The triangles are congruent by SSS or HL. The diagram shows the sequence of three rigid transformations used to map ABC onto A"B"C". What is the sequence of the transformations? rotation, then reflection, then translation rotation, then translation, then reflection reflection, then translation, then rotation reflection, then rotation, then translation
Answers
Answer:- The sequence of the transformations for the given diagram must be reflection, then rotation, then translation.
Explanation:-
Given : Four triangles which are congruent by SSS postulate or HL theorem.
According to the given diagram , the rigid transformations are as follows
1. Reflection: ΔABC is flipped about BC to form ΔA'BC such that AC=A'C and its is already given that they are congruent thus the rigid transformation used here is reflection.
2. Rotation:- ΔA'BC is rotated about point A' at some angle to form ΔA'B'C' , and they are congruent (given). Thus the rigid transformation used here is rotation.
3.Translation:- ΔA'B'C' is translated exactly right by some factor to form ΔA"B"C" ∵ all the points have changed but as these triangles are congruent (given) then corresponding parts must be equal.Thus the rigid transformation used here is translation.
The sequence should be in the order for the given transformation as, reflection, then rotation, then translation. Thus the option D is the correct option.
How to rotate, reflect, and translation the figure?Rotation, reflection and translation is the way of transformation of an figure.
Rotation- Rotation of an object is rotating it about a fixed point without changing its shape and size.Reflection- Reflecting of an object is flipping it across a line without changing its shape and size.Translation- Translation of an object is the shifting of the object without changing its dimensions, without rotating it and without reflecting it.Given information-
In the given diagram the, triangle ABC is transformation into the three stages.
First the figure ABC is just flipped into the triangle A'BC by keeping the side BC fixed.Then the triangle A'BC is rotated around the point A' and to place of A'B'C'.Finally the figure is transact right from one place to another which is A"B"C".Hence the correct sequence of the transformations is reflection, then rotation, then translation. Thus the option D is the correct option.
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Related Questions
A serving of a certain cereal has 8 grams of sugar in 1 portion. Which equation shows how the amount of sugar and the number of portions are related? The s stands for the grams of sugar and the p stands for the portions of cereal.
Answers
it would be p=1 and s=8
it helps to keep on going like a chart
ex: 1/8 2/16 3/24 etc
your gamer unstopableboy21
The equation relating sugar amount and portions in a cereal serving is s = 8p. To find how many servings of cereal are needed to consume a specific amount of sugar, moles are converted to grams, then related to the sugar content per serving.
The equation relating the amount of sugar (s) and number of portions (p) in a serving of cereal is:
s = 8p
To answer the given problem, let's relate moles of sugar to grams and servings. First, we convert moles to grams, then use the sugar content in grams per serving to find the number of servings needed to consume the specified amount of sugar.
for the final answer do i add the 5 to (x+1) making it 5x+5 or do i leave it how it is? Also how do i find the domain
Answers
It depends on what your teacher or answer key expect. You can take a hint from the fact that the given polynomials are all multiplied out.
(5x^2 +5)/(x -1)
_____
The domain of polynomials in general is "all real numbers." However, you must exclude any specific numbers that make the rational expression be undefined. This includes numbers that make the denominator of the numerator zero, as well as those that make either the numerator or the denominator of the denominator zero. In other words, you must exclude from the domain
.. x ∈ {-5, 1, 2}
What does -3.4 E + 38 mean? (In normal number terms).
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Therefore, "-3.4 E + 38" means -3.4x10^38.
The "+38" means there are 38 zeros following a 1 as the exponent. It also works with negative numbers. For example, E-3 equals 10^-3
A circle has a radius of 2 cm.
How does the circumference of the circle compare to the area?
Drag and drop a phrase to correctly complete the sentence.
A. Greater Than
B. Less Than
C. Equal To
Answers
John says the transformation rule (x, y) es002-1.jpg (x + 4, y + 7) can be used to describe the slide of the pre-image (4, 5) to the image (0, –2). What was his error?
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The appropriate transformation rule is (x -4, y-7).
_____
John's signs were in error.
Sample Response: The pre-image is the point you start with. To check the transformation rule, substitute the values of the coordinates (4, 5) into the rule. You get (4, 5) → (4+4, 5+7). Simplify to get (4, 5) → (8, 12). This is the image. Instead the rule was applied to the image. This is the source of the error.
NEED HELP ASAP AND WILL GIVE A MEDAL ***
Tammy is using a treadmill, and when she puts her hands on the bar, sensors read her heart rate. Today, the sensors are telling Tammy that she is reaching 183, which is the highest rate in her target zone. What should she do to get the most effective workout?
Increase her running speed without adjusting the incline
Use the machine to maintain or decrease her intensity
Do additional aerobic exercises immediately after the treadmill
Use the machine to increase the incline and intensity,
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1. What is the value of w? 7, 3.5, 7(sqrt)of 3, 14
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The value of w is 14.
What is the value of w?The image given is a right angled triangle. In order to determine the value of the hypotenuse, w, tan would be used.
Cos 30 = adjacent / hypotenuse
√3 / 2 = 7√3 / hypotenuse
hypotenuse = 7√3 ÷ √3/2 = 14
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What is an equation stating that two ratios are equivalent.
Answers
A proportion is an equation that shows two ratios are equivalent, such as 1/2 = 3/6. It is commonly used with unit rates and unit scales in various fields including science, engineering, and everyday measurements.
Explanation:An equation stating that two ratios are equivalent is known as a proportion. For example, the equation 1/2 = 3/6 is a proportion because it shows that the two ratios have the same value. Proportions are very useful in various aspects of mathematics and science. Notably, they are essential when dealing with unit rates and unit scales, where comparisons between two measurements are made.
A unit rate is a special kind of ratio where one of the quantities is one, such as 55 miles per hour (55/1 mph). It describes how many units of the first type of measurement corresponds to one unit of the second type of measurement. Similar in concept, a unit scale compares the dimensions of an actual object to a model or drawing. For instance, a map might have a unit scale that reads 1 inch = 100 feet, which would be written as 1 inch/100 feet.
When applying proportions in real-world scenarios, we can create conversion factors to switch from one measurement to another. This is directly applicable to cooking recipes, chemistry with mole ratios, or engineering with the transformer equation, where ratios of different quantities are kept consistent.
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Before a renovation, a movie theater had 111 seats. after the renovation, the theater has 144 seats. what is the approximate percentage increase of the number of seats in the theater? if necessary, round to the nearest tenth of a percent.
Answers
percentage increase = 33/111 x 100 = 29.8% (nearest tenths)
Kail Ryans 10 laps around the track each day each lap around the track is 400 m meters how many times around the track will she need to run a total of 12 kilometers
Answers
1 km = 1000 m
12 km = 12,000 m
Each day, she runs 10 * 400 m = 4000 m
12,000 m / 4000 m = 3
It will take 3 days.
Have a nice day
Luis strength trains two times per week. He uses 12-pound weights and performs three sets of eight repetitions. He wants to improve his frequency. What should he do?
Increase to 10 repetitions.
Increase to 15-pound weights.
Increase to four sets.
Increase to three times per week.
Answers
To improve his frequency in strength training, Luis should increase his strength training days to three times per week. Hence, the correct option is fourth.
Luis wants to improve his frequency in strength training. Since he is already training twice a week, to enhance frequency, he should consider increasing the number of days he strength trains. Therefore, the best option for Luis would be to increase to three times per week. This aligns with the muscle-strengthening activities recommendation which suggests activities should be performed on 2 or more days a week, and this can be increased over time. Luis can also regularly increase the intensity of his workouts by adding more weight or sets, to ensure continuous muscle overload and growth.
You can draw a quadrilateral with two sets of parallel lines and no right angles? @KamiBug,
Answers
What number would you add to complete the square for the equation below?x2 + 10x = 0?
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[tex](\dfrac{b}{2})^2[/tex]
to each side.
Here, the coefficient b is equal to 10. We take half of this—5—and square it to get 25. We add this to both sides of the equation.
FYI, this equation can easily be factored, so there's no need to complete the square.
Determine the equation for the parabola graphed below.
Answers
So given the vertex is at (-1, 7), this means that b = -1 and c = 7:
y = a(x + 1)^2 + 7
Then we substitute a point from the graph (aside from the vertex). The easiest is the y-intercept of (0, 5):
5 = a(1)^2 + 7
a = -2
Therefore the equation is: y = -2(x + 1)^2 + 7 = -2x^2 - 4x + 5
The equation for the parabola graphed below is [tex]y = -2(x + 1)^2 + 7 = -2x^2 - 4x + 5[/tex]
A parabola's general equation is: y = a(x - b)2 + c
Given that the vertex is located at (-1, 7), this means that b = -1 and c = 7:
y = a(x + 1)^2 + 7
Then, instead of the vertex, we replace a point from the graph. The y-intercept of (0, 5) is the simplest:
5 = a(1)^2 + 7
a = -2
As a result, the equation is as follows: [tex]y = -2(x + 1)^2 + 7 = -2x^2 - 4x + 5[/tex]
You and your friend are standing back-to-back. Your friend runs 16 feet forward and then 12 feet right. At the same time, you run 12 feet forward and then 9 feet right. You stop and throw a baseball to your friend, who catches it. How far did you throw the baseball?
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784+9=x2
793=x2
28.1602556807=x
Determine 10th term : 5,-25,125
Answers
Keep doing this until you reach the tenth term.
You will get -9,765,625.
Hope this helps!
A rectangle is 1/2 feet long and 3/4 wide what is the area of rectangle
Answers
I assume you left out "ft" from the width, so the width is 3/4 ft.
A = LW = 1/2 ft * 3/4 ft = 3/8 ft^2
A = 1/2 × 3/4
A = 0.375 or 3/8
Which of the following represents the graph of f(x) = 2(x + 3)?
A. https://cdn.flvsgl.com/assessment_images/algebra2_v14_gs-xml/93228_559e8103/08_14_17.gif
B. https://cdn.flvsgl.com/assessment_images/algebra2_v14_gs-xml/93228_559e8103/08_14_18.gif
C. https://cdn.flvsgl.com/assessment_images/algebra2_v14_gs-xml/93228_559e8103/08_14_19.gif
D. https://cdn.flvsgl.com/assessment_images/algebra2_v14_gs-xml/93228_559e8103/08_14_20.gif
Answers
the correct expression is
y=2^(x+3)
using a graph tool
see the attached figure
the answer is the option C
The vertex of this parabola is at (-1,-3) which of the following could be its equation
A. x = -2(y + 3)2 - 1
B. x = -2(y - 1)2 - 3
C. x = -2(y - 3)2 - 1
D. x = -2(y + 1)2 - 3
Answers
Option: A is the correct answer.
[tex]x=-2(y+3)^2-1[/tex]
Step-by-step explanation:We know that any general equation of a right or left open parabola is given by:
x=a(y-k)^2+h
where if a<0 then the parabola open to the left and if a>0 then the parabola opens right.
Also the vertex of the parabola is: (h,k)
Now here we are given:
Vertex (h,k)=(-1,-3)
Also a= -2 in each of the options.
Hence, we have the equation of parabola as:
[tex]x=-2(y-(-3))^2+(-1)\\\\x=-2(y+3)^2-1[/tex]
Hence, the equation of the parabola is:
[tex]x=-2(y+3)^2-1[/tex]
what is the 8th term in the following sequence 28,33,38,43.....
Answers
28, 33, 38, 43, 48, 53, 58, 63 63 is the 8th term.
Can someone please help me solve this problem????
Weston is buying a house for $215,000. He is financing $185,000 and obtained a 30-year, fixed-rate mortgage with a 6.525% interest rate. How much are his monthly payments?
$1,005.94
$1,362.48
$1,614.09
$1,172.37,
Answers
PMT=P[(r/n)/1-(1+r/n)^-ny]
where:
P=Principal Value
r=rate
n=number of compoundings/year
y=year
To solve:
*Weston is only financing $185,000.
P=$185,000
r=6.525% or 0.06525
n=12 (monthly)
year=30
PMT=185000[(0.06525/12)/1-(1+0.6525/12)^-12*30
= 185000[(.0054375)/1-(1+.0054375)^-360
= 185000[(.0054375)/1-(1.0054375)^-360
= 185000[(.0054375)/1-(0.142)
= 185000[(.0054375)/(.858)
= 185000(0.00634)
= 1,172.37
Answer: $1,172.37
MEDAL!!!!
A narrator who is not part of the story and only knows particular portion of thoughts and feelings is
A. first person
B. second person
C. third person limited
D. third person omniscient
Answers
find the positive value of x in the geometric sequence 7x-2,4x+4,3x
Answers
Let's assume k the ratio.
[tex] \left \{ {{3x=k*(4x+4)} \atop {4x+4=k*(7x-2)}} \right. \\\\ \left \{ {{3x-4kx=4k} \atop {4x-7kx=-2k-4}} \right. \\\\ \left \{ {{x(3-4k)=4k} \atop {x(4-7k)=-2k-4}} \right. \\\\ \left \{ {{x=\dfrac{4k}{3-4k} \atop {x=\dfrac{-2k-4}{4-7k} \right. \\\\ \dfrac{4k}{3-4k}=\dfrac{-2k-4}{4-7k}\\\\ 36k^2-6k-12=0\\ 6k^2-k-2=0\\ \boxed{k= \dfrac{2}{3} \ or\ k= -\dfrac{1}{2}}\\\\ x=\dfrac{4*\dfrac{2}{3} }{3-4*\dfrac{2}{3} }=8\\ x=\dfrac{4*\dfrac{-1}{2} }{3-4*\dfrac{-1}{2} }=-\dfrac{2}{5}\\ [/tex]
[tex] \boxed{x= 8 \ or\ x= -\dfrac{2}{5}}\\\\ [/tex]
The value of x = 8.
We have a geometric sequence.
We have to determine the positive value of x.
Define Geometric Sequence.A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio.
According to the question -
The Geometric sequence is -
7x - 2, 4x + 4, 3x
According to the concept of Geometric sequence -
[tex]$\frac{a(2)}{a(1)} =\frac{a(3)}{a(2)}[/tex]
[tex]$\frac{4x+4}{7x-2} =\frac{3x}{4x +4}[/tex]
(4x + 4)(4x + 4) = 3x(7x - 2)
16[tex]x^{2}[/tex] + 16x + 16x + 16 = 21[tex]x^{2}[/tex] - 6x
16[tex]x^{2}[/tex] + 32x + 16 = 21[tex]x^{2}[/tex] - 6x
38x + 16 = 5[tex]x^{2}[/tex]
5[tex]x^{2}[/tex] - 38x - 16 = 0
Solve the above quadratic equation, you will get two roots -
x = 8 and x = 0.4
Since, we need positive value, therefore -
x = 8.
Hence, the value of x = 8.
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What is the minimum number of weighings on a balance scale need to find a counterfeit coin among 8 coins if the counterfeit coin is either lighter or heavier that the other true coins (which are all the same weight.) describe the algorithm to find the counterfeit coin in this minimum number of weighings?
Answers
First you would weigh coins against each other in pairs.
-Coins 1 and 2 vs Coins 3 and 4
-Coins 5 and 6 vs Coins 7 and 8
One of the 4 pairs would weigh more or less than the other. Once you have determined that pair and whether it is more or less, then weigh the coins in that pair against each other. Use whether the pairing was more or less than the other pairing to determine which of the coins you are looking for.
To find a counterfeit coin among 8 coins with a balance scale, divide the coins and use up to 3 weighings. The algorithm involves grouping and comparing the weights, identifying the counterfeit in the imbalanced group.
Algorithm to Find a Counterfeit Coin among 8 Coins
To find a counterfeit coin among 8 coins with a minimum number of weighings on a balance scale, we need at most 3 weighings. Here is the step-by-step algorithm:
Divide the 8 coins into three groups: two groups of 3 coins each, and one group of 2 coins.Weigh the two groups of 3 coins against each other.If they balance, the counterfeit coin is in the group of 2 coins. Weigh those two coins against each other to find the counterfeit one.If the two groups of 3 coins do not balance, take the lighter or heavier group (depending on whether the counterfeit is known to be lighter or heavier) and divide the 3 coins into three groups of 1 coin each.Weigh one coin against another. If they balance, the third coin is the counterfeit. If they do not balance, the heavier or lighter coin (again, depending on the counterfeit's known weight difference) is the counterfeit.With this algorithm, the maximum number of weighings needed to determine the counterfeit coin is three.
Please show all work
Answers
.. 10x +6y = 30 . . . . . . . total distance = 30 km
1b) x +y = 4 . . . . . . . . . . total of time spent running and walking is 4 hours
2) See the graph for points and plots.
suppose the digits cannot repeat. find the number of possible two-digit and three-digit codes. 1,2,3,4,5
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Jenna's parents required her to put $10 of her $50 monthly allowance into a savings account for what percent of her monthly allowance did this represent?
Answers
Final answer:
To determine the initial amount needed in a bank account to reach $10,000 in ten years with 10% compound interest, use the compound interest formula.
Explanation:
To find out how much money you need to put in a bank account to have $10,000 in ten years with 10% interest compounded annually:
Use the formula for compound interest: A = P(1 + r/n)^(nt)
Plug in the values: $10,000 = P(1 + 0.10/1)^(1*10)
Solve for P: P = $10,000 / (1.10^10)
Calculation:
PV = FV / (1 + r/n)^(n*t)
Inserting the known values:
PV = $10,000 / (1 + 0.10/1)^(1*10)
PV = $10,000 / (1.10)^10
Calculating the exponent:
PV = $10,000 / 2.59374
Finally:
PV = $3,855.43 (approximately)
Therefore, you need to put approximately $3,855.53 into the bank account initially.
choose the answer that best completes the sentence. if you know a root of a function is -2 + sqrt3 , then __
A. 2 + sqrt3 is a possible root
B. 2 + sqrt3 is a known root.
C. -2 - sqrt3 is a possible root.
D. -2 - sqrt3 is a known root.
Answers
answer:
d. -2 - sqrt3 is a known root.
hope this helps! :o)
Answer:the answer is D
Step-by-step explanation:
What is the lateral area of this regular octagonal pyramid?(PICTURE ONE)
114.8 cm²
162.4 cm²
229.7 cm²
281.3 cm²
2.What is the slant height x of the square pyramid?(PICTURE 2)
The figure shows a square pyramid. The slant height is shown as a dashed line perpendicular to the base edge and is labeled as x. The length of the lateral edge is 8 meters. The lateral edge makes a 60 degree angle with the base edge
Express your answer in radical form.
3.What is the surface area of this square pyramid? (pICTURE 3)
Round your answer to the nearest tenth, if necessary.
43.8 yd²
66.6 yd²
105 yd²
171.6 yd²
Answers
the lateral area of the pyramid is the total area of all the lateral faces excluding the base.
In this regular octagonal pyramid, the lateral sides are triangles. As there are 8 triangles we need to find the area of all 8 sides.
Area of one lateral triangle face = 1/2 * base * slant height
slant height is the hypotenuse of the right angled triangle formed from the base of the pyramid with the perpendicular height.
slant height - l
l² = 7² + 7² = 49 *2
l² = 98
l = √98
l = 9.9
Area = 1/2 * 5.8 cm * 9.9 cm
= 28.71 cm²
There are 8 sides
total lateral area = 8 * 28.71 = 229.68 rounded off is 229.7 cm²
third option is correct - 229.7 cm²
Q2)
in the triangular face, the lateral edge makes a 60° angle with the base edge. Therefore 2 of the angles are 60° each, since the sum of the interior angles of a triangle is 180°, the third angle too is 60°. this makes the triangle an equilateral triangle with equal angles, hence equal sides.
since lateral edge is 8 cm,base edge too is 8 cm.
since this is an equilateral triangle, the perpendicular line cuts the base edge at its midpoint, bisecting the line forming 2 right angled triangles.
in the right angled triangle, height of triangle is x slant height ,
base = 8 /2 = 4 cm
hypotenuse = 8 cm
We need to find x, use Pythogoras' theorem
4² + x² = 8²
16 + x² = 64
x² = 62 - 16
x = √48
x = √4x√4x√3
= 2x2√3
= 4√3 cm
Q3)
surface area of the square pyramid
surface area of the base + surface area of triangular faces
square area = length x length
= 6.2 x 6.2
= 38.44 yd²
triangular face area = 1/2 * length * height
since the angle between lateral edge and base edge is 60°, its an equilateral triangle where all sides are equal. in this case each side is 6.2 yd.
to find the perpendicular height, use pythogoras' theorem
the perpendicular line(slant height ) cuts the base edge at its midpoint, therefore length of the right angled triangle is = 6.2/2 = 3.1 yd
slant height - l
l² + 3.1² = 6.2²
l² = 38.44 -9.61
l² = 28.83
l = 5.37
area = 1/2 *length *height
= 1/2 * 6.2 * 5.37
= 16.64 yd²
there are 4 triangles = 4 * 16.64 = 66.58 yd²
total area = 38.44 + 66.58 = 105 yd²
correct answer is 3rd option - 105 yd²
Answer:
1. 229.7cm^2
2. 4 (square root) 3 cm
3. 16.64yd^2
Step-by-step explanation:
I just took th test, and came to confirm the other guys' answers ;)
How do you do this? It's so confusing! Please help!
Answers
notice AB ⟂ BC , whilst ∡B = 30°.
now, if we run a perpendicular line from C to AB, it'll be a 90° angle at M, however ∡AMC has to be 105°, so it has to be slanted more towards A, like in the picture, and surely you already know which one is the shortest.