Which of these triangle pairs can be mapped to each other using a single translation?
pls help need it fast
Answers
Answer:- D shows the triangle pairs which can be mapped to each other using a single translation.
Explanation:-
Translation is a rigid transformation which creates a congruent image as that of the original figure such that the distance between the each point of the original figure and the image is fixed and same.
The translation mapping is given by (x,y)→(x+h,y+k) ,where h is the distance of the x coordinate of the each point of the original figure to the image and k is the distance of the y coordinate of the each point of the original figure to the image.
In figure D we can see that the distance between each point of ΔCED is equal to the distance between each point of ΔMPN. Thus it shows the triangle pairs which can be mapped to each other using a single translation.
The Figure 4 is correct as the triangle MNP and CDE can be mapped to each other using a translation.
Further explanation:
Translation can be defined as to move the function to a certain displacement. If the points of a line or any objects are moved in the same direction it is a translation.
Explanation:
The angle MNP is equal to the angle CDE.
The side PN is equal to the side ED.
The side MN is equal to the side CD.
The translation mapping of a single translation can be expressed as follows,
[tex]\left( {x,y}\right) \Rightarrow \left({x + h,y + k} \right)[/tex]
Here, h represents the distance of translation in x-axis and k represents the distance of translation in y-axis.
In Figure 1 the triangle MNP and CDE cannot be mapped to each other using a single translation.
In Figure 2 the triangle MNP and CDE cannot be mapped to each other using a single translation.
In Figure 3 the triangle MNP and CDE cannot be mapped to each other using a single translation.
In Figure 4 the triangle MNP and CDE can be mapped to each other using a translation.
Hence, the Figure 4 is correct as the triangle MNP and CDE can be mapped to each other using a translation.
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Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Triangles
Keywords: rotation, translation, triangle, rotation about point A, mapped, triangle pair, mapping, equal angles, sides.
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Which expression represents the phrase, "one third the sum of 12 and a number"?
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Planes Q and R are parallel. Lines a and b are shown on planes Q and R, respectively.
Which statement is true about lines a and b?
They are parallel lines.They are perpendicular lines.They are skew lines.They will intersect.Which inequality best represents that ice cream at −5°C is cooler than ice cream at 4°C?
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Answer:
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Step-by-step explanation:
Five less than twice what negative number squared is 157?
Answers
-5 + 2(-x^2) = 157
Now simplify:
-5 + -2x^2 = 157
-2x^2 = 162
-2x^2 - 162 = 0
2x^2 + 162 = 0
x^2 + 81 = 0
Using algebraic equation, the negative number that is squared is: -9.
What is an Algebraic Equation?An algebraic equation can be used to find an unknown value, by making the unknown value the variable.
Let the negative number that would be squared be represented by the variable, x. Thus, we have -x². Therefore:
2x² - 5 = 157
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2x² = 162
x² = 162/2
x² = 81
x = √81
x = -9
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w = 13, x = 9, y = 1.9, z = 0.5 x + 20 – 1
A. 28
B. 19
C. 30
D. 32
Answers
A = 28
The value the given expression x + 20 – 1 is, the solution is A. 28.
What is an expression?An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
here, we have,
w = 13, x = 9, y = 1.9, z = 0.5
x + 20 – 1
Since X Is 9 ,
You're Problem Would Now Be
= 9 + 20 - 1
Then You Subtract 20
And 1 Which Will Give You 19
Then , You're Left With 9 + 19
Which Is 28.
Hence, the solution is A. 28.
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If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?
Answers
It takes 1 minute to make each widget.
Suppose that a compensation professional would like to calculate the median salary. he orders four salaries as follows: $20,000, $22,000, $24,000, $26,000. what is the median salary for this data set?
Answers
First, you put them in order from least to greatest.
Then, you look to see which number is in the middle.
Since there are only four numbers given, you have to go in between two of the numbers.
The median is in between 22,000 and 24,000.
20,000 22,000 _ 24,000 26,000
The number that is equally between 22,000 and 24,000 is 23,000.
The median for the set of data is $23,000.
Hope this helps!
The median salary for the given data set of four salaries ($20,000, $22,000, $24,000, and $26,000) is calculated by averaging the two middle values ($22,000 and $24,000), resulting in a median of $23,000
To calculate the median salary from an ordered data set, you first need to determine if the number of data points is even or odd. In this scenario, there are four data points: $20,000, $22,000, $24,000, and $26,000. As the number of data values is even, the median is the average of the two middle values.
Steps to Calculate Median Salary
Arrange the salaries in ascending or descending order. This step is already completed, as the salaries are presented in order: $20,000, $22,000, $24,000, $26,000.Find the two middle salaries since the number of data points is even. In the given data set, the two middle salaries are $22,000 and $24,000.Calculate the average of these two middle salaries. Add $22,000 and $24,000 to get $46,000, then divide by 2 to obtain $23,000. This value is the median salary for the data set.Therefore, the median salary for this data set is $23,000
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2.1e-10 in standard form?
Answers
= 2.1 x 10^-10
= 0.00000000021
hope it helps
The value of 2.1e-10 = 0.00000000021
What is exponents?An exponent refers to the number of times a number is multiplied by itself.
Here e is used when the number is too large and small for the calculator.
We know 'e' represent exponents
2.1e-10, represents [tex]2.1* 10^{-10}[/tex]
= 2.1 x [tex]\frac{1}{10^{10}}[/tex]
= 2.1 x [tex]\frac{1}{10000000000}[/tex]
= 0.00000000021
Hence, 2.1e-10 = 0.00000000021
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Points J, K, L, and M are midpoints of the sides of the rectangle EFGH. Prove that quadrilateral JKLM is a rhombus by finding the lengths of the sides. The diagram is not drawn to scale.
Answers
Quadrilateral JKLM is a rhombus because its sides are all equal in length. By using the midpoints of the rectangle EFGH, we find that JK and LM are both 2a in length, and KL and MJ are both 2b in length, confirming that all four sides are equal.
To prove that quadrilateral JKLM is a rhombus, we find the lengths of its sides.
Since J, K, L, and M are midpoints of the sides of rectangle EFGH, the segments connecting them will be parallel to the sides of EFGH and half the length.
We can use the coordinates of F(-a,b), G(a,b), H(a,-b), and E(-a,-b) to find the lengths:
JK is parallel to EH and GH, so its length is half of EH and GH, and since E and G are on the same vertical line, the length of JK is a - (-a) = 2a.
KL is parallel to EG and FH, so its length is also half of EG and FH, and since E and F are on the same horizontal line, the length of KL is b - (-b) = 2b.
LM is parallel to EH and GH, hence its length is the same as JK which is 2a.
MJ is parallel to EG and FH, hence its length is the same as KL which is 2b.
Given that JK = LM and KL = MJ, and all are equal to 2a or 2b, quadrilateral JKLM has all sides of equal length. Therefore, it is a rhombus.
The probable question may be:
Points J, K, L, and M are midpoints of the sides of the rectangle EFGH. Prove that quadrilateral JKLM is a rhombus by finding the lengths of the sides. The diagram is not drawn to scale.
F(-a,b)
G(a,b)
H(a,-b)
E(-a,-b)
J(-a,0)
K(0,b)
L(a,0)
M(0,-b)
For the linear equation, x + y - 1 = 0, determine a corresponding value of y for the x-value of -6.
Answers
x + y-1 = 0
if x = 6
replace x with 6 to get
6 +y-1 =0
subtract 6 from each side
y-1 =-6
add 1 to each side
y = -5
What is the simplified form of the fifth root of x to the fourth power times the fifth root of x to the fourth power?
Answers
Answer:
The simplified form will be: [tex]x\sqrt[5]{x^3}[/tex]
Step-by-step explanation:
The given expression is: [tex]\sqrt[5]{x^4}*\sqrt[5]{x^4}[/tex]
Simplifying the above expression......
[tex]\sqrt[5]{x^4}*\sqrt[5]{x^4}\\ \\ =\sqrt[5]{x^4*x^4}\\ \\ =\sqrt[5]{x^4^+^4}\ [Exponents\ gets\ added\ while\ multiplication]\\ \\ =\sqrt[5]{x^8}\\ \\ =\sqrt[5]{x^5*x^3}\ [As\ 5+3=8] \\ \\ =\sqrt[5]{x^5}*\sqrt[5]{x^3}\\ \\ =x\sqrt[5]{x^3}[/tex]
So, the simplified form will be: [tex]x\sqrt[5]{x^3}[/tex]
Two angles form a complementary pair (sum is 90 degrees) one angle is 3x - 10 and the other angle is x + 8. Write an equation and solve for each angle.
Could somebody help? Thank you :)
Answers
4×-2=90
4x=92
X=23
One angle is 31. 23+8
The second one is 59. 3 (23)-10
Tim made a down payment of $1,000. He pays $450 for 36 months. What is the total amount he pays for the car?
Answers
1000 + 16,200 = 17,200.
He payed $17,200 for the car.
Hope this helps!
Answer:
$ 17,200
Step-by-step explanation:
Given,
The amount of down payment = $ 10000,
Also, monthly payment = $ 450,
Number of months = 36,
So, the total payment ( except down payment ) = number of months × monthly payment
= 36 × 450
= $ 16200,
Hence, the total amount paid for the car = down payment + total payment
= $ 1,000 + $ 16,200
= $ 17,200
what system of linear inequalities is represented by the graph?
Answers
y=0.5x-1
second/dotted line:
y=2x-4
your allowed values are below the first line and above the second, so the system is
I: y<=0.5x-1
II: y>=2x-4
your dotted line might also mean > instead of >=, but this depends on the notation used in class
Answer:
y > 2x - 4 and y ≤ [tex]\frac{x}{2}-1[/tex]
Step-by-step explanation:
In this question we will find the equations of the lines first then decide the inequality sign.
Dotted line in the graph passes through two points (2, 0) and (0, -4)
Let the equation of the line is y = mx + c
Where m = slope and c = y-intercept
Slope (m) of the line will be = [tex]\frac{y-y'}{x-x'}[/tex]
m = [tex]\frac{0+4}{2-0}[/tex]
m = 2
y-intercept of the line = (-4)
So, equation of the line will be y = 2x - 4
Now we see the shaded area is above the dotted line so inequality will be
y > 2x - 4
Now for the bold line
Let the equation of this line is y = m'x + c'
This line passes through points (2, 0) and (0, -1)
then slope of the line m' = [tex]\frac{y-y'}{x-x'}[/tex]
m = [tex]\frac{0+1}{2-0}[/tex] = [tex]\frac{1}{2}[/tex]
y-intercept = c = -1
Then equation of the line will be
y = [tex]\frac{x}{2}-1[/tex]
Since shaded area is below the bold line therefore, inequality sign will be "less than equal to"
Inequality of the bold line will be y ≤ [tex]\frac{x}{2}-1[/tex]
System of the linear inequalities will be
y > 2x - 4 and y ≤ [tex]\frac{x}{2}-1[/tex]
Using the given information, which lines, if any, can you conclude are parallel? Justify your conclusion with a theorem or postulate.
Answers
a and b are paralell
You are returning from a trip to England with €100 euro. The exchange rate is USD/EUR 1.3847 . How much in US dollars should you receive
Answers
Using the exchange rate of USD/EUR 1.3847, you need to multiply your €100 by 1.3847 to determine the amount in US dollars, which is USD 138.47. Therefore, you will receive USD 138.47 for your €100.
You are returning from a trip to England with €100 euro, and the exchange rate is USD/EUR 1.3847. To calculate how much in US dollars you should receive, you use the exchange rate to convert euros to USD.
Start with the amount in euros: €100.Multiply by the exchange rate: 100 × 1.3847 = 138.47.Therefore, you should receive USD 138.47.
Find the value of angle c?? Please help
Answers
180 = 5x + 30
Subtract 30 from both sides
150 = 5x
Divide both equations by 5
30 = x
Now since a and c are vertical angles a = c
So plug in 30 for x
2(30) + 10 = c
60 + 10 = c
70 = c
Jaime had $37 in his bank account on Sunday. The table shows his account activity for the next four days. What was the balance in Jaime’s account after his deposit on Thursday?
Jaime’s Bank Acc.
______________________
| Day | Deposit | withdrawal |
| Mon| $17.42 | none |
| Tues| None | -$12.60 |
| Wed| None | -$9.62 |
| Thur| $62.29 | none |
———————————————
A) $57.48
B) $59.65
C) $94.49
D) $138.93
(I would really appreciate
it if someone will help me)
Answers
on Mon $37+$17.42=$54.42
on Tue $54.42-$12.6=$41.82
on Wed $41.82-$9.62=$32.20
on Thur $32.20+$62.29=$94.49
so the correct answer is C
Answer:
Option C. $94.49
Step-by-step explanation:
Jaime had a balance in his bank account on Sunday = $37
The table shows his account activity for the next four days.
From the given table we add all the deposits to his balance and then subtract all the withdrawals.
Balance on Sunday + Deposits
= 37.00 + 17.42 + 62.29 = $ 116.71
Now we subtract all the withdrawals
= 116.71 - (12.60 + 9.62)
= 116.71 - 22.22 = $94.49
The balance would be $94.49 in Jaime's account after his deposit on Thursday.
Sal currently has an account balance of $2,835.48. He opened the account five years ago with a deposit of $2310.72. If the interest compounds twice a year, what is the interest rate on the account?
Answers
A=p (1+r/k)^kt
A future value 2835.48
P present value 2310.72
R interest rate?
K compounded twice a year 2
T time 5 years
Solve the formula for R
R= [(A/p)^(1/kt)-1]×k
R=((2,835.48÷2,310.72)^(1÷10)−1)×2
R=0.0414×100
R=4.14%
Hope it helps!
In the diagram below, what is the approximate length of the minor Arc de? "if you can, explain please"
Answers
To find DE = 2 x pi x 15 = 94.25 cm. Then you divide 94.25 by 4 = 23.56 which round to one decimal point is 23.6 cm
Answer:
D) 23.6 cm
Step-by-step explanation:
We first find the circumference of the circle. Circumference is given by the formula
C = 2πr, where π = 3.14 and r is the radius. The radius of our circle is 15 cm; this gives us
C = 2(3.14)(15) = 94.2.
Next we find the portion of the circumference associated with the given arc. The measure (in degrees) of the arc is 90°; this makes it 90/360 of the circle. 90/360 simplifies to 1/4; this means this arc is 1/4 of the circumference:
1/4(94.2) = 23.55
This rounds to 23.6.
Find the turn of sonnet 73. what is its logical relationship to what comes before
Answers
Final answer:
The volta in Sonnet 73 is a shift that occurs between lines eight and nine, serving to transition from metaphors of aging to considering their impact on love. This turn is common in sonnets, marking a change in argument or tone.
Explanation:
Finding the Volta in Sonnet 73
The volta, or the turn, in a sonnet marks a shift in thought or argument and is crucial to understanding the poem's structure and meaning. In Sonnet 73, the volta can be identified between lines eight and nine, where the poet moves from reflecting on the images that convey the passage of time and coming to terms with mortality, to directly addressing the beloved and discussing the importance of this realization for their relationship. The logical relationship between the octet (the first eight lines) and the following sestet (the last six lines) in Sonnet 73 is that the octet sets up a series of metaphors about aging and the passage of time, which the sestet then responds to by contemplating the impact of these realizations on love and connection.
The Petrarchan sonnet typically follows a structure with an octave that presents a problem that is resolved or responded to in the following sestet. Although the rhyme scheme might vary, the purpose of the volta remains the same across different sonnets: it signifies a pivot or shift in the argument or mood of the poem.
The reference to Shakespearian and Petrarchan sonnet styles in the question helps us understand that the student likely confuses the structure. Sonnet 73 is a Shakespearian sonnet that consists of three quatrains and a concluding couplet, with the volta being a conceptual rather than structural shift in Shakespeare's sonnets, typically occurring at the start of the third quatrain or the couplet.
The radius of a large sphere is 8 times the radius of a small sphere. the surface area of the large sphere is how many times the surface area of the small sphere?
Answers
small sphere's radius = r, R = 8r
surface area of a sphere (SA) = 4×pi×radius^2
So what we need is the SA of the larger in terms of the smaller sphere, so if:
SA (of R) = 4×pi×R^2, then plug in "8r" for "R"...
SA = 4×pi×(8r)^2 = 4×3.14×64r^2
SA = 12.57×64r^2 = 804 r^2
Therefore the SA of the larger sphere is 804 times the SA of the smaller sphere.
I hope that makes sense!
The large sphere is 64 times the surface area of the small sphere.
What is a sphere?A sphere is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. That given point is the centre of the sphere, and r is the sphere's radius.
Given that, the radius of a large sphere is 8 times the radius of a small sphere.
Let the radius of a small sphere be x, then the radius of a large sphere is 8x.
We know that, the surface area of a sphere is 4πr².
Here, surface area of a small sphere = 4πx²
The surface area of a large sphere = 4π(8x)²
= 256πx²
Now, 256πx²/4πx² =64
Therefore, the large sphere is 64 times the surface area of the small sphere.
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WORTH 40 POINTS!
What is the value of the expression All of 2.6 multiplied by 10 to the power 9 over all of 1.3 multiplied by 10 to the power 2?
1.3 × 107
2.0 × 107
1.3 × 1011
2.0 × 1011
Which shows the expressions in the order they would appear on a number line from least to greatest2 to the power of 3, square root of 5, square root of 20, square root of 11, 11 over 9
2 to the power of 3, square root of 11, 11 over 9, square root of 20, square root of 11
11 over 9, square root of 5, square root of 11, square root of 20, 2 to the power of 3
11 over 9, 2 to the power of 3, square root of 5, square root of 20, square root of 11
Which rational number equals 0 point 1 with bar over 1?1 over 11
1 over 10
1 over 9
1 over 8
Answers
Answer:
4 to the power of 3, square root of 40, square root of 13, square root of 7, 14 over 9
Step-by-step explanation:
i took the test
it's the other way around.
Answer:
A
Step-by-step explanation:
The average annual rainfall in California is 0.564 of a meter per year. What is the value of the digit 4 in that number
Answers
Evaluate 3/2y - 3 + 5/3z when y = 6 and z = 3
Answers
3/2(6) -3 + 5/3(3)
18/2 - 3 + 15/3
Divide.
9 - 3 + 5
Subtract 9 - 3
6 + 5 = 11
Hope this helps!
To solve the expression, you should substitute the provided values for y and z then simplify the resulting expression. The solution is 11.
Explanation:To evaluate the expression 3/2y - 3 + 5/3z when y = 6 and z = 3, first, we should substitute the values of y and z into the expression.
So, the expression becomes 3/2*6 - 3 + 5/3*3. Multiply to reduce fractions: 9 - 3 + 5. This simplifies to 11.
So the value of the given expression when y = 6 and z = 3 is 11.
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The angles with measures x and 4x are complementary angles. which is the value of x?
Answers
x+4x=90
5x=90
x=18
Answer:
x=18 degrees
Step-by-step explanation:
Hello
by definition, two angles are called complementary angles, if the sum of their degree measures is 90. Each angle is called complement of the other.
A = angle 1=x
B=angle 2 =4x
A and B are complementary angles,hence
A+B=90
replacing
[tex]x+4x=90\\\\5x =90\\x=\frac{90}{5} \\x=18\ degrees[/tex]
A=18 degrees
B=4*x
B=72 degrees
x=18 degrees
The length of a rectangle is four times its width. if the area of the rectangle is 400 yd2 , find its perimeter.
Answers
L = 4W
A = LW
400 = (4W)(W)
400 = 4w^2
4W^2 = 400
W^2 = 100
W = 10
The width is 10 yd, and the length is 40 yd.
The point (-7, -24) is on the terminal ray of angle θ which is in standard position. A student found the six trigonometric values for angle θ. The student’s answers are shown
Answers
The student wrongly calculated the value of [tex]\rm tan\theta[/tex], [tex]\rm sin\theta[/tex], [tex]\rm cosec\theta[/tex], and [tex]\rm cot\theta[/tex] and this can be determined by using the Pythagorean theorem and trigonometric functions.
GIven :
The point (-7, -24) is on the terminal ray of angle θ which is in standard position.
To determine the trigonometric function first determine the value of the hypotenuse and to determine the value of the hypotenuse, the Pythagorean theorem can be used.
[tex]\rm H^2 = P^2 + B^2[/tex]
where H is the hypotenuse, B is the base, and P is the perpendicular.
Now, substitute the value of known terms in the above equation.
[tex]\rm H^2 = 7^2+24^2[/tex]
[tex]\rm H^2=49+576[/tex]
[tex]\rm H^2 = 625[/tex]
H = 25
Now, the values of the trigonometric functions are as follows:
[tex]\rm cos\theta=\dfrac{-7}{25}[/tex]
[tex]\rm sin\theta=\dfrac{-24}{25}[/tex]
[tex]\rm tan\theta=\dfrac{24}{7}[/tex]
[tex]\rm cosec\theta=\dfrac{25}{-24}[/tex]
[tex]\rm sec\theta=\dfrac{25}{-7}[/tex]
[tex]\rm cot\theta=\dfrac{7}{24}[/tex]
The student wrongly calculated the value of [tex]\rm tan\theta[/tex], [tex]\rm sin\theta[/tex], [tex]\rm cosec\theta[/tex], and [tex]\rm cot\theta[/tex].
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To find the six trigonometric values for angle θ (-7, -24) on the terminal ray, we can use sine, cosine, tangent, cosecant, secant, and cotangent ratios.
Explanation:The given point (-7, -24) lies on the terminal ray of an angle in standard position, denoted by θ. To find the six trigonometric values for angle θ, we can use the values of the coordinates of the point. The coordinate (-7) represents the x-value (adjacent side) and the coordinate (-24) represents the y-value (opposite side).
We can use the trigonometric ratios: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot), to find the values.
Here, sinθ = y/r = (-24)/7.6, cosθ = x/r = (-7)/7.6, tanθ = y/x = (-24)/(-7), cscθ = 1/sinθ, secθ = 1/cosθ, and cotθ = 1/tanθ. By substituting the respective values, we can find all six trigonometric values.
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