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After the translation, the triangle stays in quadrant IV. It then reflects over to quadrant I, only to rotate back to quadrant IV again. The size and shape does not change. These transformations are known as "rigid transformations" which preserve segment lengths (aka keep them the same). So the final triangle is congruent to the original triangle. All that has happened is that it has moved around.
Related Questions
What is the length of line segment XZ
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The line segment XZ has a length of 16 units. Hence, the 3rd option is the correct choice. Computed using the tangent to the circle and the Pythagoras Theorem.
How is a tangent inclined to the circle?A tangent to a circle is always perpendicular to it, that is, the radius drawn from the center of the circle to the tangent, is always perpendicular to it.
What is the Pythagoras Theorem?According to the Pythagoras Theorem, in a right triangle, the square of the hypotenuse, that is, the side opposite to the right angle, is equal to the sum of the squares of the legs, that is, the other two sides.
How to solve the question?In the question, we are asked to find the length of the line segment XZ.
Firstly, we name the center of the circle O.
The diameter of the circle is given to be 12 units.
Thus, its radius = 12/2 = 6 units,
Joining the radius OW, we get a right triangle OWZ, as the radius from the center of the circle to the tangent is always perpendicular.
In the right triangle OWZ, by Pythagoras Theorem, we can write:
OZ² = OW² + WZ² {Since, OZ is the hypotenuse},
or, (k + 6)² = 6² + (k + 4)² {Since, OZ = OY + YZ = Radius + k = 6 + k, and OW = Radius = 6},
or, k² + 12k + 36 = 36 + k² + 8k + 16 {Using the formula (a + b)² = a² + 2ab + b²},
or, k² + 12k - k² - 8k = 36 + 16 - 36 {Rearranging},
or, 4k = 16 {Simplifying},
or, k = 4 {Simplifying}.
Now, XZ = XY + YZ = Diameter + k = 12 + 4 = 16 units.
Thus, line segment XZ has a length of 16 units. Hence, the 3rd option is the correct choice. Computed using the tangent to the circle and the Pythagoras Theorem.
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How many 5-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetition of digits is not allowed? a.119 b.16,807 c.2520 d.120
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c. 2520
Explanation:
Repetition is not allowed, therefore:
1st digit can be any of the given 7 numbers
2nd digit can be any of the remaining 6 numbers
3rd digit can be any of the remaining 5 numbers
4th digit can be any of the remaining 4 numbers
5th digit can be any of the remaining 3 numbers
This means that:
number of possible combinations = 7 * 6 * 5 * 4 * 3 = 2520 numbers
Hope this helps :)
if 0.75 pounds of chicken cost $2.10, how much does the chicken cost per pound?
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Choose an even number between 24 and 35. Draw a picture and explain why it is an even number.
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the area of a rectangle is 95 square yard. if the perimeter is 48 yards find the length and width of rectangle
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according to the condition w+l=48 and w*l=95.
Using these two equation:
[tex] \left \{ {{l+w=48} \atop {lw=95}} \right. \ =\ \textgreater \ \ \left[\begin{array}{ccc}l=24- \sqrt{481};w=24+ \sqrt{481}\\ \\l=24+ \sqrt{481};w=24- \sqrt{481}\end{array}[/tex]
The arithmetic sequence 2, 4, 6, 8, 10, . . . represents the set of even natural numbers. What is the 100th even natural number? a100 =
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Answer: The 100th even natural number is 200.
Step-by-step explanation: Given that the following arithmetic sequence represents the set of natural numbers :
2, 4, 6, 8, 10, . . ..
We are given to find the 100th even natural number, i.e., the 100-th term of the sequence.
We know that
the n-th term of an arithmetic sequence with first term a and common difference d is given by
[tex]a_n=a+(n-1)d.[/tex]
For the given sequence, we have
a = 2 and d = 4 - 2 = 6 - 4 = . . . =2.
Therefore, the 100-th term of the sequence will be
[tex]a_{100}=a+(100-1)d=2+99\times2=2+198=200.[/tex]
Thus, the 100th even natural number is 200.
when the figure below is rotated 90 degrees counterclockwise about the origin what would be the new coordinates of point c?
a (-5,3)
b (3,-5)
c (5,-3)
d (5,3)
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When a point is rotated 90 degrees counterclockwise about the origin, its new coordinates can be found by swapping the x and y coordinates and changing the sign of the new y coordinate. In this case, the new coordinates of point C would be (-3,-5).
Explanation:When a point is rotated 90 degrees counterclockwise about the origin, its new coordinates can be found by swapping the x and y coordinates and changing the sign of the new y coordinate.
In this case, point C has coordinates (5,-3). When we rotate it, the new x coordinate becomes -3 and the new y coordinate becomes -5. Therefore, the new coordinates of point C would be (-3,-5).
There are 5.28 cups of pudding to be put into 6 dishes.How much pudding should be put into each dish to make it equal?
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Note: In order to divide decimals, you move the decimal in the divisor (the number the other nimber is being divided by) by whatever amount to make it whole, and then do the same to the dividend by moving the decimal places of that number. Add 0's to the empty spots, and then divide like you would regular numbers. You may not need this now, but if you get questions like this and you can't use a calculator, it will really help.
A camper attaches a rope to the top of her tent to give it more support. She stakes the rope, which is 8 ft long, to the ground at a distance of 6 feet from the middle of her tent. About how tall is her tent? An image shows the tent, the staked rope, and the measurements as a right triangle. The height of the triangle is unknown. The base of the triangle is 6 feet. The hypotenuse is 8 feet.
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The support given to the tent forms a right triangle.
The height of the tent is 5.3 ft
The given parameters are:
[tex]\mathbf{Base = 6}[/tex]
[tex]\mathbf{Hypotenuse= 8}[/tex]
The height is calculated as follows:
[tex]\mathbf{Hypotenuse^2 = Base^2 + Height^2}[/tex]
Substitute known values
[tex]\mathbf{8^2 = 6^2 + Height^2}[/tex]
This gives
[tex]\mathbf{64 = 36 + Height^2}[/tex]
Collect like terms
[tex]\mathbf{Height^2 = 64 - 36 }[/tex]
[tex]\mathbf{Height^2 = 28 }[/tex]
Take square roots
[tex]\mathbf{Height = 5.3 }[/tex]
Hence, the height of the tent is 5.3 ft
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Write the rate using fraction form. Lisa ran 15 laps in 5 mins
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3laps in 1minute
What is the mixed number form for 56.4?
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Please make brainliest! ☺
for the simple harmonic motion equation d=2sin(pi/3t), what is the frequency?
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1/6
Answer:
Frequency of [tex]d=2\sin (\frac{\pi t}{3})[/tex] is [tex]\frac{1}{6}[/tex].
Step-by-step explanation:
We have the harmonic equation as, [tex]d=2\sin (\frac{\pi t}{3})[/tex].
It is known that,
If a function f(x) has a period P, then the function cf(bx) has period [tex]\frac{P}{|b|}[/tex].
So, we have,
As the function [tex]\sin t[/tex] has [tex]2\pi[/tex], then [tex]d=2\sin (\frac{\pi t}{3})[/tex] will have period [tex]\frac{2\pi}{\frac{\pi}{3}}[/tex] = 6
Further, the frequency of a function is the reciprocal of its period.
Thus, the frequency of [tex]d=2\sin (\frac{\pi t}{3})[/tex] is [tex]\frac{1}{6}[/tex].
A central angle measuring 150° intercepts an arc in a circle whose radius is 6. What is the area of the sector of the circle formed by this central angle? 15π 24π 30π 36π
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Answer: 15
Step-by-step explanation: its 15
the system of equations n= 2p+3 and n= 5+p is graphed what is the solution to the system of equations
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.. (p, n) = (2, 7)
Step-by-step explanation:
Graph is not given.
We have
n= 2 p+3
and
n= 5+p
That is
2 p+3 = 5 + p
p = 5 - 3
p = 2
Substituting in n= 5+p
n = 5 + 2 = 7
So the solution is n = 7 and p = 2
Leia cuts congruent triangular patches with an area of 63 square centimeters from a rectangular piece of fabric that is 27 centimeters long and 21 centimeters wide. How many of the patches can Leia cut from 33 pieces of the fabric?
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Leia can cut a total of 297 triangular patches from 33 pieces of fabric, with each piece yielding 9 patches.
To calculate how many triangular patches can Leia cut from 33 pieces of fabric, we first need to find out how many patches can be cut from a single piece of fabric. The area of each triangular patch is 63 square centimeters. The area of the fabric is length * width, which is 27 cm * 21 cm = 567 square centimeters.
Now, if we divide the area of the fabric by the area of one triangular patch, we get the number of patches per fabric piece: 567 cm2 / 63 cm2 = 9 patches per fabric piece.
Since Leia has 33 pieces of fabric, the total number of patches she can cut is 9 patches * 33 pieces = 297 patches.
caculate the distances tarryn if she drives 7/8 mile each way to and from work, 5 days a week
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She will cover 35/8 miles.
What is Unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
total distance in miles = 7/8 miles per day
So, in 5 days in a week.
She will cover
=5*7/8
=35/8 miles.
Hence, She will cover 35/8 miles.
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what is (½)3. ???????
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[tex] \frac{1}{2} \times 3 = \frac{1 \times 3}{2} = \frac{3}{2} = 1\frac{1}{2}[/tex]
[tex] (\frac{1}{2})^{3} = \frac{1^{3}}{2^{3}} = \frac{1}{8}[/tex]
The sale price of an item is $15 after a 70% discount is applied. What is the original price of the item?
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determine which statement is true about the zeros of the function graphed below
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Answer:
B
Step-by-step explanation:
Geoff planted dahlias in his garden. Dahlias have bulbs that divide and reproduce underground. In the first year, Geoff’s garden produced 6 bulbs. In the second year, it produced 12 bulbs, and in the third year, it produced 24 bulbs. If this pattern continues, how many bulbs should Geoff expect in the eighth year?
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x---------------> number of bulbs produced per year
n--------------> number of years
we know that
the pattern can be modeled through the following equation
x=6*[2^(n-1)]
for n=1 year
x=6*[2^(1-1)]----------> 6 bulbs
for n=2 year
x=6*[2^(2-1)]----------> 12 bulbs
for n=3 year
x=6*[2^(3-1)]----------> 24 bulbs
for n=8 year
x=6*[2^(8-1)]----------> 6*128=768 bulbs
the answer is 768 bulbs
Final answer:
Geoff's garden exhibits exponential growth of dahlia bulbs, doubling each year. By following this pattern, Geoff should expect to have 768 bulbs in the eighth year.
Explanation:
Geoff’s dahlia bulbs are showing a pattern of doubling in quantity each year. This is an example of exponential growth, a concept commonly explored in mathematics. To determine the number of bulbs Geoff can expect in the eighth year, we need to continue this pattern.
In the first year, there are 6 bulbs. The second year has 12 bulbs which is 6 multiplied by 2. The third year has 24 bulbs, which is 12 multiplied by 2. This pattern suggests that every year, the number of bulbs is the previous year's total multiplied by 2.
By following this pattern, to find the number of bulbs in the eighth year, we calculate:
Fourth year: 24 bulbs × 2 = 48 bulbs
Fifth year: 48 bulbs × 2 = 96 bulbs
Sixth year: 96 bulbs × 2 = 192 bulbs
Seventh year: 192 bulbs × 2 = 384 bulbs
Eighth year: 384 bulbs × 2 = 768 bulbs
Therefore, Geoff should expect to have 768 bulbs in his garden in the eighth year if the pattern of doubling the number of bulbs each year continues.
factor a^2b^2-7ab+10
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The factored form of −7ab+10 is (ab−5)(ab−2).
Explanation:To factor the expression −7ab+10, we look for two binomials whose product gives the original expression. In this case, the factors are
(ab−5)(ab−2).
Expanding
(ab−5)(ab−2) using the distributive property, we get:
(ab−5)(ab−2)=(ab)(ab)−(ab)(2)−(5)(ab)+(5)(2)
Simplifying each term, we get:
−2ab−5ab+10
Combining like terms, we have:
−7ab+10
Therefore, the factored form of −7ab+10 is (ab−5)(ab−2).
A rectangular prism has a length of 114 centimeters, a width of 4 centimeters, and a height of 314 centimeters.
What is the volume of the prism?
Enter your answer in the box as a simplified mixed number or a decimal.
cm³
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The volume of the prism is 143184 cm^3
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WORK: 114*4=456*314=143184
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Have a great day!
The blue shape is a dilation of the black shape. What is the scale factor of the dilation?
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blue shape:
(-5.10)
black shape:
(-1,2)
As one figure is the dilatation of another then:
k (-1,2) = (- 5,10)
From here we know:
-k = -5
Equivalently:
2k = 10
Where we conclude:
k = 5
Answer:
The scale factor of the dilation is:
k = 5
Answer:
the asnwer is 5
Step-by-step explanation:
i did this question
Marcy bought 1/4 pound of chocolate covered caramels at $2.69 a pound and 1/4 pound of coffee at $3.50 a pound how much did the candy cost
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a bin size of __ is most appropriate for the data set shown above??
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D) 10.
Hope I helped :-)
The mode of a set is the number that occurs the most in a set.
True False
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A girl throws a 2 kg rock with a net force of 6 N. What is the acceleration of the rock?
12m/s²
0.33m/s²
8m/s²
3m/s²
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acceleration = 3 m/s²
Explanation:
From Newton's second law:
Force = mass * acceleration
We are given that:
Force = 6 Newton
mass = 2 kg
Substitute with the givens in the above equation to get the acceleration as follows:
Force = mass * acceleration
6 = 2 * acceleration
acceleration = 6 / 2 = 3 m/s²
Hope this helps :)
A massless beam supports two weights as shown. 685 n w l 4 l 4 l 2 l a b find w such that the supporting force at a is zero. answer in units of n.
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Final answer:
To find the weight W such that the support force at A is zero, the principle of static equilibrium is used. By taking moments about point B and setting the sum of moments to zero, W is found to be 342.5 N.
Explanation:
The question requires the application of the principles of static equilibrium to find the unknown weight W that would set the supporting force at point A to zero. In static equilibrium, the sum of all forces and the sum of all torques (moments) about any point must be zero.
We can analyze the forces acting on the beam by taking moments about point B to find the value of W. Because the support at A is required to exert no force, we only consider the gravitational force due to the beam's weight and the weight applied at point B. By setting the sum of moments about B to zero, we can solve for W.
Using the conditions for static equilibrium:
Sum of vertical forces = 0
Sum of moments (torques) = 0
The moment leverage for the 685 N weight is at L/4, and for the unknown weight W, it is at L/2. Assuming the beam is massless the equation for the sum of moments around point B is:
(685 N) * (L/4) - (W) * (L/2) = 0
Solving for W:
W = (685 N) / 2
Thus, W is equal to 342.5 N.
what is -20 divide it by -2
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when you divide two negative numbers, the answer becomes positive:
-20/-2 = 10
10 is your answer
Note for multiplying and dividing:
two positive numbers will give you a positive answer
one negative numbers and one positive number will give you a negative answer
two negative numbers will give you a positive answer
hope this helps
What’s the sum of 2/5 and 2/4
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5 x 4 = 20
2 x 4 = 8
2 x 5 = 10
8/20 + 10/20 = 18/20
18/20, or 9/10 simplified, is your answer
Hope this helps