Describe a sequence of transformation that maps triangle DOG onto triangle CAT
Answers
The transformation of the function is given by reflection along y axis and a translation of 5 units up
What is Reflection?Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.
The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).
Given data ,
Let the transformation be represented as A
Now , the equation will be
Let the triangle be represented as ΔODG
Now , the coordinates of ΔODG is
O = O ( -1 , -2 )
D = D ( -5 , -3 )
G = G ( -2 , -4 )
Now , the transformed triangle is ΔACT
The coordinates of ΔACT is
A = A ( 1 , 3 )
C = C ( 5 , 2 )
T = T ( 2 , 1 )
Now , on reflecting the triangle ΔODG along y axis , we get
When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse
So , the coordinates of triangle O'D'G' , we get
O' = O' ( 1 , -2 )
D' = D' ( 5 , -3 )
G = G' ( 2 , -4 )
Now , translating the triangle ΔO'D'G' up by 5 units , we get
The y coordinate of the triangle gets incremented by 5
So ,
A = O' ( 1 , -2 + 5 )
C = C ( 5 , -3 + 5 )
T = T ( 2 , -4 + 5 )
And , the coordinates of the triangle ΔACT is
A = A ( 1 , 3 )
C = C ( 5 , 2 )
T = T ( 2 , 1 )
Hence , the transformation is reflection along y axis and followed by translation of 5 units up
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Related Questions
the range of daliyh temperatures during march was 32 degreed and the range of the daily temperatures during july was 8 degrees which month had a greater difference between the hottest abd coldeest temperaturw4
Answers
Difference between coldest and hottest temperature was greater in march than July.
What is range?The range is the difference between the highest and lowest values within a set of numbers. To calculate range, subtract the smallest number from the largest number in the set.
Given,
Range of temperature in march = 32°
⇒ difference in temperature in march ΔT = 32°
Range of temperature in July = 8°
⇒ difference in temperature in July Δt = 8°
By the above observation
ΔT > Δt .
difference in temperature in march > difference in temperature in July.
Hence, In month of march, there was greater difference between the hottest and coldest temperature than in month of July.
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Can you help me with this
Answers
Answer:
m = 2
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
We see the y increase by 4 and the x increase by 2, so the slope is
m = 4/2 = 2
So, m = 2
if x-3 is directly proportional to the square y and x=5 when y=2 find x when y=6
Answers
Answer:
If x-3 is directly proportional to the square of y, then we can say that:
(x-3) = ky^2
Where k is a constant of proportionality.
If x=5 when y=2, we can substitute these values into the equation to find the value of k:
(5-3) = k(2)^2
2 = 4k
k = 0.5
Now that we have the value of k, we can use it to find the value of x when y=6:
(x-3) = (0.5)(6)^2
x-3 = 18
x = 21
So, if x is directly proportional to the square of y and x=5 when y=2, then x=21 when y=6.
Simplify the expression.
[tex](1+\frac{x}{y} )(\frac{4y^{2} }{x^{2} -y^{2} } )[/tex]
Answers
Answer:
4y / x-y
Step-by-step explanation:
First change 1 to y/y. This allows us to rewrite the first term as a single fraction.
We can also factor the denominator of the second term.
x^2 - y^2 factors into (x - y)(x + y)
The y cancels and also the term x+y cancels. See image.
200 Litres of a punch that contains 35% fruit juice is mixed with 300 L of another punch. The resulting fruit
punch is 20% fruit juice. Find the percent of fruit juice in the 300L of punch.
Please help me, (with show of math)
Answers
Yes, because as x increases, y increases and because all of the pairs represent the same ratio.
What does it mean when a ratio is proportional?When two sets of provided numbers change in proportion, the ratios are said to be directly proportional if they do so in the same direction.
If two ratios or fractions are equivalent, it may be shown using the proportion formula. By dividing the supplied numbers, we may determine the value that is missing. You may write the percentage formula as a: A and d are the extreme terms, and b and c are the middle terms, according to the formula b::c: d = a/b = c/d.
Yes, because as x increases, y increases.
Yes, because all of the pairs represent the same ratio.
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Complete the table with values for x or y that make this equation true : 3x+y=15.
Answers
The table with values for x or y that make this equation true : 3x + y = 15 are
x 2 4 6 0 3 5 7/3
y 9 3 -3 15 6 0 8
What is solving an equation?
One-step equations can be solved in four different ways: by adding, subtracting, multiplying, and dividing. In an equation, both sides will remain equal if we add the same amount to each side.
Consider, the given equation: 3x + y = 15
We have to complete the given table for the values of x and y.
Plug x = 2 in the given equation.
⇒ 3(2) + y = 15
6 + y = 16
y = 9
Plug y = 3 in the given equation.
3x + 3 = 15
3x = 12
x = 4
Plug x = 6 in the given equation.
3(6) + y = 15
18 + y = 15
y = -3
Plug x = 0 in the given equation.
3(0) + y = 15
y = 15
Plug x = 3 in the given equation.
3(3) + y = 15
9 + y = 15
y = 6
Plug y = 0 in the given equation.
3x + 0 = 15
3x = 15
x = 5
Plug y = 8 in the given equation.
3x + 8 = 15
3x = 7
x = 7/3
Hence, the table with values for x or y that make this equation true : 3x+y=15 are
x 2 4 6 0 3 5 7/3
y 9 3 -3 15 6 0 8
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fill in the table using this function rule. y=6x-36
Answers
There was no table so I created one
From the equation I can see at 0, y = -36
From there I used positive numbers from 0 and substituted them into the equation for a y solution.
Simplify by using order of operations:
4+(9 x 2) divided by (4 - 1) -4
Answers
4+(9x2)/(4-1)-4
4+18/3-4
4+6-4
10-4
I need help solving for x
Answers
To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the equation. Simplify the values to find the result.
What Does Solve for x Mean?Let's begin with a straightforward equation: x + 2 = 7.
How do you obtain X on your own?
Take away two from both sides.
⇒ x + 2 - 2 = 7 - 2\s⇒ x = 5
Check the solution, x = 5, by reentering it into the equation. We get 5 + 2= 7.
R.H.S. L.H.S.
Utilizing triangle properties or the Pythagorean theorem, we can get a solution for the unknown side or angle of a triangle.
With the aid of an example, let's clarify how to solve for x in a triangle.
Two of ABC's legs, which measure 7 units and 24 units respectively, are right-angled at B. Look for the hypotenuse X.
By using the Pythagorean theorem to ABC,
We obtain AC2 = AB2 + BC2, where x2 = 72 + 242, 49 + 576, and 625 where x2 = 625.
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Is (x 5) a factor of f(x) = x3 − 4x2 3x 7? explain your reasoning.
Answers
(x+5) is not a factor of f(x) because x = -5 does not satisfy the given equation f(x) = x³ - 4x² + 3x + 7.
Step 1. First we solve the equation x +5 = 0, we get
x = -5
Step 2. By putting the value of x = -5 in f(x) check whether we get a zero or a number other than zero.
If we get zero then x+5 is a factor of f(x) and if we get a number other than zero then x+5 is not a factor of f(x)
f(-5) = (-5)³ − 4(-5)² + 3(-5) + 7 = - 233
Since we got -233 and not 0. Therefore, (x+5) is not a factor of f(x).
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How do the faces of
a three-dimensional figure determine che
two-dimensional shapes created by slicing
the figure?
Answers
The process of the faces of a three-dimensional figure determine two-dimensional shapes created by slicing the figure is explained below.
The term three dimensional figure is defined as solid shapes or figures that have three dimensions.
Basically these kind of shapes has length, width and height are the dimensions of 3D shapes and the common names of these shapes are cube, cuboid, cone, cylinder and sphere.
Where as the two dimensional figure is defined as horizontal and vertical axes that is x-axis and y-axis) and it is also known as 2d shapes are flat figures that have only length and width. And thus shapes do not have thickness or height.
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y=1/4x+3 in standard form
Answers
Answer:
Step-by-step explanation:
2
EU Migration Study
Discussion Question: In the EU migration study, 257 of the 583 immigrants
sampled were male. Let's assume the Trump/Farage claim is true: 60% of all
immigrants are male (p = 0. 60). What is the probability of obtaining 257 or fewer
males in a sample of 583 immigrants? Does this probability make you doubt the
Trump/Farage claim? Why or why not?
P
Normal(up= 0. 6, Op=. 020)
ộ ô
Ô P
ppp
PPPP
ppppppp
Skew The
Scrint
Answers
This probability does not support the Trump/Farage claim that 60% of all immigrants are male.
What is the probability?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes, and how likely they are.
The probability of obtaining 257 or fewer males in a sample of 583 immigrants can be found using the binomial probability formula, which calculates the probability of a specific number of successes (male immigrants) in a fixed number of trials (sample size) with a fixed probability of success (p = 0.60).
Using the binomial formula, the probability of obtaining 257 or fewer males in a sample of 583 immigrants can be found by summing the probabilities of obtaining 257 males, 256 males, 255 males, etc. up to 0 males.
Using a binomial calculator, we can find that the probability of obtaining 257 or fewer males in a sample of 583 immigrants is about 0.04.
This probability is quite low, which suggests that it is unlikely to obtain 257 or fewer males in a sample of 583 immigrants if the proportion of male immigrants is actually 60%.
Therefore, this probability does not support the Trump/Farage claim that 60% of all immigrants are male.
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Two shipping companies charge different amounts to ship a package. Company A charges a fee of $6.50 and $0.35 for each pound. Company B charges a fee of $7.25 and $0.25 for each pound. Write an equation that could be used to find p, the number of pounds each package would have to weigh for the total cost of shipping the packages to be the same.
Answers
The number of pounds each package would have to weigh for the total cost of shipping the packages to be the same will be 7.50 pounds.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The cost to transport an item varies between two shipping providers. The price charged by Company A is $6.50 plus $0.35 per pound. Charges from Company B are $7.25 plus $0.25 per pound.
Let 'p' be the number of pounds and 'T' be the total cost of shipping. Then the equations are given as,
T = 0.35p + 6.50
T = 0.25p + 7.25
If the total cost of shipping the packages is to be the same. Then the number of pounds is given as,
0.35p + 6.50 = 0.25p + 7.25
0.35p - 0.25p = 7.25 - 6.50
0.10p = 0.75
p = 7.50 pounds
The number of pounds each package would have to weigh for the total cost of shipping the packages to be the same will be 7.50 pounds.
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I’m doing math homework and is about functions they said f(x)= x-3 and g(x)= √x-2
After I set them up I have this
am I supposed to just add the numbers or is there something else to do?
√ (x-3)-2
Answers
Answer: It looks like you are trying to find the value of the function h(x) = √ (x-3) - 2.
To find the value of this function for a given value of x, you need to substitute the value of x into the function definition and simplify the expression.
For example, if you want to find the value of h(x) for x = 5, you would substitute 5 for x in the function definition and simplify the expression to get:
h(5) = √(5-3) - 2
= √2 - 2
= 1.4 - 2
= -0.6
Therefore, the value of h(x) for x = 5 is -0.6.
You can follow this same process to find the value of h(x) for any other value of x. Just be sure to substitute the correct value of x into the function definition and simplify the expression to find the final result.
Step-by-step explanation:
Answer:
g[f(x)]
Step-by-step explanation:
Given functions:
[tex]f(x)=x-3[/tex]
[tex]g(x)=\sqrt{x}-2[/tex]
Composite functions are when the output of one function is used as the input of another.
Therefore, to create √(x-3)-2, substitute the function f(x) in place of the x in function g(x):
[tex]\begin{aligned}\implies g[f(x)]&=\sqrt{f(x)}-2\\&=\sqrt{x-3}-2\end{aligned}[/tex]
In 2010, the population of a city was 59,000. From 2010 to 2015, the population grew by 7.3%. From 2015 to 2020, it fell by 5.3%. To the nearest whole number, by what percent did the city grow from 2010 to 2020?
Answers
To the nearest percent, the percent by which the population grew from 2010 to 2020 is; 2%
How to find the percentage growth?Percentage increase is defined as the difference between the final value and the initial value, expressed in the form of a percentage.
Now, we are told that;
Initial Population in 2010 = 59000
From 2010 to 2015, the population grew by 7.3%. Thus;
Population in 2015 = 1.073 * 59000 = 63307
Now, we are told that from 2015 to 2020, it fell by 5.3%. Thus;
Population in 2020 = 63307 * (100% - 5.3%)
= 59952
Thus, percentage increase from 2010 to 2020 = (59952 - 59000)/59000) * 100% = 1.61% ≈ 2%
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5.07 - 2.148
????????????
Answers
Answer:
Step-by-step explanation: 2.922
Answer: 2.922
Step-by-step explanation: (Look at the attachment for the best experience, or idea) So, as you can see in the attachment below, we first need to line up the decimal points with one another. They subtract in line with the other decimals and borrow. As we know, our answer is 2.922.
6 less than 3 times a number 42 what is the number
Answers
Answer: -120
6 less than is 6 - and 3 times a number 42 is 3 x 42 so...
6 - (3 x 42) = -120
Find the x and y Intercept of x + 2y = -14
Answers
Answer:
Y-intercept: (0, -7)
X-intercept: (-14,0)
Step-by-step explanation:
To find the y-intercept, we need to put 0 in for x
0 + 2y = -14
2y = -14
y = -7
So, the y-intercept is located at (0, -7)
To find the x-intercept, we need to put 0 in for y
x + 2(0) = -14
x = -14
So, the x-intercept is located at (-14,0)
Step-by-step explanation:
To find the y-intercep, we need to put 0 in for x
0 + 2y= -14
2y = -14
y = - 7
So, the y - intercept is located at ( 0, - 7)
WOMENA NGO provides transport refund to every member who attend a seminar as below. a Trainer of trainers (TOT) is given 40% of the money, a Trainer is given 30% of the money,a student lead and other participants share the remaining percentage equally.As a learner,using the knowledge of angles,drawing figures and percentages, draw a pie chart that would help the organization distribute the Transport refund. (Use radius of 4cm)
Answers
Therefore , the solution to the given question of percentage comes out to be 7.89.
What is a percentage?A% is a number that represents the percentage of 100 that it is, and it can also be stated as a decimal or a fraction. To convert a percentage to a fraction, place 100 in the denominator and the percentage number in the numerator.
Here,
Given : 40% of the money, a Trainer is given
30% of the money ,a student lead
Find the discount
40 * .15 = 6
Take this from the original price
0.30* 6.3 =1.89
The sale price is 6 + 1.89 =7.89
Therefore , the solution to the given question of percentage comes out to be 7.89.
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A building with a height of 48 meter casts a shadow that is 30 meter long. A person standing next to the building casts shadow that is 0.8 meter long. How tall is the person
Answers
The height of the person is approximately 0.426 meters or 42.6 cm.
We can use the concept of similar triangles to solve this problem. The height of the building and the length of its shadow form a right triangle, with the height as the opposite side and the shadow as the hypotenuse. The person and their shadow also form a similar right triangle, with the height of the person as the opposite side and the shadow as the hypotenuse.
We can set up the following proportion:
(Height of building)/(length of shadow) = (height of person)/(length of shadow)
48/30 = h/0.8
Solving for h, we get:
h = (48/30) * 0.8 = 0.533 * 0.8 = 0.426
Therefore, the height of the person is approximately 0.426 meters or 42.6 cm.
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Leo's bank balances at the end of months 1, 2, and 3 are $1,500.00, $1,530.00, and $1,560.60, respectively. The balances form a geometric sequence.
What will Leo's balance be after 8 months?
Leo's bank balance will be $
after 8 months.
Answers
Leo's balance after 8 months is $1725.
What is a geometric sequence?A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.
Example:
2, 4, 8, 16 is a geometric sequence.
We have,
1500, 1530, and 1560 is a geometric sequence.
First term.
a = 1500
Common ratio.
r = 1.02
The nth term of a geometric sequence is a[tex]r^{n-1}[/tex].
Now,
For n = 8,
8th term.
= 1500 x [tex]1.02^7[/tex]
= 1500 x 1.15
= 1725
Thus,
The balance after 8 months is $1725.
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I NEED ANSWERS ASAP!!!!!!!!!!!
If WY is 4. 6, what is MZ? Round your
answer to the nearest tenth. Write NA if there
is not enough information given.
Answers
NA (There is not enough information given to determine the value of MZ)
In this question, we are given that WY is 4.6 for us to find the value of MZ We need more information to be in a position to answer this. More information includes maybe we know the value of M or at least having some relationship between WY and MZ for us to draw a conclusion and come up with the value of MZ. If at all we had a common value in WY and MZ say M then it could be easier to come to a conclusion and finally get the value of MZ.
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Determine the range of f(x) = x + 51.
A-{yl-00
B-{y 1-5
C-{y|0 ≤y <∞0}
D-{y | 5 ≤y < 00}
Answers
Answer:
90670998.89999999999999
Donny is raising money for the school charity drive by mowing lawns for $9.75 per lawn. How much will he raise for the drive?
is this proportional or non proportional and why.
Answers
For two numbers to be proportional, they need to be directly increasing or decreasing in a constant ratio.
If Donny makes $9.75 per lawn, we can make a table that looks like this:
1 Lawn = $9.95
2 Lawns = $19.90
3 Lawns = $29.85...
And so on.
You can see this is proportional because it has a constant ratio between both elements.
(1 to 9.95)
So, it is proportional.
A boat is traveling due east for 130 miles. The boat travels another 72 miles at a bearing N38E. Determine the distance, direction angle, and bearing of the boat from its original location.
Answers
The distance of the boat is 191.2 miles, 12.8° and N12.8E from the original location.
Using Trignometry to find the boat's distance:To calculate the distance, direction angle, and bearing of the boat from its original location, we will need to use trigonometry to determine the final position of the boat.
a) The distance traveled in the eastward direction is 130 miles. Then, using the bearing of N38E, we can calculate the northward and eastward distances traveled in the second leg of the journey. The bearing of N38E can be thought of as an angle of 38 degrees measured clockwise from due east.
Using trigonometry to calculate the northward distance traveled, we have,
(72 miles) * (sin 38°)
= 36 miles
And the eastward distance traveled is (72 miles) * (cos 38°)
= 59.04 miles.
The final position of the boat is at a distance can be calculated by:
130 miles east + 59.04 miles east
= 189.04 miles east and 36 miles north from the original location.
b) To find the distance from the original location, we use the Pythagorean theorem,
d = [tex]\sqrt{189.04^{2} +36^{2} }[/tex]
d = 191.2 miles
To find the direction angle, we use arctan(north/east) = arctan(36/189.04) = 12.8°
Bearing is the direction angle measured clockwise from north. So, bearing = 12.8°
Hence, the final position of the boat is 191.2 miles, 12.8°, and N12.8E from the original location.
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Which is the product of 15 [tex]\frac{5}{12}[/tex]
( 100 POINTS )
Answers
Answer:
[tex] \sf \: \frac{75}{12} \: (or) \: 6.25[/tex]
Step-by-step explanation:
Given problem,
[tex] \sf \rightarrow \: 15 \times \frac{5}{12} [/tex]
Let's solve the problem,
[tex] \sf \rightarrow \: 15 \times \frac{5}{12} [/tex]
[tex] \sf \rightarrow \: \frac{(15 \times 5)}{12} [/tex]
[tex] \sf \rightarrow \: \frac{75}{12} = 6.25[/tex]
Hence, the product is 6.25.
Identify the surface whose equation is given.
p = sin θ sin φ
Answers
Therefore , the solution of the given problem of trigonometry comes out to be surface x² + y² + z² = p².
What is trigonometry?Trigonometry is the discipline of mathematics that studies correlations between angles and sides of triangles. Trigonometry is present in all of geometry because every straight-sided shape may be reduced to a set of triangles. Remarkably intricate connections exist between trigonometry and other areas of mathematics, particularly calculus, real or complicated, exponentials, logarithms, and infinite series.
Here,
Given:
p = sinθ sin∅
To Locate:
the equation's surface
Solution:
adding p to both sides of the equation
p sinθ sin∅ = p²
p sinθ sin∅ = p²
p sinθ sin∅ =y
x²+y²+z²=y
x² + y² - y+ z² = 0
x²+ (y - 1/2)²+ z² = 1/4
r² =1/4, r= √1/4,
The surface of the sphere having a radius of 1/2 and a center at (0, 1/2, 0) is designated as 1/4.
Sphere-centered coordinates
x = sin p sin
y = sin(p), sin(p),
z = p cos∅
x² + y² + z² = p²
Therefore , the solution of the given problem comes out to be surface
x² + y² + z² = p².
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Help
1. 4 < 7 Multiply both sides by 3, then by 2, then by 4, then by 9
2. 11 > -2 Add 3 to both sides, then add 3, then add (-4)
3. -2 \leq -2 Subtract 6 from both sides, then 8, and then 2
4. -4 < 8 Divide both sides by -4, then by -2
5. Write a short explanation of the effects of the above operations. Did this affect the inequality sign? Was it still true? Why or why not?
Answers
The short explanation of the effects of the above operations will not affect the inequality.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
1. 4 < 7 Multiply both sides by 3, then by 2, then by 4, then by 9, then we have
4 x 3 x 2 x 4 x 9 < 7 x 3 x 2 x 4 x 9
864 < 1512
2. 11 > -2 Add 3 to both sides, then add 3, then add (-4)
11 + 3 + (-4) > - 2 + 3 + (-4)
10 > - 3
3. -2 ≤ -2 Subtract 6 from both sides, then 8, and then 2
-2 - 6 - 8 - 2 ≤ -2 - 6 - 8 - 2
- 18 ≤ - 18
4. -4 < 8 Divide both sides by -4, then by -2
- 4 / (-4) > 8 / (-4)
1 / (-2) > - 2 / (-2)
- 1/2 < 1
The short explanation of the effects of the above operations will not affect the inequality.
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Y=6 and x=-1 parallel or perpendicular line
Answers
Answer:
perpendicular
Step-by-step explanation: