Geometry Question: Determine the lengths of each side of triangles LMN and L'M'N'.
What can we conclude about all of the side lengths?
Using your knowledge about parallel lines,
why must all of the angles be congruent?
Answers
The lengths of each side of the triangle LMN are, LM = 4 units, MN = 3.606 units, and NL = 2.236 units.
The lengths of each side of the triangle L'M'N' are, L'M' = 4 units, M'N' = 3.606 units, and N'L' = 2.236 units.
We can conclude that all corresponding sides are equal, and the two triangles are congruent.
All angles must be congruent, as the image L'M'N' has been parallelly translated from the preimage LMN.
The coordinates of the image are L' (-4, 1), M' (-4, 5), and N' (-2, 2). The length of each side of the triangle LMN:
LM = √((2 - 2)² + (-6 - (-2))²),
or, LM = √((0² + (-4)²),
or, LM = √16 = 4 units.
MN = √((2 - 4)² + (-2 - (-5))²),
or, MN = √((-2)² + (3)²),
or, MN = √(4 + 9) = √13 = 3.606 units.
NL = √((4 - 2)² + (-5 - (-6))²),
or, NL = √((2)² + (1)²)
or, NL = √(4 + 1) = √5 units = 2.236 units.
The length of each side of the triangle L'M'N':
L'M' = √((-4 - (-4))² + (5 - 1)²),
or, L'M' = √((0² + (4)²),
or, L'M' = √16 = 4 units.
M'N' = √((-4 - (-2))² + (5 - 2)²),
or, M'N' = √((-2)² + (3)²),
or, M'N' = √(4 + 9) = √13 = 3.606 units.
N'L' = √((-4 - (-2))² + (1 - 2))²),
or, N'L' = √((2)² + (1)²)
or, N'L' = √(4 + 1) = √5 units = 2.236 units.
Now, since LM = L'M', MN = M'N', and NL = N'L', that, is all the corresponding sides are equal, we can conclude that all corresponding sides are equal, and the two triangles are congruent.
Since the triangles are congruent, the image L'M'N' has been parallelly translated from the preimage LMN.
Thus, all angles must be congruent, as the image L'M'N' has been parallelly translated from the preimage LMN.
Every point moves the same amount and in the same direction throughout a translation. As a result of the picture being identical in size and shape to the preimage, a translation is referred to as a rigid transformation or isometry.
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Related Questions
anyone think they can help me??
Answers
The kind of transformation that is illustrated based on the information given is reflection.
What is transformation?It should be noted that transformation simply means the change in the position of an object while maintaining the length and other properties.
In this case, the kind of transformation that is illustrated based on the information given is reflection.
This is the flipping of the pre image and then producing the mirror image.
Here, there'll be no change in the shape of the size. This depicts congruency.
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Find the length of the arc on a circle with a radius of 2.4 kilometers and is intercepted by a central angle measuring 150°. leave your answer in terms of π.
Answers
If the radius of the circle exists 2.4 kilometers and is intercepted by a central angle measuring 150° then the length of the arc exists 5π inches.
What was the relation between the central angle and its intercepted arc?If the vertex of an angle exists in the center of the circle and the two sides of the angle are radii in the circle, then this angle exists named a central angle.Each central angle exists subtended by the opposite arc, the name of the arc exists the starting point and the finish point of the angle.There exists a relation between the central angle and its subtended arc the measure of the central angle equals half the measure of its subtended arc.The length of the subtended arc relies on the measurement of its central angle and the length of the radius and the measure of the arc.The measurement of the circle exists at 360°.The length of the circle exists at 2πr.The radius of the circle r = 2.4 kilometers
The measure of the central angle exists at 150°.
The length of the arc = central angle/360 × 2πr
The length of the arc = 150°/360° × 2 × π × 2.4 = 2π
The length of the arc exists 2π kilometers.
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HELP!
On a coordinate plane, 2 parallelograms are shown. Parallelogram 1 has points (0, 2), (2, 6), (6, 4), and (4, 0). Parallelogram 2 has points (2, 0), (4, negative 6), (2, negative 8), and (0, negative 2). How do the areas of the parallelograms compare? The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2. The area of parallelogram 1 is 2 square units greater than the area of parallelogram 2. The area of parallelogram 1 is equal to the area of parallelogram 2. The area of parallelogram 1 is 2 square units less than the area of parallelogram 2.
Answers
The areas of the parallelograms can be compared as: A. The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2.
What is a parallelogram?A parallelogram refers to a geometrical shape and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.
How to calculate the area of a triangle?Mathematically, the area of a triangle can be calculated by using this formula:
Area = ½ × b × h
Where:
b represents the base area.h represents the height.How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula;
A = LW
Where:
A represents the area of a rectangle.l represents the length of a rectangle.w represents the width of a rectangle.Next, we would determine the area of the two parallelograms as follows:
Area of parallelogram 1 = Area of red-rectangular figure - Area of triangle A - Area of triangle B - Area of triangle C - Area of triangle D.
Substituting the given parameters into the formula, we have;
Area of parallelogram 1 = (6 × 6) - (½ × 4 × 2) - (½ × 2 × 4)- (½ × 4 × 2) - (½ × 2 × 4)
Area of parallelogram 1 = 36 - 4 - 4 - 4 - 4
Area of parallelogram 1 = 36 - 16
Area of parallelogram 1 = 20 units².
For parallelogram 2, we have:
Area of parallelogram 2 = Area of blue-rectangular figure - Area of triangle P - Area of triangle Q - Area of triangle R - Area of triangle S.
Substituting the given parameters into the formula, we have;
Area of parallelogram 2 = (8 × 4) - (½ × 2 × 2) - (½ × 6 × 2)- (½ × 2 × 2) - (½ × 2 × 6)
Area of parallelogram 2 = 32 - 2 - 6 - 2 - 6
Area of parallelogram 2 = 32 - 16
Area of parallelogram 2 = 16 units².
Difference = Area of parallelogram 1 - Area of parallelogram 2
Difference = 20 - 16
Difference = 4 units².
In conclusion, we can infer and logically deduce that the area of parallelogram 1 is 4 square units greater than the area of parallelogram 2.
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Round 51.6172 to the
thousandths place.
Answers
Answer:
51.617
Step-by-step explanation:
tythe answer is 51.617 hope it helps
Explanation: The thousandths place is 51.6172 (Underlined is the thousandths) and since 2 is closest to zero we get an answer of 51.617.
Answer: 51.617
:)
Can you help me solve this, please?
Answers
Answer:
Step-by-step explanation:
When training models, you would typically place your data into three buckets: Train, Test, and Hold Out. What is the purpose of having hold-out data
Answers
Answer:
So, having "hold-out" data allows you to have a nonpartisan set of data (so to speak) for you to refer to later, once you have made use of the "train" and "test" sets. That way you can make a fair assessment as to the difference between the new and old ('hold-out") sets.
Or if you need to repeat the experiment or model again - then you can refer to the "hold out data"
Den pushes a desk 400 cm across the floor. he exerts a force of 10 n for 8 s to move the desk. what is his power output? (power: p = w/t)
Answers
The power output is = 5W
Correct option is B.
What is Power ?Power is the quantity of energy that is transferred or transformed in a certain length of time. The unit of power is the watt, which in the International System of Units is equivalent to one joule per second.. Power may also be referred to as activity in earlier writings. The scalar property of power
Power is characterized as the rate at which a thing performs labor.
According to the given information:P = W/T ..... (1)
Work is calculated as the product of force applied to an item and the distance that object has traveled.
W = F.s
When we plug this value into the equation above, we get:
P = (F. s)/t
where,
power = P =?W
F = 10N Force Exercised
s = Displacement = 400cm = 4m (1 meter = 100 centimeters).
t = Time required = 8s
Using the values in the equation above, we obtain
P = (10 x 4)/8
P = 5W
Hence, the correct option is Option b.
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I understand that the question you are looking for is :
Den pushes a desk 400 cm across the floor. He exerts a force of 10 N for 8 s to move the desk.
What is his power output? (Power: P = W/t)
a. 1.25 W
b. 5 W
c. 40 W
d.500 W
Given: the equation of a parabola is x2 = 8y. step 4: where does the focus for the given parabola lie?
Answers
The vertex of the given parabola [tex]$x^{2}=8 \mathrm{y}$[/tex] exists (0, 0).
What is the vertex of a parabola?The vertex of a parabola exists as the point at the intersection of the parabola and its line of symmetry. The vertex of the parabola exists as the minimum point on the graph for a positive right-handed parabola.
Given the equation of parabola exists [tex]$x^{2}=8 y$[/tex].
[tex]$\mathrm{y}=x^{2} / 8[/tex]
General vertex form for any given parabola exists [tex]$\mathrm{y}=\mathrm{a}(x-a)^{2}+\mathrm{b}$[/tex]
where (a, b) exists the coordinates of the vertex.
For this function it exists [tex]$\mathrm{y}=1 / 8(x-0)^{2}+0$[/tex]
The vertex of the given parabola exists at (0, 0).
Therefore, the vertex of the given parabola [tex]$x^{2}=8 \mathrm{y}$[/tex] exists (0, 0).
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Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answers
Answer:
Bottom left
Step-by-step explanation:
Since the slope has to be positive it can't be the ones on the right side since both of them are negative. And the bottom left one is rising 3 and running 4. (formula = rise/run). See image.
Select the statement that describes this expression: 10 + fraction 1 over 4x (5 + 3) − 3.
A) 10 more than fraction 1 over 4 of the sum of 5 and 3, then subtract 3
B) fraction 1 over 4 of 10 times the sum of 5 and 3, minus 3
C) 3 more than 3 plus 5 multiplied by fraction 1 over 4, then add 10
D) 10 times fraction 1 over 4 plus 3 and 5, minus 3
Answers
Answer:
B
Step-by-step explanation:
because i said so
[tex]\sqrt{2a-14} =2[/tex]
Answers
Answer:
a = 9
Step-by-step explanation:
[tex]\sqrt{2a-14} = 2[/tex]
2a - 14 = 4
2a = 18
a = 9
Answer:
The answer to this question is a = 9.
Step-by-step explanation:
To solve this problem, we need isolate the variable "a" on one side of the equation. Our first step must be to remove the square root. To do this, we should perform the inverse operation, which is squaring both sides.
√2a - 14 = 2
(√(2a - 14))² = 2²
2a - 14 = 4
Next, we should add 14 to both sides of the equation to get the variable term by itself.
2a - 14 + 14 = 4 + 14
2a = 18
Finally, we should divide both sides of the equation by 2 to remove the coefficient from the variable term.
a = 9
Therefore, the correct answer is a = 9.
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Malik randomly picked two numbers from 1 to 9 (including 1 and 9). the same number could be picked more than once. the first of the two numbers he picks is odd and less than 5. what is the probability that the sum of the two numbers malik picks is less than 5, given that the first number is odd and less than 5?
Answers
The probability that the sum of the two numbers Malik picks is less than 5, given that the first number is odd and less than 5 is 0.0494.
What is a probability?Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about how probable an event is to happen, or its chance of happening.
Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
Probability of an event P(E) = Number of favourable outcomes/Total number of outcomes.
Calculation for the given condition;
Either 1 or 3 must be present if a given integer is odd and smaller than 5.
The likelihood that it was picked from a set of nine numbers is (2/9).
The probability that the first integer is 1 is 50/50.
If it is and their combined number is less to 5, the second number will either be 1, 2, or 3.
The likelihood that it was picked out of the nine numbers is (3/9).
Additionally, there is a 50/50 probability that the first digit will be 3.
A second number is 1 if it is and the sum would be less than 5.
It was selected with a 1 in 9 chance of being one of the other 8 numbers.
The total probability is;
= (2/9) times [ (0.5 x 3/9) + (0.5 x 1/9) ]
= (2/9) times [ (1.5/9) + (0.5/9) ]
= (2/9) times [ 2/9 ] = 4/81
= 0.0494
Therefore, the probability that the sum of the two numbers malik picks is less than 5 is 0.0494.
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Answer:
See image
Step-by-step explanation:
Plato
What is the value of y?
Enter your answer in the box.
y =
Answers
Answer:
64°
Step-by-step explanation:
This is a question on angle properties.
Angle y + 37 + 79 = 180 (Sum of angles in a triangle)
Angle y + 116 = 180
Angle y = 180 - 116 = 64°
Jay received a holiday bonus in the amount of 66⅔% of his daily salary. Jay earns $300 each day. How much was his holiday bonus?
Answers
Answer: $200
Step-by-step explanation:
We will find 66⅔% of $300 to see how much Jay received. A percent divided by 100 becomes a decimal.
66⅔% / 100 ≈ 0.667
0.667 * $300 = $200
Resolver por igualación
2x+3y=2
6x+12y=1
Answers
Answer:
[tex]x = 3.5[/tex]
[tex]y\approx1.666666667[/tex]
Step-by-step explanation:
To solve simultaneous equations, at least one of our variables must have the same coefficient. We can easily multiply the first equation by 4 to get 12y on both sides, so let's do that:
[tex]8x + 12y = 8[/tex]
No let's subtract the second equation from the first equation to get the third equation:
[tex]2x = 7[/tex]
Solve:
[tex]x = 3.5[/tex]
Now, we can substitute this value into one of the original equations - let's use the second one:
[tex]21 + 12y = 1[/tex]
Solve:
[tex]12y = - 20[/tex]
[tex]y = - \frac{ - 20}{12} = \frac{ - 10}{6} = - \frac{5}{3} \approx - 1.66666666667[/tex]
Find the area of the polygon with vertices
A(0,5), B(0,2), C(-3,2), and D(-3,5)?
Answers
Answer: 9
Step-by-step explanation:
assuming that each box is 1 square inch then, you would get 9 square inches.
0,5 go down three to get 0,2
0,2 go left three to get -3,2
-3,2 go up three to get -3,5
-3,5 go right three to get 0,5
so you end up with a 3-by-3 box
Very much appreciated skin!!!
Answers
Answer:
6
Step-by-step explanation:
Given an isosceles triangle the two sides opposite of congruent angles are equal to eachother, so you can create an equation setting the two sides equal to eachother and solve for x.
[tex]x+4=3x-8\\x=3x-12\\-2x=-12\\x=6[/tex]
The length of AC is simply x, therefore 6
Which table represents a linear function?
The table shows the number of grapes eaten over several minutes.
What is the rate of change for the function on the table?
15 grapes eaten per minute
15 minutes to eat each grape
60 grapes eaten per minute
60 minutes to eat each grape
Answers
The rate of change for the function on the table is; 15 grapes eaten per minute.
What is the rate of change of the function described by the table?It follows from the complete question that the table given indicates that;
after 1min, 15 grapes had been eaten, after the next minute, 30 grapes had eaten, after the 3rd minute, 45 grapes had already been eaten.On this note, it is conclusive that the rate of change of the function represented by the table is; 15 grapes eaten per minute.
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Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles
Answers
The height of the triangle is 11.3 in. The correct option is C. 11.3 in
Calculating height of triangleFrom the question, we are to determine the height of the given triangle
The height of the given triangle is x in.
Now, we will determine the value of x
In the diagram, we can observe that the height divides the triangle into two equal halves
Thus,
By the Pythagorean theorem, we can write that
12² = x² + 4²
144 = x² + 16
144 - 16 = x²
∴ x² = 144 - 16
x² = 128
x = √128
x = 11.3
Hence, the height of the triangle is 11.3 in. The correct option is C. 11.3 in
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Find the least number should 2028 be multiplied so that the product is a perfect
square?
Answers
Thus, 2028 needs to be multiplied by 3 to become a perfect square. Therefore, the number 6084 has 3 pairs of equal prime factors . Hence, the smallest number by which 2028 must be multiplied so that the product is a perfect square is 7
The navy reports that the distribution of waist sizes among male sailors is approximately normal, with a mean of 32.6 inches and a standard deviation of 1.3 inches. part a: a male sailor whose waist is 34.1 inches is at what percentile? explain your reasoning and justify your work mathematically. (5 points) part b: the navy uniform supplier regularly stocks uniform pants between sizes 30 and 36. anyone with a waist circumference outside that interval requires a customized order. describe what this interval looks like if displayed visually. what percent of male sailors requires custom uniform pants? show your work and justify your reasoning mathematically. (5 points) (10 points)
Answers
Using the normal distribution, it is found that:
a. A male sailor whose waist is 34.1 inches is at the 87.5th percentile.
b. 5.7% of male sailors requires custom uniform pants.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 32.6, \sigma = 1.3[/tex]
For item a, the percentile is the p-value of Z when X = 34.1, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (34.1 - 32.6)/1.3
Z = 1.15
Z = 1.15 has a p-value of 0.875.
Hence 87.5th percentile.
For item b, the proportion who does not require an special order is the p-value of Z when X = 36 subtracted by the p-value of Z when X = 30, hence:
X = 36:
Z = (36 - 32.6)/1.3
Z = 2.62
Z = 2.62 has a p-value of 0.996.
X = 30:
Z = (30 - 32.6)/1.3
Z = -2
Z = -2 has a p-value of 0.023.
0.996 - 0.023 = 0.943.
Hence the proportion who requires an special order is:
1 - 0.943 = 0.057.
5.7% of male sailors requires custom uniform pants.
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Jesse and Mark are jogging along the route shown at a rate of 12 miles per hour. They start by jogging south along Capitol Street for 1 mile, then turn east on H Street and jog for 1.75 miles. At that point, Jesse is tired and decides to walk home along Florida Avenue at a rate of 5 miles per hour. Mark plans to jog back the way they came. Jesse wants to find out who will arrive home first and by how much time. Which statements should he consider when solving the problem? Check all that apply
Answers
Answer:
the answer is 1,2,4,5 and 7.
Answer: The answer is A,B,D,E,G
Step-by-step explanation: just trust me and enjoy your write answers. Have a nice day.
Find the perimeter of the shaded figure. PLS ASAP
Answers
Answer:
54
Step-by-step explanation:
pls answer this i will mark brainlest
Answers
Answer:
Answer is a
Step-by-step explanation:
it is the only answer that makes sense
find the prime factorization of 11250
Answers
Answer:
2 x 3 x 3 x 5 x 5 x 5 x 5
Step-by-step explanation:
see picture
Find the surface area of this composite solid.
Answers
Answer: C, 93m^2
Step-by-step explanation:
first step is to find the surface area of the base. it's 3x3, so that would be 9m^2. the sides of the rectangular prism are 5x3, so one side is 15m^2. there are 4, so 15x4=60m^2. now for the top, which is a triangular prism. each side has a height of 4 and a base of 3. the area of a triangle is 1/2bh, so 1/2(3)(4), which is 6. 4 of these makes 24 m^2. add up all of final numbers to get 9+60+24. this comes to 93m^2, or C.
HELP PLEASE!!
20 points for grabs
Answers
Step-by-step explanation:
....................
x=4
Replace x with 4
(5/4)(4)+2=2y
5+2=2y
7=2y
y=3.5
Drag each length to the correct location on the triangle. each length can be used more than once, but not all lengths will be used. what are the missing side lengths for the triangle? 10 5
Answers
Applying the trigonometry ratios, the missing lengths for right triangle ABC are: 12 and 8√3.
What is Trigonometry Ratios?Trigonometric ratios are defined as the values of all trigonometric functions based on the right-angled triangle's side ratio. The trigonometric ratios of any acute angle in a right-angled triangle are the ratios of its sides to that angle.
According to the given information:Reference angle (∅) = 60
Adjacent = 4√3
Opposite = ?
Apply TOA:tan 60 = opp/adj
tan 60 = Opp/4√3
√3 = opp/4√3
Opposite = √3 × 4√3
Opposite = 12
Find the other missing side:Reference angle (∅) = 60
Adjacent = 4√3
Hypotenuse = ?
Apply CAH:cos 60 = adj/hyp
cos 60 = 4√3/hyp
hyp = 4√3/cos 60
hyp = 4√3/1/2
hyp = 4√3 × 2
hyp = 8√3
Therefore, applying the trigonometry ratios, the missing lengths for right triangle ABC are: 12 and 8√3.
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how do I calculate y=3x - 2 without knowing thw value of x
Answers
Answer:
Step-by-step explanation:
easy
y=3x-2
-3x+y=-2
-3x=-2-y
x=2/3+1/3y
the selling price of a mobile after discount is 10000.if the discount is 10% find the mp
Answers
Answer:
Rs.11,111.11 (2 d.p.)
Step-by-step explanation:
The original price of the mobile is 100% of the price.
Therefore, the price of the mobile after a discount of 10% is 90% of the original price.
Let x be the original price.
If the price of the mobile after the discount is Rs.10000 then:
⇒ 90% of x = Rs.10000
⇒ 0.9x = 10000
⇒ x = 10000 ÷ 0.9
⇒ x = 11111.11 (2 d.p.)
M.P. =Rs 11111.1111
Answer:
Solution Given:
Selling price (S.P.) = Rs 10,000.
Discount =10%
Marked Price (M.P.)=?
we have
M.P. = S.P. + discount% of M.P.
keeping M.P. on same side
M.P. - discount% of M.P=S.P.
substituting value
M.P. - 10% of M.P.= Rs 10,000
taking common M.P.
M.P.(1-10%)=Rs. 10,000
we know that %=1/100
M.P.(1-10/100)=Rs 10,000
(9/10)M.P.= Rs 10,000
M.P.= Rs 10,000*10/9
M.P.=Rs11111.1111