Define what an inverse function is in terms of domain and range.

and

Define what a function is in terms of domain and range.

Answer:

im not sure

Step-by-step explanation:

Answer:

All real numbers

Step-by-step explanation:

The domain of this is all real numbers.  The x values will never keep going down (to negative infinity) and will also never stop growing (to positive infinity).

The domain of a function consists of all possible input values. For a student's major (X), it includes all university majors, for the number of classes taken (Y), it's non-negative integers up to a maximum number, and for the amount spent on books (Z), it's any non-negative real number. X, Y, and Z are random variables as they are determined after an experiment like a survey.

The domain of a function refers to the set of all possible input values that the function can accept. For the cases given:

X, Y, and Z are considered random variables because their values are determined by the outcome of some experiment or random process, like a survey or an academic semester, and are only known once that process is complete. If Z were to equal -7, that would not be a possible value because you cannot spend a negative amount on books; hence, Z must always be non-negative.

Two essential characteristics of a discrete probability distribution include a finite or countably infinite set of values, and the sum of probabilities of all possible values must equal 1.

Considering a geometric experiment, such as drawing cards from a 52-card deck until a specific card is drawn:

Answer:

Part 41) The solutions are 3 and 1

Part 42) The solution is 2 only

Step-by-step explanation:

Part 41) we have

[tex]\left|5x-9\right|=x+3[/tex]

step 1

Find the first solution (case positive)

[tex]+(5x-9)=x+3[/tex]

[tex]5x-x=3+9[/tex]

[tex]4x=12[/tex]

[tex]x=3[/tex]

step 2

Find the second solution (case negative)

[tex]-(5x-9)=x+3[/tex]

[tex]-5x+9=x+3[/tex]

[tex]5x+x=9-3[/tex]

[tex]6x=6[/tex]

[tex]x=1[/tex]

therefore

The negative case was resolved incorrectly

The solutions are 3 and 1

Part 42) we have

[tex]\left|n-7\right|=3n-1[/tex]  

step 1

Find the first solution (case positive)

[tex]+(n-7)=3n-1[/tex]    

[tex]3n-n=-7+1[/tex]

[tex]2n=-6[/tex]

[tex]n=-3[/tex]

Verify

For n=-3

substitute

[tex]\left|-3-7\right|=3(-3)-1[/tex]

[tex]\left|-10\right|=-9-1[/tex]  

[tex]10=-10[/tex]   ------> is not true

therefore

[tex]n=-3[/tex] -------> is not a solution

step 2

Find the second solution (case negative)

[tex]-(n-7)=3n-1[/tex]

[tex]-n+7=3n-1[/tex]

[tex]3n+n=7+1[/tex]

[tex]4n=8[/tex]

[tex]n=2[/tex]

therefore

The solution is 2

orthogonal = perpendicular.

an altitude in a triangle is the perpendicular distance stemming from a vertex.

where all these orthogonal segments meet is the ORTHOcenter.

The described point M is a Orthocenter.

"The orthocenter is the point where all the three altitudes of the triangle cut or intersect each other. Here, the altitude is the line drawn from the vertex of the triangle and is perpendicular to the opposite side. Since the triangle has three vertices and three sides, therefore there are three altitudes."

"The orthocenter will vary for different types of triangles such as Isosceles, Equilateral, Scalene, right-angled, etc. In the case of an equilateral triangle, the centroid will be the orthocenter. But in the case of other triangles, the position will be different. Orthocenter doesn’t need to lie inside the triangle only, in case of an obtuse triangle, it lies outside of the triangle."

In this figure, the altitudes of triangle JKL is given.

Since, these are altitudes they interest each other at orthocenter.

Hence, A is the correct answer.

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Answer:

It is 27.35 ft up the house

Step-by-step explanation:

The hypotenuse of the right triangle is 28  and the base is 6

We can use the pythagorean theorem to find how high it is

a^2 + b^2 = c^2

6^2 + b^2 = 28^2

36 + b^2 = 784

Subtract 36 from each side

36-36 + b^2 = 784-36

b^2 = 748

Take the square root of each side

b =sqrt(748)

b =27.34958866

It is 27.35 ft up the house

Answer:

  80 in.

Step-by-step explanation:

The dimensions of the dilated picture are ...

  4·4 in = 16 in . . . by . . . 4·6 in = 24 in

Then the perimeter of the painting is the sum of the lengths of its sides ...

  16 in + 24 in + 16 in + 24 in = 80 in

Answer:

80in

Step-by-step explanation:

The scale factor of the dilation is 4, so a 1 inch by 1 inch square on the photograph represents a 4 inch by 4

inch square on the painting.

The height of the image is the product of the height of the preimage and the scale factor.

w=4(6)=24

in

.

The width of the image is the product of the width of the preimage and the scale factor.

h=4(4)=16

in

.

So, the perimeter is

P=2(16)+2(24)=80

in

.

The figure shows two rectangles. The larger rectangle is 16 inches long and 24 inches wide. The smaller rectangle is 4 inches long and 6 inches wide. The sides of the larger rectangle are parallel to the corresponding sides of the smaller one, respectively.

Therefore, the perimeter of the painting is 80

inches.

(sin x)/(1-cosx) + sinx/(1-cosx) =

2 csc x

We have like denominators.

Just add the numerators.

(2 sin x)/(1 - cos x) = 2 csc x

[1/(1 - cos x)](2 sin x) = 2 csc x

Take it from here.

Answer:

a ) sin x ( \frac{sinx}{cosx}*cosx- \frac{cosx}{sinx}+*cos x)= \\ sinx(sinx- \frac{cos^{2} x}{sin^{2} x})=
sin^{2}x-cos^{2} x=1-cos^{2}x-cos^{2} x= \\ 1-2cos^{2}x    

b ) 1 +  \frac{1}{cos^{2} x} *sin^{2} x=1+ \frac{sin^{2} x}{cos^{2} x} = \\  \frac{cos {2} x+sin x^{2} x}{cos^{2} x} = \frac{1}{cos^{2} x} =sec^{2} x

c) \frac{sinx}{1-cosx} + \frac{sinx}{1+cosx}= \frac{sin x ( 1+cosx)+sinx(1-cosx)}{1-cos^{2} x} = \\  \frac{sinx+sinxcosx+sinx-sinxcosxx}{1-cos^{2}x }= \\  \frac{2sinx}{sin^{2} x}   =  \frac{2}{sinx}=2 csc x  

d) -tan ^{2}x+sec ^{2}x=- \frac{sin ^{2} x}{cos ^{2} x} + \frac{1}{cos^{2} x} = \\  \frac{1-sin^{2x} }{cos ^{2}x }= \frac{cos^{2} x}{cos^{2}x }  =1  

Step-by-step explanation:

The number tab allows percentage symbol in the spreadsheet which corresponds to option B.

To display the total percentage symbol in the spreadsheet, Diane should select the Numbers tab in the Format Cells dialog box. This tab allows her to customize the display of numbers and apply percentage formatting.

Answer:

2 out of 5 or 6 out of 15

Step-by-step explanation:

In this pattern, there is two people ordering it every five times. You can write it out as 6/15 or simplify it as 2/5 (six-fifteenths and two-fifths)

The simulated probability that a customer will order the small beverage is:

                 [tex]\dfrac{2}{5}=0.4[/tex]

The  1, 2, and 3 to represent small, medium, and large, respectively.

The simulation is as follows:

2   2   3   1   1   2   2   3   1   1    3    2   1    1    3

There are a total outcomes= 15

Also, the number of outcomes that the customer will order small beverage is: 6

( Since,  6 times such that 1 has occurred.

As 1 represent the simulation that the beverage comes in small size )

Hence, the simulated probability is:

       [tex]\dfrac{6}{15}=\dfrac{2}{5}=0.4[/tex]

Answer:

  Kira used published data that is quantitative

Step-by-step explanation:

Online census data is published data. It is numerical by nature, hence quantitative.

Answer:

Kira used published data that is quantitative.

Step-by-step explanation:

Firstly, we need to identify if the data is qualitative or quantitative.

The data is average number of people living in the homes.

Qualitative data as its name indicates is an attribute or characteristic. It can not be measured e.g color. Quantitative data is such a data which can be counted or measured.

Since the average number of people can be counted and measured, the data is Quantitative.

In an observational study the individuals are observed. In the given case, Kira did not observed the individuals to gather the data, rather she used an Online resource to gather the data.

Therefore, the correct answer will be:

Kira used published data that is quantitative.

Answer:

is this multiplication?

if so, 4.33

Step-by-step explanation:

just use division:

15.57/3.6=4.325 or rounded to two decimal places 4.33

Answer:

x = 1 and y = -4

Step-by-step explanation:

It is given that,

-2x = 2 + y

-2x - y = 2 ---(1)

-6x - y = -2   ----(2)

To find the solution of equations

Step 1: Subtract eq(2) from eq(1)

-2x - y = 2 ---(1)

-6x - y = -2  ----(2)

4x + 0 = 4

x = 4/4 = 1

Step 2: Substitute the value of x in eq (1)

-2x - y = 2 ---(1)

-2*1 - y = 2

-2 - y = 2

y = -2 - 2 = -4

Therefore x = 1 and y = -4

Answer:

i need it too

Step-by-step explanation:

Answer:

  3 1/3 ft²/h

Step-by-step explanation:

To find the unit rate, divide square feet by hours:

(5/6 ft²)/(1/4 h) = (5/6)(4/1) ft²/h = 10/3 ft²/h = 3 1/3 ft²/h

Answer:

The slope is 3

Step-by-step explanation:

The formula for finding slope is change in y over change in x. Also known as rise over run. Go up 3 and go right 1 to get from one point to the next.

Answer:

=3

Step-by-step explanation:

Lets consider any 2 points on the line such as (0,2)  and  (1,5).

The slope of a line = Δy/Δx

Δy = y₂-y₁

Δx = x₂-x₁

y₁=2

y₂=5

x₁=0

x₂= 1

we can now use these values from the two points on the line.

Gradient= (5-2)/(1-0)

=3

Answer:

The point is (3 , 6)

Step-by-step explanation:

* Lets explain how to solve this problem

- We want to reflect the point (x , y) across the line y = a, where a

 any constant

- The line y = a is a horizontal line, means parallel to x-axis

- We will change the y-coordinates only because we will move

 up and down

- We will move the point and the line by a units down if a is positive

 or up if a is negative to make the line is the x-axis and also move the

 point by a units as the line

- Then we will reflect the new point across the x-axis means we will

  change the sign of y-coordinate

- After that we will add the value of a again to the y-coordinate to

 the point after reflection

* Lets solve the problem

∵ The point is (3 , 4)

∵ The point will reflect across the line y = 5

- We take the line 5 units down to be the x-axis and also we will take

 the point down 5 units

∴ The point = (3 , 4 - 5) = (3 , -1)

- Now reflect the point across the x-axis by change the sign of the

 y-coordinate

∴ The new point is (3 , 1)

- Now add the y-coordinate of the new point the 5 units which we

 subtracted before

∴ The image of the point P after reflection across the line y = 5 is

  (3 , 1 + 5) = (3 , 6)

* The point is (3 , 6)

Answer:

The smaller the sample of people Percy observes, the easier it is to not match the percentage given in the table.

Answer:The smaller the sample of people Percy observes, the easier it is to not match the percentage given in the table.

Step-by-step explanation:

The smaller the sample of people Percy observes, the easier it is to not match the percentage given in the table.

Answer:

  Let (x+1) = the larger number

Step-by-step explanation:

Two consecutive numbers differ by 1. The larger is 1 more than the smaller. The expression for 1 more than x is (x+1).

Answer:

[tex]\large\boxed{d.\ -16\dfrac{2}{3}}[/tex]

Step-by-step explanation:

[tex]-3x=50\qquad\text{divide both sides by (-3)}\\\\\dfrac{-3x}{-3}=\dfrac{50}{-3}\\\\x=-16\dfrac{2}{3}[/tex]

Answer:

B. T–5,0 ∘ R0,90°(x, y)

Step-by-step explanation:

Just took Quiz.

Transformation involves changing the size and position of a shape.

The transformation rule from DEF to D"E"F is [tex]\mathbf{(b)\ T-5,0 \circ R0,90^o(x, y)}}[/tex]

From the complete question (see attachment), we have the following observations.

The 90 degrees counterclockwise rotation is represented as:

[tex]\mathbf{R0,90^o(x, y)}[/tex]

The left translation by 5 units is represented as:

[tex]\mathbf{T-5,0(x, y)}[/tex]

When both transformations are combined, we have:

[tex]\mathbf{T-5,0 \circ R0,90^o(x, y)}}[/tex]

Hence, the transformation rule from DEF to D"E"F is [tex]\mathbf{(b)\ T-5,0 \circ R0,90^o(x, y)}}[/tex]

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Answer:

  diameter = m - c

Step-by-step explanation:

In ΔABC, let ∠C be the right angle. The length of the tangents from point C to the inscribed circle are "r", the radius. Then the lengths of tangents from point A are (b-r), and those from point B have length (a-r).

The sum of the lengths of the tangents from points A and B on side "c" is ...

  (b-r) +(a-r) = c

  (a+b) -2r = c

Now, the problem statement defines the sum of side lengths as ...

  a+b = m

and, of course, the diameter (d) is 2r, so we can rewrite the above equation as ...

  m -d = c

  m - c = d . . . . add d-c

The diameter of the inscribed circle is the difference between the sum of leg lengths and the hypotenuse.

Answer:

Required probability = 1/6

Step-by-step explanation:

It is given that,

A red die is tossed the a green die is tossed

The possible outcomes of getting number greater than three when tossing red die  are, 4, 5, and 6

The probability of tossing red die = 3/6

The possible outcomes of getting number less than three when tossing green die  are 1 and 2

Probability of tossing green = 2/6

To find the required probability

Probability of getting red die shows greater than three and gree die shows less than three = (3/6)*(2/6) = 1/6

Variance

The standard deviation is related to the variance. The standard deviation measures the variation or dispersion of a set of data and is represented by the Greek letter sigma [tex]\sigma[/tex], while the variance measures how far a set of  numbers are spread out from their average value. The variance is obtained by squaring the standard deviation, so the variance can be found as [tex]\sigma^{2}[/tex]

given that 1 ox eats as much as 10 sheep:

4 oxen = 40 sheep

therefore,

first farmer:  the equivalent of 40 sheep

second farmer:  30 sheep

that means 30+40 = 70 animals eating

$140 ÷ 70 = $2

so it is $2 per eat

2 x 40 = $80 for the first farmer's oxen

2 x 30 = $60 for the second farmer's sheep

Answer:

$80

Step-by-step explanation:

Since if 1 ox is equal to 10 sheep, then the first farmer posesses the equivalent of 40 sheep. With 70 sheep in total, then one sheep is worth 2 dollars. The first farmer has a total of 4 oxen, equivalent to 40 sheep. 40 times 2 is 80, so the answer is 80 dollars

Answer:

Step-by-step explanation:

If you want to compare the 2 slopes, you first have to know what they are.  From the table we can find it by plugging in some numbers to the slope formula and doing the math on it:

[tex]m=\frac{-10-(-15)}{0-(-1)}[/tex]

which gives us a slope of 5.

From the equation, which is in y = mx + b form, m stands for slope.  The number in the m position is 2.  In a sentence:

The slope found in the values from the table, 5, is greater than the slope found in the linear equation, 2.

Part B:  The y-intercept exists where x = 0.  Looking at the values in the table, where x = 0, y = -10.  So the y-intercept of the line in the table is -10.  In y = mx + b, the linear equation, 8 = b, which is also the y-intercept.  So the y-intercept in the table is -10 and the y-intercept in the equation is 8.  The y-intercept is greater in the equation than in the table because 8 is greater than -10

Answer:

200 CDs

Step-by-step explanation:

80 is 40% of 200

40% - 80

100% - x

[tex]x=\dfrac{100\%\cdot80}{40\%}=200[/tex]

200 CDs

Answer:

[tex]110x+29y=333[/tex]

Step-by-step explanation:

Will's meal of grilled chicken strips and carrots contained a total of 333 calories.

The bag of grilled chicken strips contained x servings of 110 calories each, making total 110x.

The bag of carrots contained y servings of 29 calories each making total 29y.

So, the equation that represents the number of servings of chicken strips and carrots that Will may have eaten

[tex]110x+29y=333[/tex]

Answer:

  46°

Step-by-step explanation:

When secants intersect each other and a circle, the external angle (A) is half the difference of the intercepted arcs:

  ∠A = (arcDC -arcBC)/2

  12° = (arcDC -22°)/2 . . . . . . . fill in the given numbers

  24° = arcDC -22° . . . . . . . . . multiply by 2

  46° = arcDC . . . . . . . . . . . . . add 22°

Answer:

5 = 2x + 1

Step-by-step explanation:

let James be x , then 1 mile more than twice number of mile of James will be 2x + 1 therefore the total number of miles biked by carolina will be 2x + 1 = 5

The equation 5 = 1 + 2x represents the number of miles Jack biked, option fourth is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let x be the number of miles James biked.

Then, according to the problem:

Carolina biked 1 mile, more than twice the number of miles James biked.

5 =  1 + 2x  (as the Carolina biked a total of 5 miles)

Thus, the equation 5 = 1 + 2x represents the number of miles Jack biked option fourth is correct.

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