By applying the rigid transformations of reflection on y-axis, vertical compression and vertical translation, we find the transformed function based on f(x) = 2ˣ is f''(x) = (1/3) · 2⁻ˣ + 2.
How to derive a function by using rigid transformations
Rigid transformations are transformations applied on functions such that their Euclidean distance is conserved. In this problem we must use the following rigid transformations to determine an expression based on f(x) = 2ˣ.
Reflection on y-axis
f'(x) = f(-x) (1)
f'(x) = 2⁻ˣ
Vertical compression
f''(x) = k · f'(x) (2)
f''(x) = (1/3) · 2⁻ˣ
Vertical translation
f'''(x) = f''(x) + c (3)
f''(x) = (1/3) · 2⁻ˣ + 2
By applying the rigid transformations of reflection on y-axis, vertical compression and vertical translation, we find the transformed function based on f(x) = 2ˣ is f''(x) = (1/3) · 2⁻ˣ + 2.
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help asap, please and thank you
By understanding the proportions of each section with respect to the entire hexagon we have:
{1, 1/2, 1/3, 1/6} {6, 3, 2, 1}{3, 3/2, 1, 1/2}{2, 1, 2/3, 1/3}How to construct a diagram related to possible sections of a hexagonThe first row represents the proportion of each section with respect to the entire hexagon, which is shown below:
{1, 1/2, 1/3, 1/6}
The elements of the second row are obtained by mutiplying all the elements of the first row by 6:
{6, 3, 2, 1}
The elements of the third row are calculated by multiplying all the elements of the first row by 3:
{3, 3/2, 1, 1/2}
And the elements of the fourth row are determined by multiplying all the elements of the first row by 2:
{2, 1, 2/3, 1/3}
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A state health department was considering a new policy that would require all school-age children to receive the varicella (Chicken Pox) vaccine. In order to evaluate the need for such a requirement, health department epidemiologists were asked to determine the incidence of varicella in a randomly-selected fifth-grade class. During the previous school year, the class had 20 students, 5 of whom had varicella before entering fifth grade and 2 of whom developed varicella during fifth grade. What was the incidence of varicella during the fifth grade
The incidence rate of varicella is 13 per 100 if there were 20 students and 5 of whom got vaccinated before fifth grade.
Given Total students of 100 in which 5 had varicella before entering fifth grade and 2 of whom developed varicella during fifth grade.
We have to find the incidence rate of varicella means requirement of vaccine in proportion form.
So we want the incidence rate, which is the number of people who caught the disease who were at risk to it. So we have 20 people in the class in total. But we said that five of them already had it and they were told that they are immune. So we have 15 people in the class who are at risk, then two people caught it. and so the incidence rate is going to be two divided by 15, which you can check is Not .13 recurring. And so as a percentage We just times by 100 this is going to be 13/ 100.
Hence the incidence of varicella during the fifth grade is 13/100.
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Question 9 Eight wooden spheres with radii of 3 inches are packed snuggly into a cube-shaped box 12 inches on one side. The remaining space is filled with packing beads. What is the volume occupied by the packing beads
Bob can chop down 10 trees in 30 minutes, while Frank can chop down 15 trees in 30 minutes. Working together, how long will it take them to chop down 100 trees
It will take 120 minutes to chop down 100 trees.
Bob chops 10 trees in 30 minutes, so he can chop 100 trees in 300 minutes.
Frank chops 15 trees in 30 minutes, so he can chop 100 trees in 200 minutes.
Solve this using the following equation:
15 / 30 = 100 / x
Solving for x gives 120 minutes.
The unitary approach is a way of solving a hassle via first locating the price of a single unit, after which locating the necessary cost with the aid of multiplying the single unit fee.
The formula of the unitary approach is to find the cost of a single unit after which multiply the cost of an unmarried unit via the quantity of units to get the important price.
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write an exponential function that includes the following given pair of points.
(1,-2) and (2,-4)
Answer:
[tex]f(x)=-2^x[/tex]
Step-by-step explanation:
So generally an exponential equation is expressed in the form: [tex]f(x)=a(b)^x[/tex] and: [tex]b=1+r\text{ or }b=1-r \text{ depending on whether it's decaying or growing}[/tex]. In this case we see that as x increased by 1, the y-decreases, BUT the absolute value is increasing, so it's really just reflected.
Plug in known values:
[tex]-2=a(b)^1[/tex]
[tex]-4=a(b)^2[/tex]
So if you think about it. you really have
-2 = a * b
-4 = a * b * b
since ab = -2, then we can substitute this into the second equation
-4 = -2 * b
-4 = -2b
Divide both sides by -2
b = 2
You can also deduce that b=2, by realizing to go from -2 to -4, you have to subtract 100% of -2 from -2. This means r=1, so b=1+1, b=2
Anyways, now it's time to solve for a, by plugging in a point as well as b.
-4 = a(2)^2
-4 = 4a
-1 = a
You can verify this by using the other point
-2 = -(2)^1
-2 = -(2)
-2 = -2
So the equation is: [tex]f(x)=-2^x[/tex]
Question 1 of 10
A triangle has two sides of lengths 7 and 9. What value could the length of
the third side be? Check all that apply.
A. 5
B. 13
C. 2
D. 22
E. 10
F. 8
Answer:
A, B, E and F.
Step-by-step explanation:
A triangles side must be larger than the difference of the other sides, and smaller than the sum of the other sides. So in this case we could create an equation such as, 9-7<x<9+7. From this equation we can conclude that this side can be between 2 and 16. So, A, B, E and F all work.
Nora and her children went into a grocery store and see by $5 worth of apples and bananas each Apple cost $1 each banana costs $0.50. She bought 3 times as many bananas as apples. By following the stars below determine the number of apples, x, and the number of banana, y, that Nora bought.
Solving a system of equations, we will see that Nora bought 2 apples and 6 bananas.
How many apples and bananas Nora did bought?Let's define the variables:
x = number of apples.y = number of bananas.We know that She buys 3 times as many bananas as apples.
y = 3*x
The total cost is $5.
x*$1 + y*$0.50 = $5
Then we have a system of equations:
y = 3*x
x*$1 + y*$0.50 = $5
Replacing the first equation into the second one we get:
x*$1 + (3x)*$0.50 = $5
Now we can solve this for x.
x*$1 + x*$1.50 = $5
x*$2.50 = $5
x = $5/$2.50 = 2
So She bought 2 apples, and:
y = 3*x = 3*2 = 6
And 6 bananas.
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What is the circumference of a circle (to the nearest
whole number) whose diameter is 12?
Answer:
A
Step-by-step explanation:
The formula for circumference is π×diameter.
π×12= 37.6991, which can be rounded up to 38.
Solve the inequality
x² + 2x + 1 < 0.
Hello
x² + 2x + 1 < 0 ⇔ (x + 1)² < 0
S = {∅} because a² ≥ 0
A six sided die is rolled three times. Find the probability that the result is an even number for every roll.
A. 1/9
B. 3/8
C. 1/3
D. 1/8
[tex]|\Omega|=6^3\\|A|=3^3\\\\P(A)=\dfrac{3^3}{6^3}=\left(\dfrac{3}{6}\right)^3=\left(\dfrac{1}{2}\right)^3=\dfrac{1}{8}=12.5\%[/tex]
Evaluate the expression
a. tan(arctan 25) =
Step-by-step explanation:
Newton's second law of motion describes the relationship between force and acceleration. They are directly proportional. If you increase the force applied to an object, the acceleration of that object increases by the same factor. In short, force equals mass times acceleration.
Triangle A B C is shown. The length of side A is 12 inches, the length of side B is 6 StartRoot 3 EndRoot, and the length of side C is 6 inches.
What are the angle measures in triangle ABC?
m∠A = 90°, m∠B = 30°, m∠C = 60°
m∠A = 60°, m∠B = 90°, m∠C = 30°
m∠A = 90°, m∠B = 60°, m∠C = 30°
m∠A = 60°, m∠B = 30°, m∠C = 90°
The angle measures in triangle ABC are (d) m∠A = 60°, m∠B = 30°, m∠C = 90°
How to determine the angle measures?The side lengths are given as:
AB = 12 inches
BC = 6√3 inches
CA = 6 inches
From the list of options, the angles are 30°, 60° and 90°, respectively.
In a triangle, the angle opposite the largest side is the largest angle and vice versa.
This means that:
∠C = 90° --- opposite AB
∠A = 60° --- opposite BC
∠B = 30° --- opposite CA
Hence, the angle measures in triangle ABC are (d) m∠A = 60°, m∠B = 30°, m∠C = 90°
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Complete question
The length of side AB is 12 inches, the length of side BC is 6√3, and the length of side CA is 6 inches.
See attachment
(C.) m∠A = 90°, m∠B = 60°, m∠C = 30°
Got it wrong, the correct answer was revealed to be C.
Triangle XYZ was reflected across m and then dilated to form a similar triangle. Which triangle represents the image?
Triangle X Y Z is reflected across line m. It is rotated about point X prime and then is dilated to form a smaller triangle.
Triangle X Y Z is reflected across line m and then is dilated to form smaller triangle X prime Y prime Z prime.
Triangle X Y Z is reflected across line m to form triangle Z prime Y prime X prime.
The triangle that represents the image is; Option B; Triangle X Y Z is reflected across line m and then is dilated to form smaller triangle X prime Y prime Z prime.
How to carry out Transformations?From the given transformation as seen in the attached image, we can say that;
In Option A, the triangle is first reflected across m and then reflected across the vertical line. Then, it is dilated.
In Option C, the triangle is reflected across m but the angles are not preserved.
In Option B, the triangle is reflected across m and then dilated and as such is a correct image similar to the original triangle.
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It's Option B.
(You can also call it the middle one, up to you <3)
Tayli wishes to advertise her business, so she gives packs of 13 red flyers to each restaurant owner and sets of 20 blue flyers to each clothing store owner. At the end of the day, Tayli realizes that she gave out the same number of red and blue flyers. What is the minimum number of flyers of each color she distributed?
The minimum number of flyers of each color distributed is 1.
What is the minimum flyer distributed?
In order to determine the minimum number of flyers of each color distributed, the common factor of 13 and 20 has to be determined. The factor of a number is a number that divides another number perfectly without any remainder.
Factors of 13 = 1, 13
Factors of 20 = 1, 2, 4, 5, 10, 20
Common factor = 1
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Audrey is driving to a concert and needs to pay for parking. There is an automatic fee of $6 just to enter the parking lot, and when she leaves the lot, she will have to pay an additional $2 for every hour she had her car in the lot. How much total money would Audrey have to pay for parking if she left her car in the lot for 5 hours? How much would Audrey have to pay if she left her car in the lot for tt hours?
Answer:
a. $16
b. $26
Step-by-step explanation:
a. 6+2(5)= 16
b. im assuming tt means ten 6+2(10)=26
If Audrey leaves her car in the lot for "t" hours, she would have to pay a total of $6 + $2t for parking.
If Audrey leaves her car in the parking lot for 5 hours, she will have to pay the initial fee of $6 plus $2 for each hour she parked. For 5 hours, she will pay:
Initial fee: $6
Additional fee for 5 hours: $2 * 5 = $10
Total parking cost: $6 + $10 = $16
If Audrey leaves her car in the parking lot for "t" hours, the total parking cost can be calculated as:
Total parking cost = Initial fee + Additional fee for "t" hours
Total parking cost = $6 + $2t
So, if Audrey leaves her car in the lot for "t" hours, she would have to pay a total of $6 + $2t for parking.
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2 c) factorize : x² - 2xy + y²
Answer:
(x-y)²
Since, it's formula of (x+y)² ...
Hello!
This is an identity :
[tex]\boxed {(x - y)^2 = x^2 - 2xy + y^2}[/tex]
∴ The factors are (x - y) and (x - y).
Rashad is considering two designs for a garden. In Design 1 he would use fencing to surround a square plot of land that has an area of 1,296 square feet. In Design 2 he would divide a plot of land into two rectangular sections, each 15 feet by 36 feet, and surround the plot with fencing, as well as place fencing along the dividing line of the two sections.
Two designs for a garden are shown. Design 1 is a square with an area of 1,296 square feet. Design 2 is 2 rectangles with lengths of 15 feet and 36 feet that are connected at one side.
Which plan would cost less in fencing? Explain.
Design 1, because it requires 12 fewer feet of fencing than Design 2
Design 1, because it requires 24 fewer feet of fencing than Design 2
Design 2, because it requires 12 fewer feet of fencing than Design 1
Design 2, because it requires 24 fewer feet of fencing than Design 1
The plan that would cost less in fencing is B. Design 1, because it requires 24 fewer feet of fencing than Design 2.
How to depict the information?From the information given, Design 1 would use fencing to surround a square plot of land that has an area of 1,296 square feet and Design 2 would divide a plot of land into two rectangular sections, each 15 feet by 36 feet.
Therefore, the plan that would cost less in fencing is Design 1, because it requires 24 fewer feet of fencing than Design 2.
In conclusion, the correct option is B.
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Answer:
B
Step-by-step explanation:
HELP HELP HELP
Quick algebra 1 questions
Hello:
Okay, this problem should be taken in a series of steps:
What is the slope's formula?
[tex]\rm\hookrightarrow \frac{y_2-y_1}{x_2-x_1}[/tex]
(x₁,y₁) -- first point(x₂,y₂) -- second pointOkay, now let's use this knowledge
10. (5,-19) and (-5,21)
[tex]Slope = \frac{21--19}{-5-5} =\frac{40}{-10}=-4[/tex]
11. (12,1) and (12, -1)
[tex]Slope = \frac{-1-1}{12-12} =\frac{-2}{0}[/tex]
12. (8,7) and (4,7)
[tex]Slope = \frac{7-7}{4-7} =0[/tex]
Answer:
Question 10: -4Question 11: undefinedQuestion 12: 0Hopefully that helps!
please help me!!
20 points
Answer:
182 [tex]yd^{2}[/tex]
Step-by-step explanation:
Area of a parallelogram: bh
bh
= 13(14)
= 182 sq. yds
A survey conducted by a reputed Business School in Texas among 400 students showed that students spend on an average $500 for textbooks in a year. The sample standard deviation was $80. What is the confidence interval for the average amount spent on textbooks in a year if the desired level of confidence is 99%
[489.68, 510.32] is the confidence interval for the average amount spent on textbooks in a year if the desired level of confidence is 99%.
n=400
sample mean (x)=500
sample standard deviation (s)=80
99% confidence interval for mean
α=0.01
critical value [tex]Z_{\frac{a}{z} }[/tex] =2.58
Standard error of sample mean Sx = [tex]\frac{s}{\sqrt[]{n} }[/tex] = [tex]\frac{80}{\sqrt[]{400} }[/tex] = [tex]\frac{80}{20}[/tex] = [tex]4[/tex]
∴ Sx = 4
Confidence interval (μ)
μ= [tex]x[/tex] ± [tex]Z_{\frac{a}{z} }[/tex] [tex]\frac{s}{\sqrt[]{n} }\\[/tex]
μ= [tex]x[/tex] ± [tex]Z_{\frac{a}{z} }[/tex] (Sx)
=500 ± 2.58(4)
=500 ± 10.32
lower limit = 500 - 10.32 = 489.68
upper limit= 500 + 10.32= 510.32
Hence, [489.68, 510.32] is the confidence interval for the average amount spent on textbooks in a year if the desired level of confidence is 99%.
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What is the gradient of the graph shown?
Answer:
Step-by-step explanation:
Answer:
gradient= change in y intercept ÷change in x intercept
gradient=-2-0 ÷3-0
gradient=
What is the additive identity for 2 x 4 matrices?
Answer:
The additive identity matrix would be a zero matrix (all its entries are zeros .) The sum between two matrices can be done if and only if the two matrices are similar, that means that they have the same numbers of rows and columns.
Step-by-step explanation:
find the volume of a cone with a base diameter of 6ft and a height of 12ft
Answer:
452.389 cubic feet
Step-by-step explanation:
Answer:
Step-by-step explanation:
The formula for finding the volume of the cone: [tex]\pi r^2h/3[/tex]
Height= 12ft
Diameter= 6, radius= [tex]\frac{6}{2}[/tex]= 3
[tex]\frac{22}{7} *3^2*\frac{12}{3} \\\\\frac{22}{7} *3^2*2\\\frac{22}{7} *9*2\\\\\frac{22}{7} *18\\\\56.57[/tex]
Place valu of 4 in 65400 is
Answer:
hundreds place in what the place value of the number 4 in 65400 the 6 is the hundred thousand place the 5 is the thounds place the four is the hundred place. The first zero is the 10th place. in the seconds, zero is the one place value
Answer:
The value 4 is in the hundreds place.
Step-by-step explanation:
We have the number 65400. The last digit in the number is 0, the 0 is in the ones place. The next number, which is also 0, is in the tens place. The next number after that is a 4, which is in the hundreds place. This shows that the 4 is in the hundreds place.
ten-thousands thousands hundreds tens ones
6 5 4 0 0
Hope this helps!
If not, I am sorry.
what is the answer to 12y+d=−19y+t for y
Answer:
12y + d = -19y + t
31y + d = t
31y= - d + t
y = (- d + t ) / 3 ;)
Answer:
y = (t-d) / 31
Step-by-step explanation:
12y + d = -19y + t
12y + 19y = t - d
31y = t - d
y = (t-d) / 31
can you please answer the question?
The trigonometric expression [tex]\frac{\tan^{2} \alpha}{\tan \alpha - 1} + \frac{\cot^{2} \alpha}{\cot \alpha - 1}[/tex] is equivalent to the trigonometric expression [tex]\sec \alpha \cdot \csc \alpha + 1[/tex].
How to prove a trigonometric equivalence
In this problem we must prove that one side of the equality is equal to the expression of the other side, requiring the use of algebraic and trigonometric properties. Now we proceed to present the corresponding procedure:
[tex]\frac{\tan^{2} \alpha}{\tan \alpha - 1} + \frac{\cot^{2} \alpha}{\cot \alpha - 1}[/tex]
[tex]\frac{\tan^{2}\alpha}{\tan \alpha - 1} + \frac{\frac{1}{\tan^{2}\alpha} }{\frac{1}{\tan \alpha} - 1 }[/tex]
[tex]\frac{\tan^{2}\alpha}{\tan \alpha - 1} - \frac{\frac{1 }{\tan \alpha} }{\tan \alpha - 1}[/tex]
[tex]\frac{\frac{\tan^{3}\alpha - 1}{\tan \alpha} }{\tan \alpha - 1}[/tex]
[tex]\frac{\tan^{3}\alpha - 1}{\tan \alpha \cdot (\tan \alpha - 1)}[/tex]
[tex]\frac{(\tan \alpha - 1)\cdot (\tan^{2} \alpha + \tan \alpha + 1)}{\tan \alpha\cdot (\tan \alpha - 1)}[/tex]
[tex]\frac{\tan^{2}\alpha + \tan \alpha + 1}{\tan \alpha}[/tex]
[tex]\tan \alpha + 1 + \cot \alpha[/tex]
[tex]\frac{\sin \alpha}{\cos \alpha} + \frac{\cos \alpha}{\sin \alpha} + 1[/tex]
[tex]\frac{\sin^{2}\alpha + \cos^{2}\alpha}{\cos \alpha \cdot \sin \alpha} + 1[/tex]
[tex]\frac{1}{\cos \alpha \cdot \sin \alpha} + 1[/tex]
[tex]\sec \alpha \cdot \csc \alpha + 1[/tex]
The trigonometric expression [tex]\frac{\tan^{2} \alpha}{\tan \alpha - 1} + \frac{\cot^{2} \alpha}{\cot \alpha - 1}[/tex] is equivalent to the trigonometric expression [tex]\sec \alpha \cdot \csc \alpha + 1[/tex].
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isha wants to paint the four walls of her living room.
Each wall is 2.6 m high and 3.5 m long.
One wall has a door of 2.2 m by 0.8 m.
Tins of paint cost £11 per 2 litre tin.
Each litre of paint can cover 8 m2 of wall.
There is an offer of: Buy 2 tins get the 3rd at half price.
How much will Aisha pay to paint her living room?
The amount Aisha would pay to paint her living room is £38.50.
What is the cost of painting the living room?The first step is to determine the area of the walls that do not have doors.
Area of a wall = length x width
3 x (2.6 x 3.5) = 27.30 m²
Dimensions of the wall with the door : (2.6m - 2.2m) x (3.5 - 0.8) = 0.4m x 2.7m
Area of the wall with the door : 0.4m x 2.7m = 1.08 m²
Total area of the walls: 27.30 m² + 1.08 m² = 28.38 m²
Number of paint tins needed for the walls : 28.38 / 8 = 3.55 = 4 tins
Cost of the paint tins : (11 x 3) + (0.5 x 11) = £38.50
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Select the correct answer from each drop-down menu.
How can you summarize the ruler placement postulate?
The summary of the ruler placement postulate is given as:
there is a one-to-one correspondence between the set of points on the line and the set of real numbers, and.the distance between two points equals the absolute value of the difference between the corresponding numbers.What is the ruler placement postulate?This states that the points of a line can be matched and correspond to a set of points on the line and the set of real numbers,
Therefore, based on the fact that your question is incomplete, a general overview of the ruler placement postulate is given to give you a better understanding of the concept.
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Answer: You can measure the positive distance between points A and B by using either point as zero
Step-by-step explanation:
Given a line segment containing the points A,B, & C, in order, if AB is 11 and BC is 12, then the length of AC would be ____.
Answer:
23 or 1
Step-by-step explanation:
for answer 23: we considered the segment ABC which means A is the leftest point and C is the rightest point. then AC = AB+BC
for answer 1: we considered the segment CAB which means C is the leftest point, and B is the rightest point. Then AC = CA = BC-AB = 12-11=1
A grocery store is offering a sale on bread and soup. Khalil buys four cans of soup and loaves of bread for $11.67. Ronda buys eight cans of soup and one loaf of bread for $12.89.
a) rite equations for both Khalil's and Ronda's purchases.
b)solve the system to find the price of one can of soup and the price of one loaf of bread.
please help :((
Answer:
a. The equation should be
4x + 3y = $11.67
8x + y = $12.89
b. The price of one can of soup and the price of one loaf of bread is $1.355 and $2.09
The calculation is as follows:
here we assume the soup be x and bread be y
So, the equations are
4x + 3y = $11.67 .........(1)
8x + y = $12.89.........(2)
Here we need to multiply by 2 in equation 1
8x + 6x = $23.34
8x + y = $12.89
5y = $10.45
y = $2.09
Now x should be
8($2.09) + y = $12.89
x = $1.355
Hope this helps :)
Answer:
A)
Khalil: 4s + 1b = 11.67
Ronda: 8s + 1b = 12.89
B)
Can of soup = $0.305
Loaf of Bread = $10.45
(Please mark brainliest)
Step-by-step explanation:
Make s a can of soup
Make b a loaf of bread
A)
Khalil: 4s + 1b = 11.67
Ronda: 8s + 1b = 12.89
B)
12.89 - 11.67 = 1.22
1.22 / 4 = 0.305
11.67 - 1.22 = 10.45
Can of soup = $0.305
Loaf of Bread = $10.45