Rectangle ABCD is given by these coordinates: A(4,1), B(2,3), C(5,6), D(7,4). Select all the transformations that will carry the rectangle onto itself. First option: a rotation 270° counterclockwise, then a rotation 90° counterclockwise Second option: a translation 10 units left, 5 units down, 10 units right, and 5 units up Third option: a reflection across the y-axis, then a rotation 270º counterclockwise about the origin Fourth option: a reflection across the x-axis, then a translation 5 units left, then a reflection across the y-axis, then a translation 5 units right Fifth option: a reflection across the y-axis, then a translation 9 units right
Given the rectangle ABCD, whose vertices are:
[tex]A\mleft(4,1\mright),B\mleft(2,3\mright),C\mleft(5,6\mright),D\mleft(7,4\mright)[/tex]You can apply the transformations shown in each option, in order to determine all the transformations that will carry the figure onto itself:
• First option:
By definition, the rule for a rotation of 270 degrees counterclockwise is:
[tex](x,y)\rightarrow(y,-x)[/tex]And the rule for a rotation of 90 degrees counterclockwise is:
[tex](x,y)\to(-y,x)[/tex]Therefore, you can choose any vertex of the rectangle and apply the first rule and then the second rule:
[tex]A\mleft(4,1\mright)\rightarrow A^{\prime}\mleft(1,-4\mright)\rightarrow A^{\doubleprime}\rightarrow(4,1)[/tex]Notice that the coordinates of point A'' are equal to the original point A.
• Second option:
The rule for a translation of 10 units left and 5 units down is:
[tex](x,y)\rightarrow(x-10,y-5)[/tex]And the rule for a translation of 10 units right, and 5 units up is:
[tex](x,y)\rightarrow(x+10,y+5)[/tex]Then, applying the transformations indicated, you get:
[tex]\begin{gathered} A\mleft(4,1\mright)\rightarrow A^{\prime}(4-10,1-5)=A^{\prime}(-6,-4) \\ \\ A^{\prime}(-6,-4)\rightarrow A^{\prime\prime}(-6+10,-4+5)=A^{\doubleprime}(4,1) \end{gathered}[/tex]Notice that point A'' and point A are equal.
• Third option:
The rule for a reflection across the y-axis is:
[tex](x,y)\rightarrow\mleft(-x,y\mright)[/tex]Then, applying that transformation and then applying the rule for a rotation of 270 degrees counterclockwise about the Origin (shown in the explanation of the First option), you get:
[tex]A(4,1)\rightarrow A^{\prime}(-4,1)\rightarrow A^{\doubleprime}(1,4)[/tex]The points A and A'' are different.
• Fourth option:
The rule for a reflection across the x-axis is:
[tex](x,y)\rightarrow(x,-y)[/tex]For a translation of 5 units left is:
[tex](x,y)\rightarrow(x-5,y)[/tex]And for a translation of 5 units right:
[tex](x,y)\rightarrow(x+5,y)[/tex]Therefore, knowing those rules and also knowing the rule for a reflection across the y-axis, you can apply all the transformations indicated in the third option, you get:
[tex]A\mleft(4,1\mright)\rightarrow A^{\prime}\mleft(4,-1\mright)\rightarrow A^{\doubleprime}(4-5,-1)=A^{\doubleprime}(-1,-1)[/tex][tex]A^{\doubleprime}(-1,-1)\rightarrow A^{\doubleprime}^{\prime}(1,-1)\rightarrow A^{\doubleprime\prime^{\prime}}(6,-1)[/tex]Notice that the points A and A'''' do not have the same coordinates.
• Fifth option:
Knowing the rule for a reflection across the y-axis, and knowing that to translate a point 9 units right you must add 9 to the x-coordinate of the points, you get:
[tex]A\mleft(4,1\mright)\rightarrow A^{\prime}\mleft(-4,1\mright)\rightarrow A^{\doubleprime}(-4+9,1)=A^{\doubleprime}(5,1)[/tex]Notice that the points A and A'' do not have the same coordinates.
Hence, the answers are:
• First option.
,• Second option.
Which relations are functions?
The most appropriate choice for functions will be given by -
First and second options are correct
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here Domain of function is obtained from x axis and range of the function is obtained from y axis
For the first option
Every element of domain has a unique image
So first graph is a function.
First option is correct
For the second option
Every element of domain has a unique image
So second graph is a function.
Second option is correct
For the third option
x = 3 has been mapped to every element of y axis
So ]x = 3 has infinite number of images.
Third graph is not a function.
Third option is wrong
For the fourth option
Every point on x axis has been mapped to two elements
So every element of x axis has two images.
Fourth graph is not a function
Fourth option is wrong.
So First and second option are correct
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y = (x - 2)² -6
What is the vertex?
Which represents the inverse of the function f(x) = 4x?Oh(x) = x + 4O h(x) = x - 4Oh(x) =O h(x) = x
Let y=f(x). To find the inverse of f, isolate x:
[tex]\begin{gathered} f(x)=4x \\ \Rightarrow y=4x \\ \Rightarrow x=\frac{1}{4}y \end{gathered}[/tex]Let x=f^{-1](y). Then:
[tex]f^{-1}(y)=\frac{1}{4}y[/tex]Evaluate the inverse of f at y=x:
[tex]f^{-1}(x)=\frac{1}{4}x[/tex]Therefore, the rule of correspondence of the inverse of f is given by the expression:
[tex]\frac{1}{4}x[/tex]Complete the proof below that utilizes the Triangle Inequality Theorom.
1. Firstly, statement 1 is given in the question.
[tex]\bar{PL}\left|\right|\bar{MT}\text{ }\rightarrow\text{ 1. Given}[/tex]2. When two lines cut through two parallel lines, the alternate interior angles are congruent(equal)
So;
[tex]\measuredangle P\cong\measuredangle T\text{ }\rightarrow\text{ Alternate interior angles are equal}[/tex]3. Given
4. PK = KT
Since K is the mid point of PT as stated in the question, then PK will be of equal length as KT.
[tex]PK=KT\text{ }\rightarrow\text{ Since K is the midpoint of }\bar{PT}[/tex]5. Vertically opposite angles are equal.
So;
[tex]\measuredangle PKL=\measuredangle TKM\text{ }\rightarrow\text{ Vertical angles Theorem}[/tex]6. when two corresponding angles and the included side are respectively equal, a triangle is said to be congruent.
[tex]\Delta PKL\cong\Delta TKM\text{ }\rightarrow\text{ Congruent triangles (SAS- two sides and one including side are equal)}[/tex]7. The Triangle Inequality theorem states that the sum of two sides of a triangle is greater than the third side.
[tex]PK+KL>PL\text{ }\rightarrow\text{ Triangle Inequality Theorem}[/tex]8. CPCTC means that Corresponding Parts of Congruent Triangles are Congruent.
The corresponding sides of the two congruent triangles are;
[tex]\begin{gathered} \bar{KL}=\bar{KM} \\ \bar{PK}=\bar{KT} \\ \bar{PL}=\bar{MT} \end{gathered}[/tex]So;
[tex]\begin{gathered} \bar{KL}=\bar{KM}\text{ .} \\ \bar{PK}=\bar{KT}\text{ }\rightarrow\text{ CPCTC} \\ \bar{PL}=\bar{MT}\text{ .} \end{gathered}[/tex]9. The final one is a conbination of CPCTC and Triangle Inequality theorem
[tex]\bar{PK}+\bar{KM}>\bar{PL}\text{ }\rightarrow\text{ since }PK+KL>PL\text{ and }\bar{KL}=\bar{KM}[/tex][20 points]Practice analyzing stretches and shrinks of exponential
functions.
Consider the exponential function f(x) = 2(3¹) and its
graph.
ty
8
The initial value of the function is
The base of the function is
The function shows exponential
The function's initial value is 2, its base value is 3, and it exhibits exponential growth.
What is meant by initial value?An initial value of a function denotes the function's y-intercept. The constant of an equation can also be used to find initial values. Understanding the y-intercept will help you with graph functions. Substitute 0 0 for x x and solve for y y to confirm the initial value. A differential equation with some initial conditions is used to solve an initial value problem. For instance, with initial conditions y(0)=1, dy/dx = x. An initial value problem (IVP) in multivariable calculus is an ordinary differential equation with an initial condition that specifies the value of the unknown function at a given point in the domain. In physics or other sciences, modeling a system frequently entails solving an initial value problem.To learn more about initial value, refer to:
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Find the value of x in each case.
The variable x has a value of 22.5 degrees
What are angles?Angles are the measure of space when two or more lines intersect.
How to determine the value of x?The figure represents the given parameter
On the figure, we have the following angle measures
AED = 2x
BEF = 4x
EBC = 6x
Using the above as a guide, we have the following angle measures
BAE = AED = 2x ---- Corresponding angles
BEA = 180 - BEF ---- Angle on a straight line
BEA = 180 - 4x
ABE = 180 - EBC ---- Angle on a straight line
ABE = 180 - 6x
The sum of angles in a triangle is 180
So, we have
BAE + BEA + ABE = 180
This gives
2x + 180 - 4x + 180 - 6x = 180
Evaluate the like terms
-8x = -180
Divide both sides by -8
x = 22.5
Hence, the measure of x is 22.5
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x - 0.1x = 54solve for x
The equation to solve:
[tex]x-0.1x=54[/tex]We can subtract the like terms on the left hand side:
[tex]\begin{gathered} (1-0.1)x=54 \\ 0.9x=54 \end{gathered}[/tex]Now, we can divide both sides by 0.9 and solve for x. Shown below:
[tex]\begin{gathered} \frac{0.9x}{0.9}=\frac{54}{0.9} \\ x=60 \end{gathered}[/tex]The answer is
[tex]x=60[/tex]Answer: x = 60
Step-by-step explanation:
To solve for x, we will isolate the variable with simplifying and reverse operations.
Given:
x - 0.1x = 54
Subtract 0.1 from 1:
0.9x = 54
Divide both sides of the equation by 0.9:
x = 60
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y = 3900(0.937)
ANSWER
This function represents a decay. The rate of decrease is 6.3%
EXPLANATION
When the growth/decay factor is less than 1, the function represents a decay:
[tex]y=a(b)^x[/tex]b is the growth/decay factor.
For a function that represents decay, the decrease factor is:
[tex]b=1-r[/tex]where r is the rate of decrease. In this case, b = 0.937. We can find r:
[tex]\begin{gathered} 0.937=1-r \\ r=1-0.937 \\ r=0.063 \end{gathered}[/tex]To know the rate as a percentage, we have to multiply it by 100:
[tex]r=0.063\times100=6.3\text{ \%}[/tex]Predict using the equation of the trend line y=25X+150 what will the y value be when x =23?
Given the equation of the line :
[tex]y=25X+150[/tex]We need to find the value of y when x = 23
So, substitute with x = 23 at the given equation
[tex]\begin{gathered} y=25\cdot23+150 \\ y=575+150 \\ \\ y=725 \end{gathered}[/tex]So, the answer is : y = 725
Answer:
725
Step-by-step explanation:
Hello!
You can substitute 23 for x in the equation y = 25x + 150, to find the predicted y-value.
Solve for y
y = 25x + 150; x = 23y = 25(23) +150y = 575 + 150y = 725The value of y at x = 23 is 725.
How many ways can twelve jurors be assigned seats in the courtroom?
The number of ways to arrange 12 jurors willbe given as,
[tex]\begin{gathered} n!=(n-1)(n-2)! \\ W\text{here n is the number of jurors } \\ n=12 \end{gathered}[/tex]Therefore,
For 12 jurors we will have the number of ways as
[tex]\begin{gathered} 12!=12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1 \\ =479,001,600\text{ ways} \end{gathered}[/tex]Therefore,
12 jurors can be assigned seats in a courtroom in 479,001,600 ways
What is the word for added and subtracted parts of an expression
Answer:
Step-by-step explanation:
answer: terms
hope that is what you mean!
Determine if the pair of solids are similar. If NO explain
Given:
There are given that the two solid to find the similar or not.
Explanation:
To determine whether the solid pair are similar or not, we need to set their dimension with proportion.
So,
From the dimensions of solid:
The radius of the given solids is 14 yd and 4 yd.
The height of the solids is 20 yd and 6 yad.
Now,
We need to set the proportion:
[tex]\begin{gathered} \frac{14}{4}=\frac{7}{2} \\ \frac{20}{6}=\frac{10}{3} \end{gathered}[/tex]So,
[tex]\frac{7}{2}\ne\frac{10}{3}[/tex]Final answer:
Hence, the given pair of solid is not similar because their proportion has not equal.
Consider the function f(x) = 4 - 2x ^ 2 on the interval \ -6,6] Find the average or mean slope of the function on this interval , i.e. (f(6) - f(- 6))/(6 - (- 6)) =
f(x) = 4 -2x^2
First we need to find f(6)
f(6) = 4 - 2( 6) ^2 = 4 - 2(36) = 4 - 72 = -68
Then we need to find
f(-6) = 4 - 2( -6) ^2 = 4 -2( 36) = 4 - 72 = -68
Now we find the average or mean slope
The mean slope is zero
Now f'(c) must equal 0
The derivative is -4x and evaluated at c
-4c
This must be equal to 0
-4c =0
Solving for c
c=0
Solve in simplest form
-6x(-4/3)
Answer:
-6x(-4/3) in simplest form is 8x :)
−6x(−4/3)
=(−6/1)(−4/3)
=(−6)(−4)/(1)(3)
=24/3
=8x
Answer:
8x
Step-by-step explanation:
So, you have -6x(-4/3)
-4/3 could be written as a division problem, or we could just call it a fraction. And -6x is the same thing as -6x/1, so we can write that as a fraction as well. So, we multiply.
Numerators: -4 times -6=24, and we throw the x on, so we have 24x
Denominators: 3 times 1 = 3, so the denominator is 3
So, we have 24x/3, which simplifies to 8x
the architectures that group of elementary students and teachers from 32 schools who pick up trash at the Lock of parts
the answer is: each school picked up 12/128 tons
if I get the graph correct, every cross indicate the quantity under it. (an x above 1/8 means that there is 1/8 of a ton collected)
then, we need to add up the total amount of tons they collected.
we have 6 crosses in 1/8, 8 crosses in 1/4 and 2 crosses in 1/2. then we do:
[tex]6\cdot\frac{1}{8}=\frac{6}{8}=\frac{3}{4}[/tex][tex]8\cdot\frac{1}{4}=\frac{8}{4}=2[/tex][tex]2\cdot\frac{1}{2}=1[/tex]we add everithing:
[tex]\frac{3}{4}+2+1=3+\frac{3}{4}=\frac{12}{4}+\frac{3}{4}=\frac{15}{4}[/tex]the total amount of trash collected is 15/4 tons (3.75 tons)
there are 32 schools, then we need to divide the amount of trash by the amount of schools:
[tex]\frac{15}{4}\div32=\frac{15}{4}\cdot\frac{1}{32}=\frac{15}{4\cdot32}=\frac{15}{128}[/tex]every school got 15/128 tons of trash
Kristen make $16 per hour and worked 34 hours last week. How many dollars she made : Mark make $14 per hour and worked 46 hours last week. How many dollars he make :How many hours must Kristen and mark work in order for their pay/savings to be equal ?If Kristen and mark combine their saving how many they will have ?
first question
Kristen make $16 per hour
last week he worked for 34 hours
1 hour ==== $16
35 hours ==== $x
cross multiplication
x * 1 = 16 x 34
x = $544
Second question
for mark
make $14 per hour
he worked 46 hours last week
total amount made
1 hour ===== $14
46 hours =====$x
1 * x = 14 x 46
x = $644
Mark make $644 last week
for the fourth question
if mark and kristen combined their savings
mark make $644 and kristen make $544
their saving combines is
$644 + $544
= $1,188
Their saving combines is $1, 188
if mark works for 46 hours and make $644
if marks works for 34 hours and make $544
how many hours will they work
let the number of hours be x
equating the two equation
Simplify the expression.2.7 - 5.2n - 4n + 6= ? Help me solve this
To simplify the expression, we need to operate the like terms, then:
[tex]2.7-5.2n-4n+6[/tex][tex]2.7+6-5.2n-4n[/tex]Therefore:
[tex]8.7-9.2n[/tex]Matt has five times as many stickers as David. How many stickers must Matt give David so that they will each have 180 stickers?
Matt must give David 120 stickers
Explanation:Let the number of stickers that Matt has be m
Let the number of stickers that David has be d
If each of them ends up with 180 stickers each:
the total number of stickers available = 2(180)
the total number of stickers available = 360
Matt has 5 times has many stickers has David
m = 5d
Note that:
Matt's stickers + David's stickers = 360
m + d = 360
5d + d = 360
6d = 360
d = 360/6
d = 60
David has 60 stickers
m = 5d
m = 5(60)
m = 300
Matt has 300 stickers
The number of stickers Matt must give David so that they will each have 180 stickers = 300 - 180 = 120
Matt must give David 120 stickers so that they will each have 180 stickers
Consider the system of equations.x + 2y = 8-3x – 2y = 12How do you solve the system of equations with Cramer's rule? Drag a value or determinant expression into each box to correctly solve the system using Cramer's rule.
The solution to the system of equations using Cramer's rule is given by the image at the end of the answer.
How to solve a system of equations using Cramer's rule?The solution of a system of equations using Cramer's rule is based on the use of determinants of matrices.
In the context of this problem, the system is:
x + 2y = 8.-3x - 2y = 12.The matrix for the system is:
M =
[1 2]
[-3 - 2]
The determinant of the matrix M of the system is given as follows:
|M| = -2 + 6 = 4.
(using the standard procedure to obtain the determinant of a 2 x 2 matrix).
To find the matrix for x, the x-coefficients are replaced by the right-side coefficients, that is, the results of the operations, hence:
Mx =
[8 2]
[12 - 2]
Then the determinant is:
|Mx| = 8(-2) - 2(12) = -16 - 24 = -40.
The solution for x is:
x = -40/4 = -10.
To find the matrix for y, the y-coefficients are replaced by the right-side coefficients, that is, the results of the operations, hence:
My =
[1 8]
[-3 12]
The determinant is:
|My| = 12 - (-3)(8) = 12 + 24 = 36.
Hence the solution is:
y = 36/4 = 9.
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What is the cardinal number of the set H={}?
The set is empty that is null set, so the cardinal number is zero.
The cardinal number of a finite set A is the number of distinct members present in the set and it is denoted by n(A). The cardinal number of the empty set, Ø, is 0 because Ø has zero members or no members. so n(Ø) = 0. And the cardinal number of an infinite set, cannot be found because such a set has countless members.
for example
i) If A = (-3,-2,-1,0,1,2,3) then n(A)=7.
ii) If A = (x/x is a letter of the word HYDERABAD) then n(A) = 7 because writing in the tabular form, A = (H,Y,D,E,R,A,B)
Here, the set is empty that is null set, so the cardinal number is zero.
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Whats the answer to 2^3 A) 2 x 2 x 2 ???
ANSWER:
A) 2 x 2 x 2
STEP-BY-STEP EXPLANATION:
The exponent indicates the number of times the base is multiplied. If in this case, the exponent is 3 and the base is two, the equivalent expression would be:
2 x 2 x 2
So the correct answer is:
A) 2 x 2 x 2
Jim graduated in the top 6% of his class. If the mean was 585 and the standard deviation was 134, and the distribution was normal, what was Jim's Z-score?
Answer:
see below
Step-by-step explanation:
From a z-score table look for the value .9400 this would represent the top 6% From my table this is a z-score +1.56
hola me puede ayudar
La expresión dada es
[tex](a+b)+(-c+e)^2[/tex]Primero, desarollamos el producto notable a la derecha
[tex](a+b)+(e-c)^2=(a+b)+e^2-2ec+c^2[/tex]Por tanto, la expresión final es
[tex]e^2+a+b-2ec+c^2[/tex]Usando los valores a = 2, b = -1, c = 3, d = 1, y e = 5, tenemos
[tex]\begin{gathered} 5^2+2-1-2\cdot5\cdot3+3^2 \\ 25+1-30+9 \\ 35-30=5 \end{gathered}[/tex]Por tanto, la respuesta es 5.
Adults ate 3 1/2 pizzas and kids ate 7 1/8 pizzas. How many pizza eaten in total?
Answer:
10 5/8
Step-by-step explanation:
First, we want to convert the mixed fraction to an improper fraction.
3 1/2 = 7/2
7 1/8 = 57/8
Now, we have to find the Least Common Denominator (LCD).
The LCD is 8.
We multiply the top and bottom by 4 because the denominator is 2, which multiplied by 4 is 8.
7 x 4 = 28
_ _
2 x 4 = 8
Now we have 28/8.
We add.
28/8 + 57/8 = 85/8.
85/8 simplified is 10 5/8.
Answer = 10 5/8
Hope this helps!
Btw, if this is correct, can I have Brainliest?
Thanks!
Walmart buys shoes from a factory in China for $8.50. Walmart then marks up the price of the shoes by 65% to sell to their customers. If the shoes aremarked up 65%, how much do they cost at Walmart? *
Answer
The shoes cost $14.03 at Walmart.
Explanation
The markup, the selling price and the cost price are all related through the relation
[tex]\text{Markup percent = }\frac{(Selling\text{ Price) - (Cost Price)}}{(Cost\text{ Price)}}\times100[/tex]For this question,
Markup percent = 65%
Selling Price = x = ?
Cost Price = $8.50
[tex]\begin{gathered} \text{Markup percent = }\frac{(Selling\text{ Price) - (Cost Price)}}{(Cost\text{ Price)}}\times100 \\ 65=\frac{x-8.5}{8.5}\times100 \\ \text{Divide both sides by 100} \\ 0.65=\frac{x-8.5}{8.5} \\ \text{Cross multiply} \end{gathered}[/tex]x - 8.5 = (0.65) (8.5)
x - 8.5 = 5.525
x = 8.5 + 5.525
x = $14.025
x = $14.03
Hope this Helps!!!
I need the answer for x
Answer:
x=-1
Step-by-step explanation:
make equation
-2x-3=x
-3=3x
-1=x
Answer:
x=-1
Step-by-step explanation:
-x+-x-1-1-1 = x
-2x-3=x
3x=-3
x=-1
A pattern has 12 red squares to every 84 blue circles. What is the ratio of red squares to bluecircles?Saleet
A pattern has 12 red squares to every 84 blue circles
The ratio is shown below;
[tex]\begin{gathered} \text{Ratio}=\frac{12}{84} \\ \text{Divide all through and reduce to the simplest form and you now have;} \\ \text{Ratio}=\frac{1}{7} \end{gathered}[/tex]Jeanette wants to raise $3, 200 in a marathon fundraiser. Her sponsers will donate
$35 for each (whole) kilometer she runs this summer.
The minimum amount Jeanette will have to run to reach her goal of $3, 200 is
kilometers.
It’s not 92
Jeanette need to run 91.42 km to get $3,200
How to calculate the distance :
The amount Jeanette wants to raise = $3,200
Amount her sponsers donate = $35 per KM
To find total distance she need to run is divide 3,200 by 35
so we get the distance which she need to cover.
Distance Jeanette need to run = 3200/35 = 91.42 km
The basic operation applied is division.
Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers.There are four important terms used in division. These are dividend, divisor, quotient and remainder.Dividend: The number to be divided by another number is called the dividend.Divisor: The number by which we divide another number (dividend) into equal parts is called the divisor.Quotient: The result of division is called a quotient.Remainder: The leftover number after division is called the remainder.To learn more about division refer :
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Solve: - 3 < 2x – 7 < 1 State your solution as a compound inequality:
-3 < 2x - 7 < 1
we can solve the inequality if we split the inequalities
-3 < 2x - 7
-3 + 7 < 2x
4< 2x
divide both sides by 2
2 < x
x> 2
also
2x - 7 < 1
2x < 1 + 7
2x < 8
divide both sides by 2
x < 4
so upon combining x> 2 and x < 4
2 < x < 4
The value of x is greater than 2 but less than 4
