The compositions f(g(x)) and g(f(x)) of functions f and g are shown on the graph. Which statements describe the compositions? Check all that apply. f(g(x)) = g(f(x)) for at least one value of x. The composition of f and g is commutative. f(g(0)) = 5 and g(f(–2.5)) = 5. Both f(g(x)) and g(f(x)) have the same domain. The graphs show that function composition is not commutative.

There is no value for which the missing place should be filled in order to have exactly one solution.

A Linear equation may be defined as the one which can be represented in the form ax + b = 0 where a, b are coefficients and x is the independent variable. Since the equation only has one variable that is x then the linear equation will be rightly called as linear equation in one variable. We are given the equation -2(2x - _) + 1 = 17 - 4x. We solve the equation further which results as

-4x - _ + 1 = 17 - 4x

As we can see that there is -4 in both the right-hand side as well as the left-hand side both of them gets cancelled out.

- _ +1 = 17

As we can see that there is no variable left in order to find the value so any value of missing space will not be able to give any solution.

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Answer: parallel lines are in the same slope? , but they do not intersect.

Step-by-step explanation:

because

Answer: slope, intersect

Step-by-step explanation:

As parallel lines never intersect

Circle with center (2,-3) that passes through (2,0) has an area of 9π units² in terms of π and 28.3 units² (nearest tenth).

As given in the question,

Circle with center C(2, -3)

Passes through point A(2,0)

Graph of the circle attached.

Radius of the circle 'r'

r =CA

CA = √(2-2)² +(0+3)²

     = √9

     = 3

Area of the circle = πr²

                             = π (3)²

                             = 9π units² (in terms of π)

                             = 9 ×3.14

                             = 28.26

                             = 28.3 units²

Therefore, circle with center (2,-3) that passes through (2,0) has an area of 9π units² in terms of π and 28.3 units² (nearest tenth).

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Answer:

Team 1 is 7, team 2 is 6

Step-by-step explanation:

Upper Extreme-Lower Extreme

The volume of the figure shown in the reference attachment, provided hereby with the question statement will be 6786 ft³.

As per the question statement and the reference attachment, we are provided with a figure and its dimensions.

We are required to calculate the volume of the concerned figure using the dimensional values provided.

To solve this question, we need to calculate the volumes of the bottom cuboidal part, and the top pyramidal part separately, and then add these volumes, to obtain our final desired answer.

Given, the dimensions of the bottom cuboidal part is (21ft by 18ft by 13ft).

We know that, volume of a cuboid = (length * breadth * height).

Therefore, volume of our concerned bottom cuboidal part

= (21 * 18 * 13) ft³

= 4914 ft³.

Also given, the dimensions of the top pyramidal part are as follows,

Base of the triangle  = 18 ft,

Altitude of the triangle  = 16 ft,

and length of the pyramid = 13 ft.

Therefore, Volume of the concerned pyramid

= [(1/2) * base * altitude * length]

= [(1/2) * 18 * 16 * 13] ft³

= (9 * 16 * 13) ft³

= 1872 ft³.

Therefore, Total volume of the concerned figure shown in the reference  attachment, provided hereby with the question statement will be

(4914 + 1872) ft³ = 6786 ft³

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Answer:

20 - b

Step-by-step explanation:

5a - b

substitute a for 4 because a = 4

5(4) - b

20 - b

Answer:

y= 1/2 x - 3

Step-by-step explanation:

because -3 is the y-intercept, it is where the graph crosses the y-axis

the line is increasing at a rate of 1 unit up, and 2 units to the right. meaning that the slope is 1/2

The equation of the first line is y = -1/3x - 4, while the equivalent equations of the second line are y = -2/3(x - 3)  and y = -2/3x + 2

The given parameters are

Slope, m = 5/4

Point, (x1, y1) = (1, 3)

A linear equation is represented as

y = m(x - x1) + y1

So, we have

y = 5/4(x - 1) + 3

This gives

y = 5/4x + 7/4

Hence. the linear equation is y = 5/4x + 7/4

Here, we have

(x, y) = (3, 0) and (0, 2)

A linear equation is represented as

y = m(x - x1) + y1

Where

m = (y2 - y1)/(x2 - x1)

So, we have

m = (2 - 0)/(0 - 3)

m = -2/3

So, we have

y = -2/3(x - 3)

The above equation can be rewritten as

y = -2/3x + 2

Hence, the equations are y = -2/3(x - 3)  and y = -2/3x + 2

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Radius = 12 cm

Central angle = 30°

Length of circular arc = 2πr(θ/360)

⇒ Length of circular arc = 2π x 12 (30/360)

⇒ Length of circular arc = 2π x 1

⇒ Length of circular arc = 2π = 2 x 3.14 = 6.283 cm

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The equation of the hyperbola is -(1/16) (x +4)² + (1/4) (y +2)² = 1

What is Hyperbola?

A hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set. A hyperbola is made up of two mirror images of one another that resemble two infinite bows. These two sections are known as connected components or branches.

The intersection of the two asymptotes is where the hyperbola's center is located. This is the key idea (-4,-2)

We have y orientation because the vertex at (-4,0) is above this location. The equation will take the form as a result.

-a (x + 4)

2 + b (y + 2)

In the case of certain a and b, 2 Equals 1.

Inputting (-4,0) reveals that b = 1/4.

Finally, requiring that y = x/2 be an asymptote reveals that a = 1/16.

-(1/16) (x +4)² + (1/4) (y +2)² = 1

Hence, The equation of hyperbola is -(1/16) (x +4)² + (1/4) (y +2)² = 1

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The side length of the square that provides a counterexample to the statement square units in the area of a square is greater than or equal to the number of units in the perimeter is 2 Units.

A square is a kind of a 2D figure in which all the sides are equal.

We know that the absolute perimeter of a square is the sum of the lengths of all the total sides and as we see the area of a square is (side)².

Assuming that the whole square has four units completed for each side.

The square's circumference can be calculated as is 4 sides plus 4 fours, or as seen as 16 units.

Now the area of the square will be calculated as (4) ² = 16 sq units.

Now assuming that the total side length of the square about is 2 units.

The square's perimeter is calculated as (24) = 8 units, while its total area is calculated as (22) = 4 units.

∴ 2 units make up the side length that serves as a counterexample.

Basically, herein we have to determine the absolute numbers that when are multiplied by 4 are seen to be greater than it's square such numbers are 1, 2, 3.

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Using it's concept, the probabilities for this problem are given as follows:

a) A occurs and B does not: 0.1817 = 18.17%.

b) Either occurs: 0.3434 = 34.34%.

A probability is calculated as the number of desired outcomes in the experiment divided by the number of total outcomes in the experiment.

In the context of this problem, we have two mutually exclusive events, meaning that they cannot happen together.

For item a, we have that:

The events are mutually exclusive, hence we can multiply the probabilities as follows:

p = 0.23 x 0.79 = 0.1817 = 18.17%.

For item b, we add the probability in item with the probability of B occurring and A not, found as follows:

Hence:

p = 0.1817 + 0.21 x 0.77 = 0.3434 = 34.34%.

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Answer:

+

Step-by-step explanation:

[tex]-8-(-3)=-8+3[/tex]

Answer: 32 year

Step-by-step explanation:

Let Jerrey age is 'y' year

Mell age = 2y

Now,

2y – 16 = y + 16

y = 32

∴ Mells age = 64 year

& Jerrey age = 32 year

The expression without the rational exponents is ⁴√(m^3n^5)

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

(m^3n^5)^1/4

The exponents of the above expression cannot be simplified

This means that, we simply rewrite the expression using the fourth root expression

So, we have

(m^3n^5)^1/4 = ⁴√(m^3n^5)

Hence. the equivalent expression is ⁴√(m^3n^5)

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Lake Okeechobee has a surface area of 5329 square miles, as determined by solving the given values.

The area of a square unit, such as a square mile, is calculated by multiplying two lengths. Each length in the case of square miles is measured in miles.

Given: The Okeechobee lake is 7.3 * 10 to the second power square miles in area.

We need to figure out how many square miles Lake Okeechobee covers.

Area covered in square miles = (7.3 × 10)²

                                                 = 73²

                                                 = 5329 square miles

Therefore, Lake Okeechobee covers an area of 5329 square miles which was calculated by solving the given values.

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Answer: A: A = 2.2240  B: C = 3

Hope this helped! :)

Answer: y=x^2+6x+5 ==> D

Step-by-step explanation:

y=(x+3)^2-4

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

y=x*x+3*x+3*x+3*3-4

y=x^2+3x+3x+9-4

y=x^2+6x+5 ==> D

The velocity of the cart b is found as 20/23 ft/s over the pulley.

For the given data in the question.

q's velocity is 2 feet per second.

Rope length is 39 feet.

Assume x is the distance between A and Q. (refer the image).

Assume y is the distance between Q and B. (refer the image).

As a result of the image,

x² + 12² = L²

Now, with respect to time t, differentiate the above equation.

2x(dx/dt) + 0 = 2L.(dL/dt)

For x = 5 ft and L = 13 ft

dL/dt = (5×2)/13 = 10/13

In the case of B,

y² + 12² = (39 - L)² ; from diagram.

Differentiating now,

2y(dy/dt) + 0 = -2(39 - L).(dL/dt)

At x = 5 ft and y = 23 ft.

dy/dy = -20/23

(A negative sign indicates the opposite direction)

Thus, the velocity of cart b is found as 20/23 ft/s.

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Step-by-step explanation:

In order to construct a perpendicular from a point to a given line segment: Draw two arcs crossing the line segment. Make two more arcs which intersect. Join the point where the arcs intersect to the original point.

3 is a constant, 4 is the coefficient, 5a+3+4b is written as a sum of three terms are the true statements.

The act of combining two or more items is known as addition. The process of computing the sum of two or more numbers in mathematics is called addition. It is a fundamental mathematical procedure that is frequently used in daily life. When we work with money, figure out our food bills, or figure out the time, we frequently employ addition. Mathematicians employ the action of addition to combine numbers. The sum of the given numbers is the outcome of addition, or the total of the inputted numbers.

Given that,

5a+3+4b

Select all of the true statements below.

5a+3+4b is written as a product of three factors.

3 is a constant.

4 is a coefficient.

4b and 3 are like terms.

5a+3+4b is written as a sum of three terms.

Therefore, 3 is a constant, 4 is the coefficient, 5a+3+4b is written as a sum of three terms are the true statements.

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Answer:

(-14,12)

Step-by-step explanation:

Way 1: (little more complicated)
we know two things,
The two halves of the line have the same slope, and that the length from the endpoint to the midpoint is equal to the length from the midpoint to the other end point.
The slope is equal to: (6-9)/(4-(-5)) = -3/9 = -1/3
The length is equal to (using the Pythagorean theorem):
height = delta y = 9 - 6 = 3
length = delta x = 4 - (-5) = 9
3^2+9^2=hypotenuse^2
9+81 = h^2
h = sqrt(90)
So, the let's say point Q has the coordinate (a, b).
The formula of the slope would give us (b-9)/(a-(-5)) = -1/3
The formula of the hypotenuse would give us (b-9)^2+(a-(-5))^2 = 90
solving the system of equations, we would get that a = -14 and b = 12, so the point is (-14,12)
Make sure to be careful, however, because you will get two points with this system of equations. Only one works
Way 2:
since from point P to the midpoint we went to the left by 9 and up by 3, from the midpoint to point Q, we would go left by 9, and up by 3.
from the midpoint (-5,9), go left by 9, so x decreases by 9 to get (-14, 9).
go up by 3, so y increases by 3 to get (-14,12). This agrees with our other answer

Answer:

$29

Step-by-step explanation:

First you divide 290.44 by 10 which would equal 29.044, then you would round both 4's down to 0 which would get you $29.

Answer: 4.2; √19; 3√64

Step-by-step explanation: 4.2; 4.35889894354; 24

1,470

Step-by-step explanation:

because if he 4 miles and than 3 miles you would add them and get 7. you would take that 7 and double the 7 and multiply it by 105 cause that's how many calories he burnt each miles he ran then you would get the total of 1470 calories

diameter = 13.93771776cm

PARALLEL LINES HAVE EQUAL GRADIENTS...MEANING THE GRADIENT OF THE NEW LINE IS ALSO

[tex] \frac{5}{6} [/tex]

I WILL USE THE GIVEN POINTS RO FIND THE VALUE OF c

[tex] 6= \frac{5}{6} ( - 1) + c \\ 6 = - \frac{5}{6} + c \\ c = 6 + \frac{5}{6} \\ c = \frac{41}{6} [/tex]

The equation now is

[tex]y = \frac{5}{6} x + \frac{41}{6} [/tex]

ATTACHED IS THE SOLUTION

Hello!

A line that is parallel to another line:

 ⇒ has the same slope

Thus the line: has a slope of 5/6

However, the line passes through (-1, 6):

 ==> let's set up the equation in point-slope form

     [tex]y - y_1=m(x-x_1)[/tex]

    [tex]y - 6 = \dfrac{5}{6} (x -(-1))\\\\y -6 = \dfrac{5}{6} x + \dfrac{5}{6} \\\\y = \dfrac{5}{6} x +\dfrac{5}{6}+6\\\\ y=\dfrac{5}{6} x + \dfrac{5}{6} +\dfrac{36}{6} \\\\y=\dfrac{5}{6} x + \dfrac{41}{6}[/tex]<== Answer:

Hope that helps!

Answer:

[tex]-7x-28[/tex]

Step-by-step explanation

[tex]-7(x-2)-28-14[/tex]

To solve this, we must first solve what is inside the parenthesis by the distributive property. We will multiply -7 by x and -2.

[tex]-7(x)=-7x\\-7(-2)=14[/tex]

So then we have:

[tex]-7x+14-28-14[/tex]

From here, we combine like terms.

7x does not have any like terms, so we just combine 14, -28, and -14.

[tex]14+(-28)+(-14)\\=-28[/tex]

So, the final answer would be:

[tex]-7x-28[/tex]

If you have any questions, please feel free to ask!

The rational sums are:

√16 + (-21/5)

√4 + 5

√36 + ∛27

The irrational sums are:

π + 24

√8 + π

3/4 + √27

√16 + (-21/5)

= 4 + (-21/5)

= 4 - (21/5)

= (20 - 21) / 5

= - 1/5

= -0.2

Hence, the sum can be expressed as p/q so it is a rational number.

π + 24

= 3.1428571429 + 24

= 27.1428571429

The sum is non-terminating, so it is an irrational number.

√8 + π

= 2.82842712 + 3.1428571429

= 5.97128426

The sum is non-terminating, so it is an irrational number.

√4 + 5

= 2 + 5

= 7

The sum is an integer so it is a rational number.

√36 + ∛27

= 6 + 3

= 9

The sum is an integer so it is a rational number.

3/4 + √27

= 3/4 + 5.1961524227

= 0.75 + 5.1961524227

= 5.9461524227

The sum is non-repeating so it is an irrational number.

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The complete question is: "The table has a set of expressions representing the sums of rational and irrational numbers. Find each sum, and indicate whether the sum is rational or irrational. Drag the labels to the correct locations on the table. Each label can be used more than once."