Consider the relation given by the graph below.
a) Is the relation a function? Why or why not?
b) Determine the domain and range of the graph.

The value of f(x) when x = 3 is 4

The definition of the piecewise function is given as:

[tex]f(x) = \left[\begin{array}{cc}-x& x \le -1\\1&x = 0\\x + 1&x \ge 1\end{array}\right[/tex]

When x = 3, the domain is [tex]x \ge 1[/tex]

At [tex]x \ge 1[/tex], the function definition is

f(x) = x + 1

So, we have:

f(3) = 3 + 1

Evaluate

f(3) = 4

Hence, the value of f(x) when x = 3 is 4

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Complete question

A piecewise function is defined as shown.

[tex]f(x) = \left[\begin{array}{cc}-x& x \le -1\\1&x = 0\\x + 1&x \ge 1\end{array}\right[/tex]

What is the value of f(x) when x=3?

Answer:

4

Step-by-step explanation:

Answer:

Step-by-step explanation:

find prime factorization of 6 and 9

6 = 2 x 3

9 = 3 x 3

Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:

LCM = 2 × 3 × 3

LCM = 18

Step-by-step explanation:

Make a line like that and add the numbers 6 and 9 ( order doesn't matter).

then look for a number that can divide both of them without a remainder first which is 3.

Divide 6 and write the Answer down under it

Divide name and write the answer under it.

look for another number that can divide those answers you got. but they aren't no numbers that can divide them without remainders anymore, so you divide 2 by 2 and write down 1 and just write down the 3 back .

then divide 3 by 3 and write down the answer which is one beneath it.

(you should keep dividing until you get everything to 1)

Then multiply together all the numbers used in dividing and that is your L.C.M.

Hope this helps.

Good luck ✅.

Answer:

Step-by-step explanation:

Answer:

[tex]x=\frac{11}{18} =0.611[/tex]

Step-by-step explanation:

1) Subtract [tex]\frac{2}{9}[/tex] from both sides.

[tex]x=\frac{5}{6} - \frac{2}{9}[/tex]

2) Simplify [tex]\frac{5}{6} - \frac{2}{9}[/tex] to [tex]\frac{11}{18}[/tex].

[tex]x=\frac{11}{18}[/tex]

Decimal Form: 0.611111

Using trigonometric identities, and equality is reached, hence the equality is proved.

These three identities are used:

Hence:

[tex]\sec^4{x} = \frac{1 + \tan^2{x}}{1 - \sin^2{x}}[/tex]

[tex]\sec^4{x} = \frac{\sec^2{x}}{\cos^2{x}}[/tex]

[tex]\sec^4{x} = \sec^2{x} \times \sec^2{x}[/tex]

[tex]\sec^4{x} = \sec^4{x}[/tex]

Equality is reached, hence the equality is proved.

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Answer:

3, 5, 7

Step-by-step explanation:

We can assign the first number as x. Since all the numbers are odd the next number will be x+2, and the last will be x+4.

3*(x+4) = 7(x)

3x+12 = 7x

12 = 4x

x = 3

x+2 = 5

x+4 = 7

Answer: The graph of g is the graph of f translated 10 units down, and [tex]g(x)=2x-10[/tex]

Step-by-step explanation:

The y-intercept of f(x) is 6, and the y-intercept of g(x) is -4, so the graph of g is the graph of f translated 10 units down.

So, the equation of g(x) is [tex]g(x)=2x-10[/tex]

Answer:

5 units right and g(x)= f(x - 5).

A line bisector is a straight line that divides a given line into two equal parts. Thus the following steps are required by Naomi to show that point D is equidistant from points  A and C.

BD ⊥ AC (given)

BD = 3 units, and AC = 8 units.

BD is the perpendicular bisector of segment AC (given)

Thus,

<BDA  ≅ <BDC (right angles formed by a perpendicular bisector)

AD ≅ DC (equal parts of a bisected line)

AD ≅ DC = 4 units

Thus joining points B to A, and B to C,

BA ≅ BC.

So that applying Pythagoras theorem to ΔABD, we have:

[tex]/hyp/^{2}[/tex] = [tex]Adj 1^{2}[/tex] + [tex]Adj 2^{2}[/tex]

[tex]AB^{2}[/tex] = [tex]3^{2}[/tex] + [tex]4^{2}[/tex]

       = [tex]\sqrt{25}[/tex]

 AB      = 5 units

So that,

BA ≅ BC = 5 units

Therefore, it can be concluded that point D is equidistant from points A and C.

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A function assigns the values. The force that will be required to move the rock is 48 lbs.

A function assigns the value of each element of one set to the other specific element of another set.

A.) The inverse of the function f(x)=1/x is,

f(x) = 1/x

y = 1/x

x = 1/y

g(x)=1/x

Hence, The inverse of the function f(x)=1/x is g(x)=1/x.

B.) The force that will be required to move the rock using the momentum,

9ft × 80lbs = 15 ft × F

F = 48 lbs

Hence, The force that will be required to move the rock is 48 lbs.

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Answer:

a

Step-by-step

explanation:

The difference betweeh the two companies' moving rates is:

(f - g)(x) =  -2x + 200

Here we have two functions:

f(x) = 3x + 400

g(x) = 5x + 200

These functions represent the moving rates for two different companies.

If we want to find the difference between the moving rates, we just need to take the difference between the functions:

(f - g)(x) = f(x) - g(x) = (3x + 400) - (5x + 200) = -2x + 200

So the difference betweeh the two companies' moving rates is:

(f - g)(x) =  -2x + 200

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The probability that if Air America books 15 persons, there will be enough seats available is 0.913.

First of all, we would determine the probability that if Air America books 15 persons, there won't be enough seats available by using binomial distribution:

P(x = 15) = 0.85¹⁵

P(x = 15) = 0.087.

Based on logic, the probability that if Air America books 15 persons, there will be enough seats available is given by:

P = 1 - 0.087

P = 0.913.

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Answer: A

Step-by-step explanation:

The line has a positive slope.

Also, the line should be shaded below.

This leaves us with D.

Answer: 4

Step-by-step explanation:

[tex]A=7.52=\frac{1}{2}ac \sin B\\\\7.52=\frac{1}{2}(a)(6)\sin 40^{\circ}\\\\a=\frac{7.52}{\frac{1}{2}(6)(\sin 40^{\circ})}\\\\a \approx 4[/tex]

Life , Health , Car are considered to be very important insurance ,  Rental Car Damage , Travel Insurance has no usage.

Insurance is safe guarding any thing which has some monetary or emotional value to it , It can be life , health , car , house , your gold etc.

Insurance protects you against something you can never predict .The life is unpredictable and Insurance is a cover to that .

As given in the question , a person can be lucky enough that he never gets to use the money that he invested in the Insurance , but not investing due to this is wrong.

This is not difference of opinion but lack of prediction of future and lack of understanding the needs of life.

Life , Health , Car , Home , Fire etc . insurance that protects the basic amenities of life are considered to be very important ,

while nowadays insurance of Rental Car Damage , Travel Insurance , these are some which has no usage beyond the fact that they cover nothing.

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[tex]\large\boxed{y=\frac{1}{4}x+2}[/tex]

The point-slope form is actually [tex]y-4=\frac{1}{4}(x-8)[/tex]; I assume there was a copy/paste issue.

Also, the correct answer is not in the answer choices given; again assuming a copy/paste issue.

Start by distributing the [tex]\frac{1}{4}[/tex] to [tex]x[/tex] and [tex]-8[/tex].

[tex]y-4=\dfrac{1}{4}x-2[/tex]

Add [tex]4[/tex] to both sides of the equation.

[tex]\begin{aligned}y-4+4&=\frac{1}{4}x-2+4\\y&=\frac{1}{4}x+2\end{aligned}[/tex]

Answer:

C

Step-by-step explanation:

9x² - 4[tex]y^{6}[/tex]

can be factored as a difference of squares , that is

(U + V)(U - V)

9x² - 4[tex]y^{6}[/tex] = (3x)² - (2y³)²

with U = 2x and V = 2y³

Answer:

U= 3x and V=2y^3

Step-by-step explanation:

9x^2= (3x)^2

4y^6 = (2y^3)^2

=(3x)^2 - (2y^3)^2

Apply this rule below

x^2 - y^2 = (x + 7) - (x - y)

(3x)^2 - (2y^3)^2 = (3x + 2y^3) + (3x - 2y^3)

= (3x + 2y^3) (3x - 2y^3)

Answer:

The answer shall be xy[(167/30)x-(65/14)y+(3/4)]

Step-by-step explanation:

the step is given in image given...

The measure of the segment JK is 0 unit

A line is the shortest distance between two points

Given the following parameters

GJ = 70.2

JH = 26.5

GK = 70.2

Determine the measure of JK

JK = JG + GK

Since JG = -GJ then;

JK = -GJ + GK

JK = -70.2 + 70.2

JK = 0

Hence the measure of the segment JK is 0 unit

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Answer:

$2.26

Step-by-step explanation:

In total, you owed them 28.21, and so you can subtract the amount you paid from the total:

28.21 - 25.95 = 2.26

So, you owe them $2.26 now.

hope this helps! have a lovely day :)

Answer:

Falde

Step-by-step explanation:

the solution is at the point of intersection of the 2 lines

the lines intersect at (- 5, 1 ) , then

the solution is (- 5, 1 )

Answer:

y = 4/5x + 2

Step-by-step explanation:

Standard equation given slope and y-intercept -> y = mx + b

After substituting variables m and b, you get y = 4/5x + 2.

The value of y in [tex]-3 = 7\left(y-\dfrac97\right)[/tex] is 6/7

The equation is given as:

[tex]-3 = 7\left(y-\dfrac97\right)[/tex]

Open the bracket

-3 = 7y - 9

Add 9 to both sides of the equation

7y = 6

Divide both sides by 7

y= 6/7

Hence, the value of y in [tex]-3 = 7\left(y-\dfrac97\right)[/tex] is 6/7

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Complete question

Solve for y

[tex]-3 = 7\left(y-\dfrac97\right)[/tex]

Answer:

121 i.e. 11²

Step-by-step explanation:

(a+b)² = a² + 2ab + b²

x² + 2 × x × 11 + 11² = (x + 11)²

Answer:

1

Step-by-step explanation:

We can find the slope using the slope formula, which is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

The order of the points doesn't matter, but the points that are farthest right (8, 8) can be our y2 and x2 and the points that are farthest left (5, 5) can be our y1 and x1.

Thus, we have [tex]\frac{8-5}{8-5}=\frac{3}{3}=1[/tex]

Answer: [tex]x\sqrt[9]{y^{2} }[/tex]

Step-by-step explanation: For all expressions in the form [tex]x^{\frac{a}{b}[/tex] , the expression is equal to [tex]\sqrt[b]{x^a}[/tex]. The denominator in a fractional exponent is the type of root it is. For example, [tex]x^\frac{1}{3}[/tex] is going to be the cubed root, or the

3rd root of x ([tex]\sqrt[3]{x}[/tex]). The numerator is what power x is raised to. For example, [tex]x^\frac{3}{2}[/tex] is going to be [tex]\sqrt{x^3}[/tex].

In fractional exponents, the square root only takes the form of the variable it is assigned to. What does that mean? Well, for [tex]xy^\frac{2}{9}[/tex], the square root only applies to the y. The x is considered a constant and can be moved out. Thus, we get [tex]x\sqrt[9]{y^2}[/tex].

Answer:

x + y = w

w > x

w > y

Step-by-step explanation:

x and y are interior angles of a triangle.

w is the exterior angle ( opposite to angles x and y ) of a triangle.

There is a formula that exterior angle of a triangle is equal to sum of two interior angles of a triangle.

So,

x + y = w

If x + y = w,

Then,

w > x

w > y

Among angles i , k , g , a  ,i and k are the exterior angles.

Given i°, k° ,g° ,a° are some angles and we have to find which angle is exterior angle.

The angle between a side of a polygon and an extended side is known as exterior angle of polygon. The sum of exterior angles of a polygon is equal to 180 degrees. We have to identify exterior angles among i° ,k° ,g° ,a°.

The angle i is an exterior angle because it is formed on a line opposite to angle d.

Angle k is also an exterior angle because it is also formed on opposite side of an angle.

Angle g is not an exterior angle.

Angle a is not an exterior angle.

Hence i and k are exterior angles among i, g, k, a.

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Answer: 5

Step-by-step explanation:

By the inscribed angle theorem.

[tex]\frac{9}{15}=\frac{2x-1}{3x}\\\\27x=30x-15\\\\-3x=-15\\\\x=5[/tex]

The graph that matches the following system of equation is; the picture of a coordinate plane with line y equals negative 4x minus 1 and line y equals minus 3 over 2 times x plus 4. They intersect at negative 2, 7.

The graph of a function y = f(x) shows the position of the x-intercepts and y-intercepts from the graph from which the slope can be drawn.

The system of linear equations can be rewritten in slope-intercept form as follows:

y = -4x - 1

y = -3/2x + 4

From the graph, the two equations intercept at point (-2,7).

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