Triangle RST was reflected over the x-axis and translated 2 units to the left to form triangle ABC. The figures are congruent.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
Reflection, translation and rotation are rigid transformation which preserve the shape and size of a figure, forming congruent figures.
Triangle RST was reflected over the x-axis and translated 2 units to the left to form triangle ABC. The figures are congruent.
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Answer:
Option A
Step-by-step explanation:
Prove that
cos^4∆ - sin^4∆ = 2cos^2∆ - 1
[tex]\cos^{4} x-\sin^{4} x\\\\=(\cos^{2} x+\sin^{2} x)(\cos^{2} x-\sin^{2} x)\\\\=\cos^{2} x-\sin^{2} x\\\\=\cos^{2} x-(1-\cos^{2} x)\\\\=2\cos^{2} x-1[/tex]
5 Quick algebra 1 questions for 50 points!
Only answer if you know the answer! :)
Step-by-step explanation:
So it's important to define what parallel is. If one line is parallel to another line, it will never intersect the other line. This means the two lines must be changing by the same amount simultaneously. In other words, they have the same slope. It's also important to remember that same slope doesn't mean they're parallel. You also have to look at the y-intercept. If they have the same y-intercept, and the same slope, then they're the same line. So two lines are only parallel, if the slopes are the same and they have different y-intercepts.
So now that you understand what's parallel let's look at some of the problems
1. So this is kind of tricky, because as I mentioned before, parallel lines have the same slope, but in this case a slope cannot be defined. For two vertical lines to be parallel, they just have to have different a different x-constant. Because x is what's constant, and if they're different, then the two lines will never intersect. This gives us the general formula for a vertical parallel line: [tex]x=a\text{ where a} \ne3[/tex] (this is specific to this problem, since the constant in the graph is x=3). Since the parallel line must pass through (-5, -4) this means that the constant for x, must be -5, because the x is constant, if it equals anything else, it will never equal -5. So the parallel line in this case will be: [tex]x=-5[/tex]
2. So the equation is already in slope-intercept form, so we don't have to solve for the slope. The slope in this case is 8, which can be determined by looking at the formula. This gives us the general formula for the parallel line: [tex]y=8x+b\text{ where b}\ne 4[/tex]. b cannot equal 4, because if it did, then we would have two lines that are the same, not parallel, otherwise b can be anything else. Since we have a point that the parallel line goes through, we can plug this in as (x, y) to solve for b: [tex]21=8(4)+b \implies21=32+b\implies -11=b[/tex]. So now this gives us the complete equation: [tex]y=8x-11[/tex]
3. The image is a bit low quality, although from what I can see the linear equation intersects the origin (0, 0) and (4, -1). This gives us the equation for the slope -1/4 (rise/run). which gives is the slope -1/4. So this gives us the general equation: [tex]y=-\frac{1}{4}x+b \text{ where b} \ne0[/tex]. b cannot equal 0, since it would then have the same y-intercept, meaning the two lines would be the same. In this case we also get some coordinates which we can plug into the equation to solve for b: [tex]-5=-\frac{1}{4}(12)+b\implies -5=-3+b\implies-2=b[/tex]. This gives us the complete formula: [tex]y=-\frac{1}{4}x-2[/tex]
4. This is similar to the vertical line, as there is a constant value, but in this case a slope can be defined, and that slope is 0; it's 0 for all horizontal lines. So we have the general equation: [tex]y=0x+b \text{ where b}\ne4[/tex]. This can be simplified to: [tex]y=b \text{ where b} \ne4[/tex]. Since the line passes through (13, -7), that means b must equal -7, because the y does not depend on x. It's a constant value. So you have the equation: [tex]y=-7[/tex]
5. [tex]y-6=\frac{3}{5}(x+5)[/tex]. So in this case we have the point-slope form. We don't need to convert it to the slope-intercept form, since all we need to form the parallel line is the slope, sort of. You technically do need the y-intercept, so you know what b cannot equal, so that you don't have the same line, but I'm assuming, the coordinates they're giving you, do not pass through the original line, but rather a parallel line. So we have the general equation: [tex]y=\frac{3}{5}x+b[/tex]. Plugging the given coordinates give you the equation: [tex]8=\frac{3}{5}(0)+b \implies8=b[/tex]. You didn't really need to do this, since if you noticed the coordinates have x=0, which means the y-value by definition is what b is equal to, since b is the y-intercept. So this gives you the equation: [tex]y=\frac{3}{5}x+8[/tex]
Tracy made a Venn diagram to compare the numbers of students in her English and history classes. How many students are in Tracy's English class?
The total number of persons that are ion Tracy's English class is given as 21.
How to find the persons in the English Class
We have the Venn diagram showing that there are 14 people in English
15 people in history
While there is a number of 7 students intersecting the two subjects.
Hence the people that attend both history and English are 7.
From here we would know that an English class would be made up of 14 + 7 persons
= 21 persons.
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At a school there are five lessons in a day in total the five lessons last 4 hours assume that each session lasts the same amount of time how many minutes long is the final lesson
Answer:
48 minutes long
Step-by-step explanation:
For a total amount of minutes the lessons are, take 4x60. 4 for the total time in the lessons and 60 for 60 minutes in an hour. 4x60= 240 minutes.
Take 240/5. 240 is the total number of minutes and with the five lessons being the same amount of time, you divide the total number of minutes by the number of lessons. 240/5= 48 minutes
Point P is located at (−2, 7), and point R is located at (1, 0). Find the y value for the point Q that is located two thirds the distance from point P to point R.
4.9
4.7
2.5
2.3
Answer:
4.7
Explanation:
A point is positioned at minus two, seven. At one, zero, you'll find point R. Determine the value of Y. Regarding point Q. That is 2/3 of the distance between points P. So, negative two becomes positive seven. So, we have minus twenty-seven and 1 common zero. So, if we place a line between these, we must calculate the distance. First, you should be aware that you may achieve this using the distance formula. I prefer to conceive of it as the Pythagorean Theorem. So, the distance is 3^2 and 7^2, which is D^2. So, 9+49=58. And, we'll take the square root of it. As a result, the square root of 58=D. And, you want to be 2/3 the distance between points P and B. So, divide this by 2/3. So, this is close to 5.1. But, you want to get the Y value; found the distance, 2/3 of the way. When the distance is 5.1 instead of round 7.6, we've arrived at point P. We want to be 5. 1 yard away on this line. This is point P and we want to be at point Q. Since it'll have the same slope. As a result, the slope will be 7/3. So, it'll be proportionate 7. Since the square root of fifty-eight is too large. Route 58/3 is the destination. The square root of 258 is canceled. Such that 7=3y/2. 7x2=14/3=4.7. It's by locating comparable figures.
pls help me asap
Find the mean and standard deviation for the set of data.
{17, 20, 4, 15, 12, 6, 14, 13, 16}
Answer:
Standard deviation = 5.1
Mean = 13
Median = 14
Step-by-step explanation:
The sample standard deviation measures the spread of a data distribution of the sample. It is usually used to estimate the population standard deviation
The mean of a set of numbers is the sum divided by the number of terms.
Arrange the data in an ascending order and the median is the middle value. If the number of values is an even number, the median will be the average of the two middle numbers.
There were three parts to Rita's race. She ran the first part, which was 4/9
of the total distance, in 20 minutes. She ran the second part, which was 2/5
of the remaining distance, in 12 minutes. She finally ran the third part in 15 minutes at a speed of 300 meter per minute.
How long was the second part of the race? What was Rita's speed in that section of the race?
The second part of Rita's race is about 1800 meters at a speed of 150 meters per minute.
Speedlet
distance covered in first Part = d1distance covered in second Part = d2distance covered in third Part = d3speed covered in first Part = s1speed covered in second Part = s2speed covered in third Part = s3Distance in second Part:
d₃ = 15 x 300
= 4500 m
d₂ = 2/5 × d₃
= 2/5 x 4500
d₂ = 1800 meters
Speed in second part:
S₂ = 1800 m / 12 min
S₂ = 150 meters per minute
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Jims backpack weighs 3 kg when filled how many pounds is this approximately?
Answer:
6.6
Step-by-step explanation:
1 kilogram to pounds is 2.2 lbs
therefore, 3kg= 2.2× 3 lbs= 6.6 lbs
Answer:
approximately 6.6 lb
Step-by-step explanation:
1 kg equals approximately 2.2 lb.
Therefore (multiplying both sides by 3) we get
3 kg equals approximately 6.6 lb
Sides that match up between two similar figures are called corresponding sides.
Use the diagram of two similar triangles to complete the proportion below.
Answer 1 box 1 :height of fox
Answer 2 Box 1 :length of trees shadow
Answer 3 box 1 :length of foxes shadow
Answer 1 box 2 :height of fox
Answer 2 Box 2 :height of tree
Answer 3 box 2 :length of foxes shadow
please help my grandmother will beat me if I get this wrong
The diagram of two similar triangles to complete the proportion is; Height of Person/Height of flower = Length of a person's shadow/Length of flowers' shadow.
How to solve similar triangles?From the concept of similar triangles, we know that If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor.
Applying this similar triangles theorem to our question, we can say that;
Height of a person/length of a person's shadow = Height of flower/length of a flower's shadow
We can rewrite this to get;
Height of Person/Height of flower = Length of a person's shadow/Length of flowers' shadow.
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You plan to conduct a survey to estimate the percentage of adults who have had chickenpox. Find the number of people who must be surveyed if you want to be 90% confident that the sample percentage is within two percentage points of the true percentage for the population of all adults.
The number of people who must be surveyed if you want to be 90% confident that the sample percentage is within two percentage points of the true percentage for the population of all adults is 1691.
The true proportion of the population is not given, so we assume it to be 0.5, that is, p = 0.5.
Hence, q = 1 - p = 1 - 0.5 = 0.5.
Confidence level given = 90%.
Z-Score corresponding to 90% confidence interval (Z) = 1.645.
We are asked to find the sample size (n) when we want to be 90% confident that the sample percentage is within two percentage points of the true percentage for the population of all adults, that is, standard error (E) = 2% = 0.02.
By the formula of standard error, we know:
E = Z√[{p(1 - p)}/n].
Substituting the values, we get
0.02 = 1.645√[{0.5*0.5}/n]
or, 0.0004 = 2.706025*0.25/n
or, n = 2.706025*0.25/0.0004 = 1691.265625 ≈ 1691 {Since the sample size has to be a whole number}.
Thus, the number of people who must be surveyed if you want to be 90% confident that the sample percentage is within two percentage points of the true percentage for the population of all adults is 1691.
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Carla is shopping for Storage Bags. At the grocery store, Brand A Storage Bags are priced $4.59 for 40 count, or Brand B Storage Bags priced $3.99 for 30 count. Which is the better buy, Brand A or Brand B?
Answer:
Brand A
Step-by-step explanation:
Comment
The question is one of finding out what the unit cost is.
Brand A: $4.59 has a count of 40
Brand B: $3.99 has a count of 30
Brand A
unit = 4.59 / 40 = 0.115
Rounded: 0.12
Brand B
unit = 3.99 / 30 = 0.133
rounded: 0.13
Brand A even with proper rounding is the better buy
Answer:
Brand A
Step-by-step explanation:
The cost comparison can be done a variety of ways. The most formal of solutions will calculate the cost per bag for the two brands.
Informal solutionThe cost for 10 bags of Brand B is $3.99/3 = $1.33. The cost for 10 more bags (40 bags instead of 30) of Brand A is $4.59 -3.99 = $0.60. This is less than the $1.33 it would cost to buy 10 more bags of Brand B, so ...
Brand A is the better buy
Formal solutionThe cost per bag is found by dividing the cost by number of bags:
Brand A: $4.59 / (40 bags) = $0.11475 per bag
Brand B: $3.99 / (30 bags) = $0.133 per bag
13¢ per bag is more than 11¢ per bag, so Brand A is the better buy.
The line graph shows the performance of stock over a 5 - day period. Describe what is misleading about the display.
The graph is misleading because it doesn't begin at zero and the graph starts on Mon.
What is a line graph?A line graph is a graph made up of segments of straight lines that connect the depicted data points.
We have a line graph shown in the picture that represents the stock price over a 5 - day period.
As we can see in the graph,
The graph starts on the Mon and price was $11.4(approximated)
Examples of "classic" deceptive graphs include those in which the vertical scale is off, skips digits, or doesn't begin at zero.
Thus, the graph is misleading because it doesn't begin at zero and the graph starts on Mon.
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What is the value of cos(Tan^-1 1)?
a. 2
b.square root 2
c. 2 square root 2
d. square root 2 over 2
Answer:
D
Step-by-step explanation:
So you have the equation: [tex]cos(tan^-1(1))[/tex]. So let's work in order and focus on the [tex]tan^-1(1)[/tex] part first. The inverse of tan is essentially taking in the value of [tex]tan(\theta)[/tex] and returning [tex]\theta[/tex]. And the value of [tex]tan(\theta)[/tex] can be defined as [tex]\frac{sin(\theta)}{cos(\theta)}[/tex]. So if you look at the unit circle, you'll need to look for two values that are exactly the same. You'll notice when the angle is 45 degrees, the value of sine, and cosine are the exact same. They're both [tex]\frac{\sqrt2}{2}[/tex]. So the inverse of tan(1 degree) = 45 degrees. Now we can literally refer to the same point, because when finding the cosine of 45 degrees, we can just use the x-value. This gives a solution of [tex]\frac{\sqrt2}{2}[/tex]
Benjamin threw a rock straight up from a cliff that was 96 ft above the water. If the height of the rock h, in feet, after t seconds is given by the equation
h=-161² +116t+96, how long will it take for the rock to hit the water?
Answer:
8 seconds
Step-by-step explanation:
When it hits the water h = 0
0 = -16t^2 + 116t + 96 ( I corrected the equation in the question)
solve for 't' using quadratic formula t = 8 s ( and - .75 s <===throw out)
How would you simplify the fraction
4/28?
O
AIA
1
0 5
1/28
Answer:
1/7
Step-by-step explanation:
Divide the top and bottom by 4 to get
1 / 7
Answer:
1/7
Step-by-step explanation:
4 and 28 are divisible by 4.
4/4 = 1
28/4 = 7
4/28 = 1/7
30 mi / h = ____ ft / min
a.
2640
c.
880
b.
264
d.
2112
Answer:
its a 2640 trust me
Step-by-step explanation:
helllppppppppppp please
Considering the volume of a rectangular prism, the limitations are given as follows:
Upper: 500, Lower: 0.
What is the volume of a rectangular prism?The volume of a rectangular prism of length l, width w and height h is given by:
V = lwh.
For the toy, the dimensions are of 1 inch, hence:
V = 1 x 1 x 1 = 1 inch³.
For the box, the dimensions are of 10 x 10 x 5 inches, hence:
V = 10 x 10 x 5 = 500 inches³.
500/1 = 500, hence the upper limit is of 500, while the lower limit is of 0.
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On his way to and home from work, John can ride his bike at a constant speed of 16 mph. If he lives 60 miles away from work, how much time does he spend commuting to, and returning from, work each day
Answer:
7.5 hours
Step-by-step explanation:
16 mph = 16 miles per hour
how much time does he spend commuting to, and returning from, work each day = 60(2) = 120 miles
120/16
= 7.5 hrs
Which side of the original parallelogram corresponds to the y-centimeter side of the enlarged parallelogram? explain how you know. a small parallelogram has a left side length of 10 centimeters and a top side length of 15 centimeters. a larger parallelogram has a left side length of x centimeters and top side length of y centimeters. not drawn to scale the ____-centimeter side corresponds to the y-centimeter side.
The 15 cm side is equivalent to the y centimeter side.
A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.
So from the given question the given figure can be inferred which is attached below
The "y" side of the parallelogram corresponds to the bigger side of the parallelogram, as seen in the figure, and the "x" side corresponds to the shorter side.
Since "y" relates to the longer side and the longer side is 15 cm, the 15 cm side is equivalent to the y centimeter side.
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graph the inequality y > |x - 4| + 3
Answer: As graphed below.
Hope this helps ♥️
how many solution does the pair of equation Y is equal to -3 and Y is equal to 6 have
Answer:
4
Step-by-step explanation:
it takes four equations
The function f(x) is shown in the graph.
f(z)
Which type of function describes f(x)?
O Exponential
Logarithmic
Rationall
Polynomial
The function f(x) is shown in the graph is (a) an exponential function
How to determine the function type?From the graph, we can see that:
The function starts from a baseIt then increases, exponentiallyOnly exponential functions have the above features
Hence, the function f(x) is shown in the graph is (a) an exponential function
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The diagram shows the intersections of several straight roads. The avenues run parallel to each other.
First Avenue and Second Avenue are parallel. Oak goes through both streets at point A and B. Main goes diagonally down through both streets and intersects with Oak Street. The distance from First to Second on Main is 280 feet. The distance from Second to the intersection of Oak is 140 feet. The distance from Point B to the intersection of Main is 113 feet.
Amana walks along Oak from point A to B. To the nearest foot, how far does she walk?
75 ft
226 ft
307 ft
347 ft
By applying the property of similar triangles, the distance Amana from point A to B walked is: B. 226 ft.
How to determine the distance?By critically observing the diagram (see attachment), we can deduce that two (2) similar triangles were formed by the First Ave. and Second Ave.
By applying the property of similar triangles, the distance Amana walked is given by:
(AB + 113)/113 = (280 + 140)/140
(AB + 113)/113 = 420/140
(AB + 113)/113 = 3
AB + 113 = 3 × 113
AB + 113 = 339
AB = 339 - 113
AB = 226 ft.
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Answer: B. 226 ft.
Step-by-step explanation: Trust Me! I got it correct on Edge.
When an antibiotic is introduced into a culture of 70,000 bacteria, the number of bacteria decreases at a continuous rate. After 5 hours, there are only 40,000 bacteria. Determine the the continuous rate. Round your answer to the nearest tenth of a percent. Use a positive sign if it is a continuous growth rate or negative sign if it is a continuous decay rate. Do not write the percent sign in your response.
Answer:
- 10.6 % per hour
Step-by-step explanation:
By 'continuous rate' I assume you mean linear bacteria/hour
40 000 - 47 000 = - 30 000 bacteria in 5 hours
- 30 000 bacteria / 5 hours = - 6000 bacteria per hour
But then you ask for percentage....so maybe you want an exponential rate
then 40 000 = 70 000 ( 1 - x)^5
where x = decimal percentage , 5 = years
solve for x = 10.588 % DECREASE per hour
Translation: (x,y)→(x+7,y+5) Coordinates: Y(−5,−4), X(−5,−1), W(−2,0), V(−2,−5)
Answer:
Y - (2,1)
X - (2,4)
W - 5,5)
V - (5,0)
Step-by-step explanation:
Translation: (x,y) → (x+7,y+5)
Coordinates:
Y(−5,−4) => (-5 + 7, -4 + 5) => (2,1)
X(−5,−1) => (-5 + 7, -1 + 5) = > (2,4)
W(−2,0) => (-2 + 7, 0 + 5) => (5,5)
V(−2,−5) => (-2 + 7, -5 + 5) => (5,0)
Write the number which is seventeen less than ten
thousand and four:
A number which is 17 less than 10,004:
10,004-17=9987
Hope it helps!
You enter a room. 2 dogs, 4 horses, one giraffe, and a duck are laying on a bed. 3 chicken are flying over a chair. How many legs are on the ground?.
Answer:
4 legs from the bed and 4 from the chair im guessing since not all have 4
Step-by-step explanation:
.
Answer:
36 legs
Step-by-step explanation:
If f(x) = 2x – 1 and g(x) = log x, compute (f – g) (x)
Answer:
(f-g) (x) = 2x – 1 - log(x)
Step-by-step explanation:
f(x) = 2x – 1
g(x) = log x
We are given the two function and want to subtract g(x) from f(x)
(f-g) (x) = 2x – 1 - log(x)
The Box-and-Whisker Plot shown displays the number of text messages sent during the previous week. What is the fewest reported number of text messages sent?
A. 82
B. 62
C. 74
D. 90
The fewest reported number of text messages sent, given the data is 62 (Option B)
Data obtained from the questionData = 62, 74, 82, 90, 99Fewest number = ?How to determine the fewest numberThe fewest number in a given data is simply defined as the smallest number in the data.
Considering the data given from the question, we can see that the smallest number in the data is 62
Thus, 62 is the fewest number in the data.
Therefore, the correct answer to the question is 62 (Option B)
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Complete question
The Box-and-Whisker Plot shown displays the number of text messages sent during the previous week. What is the fewest reported number of text messages sent? 62, 74, 82, 90, 99
A. 82
B. 62
C. 74
D. 90
What are the solutions to the quadratic equation 2x + x = 3? - 1,2/-/- 1,3/- 1, -/-/- -1, - -/-/- (A) (B) (C) (D)
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Assuming equation:}[/tex]
[tex]\mathbf{2x + x = 3}[/tex]
[tex]\huge\textbf{Solving for the equation:}[/tex]
[tex]\mathbf{2x + x = 3}[/tex]
[tex]\mathbf{2x + 1x = 3}[/tex]
[tex]\huge\textbf{Combine the like terms:}[/tex]
[tex]\mathbf{(2x + 1x) = 3}[/tex]
[tex]\mathbf{(2x + x) = 3}[/tex]
[tex]\mathbf{2x + x = 3}[/tex]
[tex]\mathbf{3x = 3}[/tex]
[tex]\huge\textbf{Divide 3 to both sides:}[/tex]
[tex]\mathbf{\dfrac{3x}{3} = \dfrac{3}{3}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathbf{x = \dfrac{3}{3}}[/tex]
[tex]\mathbf{x = 3\div3}[/tex]
[tex]\mathbf{x = 1}[/tex]
[tex]\huge\textbf{Answer:}[/tex]
[tex]\huge\boxed{\mathsf{x = 1}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]