Answers
The line of reflection of the given image is:
A reflection across y = -3
What is the Line of Reflection?A line of reflection is a line that lies between two identical mirror images, so the distance of any point of one figure from the line will equal the distance of the same point of the mirror image (flipped figure).
The definition above tells us that if we are given two images, such as mirror images of each other, the line of reflection can be determined by calculating the midpoint from any two points of the figures.
Looking at the given image, the center point of the mirror images is seen as y = -3
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Related Questions
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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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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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
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 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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Problem 5:
Find the missing side using
trigonometry:
52
18 H
AWO
Drag&Drop the correct trig function:
Cos
Tan
Rati
Circle which shortcut you use.
Multiply
Round your answer to the nearest tenth:
Give Feedback to Micrones
Sin
%
or
IN
Divide
Ans
Ans
Answers
The missing length is 11.0818 unit.
We have,
Angle = 52 degree
H = 18
Using Trigonometry
cos 52 = B/H
cos 52 = x / 18
0.615661 = x /18
x = 11.0818 unit
Thus, the missing length is 11.0818 unit.
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Circle A has a circumference of [tex]\frac{8\pi }{x+2}[/tex] units and Circle B has a circumference [tex]\frac{4\pi }{x+2}[/tex] units. What is a simplified expression for the difference in the areas of Circle A and Circle B
Answers
The simplified expression for the difference in the areas of Circle A and Circle B is = 12π/(x+2)²
Area of a Circle:The area of a circle is the space occupied by the circle in a two-dimensional plane. Alternatively, the space occupied within the boundary/circumference of a circle is called the area of the circle. The formula for the area of a circle is [tex]A = \pi r^2[/tex], where r is the radius of the circle. The unit of area is the square unit, for example, [tex]m^2, cm^2, in^2[/tex], etc.
We know that :
The formula of circle's circumference is = 2πr
We have :
Circle A has a circumference of [tex]\frac{8\pi }{x+2}[/tex] units
and Circle B has a circumference [tex]\frac{4\pi }{x+2}[/tex]
Now, First we calculate the area of circle A is:
8π/x+2 = 2πr
r = 8π/x+2 × 1/2π
r = 4/x+2
Area = πr² = (4/x+2)²π
Now, for circle B
4π/x+2 = 2πr
r = 4π/x+2 × 1/2π
r = 2/2x+2
Area =( 2/2x+2)²π
Simplified expression for the difference in the areas of Circle A and Circle B are:
(4/x+2)²π - ( 2/x+2)²π
= π/(x+2)²( 4²-2²)
= π/(x+2)²(16-4)
= 12π/(x+2)²
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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
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
The growth of a colony of bacteria is modeled by the function below, where t is the
is time in hours after the culture is begun and f(t) is the number of bacteria present.
After how many hours will there be 2000 bacteria in the colony? Round your answer
to the nearest hundredth (two decimal places).
f(t) = 500e^0.195t
Answers
namely, what is "t" when f(t) = 2000
[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{we'll use this one} }{log_a a^x = x}\qquad \qquad a^{log_a (x)}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{f(t)}{2000}=500e^{0.195t}\implies \cfrac{2000}{500}=e^{0.195t}\implies 4=e^{0.195t} \\\\\\ \log_e(4)=\log_e\left( e^{0.195t}\right)\implies \log_e(4)=0.195t\implies \ln(4)=0.195t \\\\\\ \cfrac{\ln(4)}{0.195}=t\implies 7.11\approx t[/tex]
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
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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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.
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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.
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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In the figure to the right, you are given a square ABCD. Each of its sides is divided into two segments, such that AE = BF = CG = DH. Prove that quadrilateral EFGH is a square.
First to answer gets brainliest
Answers
Answer:proving that EFGH is a square: points E,F,G,H
separate the sides of the square ABCD into two lines. if AE=BF=CG=DH then
AH=DG=EB=FC and it shows that if we connect the points E,F,G,H to each other with line we will have a square
HAE~EBF~FCG
How many ways to paint a house with 3 different colors from a pool of 12 distinct colors
Answers
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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What is the solution to this system?
(1, 0)
(1, 6)
(8, 26)
(8, –22)
Answers
How knows how do this help me please
Answers
Answer:
Step-by-step explanation:
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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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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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 :)
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).
Determine which of the following statements is true concerning the values described in column #1 and column #2. (1 point)
Column #1
Column #2
The x-coordinate of the vertex of the graph of The x-coordinate of the vertex of the graph of
y=-2x² - 4x + 12
y=x²-4x+3
O The value found in column #1 is greater than the value found in column #2.
The value found in column #1 is less than the value found in column #2.
O The value found in column #1 is equivalent to the value found in column #2.
The relationship between column #1 and column #2 cannot be determined by the information given.
8
Answers
The statement which is true concerning the values described in column #1 and column #2 is: B. The value found in column #1 is less than the value found in column #2.
How to determine the x-coordinate of the vertex of the graph?In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical expression:
Axis of symmetry, Xmax = -b/2a
Where:
a and b represents the coefficients of the first and second term in the quadratic function.
For the given quadratic function f(x) = -2x² - 4x + 12, we have:
Axis of symmetry, Xmax = -(-4)/2(-2)
Axis of symmetry, Xmax = 4/-4 = -1.
For the vertex of f(x) = -2x² - 4x + 12, we have:
f(-1) = -2(-1)² - 4(-1) + 12 = 14.
For the given quadratic function f(x) = x²-4x+3, we have:
Axis of symmetry, Xmax = -(-4)/2(1)
Axis of symmetry, Xmax = 4/2 = 2.
For the vertex of f(x) = x²-4x+3, we have:
f(2) = (2)²-4(2) +3 = -1.
Therefore, 2 is greater than -1.
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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]
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
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
