The domain for f(x) and g(x) is the set of all real numbers.

Let f(x) = 2x^2 + x − 3 and g(x) = x + 2. Find (f • g)(x).

Whenever you want to write the equation of a parallel line through some point (h, k), you can ...

Using this formula here, we get

... 2(y +5) = 3(x -2)

Your answer form requires you solve this for y.

... 2y + 10 = 3x -6 . . . . . eliminate parentheses

... 2y = 3x -16 . . . . . . . . subtract the constant on the left (10)

... y = (3/2)x -8 . . . . . . divide by 2

The formula for area of this shape is (a+b)/2 * h

a = 8

b= 12

h = 6

Area = (8+12)/2 * 6

Area = 20/2 * 6

Area = 10 * 6

Area = 60 sq. m.

To find the y value in this line, we can simply plug 2 into the variable x and solve.

2(2) + 5

4 + 5 = 9

The y value for x 2, is 9.

This can be displayed as (2, 9).

Using the slope intercept relation, the missing y value in the points given is 9.

Given the slope intercept equation :

Substituting the value of x into the equation and solving for y :

y = 2(2) + 5

y = 4 + 5

y = 9

Therefore, the value of y which is missing is 9 ; the point is( 2, 9)

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Answer:

The linear equation for the total combination age is [tex]X+7+(X+4)+7=24[/tex]

Step-by-step explanation:

If Jane is X years old today. And her brother is 4 years older then her brothers age is,

X+4.

Jane's age after 7 years = X+7

Jane's Brothers age after 7 years = (X+4)+7

So after seven years their combined age will be 24, Lets write this in an equation form,

[tex]X+7+(X+4)+7=24[/tex]

So the linear equation for the total combination age is,

[tex]X+7+(X+4)+7=24[/tex]

Answer:

B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Standard form of non-polynomials is purely to solve them.

10^4 = 10,000

2.1 * 10,000 = 21,000

Letter D, because the y intercept is on -4 and if you look at the slope and use the method "Rise over Run" you can see that the rise is one and negative a half.

Answer is: p = [tex]\frac{21}{4}[/tex]

Let's have the first number be x, the second number y, and the third number z.

Because the second number is six more than the first, y = x + 6.

Because the third number is twice the first, z = 2x.

The three numbers added together equals 26, so 26 = x + y + z.

Let's substitute y = x + 6 and z = 2x into 26 = x + y + z.  This gives us:

26 = x + x + 6 + 2x

26 = 4x + 6

We subtract 6 from both sides of the equation and divide by 4 to get:

5 = x

Now, we'll put x = 5 into our previous to equations to find y and z:

y = 5 + 6

y = 11

z = 2*5

z = 10

Let's check out answer.  10 + 11 + 5 = 26.  10 is twice of 5 and 11 is 6 more than 5.  Thus our three numbers are 10, 11, and 5.

The three numbers are 5, 11 (5 + 6), and 10 (2 * 5)

Let's call the first number x

The second number is 6 more than the first, so it is x + 6

The third number is twice the first, so it is 2x

The sum of the three numbers is 26, so we have the equation x + (x + 6) + 2x = 26

Combining like terms, we get 4x + 6 = 26

Subtracting 6 from both sides, we get 4x = 20

Dividing both sides by 4, we get x = 5

So the three numbers are 5, 11 (5 + 6), and 10 (2 * 5)

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"The correct answer is that diagrams showing how matter moves through organisms and the environment are called cycles because they depict continuous, circular pathways.

In ecosystems, matter is not created or destroyed but is continuously recycled. This recycling process occurs in a loop or cycle, where matter moves from the environment to organisms and then back to the environment. For example, in the carbon cycle, carbon dioxide is taken in by plants during photosynthesis, then passed on to animals that consume the plants, and eventually returned to the environment through processes like respiration and decomposition.

These cycles are essential for the sustainability of ecosystems because they ensure that nutrients and other materials are reused and not depleted. The term ""cycle"" reflects the repeating and ongoing nature of these processes, highlighting the interconnectedness and interdependence of organisms and their environment. By using diagrams to represent these cycles, we can visualize and better understand the complex interactions and pathways that matter follows in ecosystems."

Answer:

They make it easier to get your arms through

Answer:

6

Step-by-step explanation:

a pex

The answer is 199.198.

Answer: x = {199.28959,  0.00000278768}

Step by step explanation:

0.00216140848x² - 0.43046552x + 0.0000012=0

[tex]x = \frac{-b +/- \sqrt{b^{2}- 4ac} }{2a}[/tex]

[tex]x = \frac{-(-0.43046552) +/- \sqrt{-0.43046552^{2}- 4(0.00216140848)(0.0000012)} }{2(0.00216140848)}[/tex]

You can do each step manually or use a quadratic calculator to do the calculations.

x = 199.28959, x = 0.00000278768

Answer:

[tex]V_{E} = -22.5 / 15 = 1.5 miles/minute\\V_{F} = 7.5 / 15 = 0.5 miles/minute[/tex]

Step-by-step explanation:

To answer this problem, we must bear in mind that the express train travels 3 times faster than the freight train.

If we call F the distance that the freight train travels and we call E at the distance that the express train travels, we must have the distance between them after 15 minutes it must be 30 miles.

So

[tex]F + E = 30\\[/tex]

We also know that:

[tex]E = 3F[/tex]

Since the express train travels 3 times faster than the freight train.

So, like both equations, we have to:

[tex]F + 3F = 30\\F = 30/4\\F = 7.5 miles\\[/tex]

Then [tex]E = 7.5*3 = 22.5[/tex] miles in the opposite direction.

This is the distance you traveled in 15 minutes.

Therefore, the speed of the express train ([tex]V_{E}[/tex]) is the distance traveled between the time it did

[tex]V_{E} = -22.5 / 15 = 1.5 miles/minute\\V_{F} = 7.5 / 15 = 0.5 miles/minute[/tex]

Answer:

Step-by-step explanation:

Given that Henry  deposited $420 into a savings account. There is a $5.00 per month service fee on the account. Also, Henry decides he wants to withdraw $25 a week for spending money.

Let us convert everything into days.

30 days a month and 7 days in a week

Service charges for 30 days = 5

withdrawn amount for 7 days = 25

Let x be the total no of days

Then [tex]\frac{25x}{7} +\frac{5x}{30}= 420\\\\750x+35x=420(7)(30)\\785x=420(7)(30)\\x=112.3567[/tex]

i.e. between 3 and 4 months

We can say in 3 months this will be exhausted.

Option A

Rounded to the nearest thousand is 47,000 because the number to the right of it is not 5 or up, so this is the answer.

hope that helps :)

Your answer will turn out to be −4x^2+3x.

Simplify. Distribute -1 to all terms within the second parenthesis

-(6x² + 3x + 5) = -6x² - 3x - 5

Combine like terms

2x² - 6x² = -4x²

6x - 3x = 3x

5 - 5 = 0

-4x² + 3x is your answer

~Rise Above the Ordinary

Answer:

B: 18.9

Step-by-step explanation:

When the 12 numbers are listed in order, they are ...

... 13, 15, 18, 20, 23, 23, 27, 29, 30, 32, 36, 38

The extreme values are 13 and 38. Only the third plot has the ends of the whiskers on these values.

Since there are an even number of numbers, the median is the average of the middle two: (23 +27)/2 = 25. Only the third plot shows the median at 25.

Since each half of the data set has an even number of numbers, the 1st and 3rd quartile values are the averages of the middle two numbers in each half:

The third plot has the ends of the box in these places, confirming it is the correct choice.

The appropriate choice is the third one.

4/75 = x/60

75x = 240

divide each side by 75

x = 3.2

Davids jogging rph/rate per hour would most likely be 3.5 /3.7

First, turn the two fractions into decimals : 7/9 = .77777 7/8 = .875

Now, all of the numbers are in common form so you can identify which is largest, etc. : .875, .77777, .7

Now put the values back to fractions : 7/8, 7/9, .7

Answer:

2.72 m/s

Step-by-step explanation:

We are given that

Boy jogs=250 meters

Time taken by boy=110 seconds

We have to find the average speed in m/s

In order to find the average speed then we will divide distance by time

[tex]Average\;Speed=\frac{distance}{time}[/tex]

Using the formula then we get

Average speed=[tex]\frac{250}{110}=2.72 m/s[/tex]

Hence, the average speed=2.72 m/s

Final answer:

To calculate the average speed, the boy's distance jogged (250 meters) is divided by the time taken (110 seconds), yielding an average speed of 2.27 m/s.

Explanation:

The student's question asks how to calculate the average speed of a boy who jogs a certain distance in a given amount of time. To find the average speed, you divide the total distance traveled by the total time taken. In this case, the boy jogs 250 meters in 110 seconds.

The calculation for the average speed (v) would be:

Distance (d) = 250 meters

Time (t) = 110 seconds

Average Speed (v) = d / t

Plugging the values into the equation yields:

Average Speed (v) = 250 m / 110 s = 2.27 m/s

Hence, the boy's average speed is 2.27 meters per second.

If the street is already 24 m wide, and it is being expanded by 125%, then the correct answer is C. 30 m!

125% simply means 1 1/4.     1/4 of 24 is 6.    So, you have 24 + 6 = 30!

Answer:

The correct answer is C: the new street should be 30m wide.

Step-by-step explanation:

This is a simple problem of per-cents. Perhaps the easiest way to do it is to use a basic ‘‘rule of three’’. In this particular case the 100% is the width of the old street, i.e. 24 m; and we want to know the new width, that is 125% of the old street. So,

                   24 ---- 100%

                    x  ----- 125%

To find x we use the formula

[tex]x = \frac{24*125}{100} = 3000/100=30[/tex]

So, the width of the new street is 30m.

The solution of the system of equations and inequalities, indicates that the solution are;

In order to find the solution of the system of equations by graphing, the lines are graphed on the same coordinate plane and the point at which the two graphs intersect is the solution of the system of equations.

1) y = (1/4)·x - 4, y = (-1/2)·x - 1,

The x-coordinates at the point of intersection, can be found by noting that the y-values of both equations are the same

Please find attached the graph of the system of equations with the point of intersection, (4, -3), which corresponds to x = 4, and y = -3, created with MS Excel

The solution of the system of equations therefore is; x = 4, y = -3

2. 3·x - 2·y = 8

x - 2·y = 4

Making y the subject of both equations, we get;

y = (3/2)·x - 4

y = (1/2)·x - 2

The graph of the above two equations can be plotted on the same coordinate plane using MS Excel, is attached

The point of intersection of the two graphs is (1, -2.5)

The solution of the system of equations is therefore; x = 1, and y = -2.5

3) The solution of the system of inequalities is the feasible region, corresponding to the region that satisfies both inequalities;

Please find attached the graph of the inequalities, showing the positive region that satisfies both inequalities, which is the triangle with vertices, (0.51, 0), (1, 1), and (1.5, 0)

4) The inequalities can be graphed by making y the subject of both inequalities and graphing the equations on the same coordinate plane.

x + y > -2, therefore; y > -2 - x

6·x - y ≥ 3, therefore; y ≤ 6·x - 3

6·x - 3 = -2 - x

The points in the feasible region of the graph are; points below and on the line, y = 6·x - 3, above the line y = -2 - x, and to the right of the point (1/7, -2 1/7)

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Hello!

Answer:⇒15√6 i

Step-by-step explanation:

√-54=3√6 i

5*3√6 i

Multiply the numbers.

5*3=15

=15√6 i

Hope this helps!

Thank you for posting your question at here on brainly.

-Charlie

[tex]i=\sqrt{-1}[/tex]

[tex]5\sqrt{-54}=5\sqrt{9(-6)}=5\cdot\sqrt9\cdot\sqrt{-6}=5(3)\sqrt{(6)(-1)}\\\\=15\cdot\sqrt6\cdot\sqrt{-1}=15\cdot\sqrt6\cdot i=15i\sqrt6[/tex]