Suppose the line segments that represent Wayne Street and George Street
are reflected in the y-axis. Draw the images. Are they parallel? Explain.
Answers
If the slopes are equal, the reflected line segments are parallel.
When a line segment is reflected in the y-axis, its image is formed by reflecting each point on the segment across the y-axis.
This means that the x-coordinate of each point is negated, while the y-coordinate remains the same.
To draw the images of Wayne Street and George Street, we need to know their coordinates.
Let's assume that Wayne Street runs from (2, 3) to (6, 5), while George Street runs from (-1, -2) to (-5, -4).
When we reflect Wayne Street in the y-axis, we negate the x-coordinates and keep the y-coordinates the same.
This gives us the image of Wayne Street, which runs from (-2, 3) to (-6, 5).
Similarly, when we reflect George Street in the y-axis, we get the image of George Street, which runs from (1, -2) to (5, -4).
We need to consider the slopes of the original segments and their images.
The slope of Wayne Street is (5-3)/(6-2) = 1/2, while the slope of George Street is (-4-(-2))/(-5-(-1)) = -1/2.
When we reflect a line segment in the y-axis, its slope is negated.
So,
The slope of the image of Wayne Street is -1/2, while the slope of the image of George Street is 1/2.
Therefore, the images of Wayne Street and George Street are not parallel, since their slopes are opposite.
In fact, they are perpendicular to each other, since the product of their slopes is (-1/2) x (1/2) = -1/4, which is equal to -1 (the negative reciprocal of each other).
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Related Questions
boardwalk electronics manufactures 200,000 circuit boards per month. a random sample of 4,000 boards is inspected every week for seven characteristics. during a recent week, seven defects were found for one characteristic, and two defects each were found for the other six characteristics. if these inspections produced defect counts that were representative of the population, what are the dpmo's for the individual characteristics and what is the overall dpmo for the boards? do not round intermediate calculations. round your answers to the nearest whole number.
Answers
The overall DPMO for the boards would be 4750.
Boardwalk Electronics manufactures 200,000 circuit boards per month. A random sample of 4,000 boards is inspected every week for seven characteristics. During a recent week, seven defects were found for one characteristic, and two defects each were found for the other six characteristics. If these inspections produced defect counts that were representative of the population, the dpmo's for the individual characteristics and what is the overall dpmo for the boards would be as follows:To calculate the DPMO, the formula used is:DPMO = (Number of defects / Number of Opportunities) × 1,000,000For Characteristic
1:Number of defects = 7Number of opportunities = 4000DPMO = (7/4000) × 1,000,000= 1750For Characteristic 2:Number of defects = 2Number of opportunities = 4000DPMO = (2/4000) × 1,000,000= 500For Characteristic 3:Number of defects = 2Number of opportunities = 4000DPMO = (2/4000) × 1,000,000= 500For Characteristic 4:Number of defects = 2Number of opportunities = 4000DPMO = (2/4000) × 1,000,000= 500For Characteristic 5:Number of defects = 2Number of opportunities = 4000DPMO = (2/4000) × 1,000,000= 500For Characteristic 6:Number of defects = 2Number of opportunities = 4000DPMO = (2/4000) × 1,000,000= 500For Characteristic 7:Number of defects = 2Number of opportunities = 4000DPMO = (2/4000) × 1,000,000= 500The overall DPMO for the boards would be the sum of the DPMO of all characteristics which would be 1750 + 500 + 500 + 500 + 500 + 500 + 500 = 4750.
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[EF] is the diameter of a circle of center O and of radius R. G is a of this circle, distinct from E and F. Prove that GEF is a right triangle.
Answers
Answer:
Step-by-step explanation:
Given : O is the centre of the circle with radius r. AB, CD and EF are the diameters of the circle. ∠OAF = ∠OCB = 60°.
To Find : What is the area of the shaded region?
Solution:
∠OAF = 60°
OA = OF = Radius
=> ΔOAF is Equilateral Triangle
∠OCB = 60°
OC = OB Radius
Hence ΔOCB is Equilateral Triangle
∠AOF = 60° , ∠BOC = 60°
=> ∠COF = 180° - 60° - 60° = 60° as AC is straight Line
∠DOE = ∠COF ( vertically opposite angle )
∠DOE = 60°
ΔODE is also an equilateral Triangle
Each sector has 60 ° angle
Area of shaded region = (60/360)πr² - (√3/4) r²
= r² (π/6 - √3/4)
= (r²/6) (π - 3√3/2)
Area of 3 shaded regions
= 3 (r²/6) (π - 3√3/2)
= (r²/2) (π - 3√3/2)
(r²/2) (π - 3√3/2) is the correct answer
what number does not appear in the first 30 digits of pi? a) 1 b) 2 c) 3 d) 4 e) 0
Answers
Answer:
0
Step-by-step explanation:
What is 14x15 and what is an art teacher ordered 26 sets for class there are 100 markers in each set how many in 26 sets?
Answers
Answer: 210
Step-by-step explanation:
The value of 14x15 is 210.
If an art teacher ordered 26 sets for class and there are 100 markers in each set, then the total number of markers is:
26 x 100 = 2600
Therefore, there would be 2600 markers in 26 sets.
A circular watch has a minute hand that is 2.5 cm long.
(a) What distance does the tip of the hand move through in 20 minutes?
(b)What area of the watch face is covered by the minute hand in 30 minutes? (Pi = 3.14)
Answers
Assuming that the clock is circular, the length of the minute hand is the radius.
The distance that the tip of the minute hand moves in a given time is the length of an arc along the circle.
If s is the length of arc, then s = rθ, where r is the radius and θ is the measure (in radians) of the central angle formed by the initial position and the final position of the minute hand (measured clockwise).
(a)
r = 2.5"
20 minutes is 1/3 of an hour.
Since there are 2π radians in 1 rotation of the minute hand (1 hour),
θ = (1/3)(2π) = 2π/3.
So, s = rθ = (2.5")(2π/3) = 10π/3 inches ≈ 5.24"
(b)
A = π x ^ 2 x 2
3.14 x 15 x 15 = 706.5
The area of the watch face is covered by the minute hand in 30 minutes is 706.5
hope you understood this question
7.) IF y = a√x² and if y=0.4 when x = 4; Find
a. y in terms of x
b. y if x=100
c. x when y=1.4
Answers
The equation y = a√x² is equal to y = 0.1√x² given that y = 0.4 when
x = 4. We also found that when x = 100, y = 10 and when y = 1.4, x = 14.
Given y = a√x² and y = 0.4 when x = 4.
a. To find y in terms of x, we substitute the given values into the equation y = a√x² as follows:
0.4 = a√4²
0.4 = 4a
Dividing both sides by 4, we get:
a = 0.1
Therefore, the equation becomes:
y = 0.1√x²
b. To find y when x = 100, we substitute x = 100 in the equation y = 0.1√x² as follows:
y = 0.1√10000
y = 10
Therefore, when x = 100, y = 10.
c. To find x when y = 1.4, we substitute y = 1.4 in the equation y = 0.1√x² as follows:
1.4 = 0.1√x²
Squaring both sides, we get:
1.96 = 0.01x²
Dividing both sides by 0.01, we get:
x² = 196
Taking the square root of both sides, we get:
x = ±14
Since x represents a distance, it cannot be negative. Therefore, x = 14.
Therefore, when y = 1.4, x = 14.
In conclusion, we found that the equation y = a√x² is equal to y = 0.1√x² given that y = 0.4 when x = 4. We also found that when x = 100, y = 10 and when y = 1.4, x = 14.
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Compute the volume of the prism when d=1 when d=2 and when d=1/2
Answers
Answer: To compute the volume of a prism, we need to know the area of the base and the height of the prism. Assuming that the prism has a rectangular base, the formula for the volume of the prism is:
Volume = Area of Base × Height
Let's assume that the length and width of the rectangular base are both equal to 2d (since we don't have specific dimensions). The height of the prism is also equal to d, as given.
When d = 1:
The area of the base is 2d × 2d = 4 square units
The height is d = 1 unit
Therefore, the volume is:
Volume = Area of Base × Height = 4 × 1 = 4 cubic units
When d = 2:
The area of the base is 2d × 2d = 8 square units
The height is d = 2 units
Therefore, the volume is:
Volume = Area of Base × Height = 8 × 2 = 16 cubic units
When d = 1/2:
The area of the base is 2d × 2d = 1 square unit
The height is d = 1/2 unit
Therefore, the volume is:
Volume = Area of Base × Height = 1 × (1/2) = 1/2 cubic units
So, the volume of the prism is 4 cubic units when d=1, 16 cubic units when d=2, and 1/2 cubic units when d=1/2.
Step-by-step explanation:
Solve the inequality for u.
5u≤45
Simplify your answer as much as possible.
Answers
Answer:
u ≤ 9
Step-by-step explanation:
5u ≤ 45 ( divide both sides by 5 )
u ≤ 9
nitially 100 milligrams of a radioactive substance was present. after 6 hours the mass had decreased by 5%. if the rate of decay is proportional to the amount of the substance present at time t, find the amount remaining after 24 hours. (round your answer to one decimal place.)
Answers
If the rate of decay is proportional to the amount of the substance present at time t, then the amount remaining after 24 hours is 57.7 milligrams
Now we need to find the value of k. We know that the mass decreased by 5% after 6 hours, which means that the amount remaining is 95% of the initial amount. We can substitute these values into our formula and solve for k:
0.95 initial amount = initial amount x (1 - k x initial amount)⁶
Simplifying this equation, we get:
1 - [tex](0.95)^{(1/6)})[/tex] = k x initial amount
Solving for k, we get:
k = (1 - [tex](0.95)^{(1/6)})[/tex]) / initial amount
Now we can use this value of k to find the amount remaining after 24 hours:
Amount remaining = 100 x (1 - k x 100)²⁴
Plugging in the value of k, we get:
Amount remaining = 100 x (1 - (1 - [tex](0.95)^{(1/6)})[/tex] * 100)²⁴
Evaluating this expression, we get:
Amount remaining = 57.7 milligrams
Therefore, after 24 hours, there will be approximately 57.7 milligrams of the radioactive substance remaining.
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The data given cars a moter by graph representing Year s No. of produced below shows. shows the production of company Draw a line the data. 2013 2009 10,200/12, 400 11, 200|15, 100 18.000 2010 2011 2012
Answers
Answer:
To draw a line graph, you need to plot your data on the graph. For example, if you have the data for the number of cars produced in a year, you would plot the number of cars on the Y-axis and the year on the X-axis. Then, you would trace both lines to the point where they intersect and place a dot on the intersection. You would repeat this process for each year and then connect the dots with a line.
tan(sin^-1(-1))= _____________
Answers
Answer:
tan(sin^-1(-1)) is undefined.
The inverse sine function returns a value between -pi/2 and pi/2, and since sin(-pi/2) = -1, sin^-1(-1) = -pi/2. However, at -pi/2, the tangent function is undefined since it results in a vertical asymptote.
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The center of the circle lies on the y-axis.
The standard form of the equation is (x – 1)² + y² = 3.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answers
Answer:
Step-by-step explanation:
Statements 1, 2, 5 are all true
lynne has \$8.00$8.00dollar sign, 8, point, 00 to spend on apples and oranges. apples cost \$0.65$0.65dollar sign, 0, point, 65 each, and oranges cost \$0.75$0.75dollar sign, 0, point, 75 each. if there is no tax on this purchase and she buys 555 apples, what is the maximum number of whole oranges she can buy?
Answers
Lynne can buy 5 apples and 6 oranges with her $8.00.
The first thing to do is determine how much money Lynne spends on the apples. Since she is buying 5 apples,
we can multiply the price of each apple ($0.65) by 5: $5 * 0.65 = $3.25
Therefore, Lynne has $8 - $3.25 = $4.75 to spend on oranges.
Now we need to determine the maximum number of whole oranges that she can buy with $4.75. We can do this by dividing $4.75 by the price of each orange ($0.75): $4.75 ÷ $0.75 = 6.33.
Since we can't buy a fraction of an orange, the maximum number of whole oranges Lynne can buy is 6. Therefore, Lynne can buy 5 apples and 6 oranges with her $8.00.
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(T/F) a shadow price indicates how much the optimal value of the objective function will increase per unit increase in the right-hand side of a constraint.
Answers
The statement " a shadow price indicates how much the optimal value of the objective function will increase per unit increase in the right-hand side of a constraint" is true because shadow prices provide valuable information about the marginal value of resources and constraints in linear programming problems
A shadow price represents the marginal value of a resource or constraint in a linear programming problem. It indicates how much the optimal value of the objective function will increase if the right-hand side of a constraint is increased by one unit, while keeping all other constraints and variables fixed. The shadow price of a constraint is calculated by adding one unit to the right-hand side of the constraint and re-solving the linear programming problem.
The resulting increase in the objective function value is the shadow price of that constraint. Shadow prices are useful in making decisions about resource allocation, pricing, and capacity planning in a variety of industries such as manufacturing, transportation, and energy.
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The path of a cannon ball is modeled by the quadratic
f(x) = - 16x
2 + 120x + 10.
The graph in red and black show the same function.
What similarities and differences to do you see?
Answers
The only significant variation between the red and black graphs is the scales used for the x and y axes. The two graphs both display the same quadratic function.
What is math as a quadratic?x ax2 + bx + c = 0 is a quadratic equation, which is a second-degree polynomial problem in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
Given :
The quadratic function f(x) = -16x2 + 120x + 10 is depicted in both the red and black graphs, however, they are plotted at various scales. In comparison to the black graph, the red graph has a narrower range on both the x and y axes.
On both graphs, the parabola's vertex, or lowest point on the curve, is situated at x = 3.75 and y = 412.5.
This indicates that the cannonball's maximum height is 412.5 feet, and it does so at a horizontal distance of 3.75 feet from the cannon.
The only significant variation between the red and black graphs is the scales used for the x and y axes. The two graphs both display the same quadratic function.
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Write 39.76% as a decimal
Answers
Decimal form of number 39.76% is,
= 0.3976
We have to write,
A number 39.76% into a decimal form.
Now, We can write the number in decimal form as,
= 39.76%
= 39.76 / 100
= 0.3976
Therefore, Decimal form of number 39.76% is,
= 0.3976
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Molly is filling bags of marbles. She makes each bag so that 3 out of every 8 marbles are blue. Which equation correctly compares the number of marbles she uses, x, to the number of blue marbles, y?
Answers
The equation that correctly compares the number of marbles used, x, to the number of blue marbles, y, is y = 3/8x.
To calculate the number of marbles used, x, and the number of blue marbles, y, Molly is making, the following equation can be used: y = 3/8x. This equation states that for every 8 marbles used, 3 of them will be blue. For example, if Molly uses 24 marbles, then 3/8x = 3/8(24) = 9. Therefore, 9 of the 24 marbles will be blue. To calculate the number of blue marbles for a different number of marbles used, x, the equation can be rearranged to solve for y. For example, if Molly uses 48 marbles, then the equation can be rearranged to y = 8/3x, and then 8/3(48) = 16. Therefore, 16 of the 48 marbles will be blue.
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5% of what number is 29?
Answers
Answer:
1,45
Step-by-step explanation:
[tex] \frac{29 \times 5\%}{100\%} = 1.45[/tex]
A new cylindrical can with a diameter of 4 cm is being designed by a local company The surface area of the can is 130 square centimeters What is the height of the can? Estimate using 3 14 for x and
round to the nearest hundredth Apply the formula for surface area of a cylinder SA-28+ Ph
Answers
The height of the can is approximately 9.74 centimeter.
Define surface area of cylinderThe surface area of a cylinder is the total area of the curved and flat surfaces that make up the cylinder. It can be calculated using the formula:
SA = 2πr² + 2πrh
where r is the radius of the cylinder and h is its height.
In this case, we are given that the diameter of the can is 4 cm, which means the radius is 2 cm.
We are also given that the surface area is 130 square centimeters. Substituting these values into the formula, we get:
130 = 2π(2)² + 2π(2)h
Simplifying this equation, we get:
130 = 8π + 4πh
Subtracting 8π from both sides, we get:
122 = 4πh
Dividing both sides by 4π, we get:
h = 122/(4π) ≈ 9.74 cm (rounded to the nearest hundredth using 3.14 for π)
Therefore, the height of the can is approximately 9.74 cm.
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The straight line shown below passes through the points (3, 1) and (8, 36).
What is the gradient of this line?
Give your answer as an integer or as a fraction in its simplest form.
Answers
Answer:
the gradient of the line is 7.
Step-by-step explanation:
To find the gradient of the straight line that passes through the points (3,1) and (8,36), we use the formula:
Gradient = (change in y) / (change in x)
The change in y is the difference between the y-coordinates of the two points, which is:
36 - 1 = 35
The change in x is the difference between the x-coordinates of the two points, which is:
8 - 3 = 5
Therefore, the gradient of the straight line is:
Gradient = (change in y) / (change in x) = 35 / 5 = 7
So the gradient of the line is 7.
...................................
Answers
Answer:
america
Step-by-step explanation:america!!
can somebody help me with a.) please
Answers
Answer:
y = -1/500x² +2/5x
Step-by-step explanation:
You want the equation for the path of a football that is thrown 200 m downfield and reaches a maximum height of 20 m.
Initial heightThe initial height is not given. The equation is much more easily written if we assume it is zero, or we assume the launch height is the same height at which the ball is caught.
PointsWe know the maximum height is reached halfway between the launch point and the final point of interest. Then we're required to write the equation of a parabola that passes through the points (0, 0), (100, 20), and (200, 0).
EquationSince we know the x-intercepts, we can write the equation as ...
y = ax(x -200)
Then all we have to do is find the value of 'a' so the equation has (100,20) as a solution.
20 = a(100)(100 -200) = -10000a
a = -1/500 . . . . . divide by -10000
The equation of the path of the football is ...
y = (-1/500)(x)(x -200)
y = -1/500x² +2/5x
__
Additional comment
When x=185, y = -1/500(185)(185 -200) = 15/500(185) = 5.55 . . . meters
The domain is [0, 200]; the range is [0, 20].
To achieve that distance and height, the football would need to be thrown at a speed in excess of 119 miles per hour. For comparison, the fastest baseball pitch ever thrown was 108.1 miles per hour.
The point T(-4, -1) is rotated 90° counterclockwise around the origin. What are the coordinates of the resulting point, T?
Answers
Answer:
(1, -4)
Step-by-step explanation:
if you rotate from quadrant 3 to 4, x=-y and y=x
After the rotation of 90° clockwise about the origin, the coordinates become P'(- 1, - 4).
What is image rotation?A rotation is a type of transformation which is a turn.A figure can be turned clockwise or counterclockwise on the coordinate plane.In both transformations the size and shape of the figure stays exactly the same.Given is the coordinate of point as (-4, - 1). It is rotated by 90° clockwise about the origin.
When we rotate a figure 90 degrees clockwise about the origin, then the new coordinates will be -
A(x, y) → A(y, - x)
Then, we can write the new coordinates according to the rule as -
P(-4, - 1) → P'(- 1, - 4)
Therefore, after the rotation of 90° clockwise about the origin, the coordinates become P'(- 1, - 4).
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Does anyone understand this?
Answers
A function is a relationship between a set of inputs where each input has exactly one output. So any set will not have any x value repeated in the set.
6. Set #2 is a function, no x value repeats in the set
7. Set #4 is a function, no x value repeats in the set
8. Answer is #4, there are multiple y values for every x value. *note: look at the circle. If you had x=2, you would have a y value in quadrant 1 AND in quadrant 4, so you would have two points with the same x value. This can be represented with the vertical line test. Draw a vertical line, if the line hits two points on the line, it is NOT a function. See attachment.
9. Points (0, 2) and ( 0, -1) repeat the x value of (0) so your answer would be #4 to remove ( 0, -1) to make this set a function
10. Answer #4 = 4 would replace “a” and keep this set a function because 4 is not repeated as an x value in the set.
Solve the equation.
4π=w−6π
Answers
Answer: W=10pi
Step-by-step explanation:
the percentage of people who prefer dogs to cats is 78% for a given population. what is the standard error of the sampling distribution of sample proportions for samples of size n
Answers
The standard error of the sampling distribution of sample proportions for samples size
1) n = 35 ⇒ SE = 0.07
2) n = 100 ⇒ SE = 0.04
3) n = 250 ⇒ SE = 0.03
We know that the formula for thr standard error(SE) of the sample Proportion is:
SE = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
as the sample size increases, the standard error decreases.
Here, the percentage of people who prefer dogs to cats is 78%
so, p = 0.78
For samples of size n = 35,
SE = [tex]\sqrt{\frac{0.78\times (1-0.78)}{35} }[/tex]
SE = [tex]\sqrt{\frac{0.1716}{35} }[/tex]
SE = 0.07
For sample size n = 100,
SE = [tex]\sqrt{\frac{0.78\times (1-0.78)}{100} }[/tex]
SE = [tex]\sqrt{\frac{0.1716}{100} }[/tex]
SE = 0.041
For samples of size n = 250,
SE = [tex]\sqrt{\frac{0.78\times (1-0.78)}{250} }[/tex]
SE = [tex]\sqrt{\frac{0.1716}{250} }[/tex]
SE = 0.03
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The complete question is:
The percentage of people who prefer dogs to cats is 78% for a given population. What is the standard error of the sampling distribution of sample proportions for samples of size n=35, n=100, and n=250?
PLEASE HELP ME DUE MIDNIGHT !!!
Answers
Answer:
Column 1:
[tex]\pi/3[/tex] (given)
[tex]5\pi/4[/tex]
[tex]11\pi/6[/tex]
Column 2:
[tex]\sqrt{3}/2[/tex]
[tex]-\sqrt{2}/2[/tex] (given)
[tex]-1/2[/tex]
Column 3:
all given
Column 4:
[tex]\sqrt{3}[/tex]
[tex]1[/tex]
[tex]-\sqrt{3}/3[/tex] (given)
Step-by-step explanation:
Solved by using unit circle and inverse trig functions
The image of a composite figure is shown.
A four-sided shape with the bottom side labeled as 21.4 yards. The height is labeled 9 yards. A portion of the top side from the perpendicular to right vertex is labeled 2.2 yards. The portion of the top from the perpendicular to the left vertex is 19.2 yards.
50 POINTS PLEASE GET CORRECT
What is the area of the figure?
192.6 yd2
211.86 yd2
212.4 yd2
423.72 yd2
Answers
Answer:
area=192.6yards^2
Step-by-step explanation:
9×2.2=19.8÷2= 9.9 for area of one of the triangles
19.2×9=172.8 for area of the rectangle
21.4-19.2=2.2
2.2×9=19.8÷2=9.9
19.8+172.8=192.6
Answer: its a
Step-by-step explanation:
100 points!!!
Express the function graphed on the axes below as a piecewise function
Answers
Answer: { (-1/2)x - 1, -2 ≤ x ≤ 4
Step-by-step explanation:
Let's start with the first line:
The line passes through two points: (-5, 8) and (-2, 2). The hollow circle at (-5, 8) indicates that this point is not included in the graph, while the closed circle at (-2, 2) indicates that this point is included.
We can find the slope of the line using the two points:
slope = (change in y) / (change in x) = (2 - 8) / (-2 - (-5)) = -6 / 3 = -2
Using point-slope form, we can write the equation of the line as:
y - 2 = -2(x - (-2))
Simplifying:
y - 2 = -2x - 4
y = -2x - 2
Next, let's consider the second line:
The line passes through two points: (-2, -2) and (4, -5). The hollow circle at (-2, -2) indicates that this point is not included in the graph, while the closed circle at (4, -5) indicates that this point is included.
We can find the slope of the line using the two points:
slope = (change in y) / (change in x) = (-5 - (-2)) / (4 - (-2)) = -3 / 6 = -1/2
Using point-slope form, we can write the equation of the line as:
y - (-2) = (-1/2)(x - (-2))
Simplifying:
y + 2 = (-1/2)x + 1
y = (-1/2)x - 1
Now we can write the piecewise function:
f(x) = { -2x - 2, -5 ≤ x < -2
{ (-1/2)x - 1, -2 ≤ x ≤ 4
This piecewise function represents the two lines graphed on the given axes, where the first line is defined for x values between -5 and -2 (inclusive on -2 but not on -5), and the second line is defined for x values between -2 and 4 (inclusive on both).
What are two other ways to name <1?
Answers
Answer: <PFY and <YFP
Step-by-step explanation:
Answer:
<PFY and <YFP
Step-by-step explanation: