(Identifying Transformations LC)
Use the image to determine the type of transformation shown.
Preimage of polygon ABCD. A second image, polygon A prime B prime C prime D prime to the right of the first image with all points in the same position.
Horizontal translation
Vertical translation
Reflection across the x-axis
90° clockwise rotation
Answers
If the polygon A, B, C, D is transformed to polygon A', B', C', D' to the right of the first image with all points in the same position, then the transformation is a horizontal translation.
Option A is the correct answer.
We have,
A horizontal translation moves every point of a figure the same distance in the same direction.
In this case, since the second polygon is to the right of the first one, we know that every point of the polygon has been translated to the right by the same amount.
A vertical translation would move every point of the figure the same distance in the same direction, but vertically instead of horizontally.
A reflection across the x-axis would flip the figure over the x-axis, so points that were above the x-axis would end up below it and vice versa.
A 90° clockwise rotation would rotate the figure 90 degrees to the right.
Thus,
If the polygon A, B, C, D is transformed to polygon A', B', C', D' to the right of the first image with all points in the same position, then the transformation is a horizontal translation.
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Related Questions
witch values are solutions to the inequlity [tex]x^{2} \leq 8[/tex]
Answers
Answer:
x ≤ [tex]\sqrt[2]{2}[/tex]
Step-by-step explanation:
x² ≤ 8
[tex]\sqrt{x^{2} }[/tex] ≤ [tex]\sqrt{8}[/tex]
x ≤ [tex]\sqrt[2]{2}[/tex]
Triangle ABC
A
B
C
and triangle DEF
D
E
F
are similar. What is the measure of side DF
D
F
?
Answers
Answer:
19cm
Step-by-step explanation:
I think it's 19cm as sides BC on the green triangle measure 15cm, and EF is 25cm on the blue triangle. It also mentions that they are similar, meaning that ∆ DEF is just a translated and enlarged version of ∆ ABC
25 - 15 = 10cm
9 + 10 = 19cm
Hope this helped :)
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The height h in feet of an object shot straight up with initial velocity v in feet per second is given by h = −16t^2 + vt + c, where c is the initial height of the object above the ground. A model rocket is shot vertically up from a height of 6 feet above the ground with an initial velocity of 22 feet per second. Will it reach a height of 10 feet? Identify the correct explanation for your answer.
A. No; The discriminant is positive so the rocket will reach a height of 10 feet.
B.Yes; The discriminant is positive, so the rocket will reach a height of 10 feet.
C.No; The discriminant is negative, so the rocket will not reach a height of 10 feet.
D.Yes; The discriminant is zero, so the rocket will reach a height of 10 feet.
Answers
Answer:
B.
Step-by-step explanation:
We can use the given formula to find the time it takes for the rocket to reach a height of 10 feet:
10 = -16t^2 + 22t + 6
Rewriting the equation in standard quadratic form:
16t^2 - 22t + 4 = 0
Using the quadratic formula:
t = (22 ± sqrt(22^2 - 4(16)(4)))/(2(16))
t = (22 ± sqrt(36))/32
t = 3/4 or 1/4
Since the rocket reaches a height of 10 feet at two different times (3/4 and 1/4 seconds), it must pass through that height twice during its flight. Therefore, the rocket will reach a height of 10 feet. The correct answer is B.
How many ways to paint a house with 3 different colors from a pool of 12 distinct colors
Answers
In a choir, the number of girls is twice the number of bovs. The avera height of the boys is 150 cm and the average height of the girls is 159 cm
What is the average height of all the choir members?
Answers
Answer:
Step-by-step explanation: mark me brainliest
3 subtracted from quarter of g is 6
Answers
Answer: G=36
Step-by-step explanation:
Step 1: Write out the equation
1/4g-3=6
Step 2: Add 3 to both sides
1/4g=9
Step 3: Divide both sides by 1/4, or 0.25
G=36
NEED HELP WILL GIVE BRAINLIEST AND WILL RATE. Show work and do all 3. :)
Answers
Step-by-step explanation:
5 (4x^8) ^(-1/2) - 2 x^-3
p ^(1/2)
r ^5/3
complete the table on the relation
Answers
Use the graph to answer the question.
Graph of polygon VWXYZ with vertices at 3 comma 2, 3 comma 0, 6 comma negative 7, 9 comma 0, 9 comma 2. A second polygon V prime W prime X prime Y prime Z prime with vertices at 3 comma negative 10, 3 comma negative 8, 6 comma negative 1, 9 comma negative 8, 9 comma negative 10.
Determine the line of reflection.
Reflection across the x-axis
Reflection across the y-axis
Reflection across x = 6
Reflection across y = −4
Answers
The requried line of reflection is the x-axis.
To determine the line of reflection, we need to find the line that maps each vertex of the first polygon to the corresponding vertex of the second polygon.
We can start by reflecting the first polygon across the x-axis. This will map V to V', W to W', X to X', Y to Y', and Z to Z', as shown below:
First Polygon (VWXYZ) Second Polygon (V'W'X'Y'Z')
(3, 2) V (3, -10) V'
(3, 0) W (3, -8) W'
(6, -7) X (6, -1) X'
(9, 0) Y (9, -8) Y'
(9, 2) Z (9, -10) Z'
Next, we can compare the coordinates of each vertex in the first and second polygons to determine the line of reflection. We notice that reflecting the first polygon across the x-axis negates the y-coordinates of all vertices. Therefore, the line of reflection must be the x-axis.
Therefore, the line of reflection is the x-axis.
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birth weights for a simple random sample of 195 boys were recorded. the mean weight calculated for this sample was 3.04 kilograms and the standard deviation was 0.71 kilograms. what is the best point estimate for the birth weight of boys and construct a 90% confidence interval estimate of the mean birth weight of boys
Answers
Based on the information, we are 90% confident that the true mean birth weight of boys is between 2.956 and 3.124 kilograms.
How to calculate the valuestandard error will be:
= 0.71 / ✓(195) = 0.051 kilograms
Substituting these values into the formula, we will then get:
Confidence interval = 3.04 ± (1.645) × (0.051)
Confidence interval = 3.04 ± 0.084
Confidence interval = (2.956, 3.124)
Therefore, we are 90% confident that the true mean birth weight of boys is between 2.956 and 3.124 kilograms.
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Find the dot product for the pair of vectors
Answers
The result of -3u + 5v is the vector (12, -34).
Let's start by defining the two given vectors u and v:
u = (1, 3)
v = (3, -5)
To find the dot product of two vectors, we need to multiply their corresponding components and then add up the results. The formula for the dot product of two vectors can be written as:
u · v = u₁v₁ + u₂v₂ + ... + uₙvₙ
where u₁ and v₁ are the first components of vectors u and v, u₂ and v₂ are the second components, and so on up to un and vₙ, which are the nth components.
Using this formula, we can find the dot product of u and v as follows:
u · v = (1)(3) + (3)(-5)
= 3 - 15
= -12
So, the dot product of vectors u and v is -12.
Next, we need to calculate -3u + 5v. To do this, we need to multiply each component of vector u by -3 and add it to the corresponding component of vector v multiplied by 5. We can write this as follows:
-3u + 5v = (-3)(u₁, u₂) + (5)(v₁, v₂)
= (-3)(1, 3) + (5)(3, -5)
= (-3, -9) + (15, -25)
= (12, -34)
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A student takes a multiple-choice test that has 10 questions. Each question has four choices. The student guesses randomly at each answer. Let X be the number of questions answered correctly. Find P (4) and Find P (More than 2)
Answers
Probability of answering exactly 4 questions correctly = 0.206
P (More than 2) = 0.475
How to solve for the probability1.
ind P(4): Probability of answering exactly 4 questions correctly.
P(X=4) = (10C4) * (0.25^4) * (0.75^6)
10C4 = 10! / (4! * (10-4)!) = 210
P(X=4) = 210 * (0.25^4) * (0.75^6)
= 0.206
2. P(More than 2):P(X=0) = (10C0) * (0.25^0) * (0.75^10) ≈ 0.056
P(X=1) = (10C1) * (0.25^1) * (0.75^9) ≈ 0.187
P(X=2) = (10C2) * (0.25^2) * (0.75^8) ≈ 0.282
Now, calculate P(X>2):
P(X>2)
= 1 - (P(X=0) + P(X=1) + P(X=2))
= 1 - (0.056 + 0.187 + 0.282)
= 1 - 0.525
= 0.475
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The letters of "EAGLES" should be evenly spaced across a 63 inch wide banner, with no margins. Each letter is 8 inches wide. How many inches (x) should exist between each pair of letter?
Answers
Answer:
1 inch
Step-by-step explanation:
How do you find Exponential Decay Rate?
1+b
1-b
Answers
Answer:
Exponential decay is represented by the equation:
y = a * e^(-bx)
where:
y is the final value
a is the initial value
b is the decay rate
x is the time variable
The exponential decay rate, b, can be found by taking the natural logarithm (ln) of both sides of the equation, then rearranging to isolate the decay rate:
ln(y/a) = -bx
b = -ln(y/a)/x
So, to find the exponential decay rate, you would need to know the initial value (a), the final value (y), and the time elapsed (x). Then, you can use the formula above to calculate the decay rate, b.
The expressions "1+b" and "1-b" are not sufficient to find the exponential decay rate, as they do not contain enough information about the specific scenario or data set.
if this helps, can you please mark my answer brainliest?
A geography teacher assigns each student to write a report about one of the first 13 colonies. Students select the name of a colony by "blindly" drawing a colony's name from a bag. Once a colony has been drawn, it is not replaced.
What is the probability that the first student selects Pennsylvania and the second student selects Virginia? Round your answer to the nearest hundredth of a percent.
Answers
The probability that the first student selects Pennsylvania and the second student selects Virginia to the nearest hundredth of a percent is 0.64%.
Probability problemThe probability that the first student selects Pennsylvania is 1/13. Once Pennsylvania has been drawn, there are only 12 colonies left in the bag, so the probability that the second student selects Virginia is 1/12.
To find the probability that both events occur, we multiply the probabilities:
(1/13) x (1/12) = 1/156
To express this probability as a percentage, we multiply by 100:
(1/156) x 100 ≈ 0.64%
Therefore, the probability that the first student selects Pennsylvania and the second student selects Virginia is approximately 0.64%.
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Put the quadratic into vertex form
Answers
The vertex form of the quadratic function f(x) = 2x^2 + 8x + 7 is f(x) = 2(x + 2)^2 - 25.
How to find the vertex formTake a look at the quadratic function:
f(x) = 2x^2 + 8x + 7
In this situation, a = 2 and b = 8, yielding:
f(x) = 2(x^2 + 4x) + 7
It shtbe noted that to determine the value to add and subtract, multiply (b/2a)2 by (8/2(2))2 = 42 = 16. Inside the parenthesis, we add and subtract 16:
f(x) = 2(x^2 + 4x + 16 - 16) + 7
The expression inside the parenthesis can now be written as a perfect square:
f(x) = 2((x + 2)^2 - 16) + 7
Finally, the phrase is simplified by spreading the 2:
f(x) = 2(x + 2)^2 - 32 + 7
f(x) = 2(x + 2)^2 - 25
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What is the vertex form of the quadratic function f(x) = 2x^2 + 8x + 7
A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. No fencing is needed along the barn, and the fencing along the west side of the plot is shared with a neighbor who will split the cost of that portion of the fence. If the fencing costs $24 per linear foot to install and the farmer is not willing to spend more than $6000, find the dimensions for the plot that would enclose the most area. Leave in terms of (width, length): (,)
Answers
The dimensions of the plot that would enclose the most area are (width, length) = (125/6, 125/3).
We have,
Let's assume that the barn wall is located on the south side of the rectangular plot, and the fencing is required on the remaining three sides (east, north, and west).
Let's denote the width of the plot as x and the length of the plot as y.
Then, the length of fencing required can be expressed as:
L = x + y + x/2
where x/2 is the length of the shared fencing with the neighbor.
The cost of fencing can be expressed as:
C = 24L
Substituting the value of L, we get:
C = 24(x + y + x/2)
Since the farmer is not willing to spend more than $6000, we have:
24(x + y + x/2) ≤ 6000
Simplifying this inequality, we get:
3x + 4y ≤ 500
Now, we need to maximize the area of the rectangular plot, which is given by:
A = xy
Using the inequality constraint, we can express y in terms of x as:
y ≤ (500 - 3x)/4
Substituting this value of y in the expression for A, we get:
A = x((500 - 3x)/4)
Simplifying this expression, we get:
A = (125/4)x - (3/4)x^2
To find the value of x that maximizes A, we can take the derivative of A with respect to x and set it equal to zero:
dA/dx = 125/4 - (3/2)x = 0
Solving for x, we get:
x = 125/6
Substituting this value of x in the expression for y, we get:
y = (500 - 3(125/6))/4 = 125/3
Therefore,
The dimensions of the plot that would enclose the most area are (width, length) = (125/6, 125/3).
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Given u = 4i - 7j and v = -6i + 9j, what is u • v?
-87
-82
26
39
Answers
u • v = (4i)(-6i) + (-7j)(9j) = -24i^2 - 63j^2
Since i^2 = j^2 = -1, we have:
u • v = -24(-1) - 63(-1) = 24 - 63 = -39
Therefore, the answer is —87
perimeter of a tabe is 228 inches and the length is 18 inches which is more than twice the width. How do I find the length and width of the worktable
Answers
The width of the worktable is 32 inches, and the length of the worktable is 82 inches.
Let's assume that the width of the worktable is "w" inches.
We are given that the length is 18 inches more than twice the width, which can be expressed as:
Length = 2w + 18
The perimeter of the worktable is the sum of the lengths of all four sides.
We know that the perimeter of the worktable is 228 inches, so we can write an equation:
Perimeter = 2 × (Length + Width)
228 = 2 × (2w + 18 + w)
228 = 2 × (3w + 18)
Dividing both sides by 2:
114 = 3w + 18
Subtracting 18 from both sides:
96 = 3w
Dividing both sides by 3:
w = 32
So, the width of the worktable is 32 inches.
Now we can use this value to find the length:
Length = 2w + 18
Length = 2 × 32 + 18
Length = 82
So, the length of the worktable is 82 inches.
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How knows how do this help me please
Answers
Answer:
Step-by-step explanation:
What is the solution to this system?
(1, 0)
(1, 6)
(8, 26)
(8, –22)
Answers
What is the value of x in this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
Answers
Answer:
58.85°
Step-by-step explanation:
You want to know the measure of the angle in the right triangle that has hypotenuse 29 and adjacent side 15.
CosineThe cosine function relates angles and sides by ...
Cos = Adjacent/Hypotenuse
cos(x) = 15/29
The inverse function is used to find the angle value:
x = arccos(15/29) ≈ 58.85°
The value of x is about 58.85°.
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Determine if the statement is true or false.
Angle AEC and DEB are complementary angles and therefore add up to 180 degrees.
1. True
2. False
Answers
The statement "Angle ∠AEC and ∠DEB are complementary angles" is false.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.
Angle ∠AEC and ∠DEB are supplementary angles because the sum is 180 degrees.
Thus, the given statement is false.
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f(x)=3x-15 g(x)=1/3x+15
find f(g(x))
g(f(x))
are they inverses if do, why?
Answers
The values for the composition of functions are:
a. (f o g)(x) = -x³ - x + 1
b. (g o f)(x) = -x³ - x - 1
Here, we have,
to Determine the Value of Composite Functions:
The value of composite functions are determined by first finding the output of the inner function, which would be used as the input of the outer functions to derive the value of the composite functions.
Given the following:
f(x) = x³ + x + 1
g(x) = -x
a. To find (f o g)(x), substitute g(x) as the inner function for x into f(x):
(f o g)(x) = (-x)³ + (-x) + 1
Simplify
(f o g)(x) = -x³ - x + 1
b. To find (g o f)(x), substitute f(x) as the inner function for x into g(x):
(g o f)(x) = -(x³ + x + 1)
Distribute by -1
(g o f)(x) = -x³ - x - 1
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complete question:
If f(x)=x³+x+1 and g(x)=-x, find (f°g)(x) and (g°f)(x).
(f°g)(x)=
(c) log, 12-( log, 9+ log 1 3 log, 8), write a single form equation
Answers
log(a) + log(b) = log(ab)
log(a) - log(b) = log(a/b)
log(a^n) = n*log(a)
Using these rules, we can write:
log(12) - (log(9) + log(13) + log(8))
= log(12) - log(9138)
= log(12/9138)
= log(4/351)
Therefore, the single form equation for the expression is:
log(12) - (log(9) + log(13) + log(8)) = log(4/351)
Solve the system of equation algebraically y =
x ^ 2 + 4x + 3 y = 2x + 6
Answers
y = x ^ 2 + 4x + 3 --- Equation 1
y = 2x + 6 --- Equation 2
We can set the right-hand sides of the two equations equal to each other since they are both equal to y:
x ^ 2 + 4x + 3 = 2x + 6
Subtracting 2x + 6 from both sides, we get:
x ^ 2 + 2x - 3 = 0
We can factor the quadratic equation:
(x + 3)(x - 1) = 0
This gives us two possible solutions:
x + 3 = 0 or x - 1 = 0
Solving for x, we get:
x = -3 or x = 1
Substituting these values back into either Equation 1 or Equation 2, we can solve for y:
When x = -3, y = (-3) ^ 2 + 4(-3) + 3 = 0
When x = 1, y = 2(1) + 6 = 8
Therefore, the solution to the system of equations is (x, y) = (-3, 0) and (1, 8).
If tan A= 28 /45 and cosB= 13 12 and angles A and B are in Quadrant I, find the value of tan(A+B).
Answers
The value of Tan A + B is 6.009.
How to solve for the tangent[tex]sin^2 A + cos^2 A = 1sin^2 A = 1 - cos^2 Asin A = sqrt(1 - cos^2 A)sin A = sqrt(1 - (28/45)^2)sin A = sqrt(1 - 784/2025)sin A = sqrt(1241/2025)cos A = 28/45\geq[/tex]
We have to solve for Tan B
[tex]sin^2 B + cos^2 B = 1sin^2 B = 1 - cos^2 Bsin B = sqrt(1 - cos^2 B)sin B = sqrt(1 - (13/12)^2)sin B = sqrt(55/144)Therefore, tanB = sinB / cosB = (sqrt(55/144)) / (13/12) = (12 sqrt(55)) / 143[/tex]
[tex]tan(A+B) = (3207 \sqrt{55}) + 1804 \sqrt{124})) / (3115 - 207 \sqrt{(341)}[/tex]
= 6.009.
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Find the 7th term of the geometric sequence whose common ratio is 2/3 and whose first term is 8
Answers
we know that general term for gp is [tex]a_{n}[/tex] = a [tex]r^{n-1}[/tex]
where r = common ratio
a = first term
putting values we get
8th term = 8x 64/729
= 0.702
hence the 8th term is 0.702
Paola has enough mulch to cover 48 square feet. She wants to use it to make three square vegetable gardens of equal sizes. Solve the equation 3s2 = 48 to find s, the length of each garden side (in feet).
Answers
The length of each garden side is 4 ft.
Given that, Paola has 48 ft² of mulch, she wants to make three square vegetable gardens of equal sizes, we need to find the length of each garden side.
Let s be the length of the side of the gardens,
Since, she need 3 gardens,
So,
3 × side² = 48
3s² = 48
s² = 16
s = 4
Hence, the length of each garden side is 4 ft.
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A positive real number is 1 less than another. When 2 times the larger is added to the square of the smaller, the result is 13. Find the numbers. (If applicable, write your answers in the form p±q√r)
Answers
From the problem, we know that:
2(x + 1) + x^2 = 13
Simplifying and rearranging:
x^2 + 2x - 11 = 0
Using the quadratic formula:
x = (-2 ± sqrt(2^2 - 4(1)(-11))) / (2(1))
x = (-2 ± sqrt(48)) / 2
x = (-2 ± 4sqrt(3)) / 2
x = -1 ± 2sqrt(3)
Since the problem states that the numbers are positive, we can ignore the negative solution. Therefore, the smaller number is:
x = -1 + 2sqrt(3)
And the larger number is:
x + 1 = 2sqrt(3)
So the two numbers are -1 + 2sqrt(3) and 2sqrt(3).
