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Answer:

[tex]2x^3+ 3x^2-5x-6 = (x+2)(x+1)(2x+3)[/tex]

Step-by-step explanation:

Given polynomial [tex]g[/tex]:

[tex]g(x) = 2x^3+ 3x^2-5x-6[/tex]

A factor of polynomial is [tex](x+2)[/tex].

To find:

Equation of the polynomial as the product of linear factors.

Solution:

First of all, let us divide the polynomial [tex]g[/tex] with [tex](x+2)[/tex] to find the other factors.

As degree of polynomial is 3, when divided by a linear equation, it will result in a quadratic.

That quadratic will have 2 solutions.

Solving the quadratic in linear will give us the answer.

Result of division:

[tex]\dfrac{2x^3+ 3x^2-5x-6}{x+2} =2x^2-x-3[/tex]

Now, solving the quadratic:

[tex]2x^2-x-3 = 2x^2-3x+2x-3 \\\Rightarrow x(2x-3)+1(2x-3)\\\Rightarrow (x+1)(2x-3)[/tex]

So, the linear equation can be written as:

[tex]2x^3+ 3x^2-5x-6 = (x+2)(x+1)(2x+3)[/tex]

Complete question :

From points A and B, the distance between which is 1020 mi, two trains left simultaneously towards each other. The speed of one train was 10 mph greater than the speed of the other one. In 5 hours the trains had not met yet and were 170 mi apart. Find the speed of the trains.

Answer:

Train A = 80 miles per hour

Train B = 90 miles per hour

Step-by-step explanation:

Given that :

Distance between A and B = 1020

Let the speed of A = x

Speed of B = x + 10

Since they both left simultaneously;

Distance traveled after 5 hours will be :

Distance = speed * time

A = x * 5 = 5x

B = (x + 10) * 5 = 5x + 50

After the distance traveled by each of A and B, they are still 170 miles apart

Hence, distance covered after 5 hours ;

Total miles - miles left

1020 - 170 = 850 miles

Hence,

5x + 5x + 50 = 850

10x = 850 - 50

10x = 800

x = 80

Train A = 80 miles per hour

Train B = 80 + 10 = 90 miles per hour

First, we must determine b using slope-intercept form*, the given point, and the given slope.

[tex]-4 = -\frac{1}{3}(-9) + b\\\\-4 = -3 + b\\\\-1 = b[/tex]

Second, we need to set up the equation of the line in slope-intercept form.

[tex]y = -\frac{1}{3}x - 1[/tex]

Third, we convert the above equation to STANDARD FORM**.

[tex]y = -\frac{1}{3}x - 1\\\\\frac{1}{3}x + y = -1[/tex]

We now have our equation: [tex]\frac{1}{3}x - y = -1[/tex]

*Slope-intercept form: y = mx + b

**Standard form: ax + by = c

Answer:

slope of 10/1 or simplified to 10

Step-by-step explanation:

Answer:

slope is 10/7

Step-by-step explanation:

use the formula or plot the points on a graph to get the slope is 10/7

Answer:

3 times

Step-by-step explanation:

Firstly we calculate the number of minutes between 8 and 11 am

The number of hours is 3 hours

The number of minutes is 180 minutes since 1 hour is 60 minutes

Now out of 180, to know the number of times that they both leave, we need to get the multiples of both between 0 and 180

The multiples are;

60, 120, 180

This means that they leave together 3 times

Answer: 6

Step-by-step explanation:

[tex]6\left(-1\right)^{-4}[/tex]

[tex]6\cdot \frac{1}{\left(-1\right)^4}[/tex]

[tex]6\cdot \:1[/tex]

[tex]6[/tex]

Answer:

C, the answer is 6.

Step-by-step explanation:

If you substitute -1 into the variable "k", it would look like this equation, 6(-1)[tex]6(-1)^{-4}[/tex], if you then raise -1 to the power of -4, you would then get the value 1. Thus, 6 * 1 equals 6. C would be the correct answer.

Answer:

C 13 inches

Step-by-step explanation:

Because the plant grows two inches every week so if by the second week it is 7 inches tall just add 3 more weeks or 6 inches of growth to the 7 inches and you get your answer 13 inches

Step-by-step explanation:

I used a calculator but the answer is 1 1/6

Answer:

please make it more clear

Step-by-step explanation:

what you are asking

Answer:

X=5+h

Step-by-step explanation:

Answer:

39

Step-by-step explanation:

let the 2 digit number be ab = 10a + b ( considering place value )

The reversed  2 digit number is ba = 10b + a

The sum of the 2 digit number is

a + b = 12 ( subtract b from both sides )

a = 12 - b → (1)

Expressing as an equation

ba = ab + 54 , that is

10b + a = 10a + b + 54

Substitute a = 12 - b into the equation

10b + 12 - b = 10(12 - b) + b + 54 , simplify both sides

9b + 12 = 120 - 10b + b + 54

9b + 12 = - 9b + 174 ( add 9b to both sides )

18b + 12 = 174 ( subtract 12 from both sides )

18b = 162 ( divide both sides by 18 )

b = 9

Substitute b = 9 into (1)

a = 12 - 9 = 3

Thus

the original 2 digit number = ab = 39

The reversed 2 digit number = ba = 93

which is 54 more than the original number

Answer:

It is D

Step-by-step explanation:

Looking at the Graph the point is at 5-5i

the only polar form that solves to 5-5i is D.

Also I did it on Edge.. Good Luck!

The complex number z represented on the graph (5, -5) is given as 5√2[cos(-π/4) + isin(-π/4)] in polar form

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the complex number z represented on the graph as (5, -5). Therefore:

r = √(5² + 5²) = 5√2

Ф = tan⁻¹(-5/5) = -π/4

The complex number z represented on the graph (5, -5) is given as 5√2[cos(-π/4) + isin(-π/4)] in polar form

Find out more on equation at: https://brainly.com/question/2972832

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I think c

Step-by-step explanation:

I did it a min ago

Answer:

ur answer would be C. Angles A and H are congruent.

Step-by-step explanation:

right on edge 2021 for math

Answer: -1 would be greater than negative two, along with 20, 1000.

-2 is a negative number, so any number that is -1 or higher is greater than -2

Answer:

1,2,3

Step-by-step explanation:

Answer:

The volume of water in the pool over time from when the hose is placed in the pool until the pool is full is defined by the equation  and its graph is given below.

Explanation:

The total capacity of the pool is 20,000 gallon.

It is given that the pool contains 5000 gallons of water when a hose is placed in the pool and begins adding water at a rate of 1250 gallons per hour. So the initial volume of water is 5000.

Let the time is defined by t. So, the volume of water in the pool after time t is defined as,

The capacity of the pool is 20,000 gallon, therefore the maximum value of V(t) is 20,000.

The maximum value of t is 12, since the time is always positive, therefore we can say that,

The below graph representing the volume of water in the pool over time from when the hose is placed in the pool until the pool is full. The initial point is (0,5000) and the other point is (12,20000).

Answer:

the two points will be (0,5000) and (12,20000

Step-by-step explanation:

Answer:

x=-10 I think?? because they are congruent

Answer:

$0.69

Step-by-step explanation:

Add them all up.

Answer:

$0.64

Step-by-step explanation:

hope this helped :-)

Answer:

-20

Step-by-step explanation:

f(x)= 4x-8 f(-3)

y= 4(-3) -8

y= -12 -8

y= -20

Answer:

34-158n

Step-by-step explanation:

First factor:

8n+4-150n+30

Then combine like terms

34-158n

Answer:    -142n+34

Step-by-step explanation:(2/3)(12n)+(2/3)(6)+(-15)(10n)+(-15)(-2)

=-142n+34

√48 = 4√3

Click on the photo to view full solution

Answer:( -10,10), (-,+)

Step-by-step explanation:

Awnser:

-2

Step by Step:

To find a slope, you need to find 2 points. You can't have a line with only 1 point.

The equation for a slope is: y2-y1/x2-x1.

It doesn't matter which order you put them in.

I used (-4,1) and (-6,2).

So: 2-1/-6-(-4)

1/-6+4

1/-2

-2

Answer:

(0,6) (0,-12)

Step-by-step explanation:

The equation y = 2x - 12 represents a linear function with a slope of 2 and a y-intercept of -12.

The equation y = 2x - 12 represents a linear function with a slope of 2 and a y-intercept of -12. This means that the graph will have a positive slope, indicating a upward trend, and it will intersect the y-axis at the point (0, -12).

To sketch the graph, you can start by plotting the y-intercept at (0, -12). From there, use the slope of 2 to determine additional points by moving 1 unit horizontally (to the right) and 2 units vertically (upward) to plot another point. Repeat this process to plot more points, then connect them to form a straight line.

Keep in mind that a visual representation is essential for accurately identifying the specific graph of y = 2x - 12.

Learn more about graph here

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Answer:

f(2)=128

Step-by-step explanation:

f(x) = 2(8)^x evaluate f(2)

f(2)= 2(8)^2

f(2)=2(64)

f(2)=128

Answer:

1.5

Step-by-step explanation:

Do the reverse/opposite/check division with multiplication.

2.5 · 0.6 = 1.5  

Answer:

Option C: 74 is both a whole number and a rational number.

Step-by-step explanation:

A rational number is defined as a number which can be written as a fraction of two integers, an integer, a whole number and a natural number. The integer could be positive or negative.

Examples include -1/4, 1/2, 12

So it's obvious that the given number of 74 is a rational number.

Now, a whole number is simply a non - negative integer.

An integer is a number that is not a fraction.

Thus, examples of whole numbers are 0, 1, 2, 3, 4...

So 74 is clearly a whole number.

Therefore, we can conclude that 74 is both a whole number and a rational number.