The quadratic functions that have a graph with x-intercepts of -8 and 2 are:
y = (x + 8)(x - 2)
f(x) = -7(x + 8)(x - 2)
Options A and C are the correct answer.
We have,
To find the quadratic functions that have a graph with x-intercepts of -8 and 2, we can start by using the fact that the x-intercepts occur when y = 0.
We know that the x-intercepts are -8 and 2, so we can set up two equations:
(x + 8) = 0 and (x - 2) = 0
Solving for x in each equation, we get:
x = -8 and x = 2
Therefore, the factors of the quadratic function that has x-intercepts of -8 and 2 are (x + 8) and (x - 2).
Now we can use these factors to determine which quadratic functions have a graph with these x-intercepts.
A.
y = (x + 8)(x - 2)
Expanding this quadratic function gives:
y = x² + 6x - 16
This function has x-intercepts of -8 and 2, so it is a valid option.
B.
y = (x - 8)(x - 2)
Expanding this quadratic function gives:
y = x² - 10x + 16
This function does not have an x-intercept of -8, so it is not a valid option.
C.
f(x) = -7(x + 8)(x - 2)
Expanding this quadratic function gives:
f(x) = -7x² - 42x - 96
This function does have x-intercepts of -8 and 2, so it is a valid option.
D.
f(x) = -2x² - 12x + 32
To find the x-intercepts of this quadratic function, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
Plugging in the values from the given function, we get:
x = (-(-12) ± √((-12)² - 4(-2)(32))) / 2(-2)
x = (-(-12) ± √(144 + 256)) / (-4)
x = (6 ± √(100)) / 2
x = 3 ± 5
So the x-intercepts are -2 and 8, which means this function is not a valid option.
E.
y = x² - 5x + 8
To find the x-intercepts of this quadratic function, we can again use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
Plugging in the values from the given function, we get:
x = (-(-5) ± √((-5)² - 4(1)(8))) / 2(1)
x = (5 ± √(9)) / 2
x = 4 or x = 1
So the x-intercepts are 4 and 1, which means this function is not a valid option.
F.
f(x) = x² - 8x + 2
To find the x-intercepts of this quadratic function, we can once again use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
Plugging in the values from the given function, we get:
x = (-(-8) ± √((-8)² - 4(1)(2))) / 2(1)
x = (8 ± √(60)) / 2
x = 4 ± 2√(15)
So the x-intercepts are 4 + 2 √(15) and 4 - 2 √(15), which means this function is not a valid option.
Therefore,
The quadratic functions that have a graph with x-intercepts of -8 and 2 are:
A. y = (x + 8)(x - 2)
C. f(x) = -7(x + 8)(x - 2)
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The depth of water at a dock can be modeled as y = 3 sin(x) +7. At low tide, the water is 4 feet
deep. What is the depth of water at high tide (its maximum point)?
Step-by-step explanation:
At low tide depth = (3)(-1) + 7 = 4
at HIGH tide depth = (3) (+1) + 7 = 10 feet
What fraction is equivalent to 1/4
The numbers are: 2,4,6,8,10,12
. According to the National Highway Traffic Safety Administration, seat belt using among American
drivers and front-seat passengers passed 90% for the first time in 2016. At that time, 90.1% of
people used seat belts. If four people are selected at random, find the probability that all four
regularly use seat belts.
The probability that all four people regularly use seat belts is approximately 0.656 or 65.6%.
To find the probability that all four people regularly use seat belts, we need to use the multiplication rule of probability which states that the probability of two or more independent events occurring together is the product of their individual probabilities.
The probability that the first person uses a seat belt is 0.901, and assuming that the events of seat belt use by different people are independent, the probability that the second person also uses a seat belt is 0.901.
The probability that the third person uses a seat belt is also 0.901, and the probability that the fourth person uses a seat belt is also 0.901.
Therefore, the probability that all four people regularly use seat belts is:
P(all four use seat belts) = P(person 1 uses seat belt) x P(person 2 uses seat belt) x P(person 3 uses seat belt) x P(person 4 uses seat belt)
P(all four use seat belts) = 0.901 x 0.901 x 0.901 x 0.901
P(all four use seat belts) = 0.656
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I need help with this question
(4x+3)5=2x/6
1. The relationship between distance
measured on a map and the actual
distance on the ground
A. A sketch
B. A statement
C. Layout
D. Scale
What if the correct answer
Answer: A Map Scale.
Step-by-step explanation:
A Map Scale is the relationship with the ground.
Find the angles of △ABC given that a=11, b=20, and c=18.
Round each angle to the nearest tenth of a degree and use that rounded value to find the remaining angles.
The angles of △ABC are approximately:
A ≈ 36.1 degrees
B ≈ 55.9 degrees
C ≈ 101.3 degrees
Angles of triangle calculation.
To find the angles of △ABC, we can use the Law of Cosines, which states that:
c^2 = a^2 + b^2 - 2ab*cos(C)
where C is the angle opposite the side c.
Using the given values, we can substitute and solve for cos(C):
18^2 = 11^2 + 20^2 - 2(11)(20)cos(C)
324 = 441 + 400 - 440cos(C)
cos(C) = -17/440
C ≈ 101.3 degrees
We can now use the Law of Sines to find the other angles:
sin(A)/a = sin(C)/c
sin(A)/11 = sin(101.3)/18
sin(A) ≈ 0.593
A ≈ 36.1 degrees
sin(B)/b = sin(C)/c
sin(B)/20 = sin(101.3)/18
sin(B) ≈ 0.820
B ≈ 55.9 degrees
Therefore, the angles of △ABC are approximately:
A ≈ 36.1 degrees
B ≈ 55.9 degrees
C ≈ 101.3 degrees
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Question 4(Multiple Choice Worth 1 points)
(04.03 MC)
On a number line, point A is located at 4, point C is located at 11, and point B lies between points A and C. What is the location of B such that the ratio of AB BC is 2:3
8.2
6.8
5.9
5.6
Kaydin is trying to decide
wether to buy a season pass to UCLA's 23
home basketball games this season. The
cost of an individual ticket is $21, and the
cost of a season pass is $386. The season
pass will admit Kaydin to any home game
at no additional cost. What is the
minimum number of home basketball
games Kaydin must attend this season in
order for the cost of a season pass to be
less expensive than the total cost of
buying an individual ticket for each game
he attends?
____games
Can someone help me?
The surface area of the triangular prism is 235 cm²
How to solve an equation?An equation is an expression that uses mathematical operations to show how numbers and variables are related to each other.
The surface area of a triangular prism is gotten by adding the individual area of each surface.
For the triangular prism shown:
Surface area = 2(1/2 * 10 cm * 12 cm) + (10 cm * 5 cm) + 2(13 cm * 5 cm) = 235 cm²
The surface area is 235 cm²
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Can anybody help me on the question.
ASAP
The hanger in the illustration will have the value x = 6, and it will remain balanced.
Define equations?Mathematical expressions with two algebraic expressions on either side of the equals (=) sign are called equations. It demonstrates the equality of the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in each mathematical equation. To determine the value of an unknown variable that stands in for an unknown quantity, equations can be solved.
Here's the query,
Considering the graph,
The hanger's equation is as follows:
4x= 24
There are 4 numbers here that represent the value of the hanger.
So, x+x+x+x will be 24.
The equation is thus:
4x = 24.
Now, by resolving the equation, we can determine the value of x that balances the hanger:
4x = 24.
When you divide 4 on both sides:
x = 24/4
x = 6.
As a result, the hanger will remain in equilibrium for x = 6.
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Question attached below:
The probability that Frank gets a head and a tail in any order is 2/5.
We have,
The sample space of tossing two coins.
= {HT} x {HT}
= {HH, HT, TH, TT}
So,
The table is filled as:
First coin Second coin
Head Head
Head Tail
Tail Head
Tail Tail
Now,
The probability that Frank gets a head and a tail in any order.
= Number of required outcomes / Total outcomes
{HT, TH} = 2
{HH, HT, TH, TT} = 5
So,
= 2/5
Thus,
The probability that Frank gets a head and a tail in any order is 2/5.
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x^2+16=(x+4)^2 true or false?
Answer:
False
Step-by-step explanation:
(x+4)^2 = x^2 + 8x + 16
Side of a triangle is utility pole. Henry wouls like to know how long the guy wire, c, should be. The telephone pole is perpendicular to the ground. Henry knows that a = 20 ft and b = 15 ft. The length of the guy wire should be
The length of the guy wire should be option D √(25) ft. that is 25 ft.
What is perpendicular mean?Perpendicular means that two lines or objects intersect each other at a 90-degree angle, forming a right angle. This means that if you were to draw a line at the point of intersection, it would split the angles on either side of it into two equal parts. In simpler terms, if you imagine a horizontal line and a vertical line intersecting each other, they would be perpendicular to each other. The concept of perpendicularity is important in geometry and is used in many different applications, such as construction, engineering, and design.
We can use the Pythagorean theorem to find the length of the guy wire c. According to the theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Therefore:
c² = a² + b²
Substituting the given values:
c² = (20 ft)² + (15 ft)²
c² = 400 ft² + 225 ft²
c² = 625 ft²
Taking the square root of both sides:
c = √(625) ft
c = 25 ft
Therefore, the length of the guy wire should be 25 feet.
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Form a polynomial whose zeros and degree are given.
Zeros: 6, multiplicity 1; 3, multiplicity 2; degree 3
Type a polynomial with integer coefficients and a leading coefficient of 1 in the box below.
f(x) = (Simplify your answer.)
The polynomial with integer coefficients and a leading coefficient of 1 is (x-6) (x-3)² which in turn will be: f(x) = x³ - 12x² + 45x - 54
What is the polynomial?Based on the question, If the zeros of a polynomial are said to be 6, 3, and 3, one can say that the polynomial can be written in factored form such as
f(x) = (x - 6)(x - 3)(x - 3)
The to solve this, we have to multiply it:
f(x) = (x - 6) (x² - 6x + 9)
f(x) = x³ - 6x² + 9x - 6x² + 36x - 54
f(x) = x³ - 12x² + 45x - 54
Therefore, the polynomial with integer coefficients and a leading coefficient of 1 will be f(x) = x³ - 12x² + 45x - 54
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Random sample of 250 students taken with a population of 7500 surveyed about their majors. In the sample, 75 students were Art majors. How many students in total population are are Art majors?
Therefore, we estimate that there are 2250 Art majors in the total population.
What is proportion?In mathematics, a proportion is an equation that states that two ratios are equal. A ratio is a comparison of two quantities expressed as a fraction or a decimal. Since both sides of the equation are equal, the proportion is true. Proportions are used in many mathematical and real-world contexts, such as in geometry, finance, and statistics. They are useful for comparing and scaling quantities, and for solving problems involving unknown quantities or variables.
Here,
We can use proportions to estimate the total number of Art majors in the population based on the proportion of Art majors in the sample.
The proportion of Art majors in the sample is:
75/250 = 0.3
We can assume that this proportion is representative of the proportion of Art majors in the population.
So, if x is the total number of Art majors in the population, then we can set up the following proportion:
0.3 = x/7500
To solve for x, we can cross-multiply and simplify:
0.3 * 7500 = x
x = 2250
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A quadratic equation with opposite solutions can be found by multiplying ______
The equation will have ________.
A quadratic equation with opposite solutions can be found by multiplying a variable by its negative value. Specifically, if we start with a quadratic equation of the form:
ax^2 + bx + c = 0
We can find an equation with opposite solutions by multiplying either a or c by -1. For example, if we multiply c by -1, we get:
ax^2 + bx - c = 0
This equation will have opposite solutions if the discriminant, b^2 - 4ac, is negative. This is because the solutions of a quadratic equation are given by the formula:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
Thus, if the discriminant is negative, then the square root term will be imaginary, which means that the solutions will be complex conjugates of each other.
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Lyle uses 13 cups of shredded cheese to make a large pizza. How many cups of shredded cheese will he use to make 5 pizzas?
Answer:
65
Step-by-step explanation:
cups per pizza- 13
for 5 pizza- 13×5= 65
think of it this way you eat 2 slices of pizza in an hour, how many will you eat in 6 hours? 2x6 = 12
Trisha is collecting books to donate. The table below shows the total number of books collected, b, for different number of weeks, w. Which equation represents the relationship between the number of weeks, w, and the number of books collected, b?
The equation representing the relationship between the number of weeks (w) and the number of books collected (b):
b = 10w + 0
b = 10w
How to solveWe can observe from the table that the number of books collected increases by 10 for each week.
Thus, there is a linear relationship between the number of weeks (w) and the number of books collected (b). We can represent this relationship using the equation:
b = mw + c
where b is the number of books collected, w is the number of weeks, m is the slope (rate of change), and c is the y-intercept (number of books collected at week 0).
The slope (m) is the change in the number of books collected per week, which is 10. We can now find the y-intercept (c) by substituting one of the points from the table into the equation. Let's use the point (1, 10):
10 = 10 * 1 + c
c = 0
Now we have the equation representing the relationship between the number of weeks (w) and the number of books collected (b):
b = 10w + 0
b = 10w
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the data in the form of a table, which shows the total number of books collected (b) for different number of weeks (w).
Weeks (w) Books Collected (b)
1 10
2 20
3 30
4 40
Trisha is collecting books to donate. The table below shows the total number of books collected, b, for different number of weeks, w. Which equation represents the relationship between the number of weeks, w, and the number of books collected, b?
Is (2, 6) a solution to this system of equations?
y = 3/2x + 3
y = -9x + 1
yes
no
To determine if (2, 6) is a solution to the system of equations:
y = 3/2x + 3 ... (equation 1)
y = -9x + 1 ... (equation 2)
We need to substitute x = 2 and y = 6 into both equations and check if they are true.
Substituting x = 2 and y = 6 into equation 1, we get:
6 = 3/2(2) + 3
6 = 3 + 3
6 = 6
This equation is true.
Substituting x = 2 and y = 6 into equation 2, we get:
6 = -9(2) + 1
6 = -18 + 1
6 = -17
This equation is false.
Since (2, 6) does not satisfy equation 2, it is not a solution to the system of equations. Therefore, the answer is: no.
Question 02/08 The probability that the bus will arrive on time is 0.6 and the probability that it will be late is 0.3. What is the probability that it will arrive early?
The probability that the bus will arrive early is 0.1, or 10%.
To find the probability that it will arrive early
It is possible to calculate the likelihood that the bus will arrive early using the rule that the sum of all possible outcomes must equal 1.
P(on time) + P(late) + P(early) = 1 if P(E) is the likelihood that the bus will arrive early.
Using the probabilities as a replacement, we get:
0.6 + 0.3 + P(E) = 1.
For P(E), use the formula:
P(E) = 1 - 0.6 - 0.3 = 0.1.
Therefore, the probability that the bus will arrive early is 0.1.
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Operations with Fractions
Solve for x.
2/5+x=1
Answer:
Hello... im exhausted but ill solve it i guess
To solve for x in the equation 2/5 + x = 1, we can follow these steps:
Subtract 2/5 from both sides of the equation to isolate the x term:
2/5 + x - 2/5 = 1 - 2/5
This simplifies to:
x = 1 - 2/5
Find a common denominator for 1 and 2/5, which is 5:
x = 5/5 - 2/5
Subtract 2/5 from 5/5:
x = 3/5
So, the solution for x in the given equation is x = 3/5.
Complete the statement by filling in the blank. Write your answer on a
separate sheet of paper.
A ___________ is a frequency distribution using the means computed from all
possible random samples of a specific size taken from a population. To get the
possible samples use the formula ______, where N is the ________ and n is the ____
size to be taken. The total probability of the sample mean must be equal to ____.
A sampling distribution is a frequency distribution using the means computed from all possible random samples of a specific size taken from a population.
To get the possible samples, use the formula "N choose n", where N is the population size, and n is the sample size to be taken. The total probability of the sample mean must be equal to 1.
Since the mean of all possible samples must be equal to the population mean. The sampling distribution is an important concept in statistics as it allows us to make inferences about the population based on the characteristics of the sample, and helps us estimate parameters and test hypotheses.
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Drag each value to the correct location on the equation. Not all values will be used. Convert radians to degrees. 4 /9
4[tex]\pi[/tex]/9 radians equals 80 degrees.
How will you convert radians into degrees?To convert a radian angle to a degree angle, multiply it by 180°/[tex]\pi[/tex]. To convert a degree angle to a radian angle, multiply it by [tex]\pi[/tex]/180°.
We utilize the conversion factor that 1 radian = 180/[tex]\pi[/tex] degrees to convert radians to degrees.
So we multiply 4[tex]\pi[/tex]/9 radians by the conversion factor to get degrees:
[tex]\\\frac{4\pi }{9} * \frac{180}{\pi } \\\frac{720}{9}[/tex]
On simplifying we get,
720 / 9 = 80 degrees
As a result, 4[tex]\pi[/tex]/9 radians equals 80 degrees.
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Complete question:
attach in the image form
4x 4/8
(4/8 is a fraction)
PLEASE HELP IMMEDIATELY ♥️
Answer:
2
Step-by-step explanation:
So there are 2 ways to do this, but the easy way is to do [tex]\frac{4}{1}[/tex] x [tex]\frac{4}{8\\}[/tex]
it becomes [tex]\frac{16}{8}[/tex] then divided 16 by 8 and it's 2.
Have a good day!
Which of these is an accurate way to measure the volume of a rectangular prism
A. Fill it with water and then weigh the water.
B.Trace each face of the prism on centimeter grid paper, and then count the number of squares it comprises.
C. Measure the length and the width, and then multiply the two values.
D. pack it with unit cubes, leaving no gaps or overlaps, and count the number of unit cubes.
The correct option is (D) if unit cubes are packed into a rectangular prism without any gaps or overlaps, the volume of the prism can be calculated by counting the number of unit cubes.
What is a rectangular prism?A rectangular prism is a polyhedron in geometry that has two parallel and congruent bases.
It also goes by the name cuboid.
Six faces, each with a rectangle shape and twelve edges, make up a rectangular prism.
It is referred to as a prism because of the length of its cross-section.
There are 6 faces, 8 vertices, and 12 edges on a rectangular prism.
A rectangular prism's volume can be determined by packing unit cubes into it without any gaps or overlaps, then counting the number of unit cubes.
A rectangular prism's surface area is equal to the sum of the areas of each of its faces.
It can be calculated using the formula 2(lw+ wh+ hl).
Therefore, the correct option is (D) if unit cubes are packed into a rectangular prism without any gaps or overlaps, the volume of the prism can be calculated by counting the number of unit cubes.
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The sets D and E are given below.
D=(-1.2.4, 5, 8)
E=(-2,2. 3, 4, 6)
Find the union of D and E.
Find the intersection of D and E.
Write your answers using set notation (in roster form).
DUI- D
DAE = D
X
Ø
Ś
Answer:
D∪E = {-2, -1, 2, 3, 4, 5, 6, 8}D∩E = {2, 4}Step-by-step explanation:
You want the union and the intersection of the given sets D and E.
UnionThe union of the two sets is the list of elements in either set. It will contain all of the elements of D along with all of the elements of E, with duplicate values removed so that each element is only listed once.
D∪E = {-2, -1, 2, 3, 4, 5, 6, 8}IntersectionThe intersection of the two sets is the list of elements that appear in both sets. Any element that only appears in one of the sets is not part of the union.
D∩E = {2, 4}<95141404393>
PLEASE HELP! An ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. An agricultural association publishes tariff rates for railroad-car shipments of ethanol. Assuming that the standard deviation of such tariff rates is $1200, determine the probability that the mean tariff rate of 400 randomly selected railroad-car shipments of ethanol will be within $80 of the mean tariff rate of all railroad-car shipments of ethanol. Interpret your answer in terms of sampling error. The probability is what?
(Round to three decimal places as needed.) Thanks!
The probability that the mean tariff rate of 400 randomly selected railroad-car shipments of ethanol will be within $80 of the mean tariff rate of all railroad-car shipments of ethanol is: 0.305.
The interpretation and how to arrive at the propabilityThe interpretation of the statement that the probability of the sample mean being within $80 of the population mean is 0.305 is that if we take multiple samples of 400 ethanol railroad-car shipments, about 30.5% of the time, the sample mean tariff rate will be within $80 of the population mean tariff rate.
To arrive at the propability, we will first list the data as follows:
Standard deviation of tariff rates, σ = $1200
Sample size, n = 400
Margin of error, E = $80
Standard deviation of sample mean = σ/√n = 1200/√400 = 60
To find the probability, we need to calculate the z-score for the margin of error.
z = E / standard deviation of sample mean = 80 / 60 = 4/3.
When we use the standard normal distribution table, we will arrive at the probability of a z-score between -1.33 and 1.33. This probability is approximately 0.305.
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The probability that the friend is at least 22 minutes late is
The probability that the friend is at least 22 minutes late is 0.266
Uniform density function for a friend = x minutes late
The Friend is at least 21 minutes late
Based on the above information, the probability that the friend is at least 21 minutes late is
= (Total minutes - minimum minutes)/Total minutes
=30-22/30
=8/30
=0.266
Based on the above formula we can easily find out the probability for the friend who is at least 22 minutes late
Hence, the probability that the friend is at least 22 minutes late is 0.266
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the table shows the favirote film of 20 people complete the pie chart
The complete table for the pie chart is;
Type of Film Frequency Angle in °
Action 4 72°
Horror 11 198
Comedy 5 90
How to interpret Pie chart?From the given table used to form the pie chart, we see that;
Type of Film Frequency Angle in °
Action 4 72°
Horror 11
Comedy 5
We know that the angles in a circle is equal to 360 degrees. Thus;
Angle composed of horror and comedy = 360 - 72 = 288°
Thus;
Angle for horror film = (11/(4 + 11 + 5)) * 360°
= (11/20) * 360°
= 198°
Thus;
Angle for comedy = 288° - 198° = 90°
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PLEASE HELP
IM CONFUSED
the correct answers are E(-4, 5) and F(3, 2). According to given probabilities condition
How to solve the question?
To find the coordinates of Checkpoints E and F, we need to first understand what is meant by "located at CD's location in a 180° rotation of the course."
A 180° rotation means that we flip the course upside down, with the line segment connecting Checkpoints C and D acting as the axis of rotation. This means that Checkpoints E and F will be on the same line as CD, with E being the reflection of C and F being the reflection of D across the line CD.
To find the coordinates of E, we reflect C across the line CD. To do this, we first find the slope of the line CD:
slope = (2 - 5) / (-3 - (-4)) = -3
The midpoint of CD is:
midpoint = ((-3 + (-4))/2 , (2 + 5)/2) = (-3.5, 3.5)
The line perpendicular to CD passing through the midpoint has slope -1/(-3) = 1/3. Using point-slope form, we can find the equation of this line:
y - 3.5 = (1/3)(x + 3.5)
Simplifying, we get:
y = (1/3)x + 4
To reflect C across CD, we can find the intersection point of this line with the line passing through C and CD. This line has slope -3 and passes through (-4, 5). Using point-slope form, we can find its equation:
y - 5 = (-3)(x + 4)
Simplifying, we get:
y = -3x - 7
Setting these two equations equal to each other, we get:
(1/3)x + 4 = -3x - 7
Solving for x, we get:
x = -4
Substituting this value back into either equation, we get:
y = 5
Therefore, the coordinates of Checkpoint E are (-4, 5).
To find the coordinates of F, we reflect D across CD. We can use a similar method as above to find the line passing through D and CD:
slope = (2 - 5) / (-3 - (-4)) = -3
y - 2 = (-3)(x + 3)
Simplifying, we get:
y = -3x - 7
To reflect D, we find the intersection point of this line with the line perpendicular to CD passing through the midpoint:
y - 3.5 = (1/3)(x - (-3.5))
Simplifying, we get:
y = (1/3)x + 4
Setting these two equations equal to each other, we get:
(1/3)x + 4 = -3x - 7
Solving for x, we get:
x = 3
Substituting this value back into either equation, we get:
y = 2
Therefore, the coordinates of Checkpoint F are (3, 2).
So the correct answers are E(-4, 5) and F(3, 2).
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