24, and 5! as 5 * 4 * 3 * 2 * 1 = 120. Therefore:
Total arrangements = 10 * 24 * 120 * 120

= 345,600.

There are 345,600 possible seating arrangements with the given restrictions.

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Answer:

1) What does it mean when a polynomial equation is in standard​ form?

All terms are on one side of the equation, and zero is on the other side.

2) When factoring 6x2−7x−20 by grouping, how should the middle term be rewritten?

It should be written as 8x−15x.

3) Is the given equation a quadratic equation? Explain.

x(x−6)=−5

The equation is a quadratic equation because there is an x2-term.

4) Which of the following factored forms given below represent the correct factorization of the trinomial x2+10x+16?

(2+x)(8+x)

5) Which of the following is an example of the difference of two​ squares?

x2−9

Step-by-step explanation:

I hope this helps you out ☺

A binomial whose first term and second term can be squared, and has a subtraction sign between both squared terms represents the difference of two squares, an example of the difference of two squares is:

A. \(x^2 - 9\)

Recall:

Thus, from the options given, option A: \(x^2 - 9\) is an example of a binomial that is the difference of two squares.

9 can be expressed as \(3^2\).

In summary, a binomial whose first term and second term can be squared, and has a subtraction sign between both squared terms represents the difference of two squares, an example of the difference of two squares is:

A. \(x^2 - 9\)

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Below are the field properties or axioms of equality used to justify each step.

What is an axiom answer?

An axiom is a rule or statement that is generally accepted to be true without proof. An axiom is also called a postulate.

7(x + 3) = 4 + 3x  

7x + 21 = 4 + 3x  --- Distributive Property of Multiplication over Addition

7x + 21 = 3x + 4  --- Subtraction Property of Equality

4x + 21 = 4   ---- Commutative Property of Addition

4x = - 17         -------- Subtraction Property of Equality

1/4 * (4 * 1) = 1/4 * (- 17)    ----- Multiplication Property of Equality

x = 1/4 * (- 17)               ----- Multiplicative Identity Property

x =-17/4             ----- Multiplicative Inverse Property

Hence, Above are the field properties or axioms of equality used to justify each step.

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Answer:

195

Step-by-step explanation:

15*13=195

whereas 15*14=210 so it is the biggest and smaller than 200

The Simplified value of the "algebraic-expression" (12x³y² - 18xy)/6xy is 2x²y - 3.

An "Algebraic-Expression" represents a combination of numbers, variables, and arithmetic operations such as addition, subtraction, multiplication, and division, that represents a mathematical relationship or rule.

To simplify the expression, (12x³y² - 18xy)/6xy,  we factor out a common factor of "6xy" from the numerator;

We get,

⇒ (12x³y² - 18xy)/6xy = 6xy(2x²y - 3)/6xy,

The 6xy in the numerator and denominator cancel out,

We get,

⇒ 2x²y - 3

Therefore, the simplified expression is 2x²y - 3.

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The given question is incomplete, the complete question is

Simplify and evaluate the given algebraic expression

(12x³y² - 18xy)/6xy.

Using the rule for a dilation, it is found that:

1. The table with the coordinates is given by the first image.

2. The graph of the dilated triangle is given by the second image.

3. The rule is: (x,y) -> (1.5x, 1.5y).

When a figure is dilated by an scale factor of a, each vertex of the figure is multiplied by the scale factor of a, hence the rule is given by the following vector:

(x,y) -> (ax, ay).

The coordinates of the vertices of the pre-image are given as follows:

A(-2, -2), B(2,2), C(4, -2).

The dilation has a scale factor of 1.5, hence the rule for the calculation of each vertex of the image, considering the pre-image, is given as follows:

(x,y) -> (1.5x, 1.5y).

Then the vertices of the image will be given as follows:

A'(-3, -3), B'(3,3), C'(6, -3).

Each coordinate of A, B and C was simply multiplied by 1/2, and the triangle with these vertices is given by the second image at the end of the answer.

The problem is incomplete, and is given by the first image at the end of the answer.

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Answer:

Answer:

The advantages and disadvantages of options Options are a very unique investment vehicle so it is important to learn the unique characteristics of options before you decide to trade them. Advantages. Leverage. Options allow you to employ considerable leverage. This is an advantage to disciplined traders who know how to use leverage. Risk/reward ratio. Some strategies, like buying options, allow you to have unlimited upside with limited downside.

hope this helps:)

Answer:

the circumference of circle Q and circle Q' are the same

Step-by-step explanation: