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.

Answer:

7

Step-by-step explanation:

5 x 27 = 135

135 ÷ 20 = 6.75

round up to 7

Using the mid-point concept, we have that:

The mid-point between two points is the halfway point between them, and is found using the mean of the coordinates.

The center of the circle is the mid-point of the coordinates of the diameter, hence:

The radius is the distance between the center and the end-points of the diameter, hence, applying the formula for the distance between two points:

[tex]r = \sqrt{(5 - 2)^2 + (8 - 7)^2} = \sqrt{10} = 3.16[/tex]

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Answer:

Carrie's allowance is 7.

Step-by-step explanation:

Use the equation to find a.

a+a+8=22

First, combine like terms.

2a+8=22

Subtract 8 from both sides.

2a+8-8=22-8

2a=14

Divide 2 from both sides.

2a/2=14/2

a=7

Hope this helps!

If not, I am sorry.

#1

y=x+5

#2

y=3/8

#3

Reflection by y axis as x will be negative and shifting 2 units right

#4

y=6x+1

#5

y=x-11

#6

y=8x

Horizontally streched by 1/8 factor

Answer:

1.  Translated 5 units left.

2.  Vertical stretch by a factor of 3/8.

3.  Reflection in the x-axis, then translated 2 units down.

4.  Vertical stretch by a factor of 6, then translated 1 unit up.

5.  Translated 11 units down.

6.  Vertical stretch by a factor of 8.

7.  Vertical stretch by a factor of 1/3, then reflection in the x-axis.

Step-by-step explanation:

Transformations

For a > 0

[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}.[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}.[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}.[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}.[/tex]

[tex]a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}.[/tex]

[tex]f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $\dfrac{1}{a}$}.[/tex]

[tex]-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}.[/tex]

[tex]f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}.[/tex]

Parent function:

[tex]y=x[/tex]

[tex]\textsf{1.} \quad y=x+5[/tex]

Translated 5 units left.

[tex]\textsf{2.} \quad y=\dfrac{3}{8}x[/tex]

Vertical stretch by a factor of 3/8.

[tex]\textsf{3.} \quad y=-x-2[/tex]

Reflection in the x-axis, then translated 2 units down.

[tex]\textsf{4.} \quad y=6x+1[/tex]

Vertical stretch by a factor of 6, then translated 1 unit up.

[tex]\textsf{5.} \quad y=x-11[/tex]

Translated 11 units down.

[tex]\textsf{6.} \quad y=8x[/tex]

Vertical stretch by a factor of 8.

[tex]\textsf{7.} \quad y=-\dfrac{1}{3}x[/tex]

Vertical stretch by a factor of 1/3, then a reflection in the x-axis.

The value of a in the exponential function is 4/5.

Given the exponential function is f(x)=a(3/2)ˣ.

An function may be a mathematical relation of the subsequent form: f(x)=aˣ. where x may be a variable, and a could be a constant called the exponential of the function.

When multiplying the any function by a constant, we may expand or shrink the function in the y-direction.

y=a(b)ˣ

If a>1 then the function will enlarge.

If a<1 then the function will shrink.

When a=4/5

Then 4/5<1 means the function would shrink.

When a=5/4

Then 5/4>1 means the function would enlarge.

When a=3/2

Then 3/2>1 means the function would enlarge.

When a=7/4

Then 7/4>1 means the function would enlarge.

Hence, the given function f(x)=a(3/2)ˣ would shrink when a=4/5.

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Answer:

4/5

Step-by-step explanation:

got it right

The length of GX is 13 and the value of ∠ABX is 22.

We know that the point at which the triangle's three interior angle bisectors converge is known as the incenter. It can be thought of as the intersection of the triangle's internal angle bisectors. Due to the junction point of the central axis being the center of the triangle's inscribed circle, this point will be equally spaced from each of the triangle's sides. The center of a triangle's inscribed circle, which is the biggest circle that can fit inside the triangle, is known as the incenter.

Given that EX = 4z + 1 and  XF = 2z + 7.

Since X is the incentre of this triangle ΔABC, EX = XF = GX.

Now, 4z + 1 = 2z + 7

i.e. 4z - 2z = 7 - 1

i.e. 2z = 6

i.e. z = 6/2 = 3

Then GX = 2 * 3 + 7 = 6 + 7 = 13

Also given that ∠ABC = 44°.

Since X is the incentre of this triangle ΔABC, ∠ABX = ∠CBX

Let ∠ABX = ∠CBX = y

Now y + y = 44

i.e. 2y = 44

i.e y = 44/2 = 22

Then ∠ABX = 22°

Therefore, the length of GX is 13 and the value of ∠ABX is 22°.

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Si cada jugador tiene un total de 2 canicas y hay 5 jugadores, se espera que el número total de canicas sea 10.

Multiplica el número de canicas por el de jugadores:

Este factor se puede descomponer así:

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To solve a simultaneous equation on a graph, it is important to:

This refers to the diagram that is used to show the relationship between variables that are measured along a pair of axes.

Hence, we can see that your question is incomplete so I gave you a general overview to help you get a better understanding of the given concept.

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Answer:

Graph for (x^4+x-1)/(x-1)

Step-by-step explanation:

Graph for (x^4+x-1)/(x-1)

The required, divide is given by [tex]=x^3+x^2+x+2+\frac{1}{x-1}[/tex]

Fraction of polynomial is, in the numerator and in the denominator of a fraction there is polynomial function

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

[tex]=x^3+x^2+\frac{x^2+x-1}{x-1}\\[/tex]

[tex]=x^3+x^2+x+\frac{2x-1}{x-1}\\[/tex]

[tex]=x^3+x^2+x+2+\frac{1}{x-1}[/tex]

Thus the required, divide is [tex]=x^3+x^2+x+2+\frac{1}{x-1}[/tex].

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The line with an equation of y = x have a slope of 1 and y intercept of 0.

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

The standard equation of a line is given as:

y = mx + b

Where m is the slope of the line and b is the y intercept.

The line with an equation of y = x have a slope of 1 and y intercept of 0.

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Answer:

40/41

Step-by-step explanation:

cos = adjacent/hypotenuse

adj = 40, hyp = 41

It looks like your equations are

7M - 2t = -30

5t - 12M = 115

Solving by substitution

Solve either equation for one variable. For example,

7M - 2t = -30   ⇒   t = (7M + 30)/2

Substitute this into the other equation and solve for M.

5 × (7M + 30)/2 - 12M = 115

5 (7M + 30) - 24M = 230

35M + 150 - 24M = 230

11M = 80

M = 80/11

Now solve for t.

t = (7 × (80/11) + 30)/2

t = (560/11 + 30)/2

t = (890/11)/2

t = 445/11

Solving by elimination

Multiply both equations by an appropriate factor to make the coefficients of one of the variables sum to zero. For example,

7M - 2t = -30   ⇒   -10t + 35M = -150 … (multiply by 5)

5t - 12M = 115   ⇒   10t - 24M = 230 … (multiply by 2)

Now combining the equations eliminates the t terms, and

(-10t + 35M) + (10t - 24M) = -150 + 230

11M = 80

M = 80/11

It follows that

7 × (80/11) - 2t = -30

560/11 - 2t = -30

2t = 890/11

t = 445/11

Answer:

Step-by-step explanation:

A rational number can be in the form of a whole/natural number, integers, fractions and recurring decimals

In this case, 5 is a whole number, integer (can be a fraction too) , and of course, is a rational number.

As of which options to choose, read the above sentence carefully :)

Answer:

Natural, Integer, Rational, Whole

Step-by-step explanation:

First, we should know the definition of the word choices.

1) Natural Numbers: We can also count it as 'counting numbers'. Natural numbers are numbers that are a whole excluding the number 0. Some examples are 1, 2, 3, 4, 5 ... and so on.

2) Irrationals: They are numbers that cannot be written in a fraction form. Some examples are [tex]\sqrt{2} , \sqrt{3} , \sqrt{4} , \pi ...[/tex] etc.

3) Integers: They are a whole number that can be a negative, positive, or even a zero. Natural numbers are included in integers. Examples are -2, -1, 0, 1, 2, and so on.

4) Rationals: They are numbers that can be expressed in a fraction form, so it is the opposite of 'irrationals'. Examples are -1/2, 1/2, 2/4, 2/1 ... etc.

5) Whole Numbers: They are numbers that aren't a fraction. It can only be a positive number and a zero, so some examples would be 0, 1, 2, 3, 4, 5 ... and so on.

With these in mind, we can now solve the question. The number 5 is a natural, integer, rational, and a whole number.

Answer:

AB = 14

Step-by-step explanation:

We can add the segments together to find the total

AB + BC = AC

This will allow us to find x

4x+2 + 3x-1 = 22

Combine like terms

7x +1 = 22

Subtract 1 from each side

7x+1-1 = 22-1

7x = 21

Divide by 7

7x/7 = 21/7

x = 3

Now we can find the length of AB

AB = 4x+2 = 4(3)+2 = 12+2 = 14

the probability of making a Type I error is equal to the significance level of power. To increase the probability of a Type I error, increase the significance level. Changing the sample size has no effect on the probability of a Type I error.

The electricity of a take a look at can be expanded in a number of methods, for example increasing the pattern length, reducing the standard errors, increasing the difference between the pattern statistic and the hypothesized parameter, or growing the alpha degree.

The chance of creating a kind I mistakes is α, that's the extent of importance you put for your hypothesis check. An α of 0.05 indicates which you are inclined to accept a five% chance which you are incorrect whilst you reject the null hypothesis. To lower this risk, you have to use a decrease cost for α

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El número máximo de ocupantes es el máximo común divisor de los dos números, es decir, 10 personas por cabaña. Se debe pagar siete cabañas para minimizar costes.

En esta pregunta desconocemos la capacidad de cada cabaña, solo conocemos que todas las cabañas tienen el mismo aforo. En consecuencia, puede haber más de una respuesta, aunque con la restricción de que cada cabaña tiene el mismo número de hospedados.

Inicialmente, descomponemos factorialmente los números de adultos y niños:

Niños

40 = 2³ × 5

Adultos

30 = 2 × 3 × 5

El número máximo de ocupantes por cabaña es el máximo común divisor de los dos números, es decir, 2 × 5 = 10. Por tanto, los excursionistas deben pagar siete cabañas para minimizar costes.

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The statement which correctly compares the two functions is that: A. they have the same y-intercept and the same end behavior as x approaches ∞.

A function is a mathematical expression which can be used to define and show the relationship that exist between two or more variables in a data set.

By critically observing the graph which models the function f (see attachment), we can logically deduce that the y-intercept is at four (4).

Also, from the table of function g (see attachment), we have:

At x = 0, g(x) = g(0) = 4.

In conclusion, the statement which correctly compares the two functions is that they have the same y-intercept and the same end behavior as x approaches infinity (∞).

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Complete Question:

The graph of function f is shown.

Which statement correctly compares the two functions?

A. They have the same y-intercept and the same end behavior as x approaches ∞.

B. They have different x- and y-intercepts but the same end behavior as x approaches ∞.

C. They have the same x- and y-intercepts.

D. They have the same x-intercept and the same end behavior as x approaches ∞.

Answer: 94

Step-by-step explanation:

The area of each of the top and bottom face is [tex](4)(6)-(2)(2)=20[/tex].

The area of each of the side faces is 12.

The area of each of the faces facing out is 6.

The area of each of the 3 'inner' faces is also 6.

Adding these together,

[tex]20(2)+12(2)+6(2)+6(3)=94[/tex]

Answer:

kskwnneokjwonannwknwonw

Answer:

Hence we prefer FOIL method when multiplying two binomials.

Step-by-step explanation:

Explanation

Thus an approximate 95% confidence interval for the average enrollment of all 60,000 faculty members in the two years prior to the survey. which implies that the given statement is true.

According to the statement

Average sample =3700

SD sample =6500

Sample size =400

EV average =3700

SE average =325

Population size =3000

The boundaries of the 68% confidence interval are then 1 standard error from the estimated average:

EV average+1⋅SE average ​=3700+1⋅325=3700+325=4025

EV average−1⋅SE average =3700−1⋅325=3700−325=3375

Thus an approximate 95% confidence interval for the average enrollment of all 60,000 faculty members in the two years prior to the survey. which implies that the given statement is true.

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The measure in radians for the central angle of the circle is; 0.9 radians.

Since, the length of the arc is given as 7.2cm and it's radius is 8cm.

It follows that the angle measure of the central angle can be evaluated as follows;

7.2 = (A/6.28) × 2× 3.14 × 8

7.2 = 8A

A = 7.2/8

A = 0.9 radians.

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The value of the 1 mile is equal to 5280 feet

We have given that,

The problem involves a conversion from feet to miles.

We have to determine how many feet are in one mile.

Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.

1 mile is equal to 5280 feet

Therefore we get,

1mile=5280 feet.

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The area of regular hexagon is 166.27688 inch².

The area is the amount of space within the perimeter of a 2D shape.

Given:

side = 8 inch

Using

Area of regular hexagon = 3 √3/2 * a²

= 3 √3/2 * 8*8

=96√3

= 166.27688 inch²

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The difference between the retail and wholesale unit price is $ 0.99.

The retail price is the price that the item is sold for to the customer.

Here,

Coordinates extracted from the graph;

(4, 1)     (12, 3)

Equation of straight line (Whole sale price)

(y - y₁) = m(x - x₁)                  

where, m = (y₂-y₁)/(x₂-x₁)

then, m = (3-1) / (12-4)

            = 2/8

           = 1/4

Now,   (y - 1) = 1/4 (x - 4)

           4y - 4 = x - 4

            x = 4y

            x - 4y = 0

Now, whole sale price for 24 boxes; x = 24

           24 - 4y = 0

            4y = 24

             y = 24/4

             y = 6

The wholesale price = $ 6

The retail price = $ 6.99

The difference between retail and wholesale = Retail - Wholesale

                                                                            = 6.99 - 6

                                                                            = $ 0.99

Thus, the difference between the retail and wholesale unit price is $ 0.99.

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The tax paid by Rebecca on each cupcake was $0.15 or 15 cents, in the buying of 15 cupcakes for $47.25, where the cost of each was $3 plus taxes.

The tax is the amount paid to the government for buying and selling of goods are services.

In the question, we are informed that Rebecca bought 15 cupcakes, where each cupcake cost $3 plus taxes and the total bill to Rebecca was $47.25.

It implies that the cost of 15 cupcakes along with their taxes = $47.25.

Therefore, the cost of 1 cupcake along with its taxes = $47.25/15 = $3.15.

The cost of 1 cupcake is given as $3 plus taxes.

The total cost of 1 cupcake was $3.15.

Thus, the tax on 1 cupcake = $3.15 - $3 = $0.15 = 15 cents.

Thus, The tax paid by Rebecca on each cupcake was $0.15 or 15 cents, in the buying of 15 cupcakes for $47.25, where the cost of each was $3 plus taxes.

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solution:

1€=1.50

$x=€40

By using chain rule

1 × x =1.50×40

so,x=60

Hence,60 Australian $ can be exchanged from €1.5

Answer:

A. perimeter 200

   area         2356

B. Perimeter

C. Area

Step-by-step explanation:

A. Perimeter = 2(base+ height) = 2(62+38)= 200

BASE *HEIGHT (62*38)= 2356

Answer:

(a) Perimeter = 200 inches

    Area 2356 inches squared

(b) Area

(c) Perimeter

Step-by-step explanation:

(a) Perimeter = [tex]2(62+38)=200[/tex] inches

    Area = [tex]38\times62=2356[/tex] inches squared

(b) Area (rectangle)

(c) Perimeter (line)

Answer:Answer: We know it has a length of 10 cm, and the width is h times 2.

Step-by-step explanation: So the equation we should write is volume = 10 x (h x 2) x h.

Step-by-step explanation: