Factor the polynomial: -2x³ - 4x² - 6x

Answer:

f(3)=-11

f(-1)=1

f(-2)=4

Explanation:

For each question you would replace the x in the main equation (f(x)=-3x-2) for the number given within f(x).

Therefore,

f(3)=-3(3)-2

=-9-2

=-11

f(-1)=-3(-1)-2

=3-2

=1

f(-2)=-3(-2)-2

=6-2

=4

Making x the subject of the formula x/y -z=w is

x = y(w+z)

The subject of a formula is the variable which is expressed in terms of the other variable. For example the volume of a cylinder is V = πr^2h.

where V is the volume and r is the radius and h is the height . In the formula V is expressed in term of other variables like radius and height. Therefore V is said to be the subject of the formula

Relating the explanation with the formula x/y -z= w, here w is the subject and we need to make x the subject.

We achieve this by evacuating other variables attached to x

x/y -z= w

add both sides by z

x/y-z+z= w+z

x/y= w+z

multiply both sides by y

x/y×y=(w+z)y

therefore x= y(w+z)

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5.37 divided by 3 equal to 1.79

The calculation can be done simply by calculator however to so it manually the decimal is converted to fraction

converting to fraction

5.37 = 537 / 100

dividing by three

= 537/100 / 3

= 537/100 * 1/3

= 537/300

= 1.79

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Answer:

Tan A = Opposite/ Adjacent

Tan A = 40/9

option D

Step-by-step explanation:

On the second page, last question

Tan is given by a formula opposite divided by the adjacent

Based on the position of the angle, our opposite will be 40 and the adjacent, 9 leaving us with and equation

tan A = 40/9

Di-ane plans to walk 6000 steps on day 100.

Given, Di-ane walks 5000 steps each day. She keeps her goal to increase the 10 number of steps. The increase has been modelled using the function.  

A re-lation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a re-lationship between inputs in which each input is connected to precisely one output.

We have to write what does f(100)=6000 represent.

As given in question the function represents the number of steps. and x represent the day.

100 represents the number 100th day, f(100)=6000 represents that Di-ane walks 6000 steps on the 100th day.

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Answer:

∴ g(x) = -2x + 10

Step-by-step explanation:

Since f(x) = -x + 5,

g(x) = 2[f(x)]

      = 2(-x + 5)

      = -2x + 10

Answer:

5

Step-by-step explanation:

add the numbers up

1+2+5+5+6+6+7+8=40

divide it by 8 (because there are 8 numbers)

40/8=5

Answer: We on da same question i do not know

Step-by-step explanation:

The value of the final result when 19 is subtracted from 26 will be positive value (7).

According to the question,

We have the following expression:

26-19

Now, we have to find whether the value of this expression will be positive or negative.

We know that when two integers are of different signs then the smaller one is subtracted from the larger one but in the final result the sign remains that of the larger integer.

In this case, 26 is greater than 19 and it is positive.

So, the result will also be positive.

26-19

7

Hence, the value of the final result when 19 is subtracted from 26 will be positive (7).

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Answer:

See below

Step-by-step explanation:

By "gradient of the given line" the question is asking to find the slope of the line.  If we rearrange each equation inrto slope-intercept format of y = mx + b, we can find the slope easily, since m is the slope (b is the y-intercept).

y = 4x + 3

 The slope is 4.

y= -8x + 6

  The slope is -8

4y = 8x +3

y = 2x + (3/4)   Rearrange to y = mx + b

  The slope is 2

y+x=8

y = -1x + 8       Rearrange

    The slope is -1

y -x = 5

      y = x + 5   Rearrange

      The slope is 1

4y + 5x = 30

       y = -(5/4)x + (30/4)

       The slope is -(5/4)

The speed of boat in still water is 15 m per hour.

What is speed?

The speed of an object, also known as v in kinematics, is the size of the change in that object's position over time or the size of the change in that object's motion per unit of time, making it a scalar quantity. The instantaneous speed is indeed the upper limit of a average speed as that of the length of the interval approaches zero. The average speed of the object in a period of time is equal to the distance travelled by object divided by duration of the period. Velocity and speed are not the same thing.

The dimensions of speed are time divided by distance.

Given, speed of lazy river current = 5

distance covered = 20 miles downstream

and 10 miles upstream

Let x be the speed in still water
(x+5)T = 20

(X-5)T= 10

2(X-5) = (X+5)

X = 15

Therefore, speed of the boat in still water is 15 m per hour

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The triangles are congruent using a two-column proof and triangle congruency theorems. For that please refer to the image also and reasons are mention below.
Math congruent meaning?

If two shapes are similar in size and shape, they are congruent. We can also state that if two shapes are congruent, then their mirror images are identical.

Since the statements are already presented in your figure, only the reasons need be stated here.

1)Given

2)Given

1)Given

4)Congruent line segment definition5)

5)symmetry as a congruence trait

6) Addition and substitution aspects of equality

7)Segment addition theorem

8)Congruent line segment definition

9)Congruence postulate for AAS

According to the property of addition, if A=B, then A+C=B+C. According to the substitution property, if C=D, then A+C=B+D. (D can be substituted for C). I believe that in order to move from A=B and C=D to A+B=C+D, both qualities must be present.

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An equilateral triangle is not a right triangle for which the formula A = 1/2 bh applies. where A is the area, b is the length of the base, and h is the height. This formula does not work because all sides and angles of an equilateral triangle are equal.

Hence, An equilateral triangle is not a right triangle for which the formula A = 1/2 bh applies. where A is the area, b is the length of the base, and h is the height. This formula does not work because all sides and angles of an equilateral triangle are equal.

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Answer:

5

Step-by-step explanation:

The straight line distance between the two friends is 12 meters.

Given, On a school playground, a math teacher draws a number line with values from -10 to 10.

Also, the distance between each consecutive number is 1 meter.

Now,  Rebecca is standing at +4, and her friend Cedric is standing at -8.

We have to find the straight-line distance between the two friends, in meters.

As, the distance of Rebecca from the origin is 4 m and the distance of Cedric from the origin is 8 m.

Therefore, the distance between Rebecca and Cedric is 4 + 8 i.e. 12 m

Hence, the straight line distance between the two friends is 12 meters.

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Marques played songs in Number of movies = 5 and Number of commercials = 10

A mathematical statement proving the equality of two mathematical expressions is the essence of an equation.  For example, 8x + 3 = 12 is an equation in which the expressions 8x + 3 and 12 are separated by a 'equal' sign.

The system of equations that could be used to determine the number of commercials and the number of movies on which Marques songs were played is illustrated as 30(x + 5) + 120(x) = 900.

The variable x represents the number of times the song has been played in movies.

According to the information, Marques is a songwriter who collects royalties on his songs whenever they are used in a commercial or a movie, and she will earn $30 every time one of his songs is used in a commercial, while he will earn $120 every time one of his songs is used in a movie.

Let x be the number of times the song was heard in movies.

Marques' songs were heard in five times more commercials than in movies. x+5 will be the answer.

As a result, the equation to solve the problem will be:

30(x + 5) + 120(x) = 900

30x + 150 + 120x = 900

150x + 150 = 900

150x = 900 -150

150x = 750

x = 750/150

x = 5

Number of movies = 5

Number of commercial = x + 5

5 + 5 = 10

Therefore Marques played songs in Number of movies = 5 and Number of commercials = 10

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You are buying 3 shirts and 2 pairs of pants. You spend $300. Let x represent the price of the shirt and y represent the price of the pants.

Let

x ----> the price of the shirt

y ---> he price of the pants

we have that

The price of three shirts plus the price of two paints must be equal to $300

so 3x+2y = 300 this is the equation of the line in standard form

Convert to slope intercept form

y = mx+b

Isolate the variable y

3x+2y = 300

subtract 3x both sides

3x+2y-3x = -3x+300

2y = -3x+300

Divide by 2 both sides

y = -1.5x+150

----> equation of the line in slope intercept form

Find out the x-intercept

Remember that the x-intercept is the value of x when the value of y is equal to zero

In this problem, the x-intercept is the price of the shirt when the price of the paints is equal to zero

Using the Standard Form, identify the x-intercept of the graph

The standard form is

Ax+By = C

The x-intercept is C/A

we have

3x+2y = 300

so

300/3 = 100

The x-intercept is the point (100,0)

That means---> The price of the shirt is $100 when the price of the paints is equal to $0

Alternative method to find out the x-intercept (equation in slope intercept form)

y = -1.5x+150

For y=0

0 = -1.5x+150

solve for x

1.5x = 150

x = $100

Hence the x-intercept is the point (100,0)

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Answer:

---------------------------------------

Slope is negative and therefore it represent a negative correlation.

The matching choice is D

Answer:

d)  The slope is -0.3, which indicates a negative correlation.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Given equation:

[tex]y=3.9-0.3x[/tex]

The slope of a linear equation is the coefficient of the term in x.

Therefore, the slope of the given line of best fit is -0.3.

If the slope of the line of best line is negative, it indicates a negative correlation.

If the slope of the line of best line is positive, it indicates a positive correlation.

Therefore, as the slope is negative, it indicates a negative correlation.

Answer:

m = -27/13

Step-by-step explanation:

Given equation,

→ (2m - 27)/3 = 5m

Now the value of m will be,

→ (2m - 27)/3 = 5m

→ 2m - 27 = 5m × 3

→ 2m - 15m = 27

→ -13m = 27

→ [ m = -27/13 ]

Hence, value of m is -27/13.

Answer:

x=80 degrees

Step-by-step explanation:

all 3 angles of a triangles equals 180

We add the 2 angles 70+30=100

Now we subtract from 180

180-100=80

x=80 degrees

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The compound interest earned on an account with $700 invested at 4.5% for 2 years is $64.42.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

To calculate the compound interest earned, we use the formual below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the compound interest earned is $64.42.

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Answer:

Yes

Step-by-step explanation:

I will do question 4 so you understand: What there asking is for you to simplify.

This is how you do so.

step 1 find the numbers that have the same letter

Step 2 If you find one for example 7y and 3y you add them which is 10y

Step 3: Any letters that are by them selves and the question doesn't give you a value ignore!

Hope this helps!!

The system of inequalities that represents this scenario is;

x² - 2y ≥ 7000

2x + 5y < 1000

We are given that;

Value of company's stock = x² - 2y

Now, purchases by the company is modeled by; 2x + 5y

We are now told that the company’s goal is to maintain a stock value of at least $7,000. This means the stock value must be greater than or equal to $7000. Thus, this inequality is;

x² - 2y ≥ 7000

Now, we are told that the purchases must be kept below $1000. This means less than $1000 and as such the inequality is;

2x + 5y < 1000

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According to the substitution method, the value of x is 5 and the value of y is -2

Substitution method:

In math, substitution method, we have to substitute the value of a variable found by one equation in the second equation.

Given,

Here we have the equations:

3x + 4y = 7

2x - 3y = 16

Now, we have to solve this one by using an algebraic method.

Here we have to use the substitution method to solve this equations,

Suppose,

3x+4y=7              →(1)

and 2x-3y=16     →(2)

Taking equation (1), we have

=> 3x+4y = 7

⇒ 3x = -4y+7

⇒ x = (-4y+7)/3  →(3)

Putting x = (-4y+7)/3 in equation (2), we get

=> 2x - 3y = 16

=> 2((-4y+7)/3) - 3y = 16

⇒-8y + 14 - 9y = 48

⇒ - 17y + 14 = 48

⇒ - 17y = 48 - 14

⇒ - 17y = 34

⇒y=-2→(4)

Now, Putting y=-2 in equation (3), we get

=> x = (-4y+7)/3

=> x = (-4(-2)+7)/3

⇒ x = (8 + 7)3

⇒ x = 15/3

⇒ x = 5

∴ x = 5 and y = -2

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By evaluating the exponential equation we will see that:

a) On 2001 the population is 150.38 thousands.

b) on 2018 the population is 409.13 thousands.

We know that the population (in thousands) x years after 1998 is given by the exponential equation:

y = 123.1*(1.069)^x

a) We want to find the population in 2001, this is 3 years after 1998, so x = 3, replacing that we will get:

y = 123.1*(1.069)^3 = 150.38

So the population on 2001 will be 150.38 thousands.

b) If the equation still works for 2018, then we can use x = 20 (2018 is 20 years after 1998) then the population will be:

y = 123.1*(1.069)^18 = 409.13

So the population is 409.13 thousands.

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Length of KM using distance formula is √53.

Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage. In math, what is a distance? The length of the line segment connecting the two sites is used to measure distance between them. The shortest line segment between a point and a line will have a length equal to the distance between them.

Given,

Coordinates of K = (8,-4)

Coordinates of M = (1,-2)

Distance formula:

D = √(x₂ - x₁)² + (y₂ - y₁)²

D = √(8-1)² + (-4+2)²

D = √49 + 4

D = √53

Length of KM using distance formula is √53.

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Answer:

The answer to your problem is 540

Step-by-step explanation:

The answer is 180 because all triangles have 3 sides and a pentagon is 3 triangles formed as one so you need to do 180 x 3 which is 540

Answer:

Perimeter is the sum of length of the sides used to made the given figure. The length of each side of the yield sign is 78 centimeters.

Step-by-step explanation: