Answers
2•20•2•12= 960
Related Questions
On the Y axis, we have the profit from the trucking company and on the X axis, we have the miles the truck has traveled. The company decided that they needed to start paying for a driver at a price of 0.25 cents a mile. After this change what will happen to the x and y axis/slope?
A. Y intercept will be less and X will be less
B. Y intercept will be less and X intercept will be greater
C. Y intercept will be greater and X will be greater
D. Y intercept will be greater and X will be less
Answers
Answer:
B.
Step-by-step explanation:
Answer:
B.
Step-by-step explanation:
the description is very confusing and lacks any hint about the behavior of the curve before the change.
but ok, let's assume that the curve (line ?) is in general going up. in other words, if the traveled miles go up, so does the profit.
I also don't know how they could drive the miles without paying the driver, but again, let's assume they did.
now they pay the driver. $0.25 per mile.
this has to come out of their profit.
so, the Y (profit) values all go down by 0.25.
therefore, the y-intercept is going down too.
that eliminates C. and D.
for this to be true they have to have some overhead costs that apply even if there are 0 miles traveled (which is the meaning of the y-intercept : the y-value when x = 0).
so, the line must be in a form
y = ax + b
with "b" <> 0.
and since we assumed the line to go up (positive slope), a "sinking" line means that the x-intercept (the break-even point, where the line goes from below the x-axis and therefore negative (y) profit up into positive profit) will move to the right (become greater).
because now that they have additional costs (paying the driver), it takes longer (more driven miles) to make a positive profit.
and that eliminates A, leaving B. as the right answer.
Matt can save $225 per month that he puts into a savings
account earning 5% annual interest. How much will he have
saved after 2 years?
Answers
Answer:
FV ≈ $5,673.56
Step-by-step explanation:
To calculate the total amount that Matt will have saved after 2 years of saving $225 per month at an annual interest rate of 5%, we can use the formula for the future value of an annuity:
FV = P * (((1 + r/12)^(n*12) - 1) / (r/12))
where:
FV is the future value of the annuity
P is the periodic payment (in this case, $225 per month)
r is the interest rate per year (in this case, 5%)
n is the number of years (in this case, 2)
Substituting the given values, we get:
FV = $225 * (((1 + 0.05/12)^(2*12) - 1) / (0.05/12))
Using a calculator, we get:
FV ≈ $5,673.56
Therefore, after 2 years of saving $225 per month at an annual interest rate of 5%, Matt will have saved approximately $5,673.56.
Triangle PQR is rotated 180 degrees clockwise about the origin to produce the image Triangle P’Q’R’. Which of the following statements is TRUE abóyate Triangle P’Q’R’.
Answers
Answer:
Step-by-step explanation:
We get triangle PQR by plotting the point P (1, 4), Q (3, 1), R (2, -1) on the graph paper when rotated through 180° about the origin. The new position of the point is: P (1, 4) → P' (-1, -4) Q (3, 1) → Q' (-3, -1) R (2, -1) → R' (-2, 1) Thus, the new position of ∆PQR is ∆P’Q’R’.
20. The volume of a large crate is 84 yd³. It is 23 yd wide and 4 yd high. What is the length of the crate?
Answers
Volume = length x width x height
We are given that the volume of the crate is 84 yd³, the width is 23 yd, and the height is 4 yd. Substituting these values into the formula, we get:
84 = length x 23 x 4
To solve for the length, we can divide both sides by 23 x 4:
84 ÷ (23 x 4) = length
Simplifying the left side of the equation, we get:
84 ÷ (23 x 4) = 0.913043478
Therefore, the length of the crate is approximately 0.913043478 times the width, or:
Length ≈ 0.913043478 x 23 yd = 21 yd (rounded to the nearest whole number)
Therefore, the length of the crate is approximately 21 yards.
A rectangular flower bed measures 10m by 6m. It has a path 2m
wide around it. Find the area of the path
Answers
The area of the path is 80 square meters.
Given: A rectangular flower bed measures 10m by 6m. It has a path 2m wide around it.
To Find: The area of the path.
Solution: We need to subtract the area of the inner rectangle from the area of the outer rectangle.
So,
The outer rectangle has dimensions 14m by 10m (adding 2m to each side of the flower bed), so its area is:
A outer = 14m x 10m = 140 m²
Now,
The inner rectangle has dimensions 10m by 6m (the original dimensions of the flower bed), so its area is.
A inner = 10m x 6m = 60 m²
Now,
The area of the path.
A path = A outer - A inner
= 140 m² - 60 m²
= 80 m²
Thus, The area of the path is 80 square meters.
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12. The length of a rectangle is 6 meters longer than the width. If the total area of the rectangle is 16m², find the dimensions of the rectangle.
Answers
Answer: Let's say that the width of the rectangle is x meters. Then, according to the problem, the length of the rectangle is 6 meters longer than the width, which means that the length is (x + 6) meters.
The formula for the area of a rectangle is:
Area = Length x Width
We are given that the total area of the rectangle is 16m². Substituting the expressions for length and width, we get:
(x + 6) x = 16
Expanding the product and rearranging, we get a quadratic equation:
x² + 6x - 16 = 0
We can solve this equation by factoring or by using the quadratic formula. Factoring, we get:
(x + 8) (x - 2) = 0
This equation is satisfied when either x + 8 = 0 or x - 2 = 0. Therefore, the possible values for the width are x = -8 or x = 2. However, since the width of a rectangle cannot be negative, we reject the solution x = -8.
Therefore, the width of the rectangle is x = 2 meters. The length is 6 meters longer than the width, so the length is (2 + 6) = 8 meters.
Therefore, the dimensions of the rectangle are 2 meters by 8 meters.
Step-by-step explanation:
3. How many ways can you line up 7 books on a shelf?
Answers
Answer:
There are 5040 different ways to arrange the 7 books on a shelf.------------------------------
Use the formula for permutations:
n! = n × (n - 1) × (n - 2) × ... × 1, where n is the number of objects and ! denotes a factorial.The number of objects is n = 7 books.
Calculate the factorial:
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040A company is going to make an oil container in the shape of a cylinder. As shown below, the container will have a height of 8 m and a diameter of 10 m. The container will be made from steel (including its top and bottom). Suppose the total cost of the steel will be $13,062.40. How much will the steel cost per square meter? Use 3.14 for it, and do not round your answer.
Answers
The per square meter cost of steel will be $32. The solution has been obtained by using the cylinder.
What is a cylinder?
The cylinder, one of the most basic curvilinear geometric shapes, has long been considered to be a three-dimensional solid. It is regarded as a prism with a circle as its basis in elementary geometry.
We are given that the height of cylinder is 8 m and diameter is 10 m.
So, the radius is 5 m.
Now, using the surface area formula, we get
⇒ S = 2πrh + 2π[tex]r^{2}[/tex]
⇒ S = 2π * 5 * 8 + 2π * [tex]5^{2}[/tex]
⇒ S = 2 * 3.14 * 5 * 8 + 2 * 3.14 * 25
⇒ S = 251.2 + 157
⇒ S = 408.2 square meter
Now, it is given that the total cost of the steel will be $13,062.40.
So, per square meter cost will be:
⇒ Cost = [tex]\frac{13,062.40}{408.2\\}[/tex]
⇒ Cost = $32
Hence, the per square meter cost of steel for the cylinder will be $32.
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A student attempted to solve the system 5x + 2y = 10 and 10x + 2y = 1 by graphing. The graph and the conclusion are
below. What can you say about the student's work?
y
-10x + 2y = 1
5x + 2y = 10
The soluion is ().
O The solution is incorrect because the student did not correctly identify the intersection.
O The solution is correct and the lines are graphed correctly.
O The solution is correct, but the lines were graphed incorrectly.
O The solution is incorrect because the lines are not graphed correctly.
Answers
Answer:
Option A: The solution is incorrect because the student did not correctly identify the intersection.
Step-by-step explanation:
Solve by elimination method.
5x + 2y = 10; -10x + 2y = 1
Multiply the second equation by -1, then add the equations together.
(5x + 2y = 10)
-1 (-10x + 2y = 1)
Forms:
5x + 2y = 10
10x - 2y = -1
Add these equations to eliminate y.
15x = 9
Then solve 15x = 9 for x:
15x = 9
15/15 = 9/15 (Divide both sides by 15)
x = 3/5
Now that we've found x let's plug it back in to solve for y.
Write down the original equation:
5x + 2y = 10
Substitute 3/5 for x in:
5x + 2y = 10:
5(3/4)+2y=10
2y+3=10
2y+3-3=10+-3
2y=7
2y/2 = 7/2
y = 7/2
x = 3/5 and y = 7/2.
Comparing the identified answers to the one found by the students, it can be concluded that Option A: The solution is incorrect because the student did not correctly identify the intersection.
whats the answer to 102-38x14 divided by 7+162= help plss
Answers
Answer:
-2.5
Step-by-step explanation:
follow BIMDAS.
like my answer if you find it helpful
There is a 25% chance that a vowel is drawn from a bag of random letter tiles. what is the probability of drawing a vowel, placing it back in the bag, and then drawing a consonant
Answers
The probability of drawing a vowel, placing it back in the bag, and then drawing a consonant is 0.1875 or 18.75%.
Calculating the probability
The probability of drawing a vowel from the bag of random letter tiles is 25%. Since the tile is replaced after drawing, the probability of drawing a vowel on the second draw is also 25%.
The probability of drawing a vowel and then a consonant can be calculated by multiplying the probabilities of each event:
P(vowel and consonant) = P(vowel) x P(consonant)
= 0.25 x 0.75
= 0.1875
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i have 60 square feet of paper to wrap a box in the shape of a right rectangular prism the height of the box is 1 2/3 feet the width is 4 feet and the length is 5 1/2 feet what percent of the box will remain unwrapped if i use all the paper i has available
Answers
The percent of the box that will remain unwrapped by the 60 square feet of paper is about 20.70%
What is a percentage?A percentage is a proportion of a number expressed as fraction of a 100
The dimensions in mixed fractions can be expressed as follows;
Height of the box = 1 2/3 feet = 5/3 feet
Width of the box = 4 feet
Length of the box = 5 1/2 feet = 11/2 feet
Surface area of the box, A = 2 × (5/3) × 4 + 2 × 4 × 11/2 + 2 × (5/3) × 11/2 = 227/3 = 75 2/3 square inches
The percent of the box that will remain unwrapped is therefore;
Percentage = 60/(227/3) × 100 ≈ 79.3%
The percentage of the box that will remain unwrapped is about (100 - 79.3)% = 20.70%
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. (Adapted from Terence Blows, Northern Arizona University.) Classify as in Exercise 6 but for the following circumstances. a. The amount of caffeine in the bloodstream decreases by 50% every 5 hours or so after stopping drinking coffee. b. The amount of trash in a landfill increases by 350 tons per week. c. The amount of alcohol in the bloodstream decreases by 10 grams (the amount in a standard drink) per hour after stopping drinking. d. Your age increases every day.
Answers
The statements are classified as Exponential decay and Linear growth.
What are the classification of the statements?
a. Exponential decay: The amount of caffeine in the bloodstream decreases by 50% every 5 hours, which indicates an exponential decay process where the quantity decreases at a constant percentage rate over time.
b. Linear growth: The amount of trash in a landfill increases by 350 tons per week, which indicates a linear growth process where the quantity increases by a constant amount over time.
c. Exponential decay: The amount of alcohol in the bloodstream decreases by 10 grams (the amount in a standard drink) per hour after stopping drinking, which indicates an exponential decay process where the quantity decreases at a constant percentage rate over time.
d. Linear growth: Your age increases every day, which indicates a linear growth process where the quantity (age) increases by a constant amount (1 day) over time.
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This pattern follows the rule add 2. What is another feature of this pattern? (4 points) An image of a pattern. Term one has one dot, term two has three dots, term three has five dots, term four has seven dots. a The terms appear even, odd, even, odd. b All the terms are even. c Two terms are even, then two terms are odd. d All the terms are odd.
Answers
The correct answer is c: Two terms are even, then two terms are odd. This pattern follows the rule of adding 2, so each successive term is an even number followed by an odd number.
Number is a mathematical object used to count, measure and represent a quantity. It is used to symbolize a numerical quantity or value, and is used in various ways in mathematics, science, engineering, finance and other fields. Numbers are also used to represent relationships between objects, such as the number of sides in a triangle or the number of students in a classroom.
This alternating pattern of even and odd terms is a feature of the pattern, with two terms being even followed by two terms being odd. This pattern continues as the terms increase, with the even terms adding 2 and the odd terms adding 2 as well. This pattern is a good way to remember a sequence of numbers and can be used to help understand patterns in mathematics.
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Can someone help me with this problem, and explain how to solve it?
Answers
Thus, the height of flagpole from the ground is found as 23.34 feet.
Explain about the angle of elevation:The measurement of the angle between a person's eyes' line of sight to anything above and the horizontal line is known as the angle of elevation.
The movement of the observer's eyes determines the elevation angle. The angle of elevation is the angle formed by the line of sight and the horizontal line when a viewer is looking up at an object.
Given data:
height of boy = 5 ftDistance of boy from flagpole = 30 ft angle of elevation = 35 degreesLet the height of pole above the boy be 'h'feet.Using the trigonometric ratios in the right triangle ABE.
tan 35 = h / 30
h = 30* tan(35)
h = 18.34
Height of flagpole = 18.34 + 5 = 23.34 feet
Thus, the height of the flagpole from the ground is found as 23.34 feet.
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If P(A)=0.3, P(B)=0.2 and P(A∩B)=0.2 determine the following probabilities:
(a) P(A')
(b) P(A∪B)
(c) P(A'∩B)
(d) P(A∩B')
(e) P[(A∪B)']
Answers
The probabilities are as follows:
(a) P(A')= 0.7
(b) P(A∪B) = 0.3
(c) P(A'∩B) = 0
(d) P(A∩B') = 0.1
(e) P[(A∪B)'] = 0.7
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
(a) P(A') = 1 - P(A) = 1 - 0.3 = 0.7
(b) P(A∪B) = P(A) + P(B) - P(A∩B) = 0.3 + 0.2 - 0.2 = 0.3
(c) P(A'∩B) = P(B) - P(A∩B) = 0.2 - 0.2 = 0
(d) P(A∩B') = P(A) - P(A∩B) = 0.3 - 0.2 = 0.1
(e) P[(A∪B)'] = 1 - P(A∪B) = 1 - 0.3 = 0.7
Note: P(A) represents the probability of event A occurring, P(B) represents the probability of event B occurring, and P(A∩B) represents the probability of both events A and B occurring simultaneously. The symbol '∪' represents the union of two events, and the symbol '∩' represents the intersection of two events. The complement of an event A is represented by A'.
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4. This number line
number of minutes Diane read
week for 3 weeks.
0
200
100
300
How many minutes did she read after
the first week?
minutes
After the second week?
After the third week?
minutes
minutes
How many minutes did she read each
week? Explain how you know.
5. Diane reads the same number of minutes
each week. How many minutes does
she read after 4 weeks? After 5 weeks?
Skip count on the number line above to
find the answers.
After 4 weeks:
After 5 weeks:
minutes
minutes
Answers
4) Dane read an average of 400 minutes per week. 5) Diane will have read 2000 minutes after 5 weeks.
How to determine how many minutes did she read each week4) The number "0200100300" represents the number of minutes Diane read each week for 3 weeks. To find out how many minutes she read after the first week, we simply look at the first digit, which is "0." This means that Diane did not read any minutes during the first week.
To find out how many minutes she read after the second week, we add the digits in the first two positions, which are "02." This gives us a total of 2 x 60 = 120 minutes.
To find out how many minutes she read after the third week, we add the digits in the first three positions, which are "020." This gives us a total of 20 x 60 = 1200 minutes.
To find out how many minutes she read each week, we simply divide the total number of minutes by the number of weeks, which is 3. So Diane read a total of 1200 minutes in 3 weeks, which means she read an average of 400 minutes per week.
5) If Diane reads the same number of minutes each week, then she will read that same number of minutes after 4 weeks and after 5 weeks. To find out how many minutes she reads after 4 weeks, we can skip count by the same number repeatedly: 400, 800, 1200, 1600. So Diane will have read 1600 minutes after 4 weeks.
Similarly, to find out how many minutes she reads after 5 weeks, we can skip count again by the same number repeatedly: 400, 800, 1200, 1600, 2000. So Diane will have read 2000 minutes after 5 weeks.
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Peanuts sell for Php 10.00 per gram. Cashews sell for Php 8.00 per gram. How many grams of cashews should be mixed with 12 g of peanuts to obtain a mixture that sells for Php 9.00 per gram?
PEANUTS CASHEWS MIXTURE Number of Grams (g) 12 X 12+ X Price per grams Php 10.00 Php 8.00 Php 9.00 Total Price Phn10x12 = Php 120 8x 9 [12+x]
Answers
Answer:
Phn10x12
Step-by-step explanation:
PEANUTS CASHEWS MIXTURE Number of Grams (g) 12 X 12+ X Price per grams Php 10.00 Php 8.00 Php 9.00 Total Price Phn10x12 = Php 120 8x 9 [12+x]
330 men took 30 days to finish a work then how many men will be required to finish the same work in 11 days...???
In your birthday party there was food for 20 friends for 2 hours but 30 friends attened the party. Till how long did the food last...???
Answers
Step-by-step explanation:
data given
men 330 ,days30
men? ,days11
from
men(m) are inversely proportional todays (d)
m=k/d
330×30=k
k=9900
now,
m=9900/11m
m=900
data given
friends 20, time 2hours
friends 30, time?
from
friends (f) are inversely proportional to time (t)
f=k/t
k=20×2
k=40
now,
t=40/30
t=1.3(1:18)
answer ,men required are900answer the food will last for1:18Which is NOT the same as asking:
What is the logarithm of 1,296 if the base is 6?
Answers
Reason: log=exponent, so whenever you see a log, that means you’re solving for an exponent.
The diameter of a circle is 5 centimeters. What’s the radius? Give the exact answer in simplest form
Answers
Answer:
2.5cm
Step-by-step explanation:
you half the diameter to get the radius
3√b in exponential form
Answers
When you want to change a square root to exponential form, simply change it to the power of 1/2. And if you want to get rid of a square root, square the whole thing.
FIND THR CIRCUMFERENCE OF A CD THAT HAS A RADIUS OF 6 CENTIMETERS
___cm
Answers
Answer:
Hm
Step-by-step explanation:
The formula to find the circumference of a circle is:
Circumference = 2πr
Where "r" is the radius of the circle, and "π" (pi) is a mathematical constant approximately equal to 3.14.
Substituting the given value of radius, we get:
Circumference = 2 x π x 6
Circumference = 12π
Circumference ≈ 37.7 cm (rounded to one decimal place)
Therefore, the circumference of a CD that has a radius of 6 centimeters is approximately 37.7 cm.
^4√p7
in exponential form.
Answers
Answer:1111
Step-by-step explanation:
what is one of the zeros of the function shown in this graph?
Answers
Answer:
x = -3 and x = 1 are the two zeroes of this function. Choose one of them for your answer.
1. You go to the ice cream shop with your friends and you can choose an ice cream, a topping
and sprinkles. How many different sundaes can you make when you order one flavor of ice
cream, one topping and one color of sprinkles from the chart below? Show all possible
outcomes in a tree diagram.
Ice Cream
Chocolate
Vanilla
Strawberry
Topping
Fudge
Marshmallow
Sprinkles
Chocolate
Rainbow
How many sample spaces are there? HINT: How many possible combinations?
b. P (Chocolate, Fudge, Rainbow)
Answers
Answer:
Step-by-step explanation:
Answer:
You can make 12 possible sundaes with these toppings.
Step-by-step explanation:
Chocolate, Vanilla, and Strawberry all have 4 possible outcomes:
1. Fudge & Chocolate Sprinkles
2. Fudge & Rainbow Sprinkles
3. Marshmallow & Chocolate Sprinkles
4. Marshmallow & Rainbow Sprinkles
-------------------------------------------------------------------------------------------------------------
4 x 3 will equal 12, the total possible sundaes you can make with these toppings and ice cream flavors.
Cylinder M and cylinder N are similar. The radius of cylinder N is equal to its height, and the ratio of the height of cylinder N to the height of cylinder M is 5: 3. The surface area of cylinder N is 256 square feet greater than the surface area of cylinder M. Find the surface area of each cylinder.
Answers
The surface area of cylinder M is approximately 131.95 square feet and the surface area of cylinder N is approximately 319.77 square feet.
What is a cylinder?
A cylinder is a three-dimensional geometric shape that consists of two congruent parallel bases in the shape of circles or ellipses, and a curved surface that connects the bases. The height of a cylinder is the perpendicular distance between the bases. A cylinder is a type of prism, and it can be classified as either a right cylinder or an oblique cylinder depending on whether or not its axis is perpendicular to its bases. Right cylinders have circular bases and their axis is perpendicular to the bases, while oblique cylinders have elliptical bases and their axis is not perpendicular to the bases.
Now,
Let the radius of cylinder M be r and its height be h. Then, the radius and height of cylinder N are both 2r, since the radius is equal to the height.
Since the cylinders are similar, their dimensions are proportional, which means:
(height of N) / (height of M) = 5/3
(radius of N) / (radius of M) = (2r) / r = 2
Using the formula for the surface area of a cylinder, we can write:
Surface area of cylinder M: 2πr² + 2πrh
Surface area of cylinder N: 2π(2r)² + 2π(2r)(5/3)h
We are told that the surface area of cylinder N is 256 square feet greater than the surface area of cylinder M. So we can set up the equation:
2π(2r)² + 2π(2r)(5/3)h = 2πr² + 2πrh + 256
Simplifying and solving for h, we get:
4r² + 20rh/3 = r² + rh + 128
3r² - rh - 128 = 0
(3r + 32)(r - 4) = 0
Since the height of the cylinder cannot be negative, we take the positive solution r = 4. Then, the height of cylinder M is (3/5)(4) = 12/5, and the height of cylinder N is 2(4) = 8.
Using the formulas for surface area, we can find the surface areas of both cylinders:
Surface area of cylinder M: 2π(4)² + 2π(4)(12/5) = 131.95 square feet
Surface area of cylinder N: 2π(2(4))² + 2π(2(4))(8) = 319.77 square feet
Therefore, the surface area of cylinder M is approximately 131.95 square feet and the surface area of cylinder N is approximately 319.77 square feet.
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Brenda is fishing from a small boat. Her fishing hook is 12 feet below her, and a fish is swimming at the same depth as the hook, 16 feet away. How far away is Brenda from the fish?
Answers
Answer:
We can use the Pythagorean theorem to solve this problem. Let's call the distance Brenda is away from the fish "x". Then, we have a right triangle with legs of length 12 and x, and a hypotenuse of length 16. So:
x^2 + 12^2 = 16^2
Simplifying:
x^2 + 144 = 256
x^2 = 112
Taking the square root of both sides:
x ≈ 10.6 feet
Therefore, Brenda is approximately 10.6 feet away from the fish.
Hello, I am confused on how to answer this question.
Answers
Answer: x=14
Step-by-step explanation:
cb=10.
ac=14
The value of X will be 14.
This is a simple mathematics problem that can be solved by using ratios.
Given, AC : BC : AB = 7 : 5 : 8
AC = X ; BC = 10 ; AB = X + 2
AC/ BC = X/ 10 = 7/5 (Ratios can also be represented as fractions)
X/10 = 7/5
On Transposing,
5X = 70
X = 70/5
X = 14
Alternatively,
BC/AB = 5/8 = 10/ (X + 2)
5/8 = 10/ (X + 2)
On Transposing,
80 = 5X + 10
5X = 70
X = 14
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coordinate plane with points at A 0 comma 2 and B 2 comma 0 intersected by line f Dilate line f by a scale factor of one half with the center of dilation at the origin to create line f′. Where are points A′ and B′ located after dilation, and how are lines f and f′ related? The locations of A′ and B′ are A′ (0, 2) and B′ (0, 0); lines f and f′ intersect at point A. The locations of A′ and B′ are A′ (0, 1) and B′ (1, 0); lines f and f′ are parallel. The locations of A′ and B′ are A′ (0, 0) and B′ (2, 0); lines f and f′ intersect at point B. The locations of A′ and B′ are A′ (0, 2) and B′ (2, 0); lines f and f′ are the same line.
Answers
The answer of the given question based on the graph is , The locations of A′ and B′ are A′ (0, 1) and B′ (1, 0); lines f and f′ are parallel.
What is Scale factor?A scale factor is a number that scales, or multiplies, a quantity by some factor. It is used in mathematics to describe the relationship between corresponding measurements of two similar figures, such as triangles or rectangles.
To dilate line f by scale factor of one half with center of dilation at origin, we multiply coordinates of each point on line f by 1/2.
The equation of line f can be found by using the points A and B:
slope of line f = (0 - 2)/(2 - 0) = -1
y-intercept of line f = 2
Therefore, the equation of line f is y = -x + 2.
To find the coordinates of A' and B' after dilation, we can apply the dilation factor to each point:
A' = (0, 2)*1/2 =(0, 1)
B' = (2, 0)*1/2 =(1, 0)
So A' is located at (0, 1) and B' is located at (1, 0) after dilation.
Now let's analyze the relationship between lines f and f'. The dilation was centered at the origin, so the origin is a fixed point of the dilation. This means that the point where lines f and f' intersect must be the origin.
If we plug in x = 0 into the equation of line f, we get y = 2. This means that point A is located at (0, 2) and intersects with line f at y = 2. After dilation, point A' is located at (0, 1), which means that lines f and f' intersect at point A.
To determine the relationship between lines f and f', we can compare their equations. The equation of f' can be found by using the points A' and B':
slope of f' = (0 - 1)/(1 - 0) = -1
y-intercept of f' = 0
Therefore, the equation of f' is y = -x.
Comparing the equations of f and f', we can see that they have the same slope of -1, which means they are parallel. Therefore, the correct answer is: The locations of A′ and B′ are A′ (0, 1) and B′ (1, 0); lines f and f′ are parallel.
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