Final answer:
The point where two or more rays meet in optics is known as the focal point, which is crucial in geometric optics. For a converging lens or mirror, it's where light rays converge, while for a diverging lens or mirror, it's where light rays appear to originate.
Explanation:
The point where two or more rays or 'arms' of an angle meet in the context of geometrical optics is known as the focal point. In terms of a converging lens or mirror, the focal point is where converging light rays intersect after passing through the lens or reflecting off the mirror surface. This is a fundamental concept in the study of geometrical optics, which deals with the ray aspect of light. A ray is a straight line that originates at a point and is used in geometric optics to represent the path along which light travels.
For a converging lens, which is also known as a convex lens, parallel light rays entering the lens will refract and converge at a single point on the opposite side of the lens. This single point is the focal point. Similarly, in concave mirrors, ray diagrams show the focal point as the point where reflected rays converge or appear to converge. The distance from the focal point to the mirror along the central axis is referred to as the focal length. Conversely, for a diverging lens or mirror, the focal point is the point from which diverging light rays appear to originate.
The coordinate plane below represents a town. Points A through F are farms in the town.
graph of coordinate plane. Point A is at 1, 3. Point B is at 3, 1. Point C is at 3, negative 3. Point D is at negative 4, 2. Point E is at negative 1, 5. Point F is at negative 3, negative 3.
Part A: Using the graph above, create a system of inequalities that only contains points D and E in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above. (5 points)
Part B: Explain how to verify that the points D and E are solutions to the system of inequalities created in Part A. (3 points)
Part C: Chickens can only be raised in the area defined by y > 3x − 4. Explain how you can identify farms in which chickens can be raised. (2 points)
express 7x^3/4 in radical form
Answer:
7/34
Step-by-step explanation:
what is the length of the side of a square if the apothem is 7
Amal had 12 stuffed animals and gave 3 over 4 of them to charity. Maria had 6 stuffed animals and gave 1 third to charity Who had the most stuffed animals left?
Answer the word problem:
Taylor and Blair are driving away from each other in opposite directions. If Blairs speed is 70mph and Taylors speed is 80mph, how many hours will it be before the two are 225 miles apart?
It will take 1.5 hours (or 1 hour and 30 minutes) before Taylor and Blair are 225 miles apart.
To find out how many hours it will be before Taylor and Blair are 225 miles apart, we can set up an equation based on the distance they travel.
Since they are driving away from each other in opposite directions, their distances add up to the total distance they will be apart.
Let t be the number of hours it takes for them to be 225 miles apart.
Distance traveled by Blair = Blair's speed * time (d = r * t)
Distance traveled by Taylor = Taylor's speed * time (d = r * t)
The total distance they will be apart is 225 miles:
Blair's distance + Taylor's distance = 225 miles
(70 mph * t) + (80 mph * t) = 225 miles
Now, solve for t:
70t + 80t = 225
150t = 225
t = 225 / 150
t = 1.5
So, it will take 1.5 hours (or 1 hour and 30 minutes) before Taylor and Blair are 225 miles apart.
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A car moved at a constant velocity during the first hour. It stopped for 2 hours at a mall and then moved ahead again at a constant velocity for the next 3 hours. The car finally returned to its starting point with a constant velocity in the next 2.5 hours. Which of the following graphs best represents the car's motion?
First straight line joins ordered pairs 0, 0 and 1, 60, second straight line joins 1, 60 and 3, 60, third straight line joins 3, 60 and 6, 30 and fourth straight line joins 6, 30 and 8.5, 0
First straight line joins ordered pairs 0, 0 and 1, 60, second straight line joins 1, 60 and 3, 60, third straight line joins 3, 60 and 6, 100 and fourth straight line joins 6, 100 and 8.5, 0
First straight line joins ordered pairs 0, 0 and 1, 60, second straight line joins 1, 60 and 3, 60, third straight line joins 3, 60 and 6, 100 and fourth straight line joins 6, 100 and 9.5, 0
First straight line joins ordered pairs 0, 0 and 1, 60, second straight line joins 1, 60 and 6, 100, and third straight line joins 6, 100 and 8.5, 0
Answer:
First straight line joins ordered pairs 0, 0 and 1, 60; second straight line joins 1, 60 and 3, 60; third straight line joins 3, 60 and 6, 100; and fourth straight line joins 6, 100 and 8.5, 0.
Step-by-step explanation:
Starting at home is starting at (0, 0).
Traveling at the same velocity for an hour will connect (0, 0) to (1, 60).
Stopping at the mall for 2 hours will connect (1, 60) to (3, 60).
Going ahead again at a constant velocity for 3 hours will connect (3, 60) to (6, 100).
Returning to the starting point for 2.5 hours will connect (6, 100) to (8.5, 0).
A company has an opportunity to bid on three contracts. Determine which would be the best investment given the information in the table below.
CONTRACT
PROFIT, (P)* OF PROFIT...(P)*. TO BREAK EVEN...LOSS, (P)* OF LOSS
Southeast
$45,000, 50%...30%...$6,000, 20%
Southwest
$60,000, 35%...40%...$10,000, 25%
California
$112,000, 20%...40%...$40,000, 40%
*(P)=PROBABILITY
a) Southeast
b) Southwest
c) California
d) All contracts include a probability for loss
CONTRACT PROFIT, (P)* OF PROFIT...(P)*. TO BREAK EVEN...LOSS, (P)* OF LOSS
Southeast $45,000, 50% 30% $6,000, 20%
Southwest $60,000, 35% 40% $10,000, 25%
California $112,000, 20% 40% $40,000, 40%
I think that the best contract would be with SOUTHEAST. It probability of having a profit is higher than the other two at 50% while its probability of incurring a loss is lesser than the other two at 20%.
Despite the bigger value of its contract profit of the other two, these value will still be greatly affected by its corresponding probabilities.
Answer:
It's A. Southeast
Step-by-step explanation:
y=4x-9
y=x-3
asking another question
appreciate any answers
edit: find x and y
(x,y)
Solve 10p + 9 - 11 - p = -2(2p + 4) - 3(2p - 2)
The value of p is 0.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
Example:
33 + 3x + 4y = 7 is an expression.
24 - 87 is an expression.
We have,
10p + 9 - 11 - p = -2(2p + 4) - 3(2p - 2)
Simplifying we get,
10p - 2 - p = -4p - 8 - 6p + 6
Combining like terms.
9p - 2 = -10p - 2
Add 2 on both sides.
9p + 10p = -2 + 2
Divide 19 on both sides.
19p = 0
p = 0
Thus,
The value of p is 0.
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Does anyone know how to make these statements false with a counterexample? 1) The reciprocal of each natural number is a natural number. 2) The opposite of each whole number is a whole number. 3) There is no integer that has a reciprocal that is an integer.
When j = 32, m = 2, and p = 1/4. If j varies directly with m and inversely with p, what is the constant of variation?
When j = 32, m = 2, and p = 1/4. If j varies directly with m and inversely with p, The k is the constant of variation that is 4.
What is directly proportional and inversely proportional relationship?Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
p = kq
where k is some constant number called the constant of proportionality.
This directly proportional relationship between p and q is written as
[tex]p \propto q[/tex] where that middle sign is the sign of proportionality.
This inversely proportional relationship is denoted by
[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]
When j = 32, m = 2, and p = 1/4. If j varies directly with m and inversely with p
j = mk/p
where k is the constant of variation.
32 = 2 x k / (1/4)
Multiply both sides by 1/4.
8 = 2k
Divide both sides by 2.
4 = k
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Dominick is planning to take a vacation to either Orlando or Tampa Bay. He wants to go to the city that is warmer, on average. The box plot below shows the temperatures from the previous year during the time that Dominick will take his vacation: box plot labeled Orlando with min at 64.5, Q1 at 65.5, median at 67.5, Q3 at 71.5, max at 72.5. Box plot labeled Tampa Bay with min at 60, Q1 at 63.5, median at 66.25, Q3 at 72.5, max at 74 Which city should Dominick visit, and why? He should visit Orlando. It has a greater IQR. He should visit Orlando. The median is higher and the range is smaller, so the temperature is higher on average. He should visit Tampa Bay. The highest temperature occurred there. He should visit Tampa Bay. The range is very large, so there is a better chance that any given day will be warm.
The correct answer is option b. Dominick should visit Orlando. The median is higher and the range is smaller, so the temperature is higher on average.
Option b is correct because if Orlando has a higher median temperature, this suggests that the middle value of the temperatures in Orlando is higher than in Tampa Bay. Additionally, a smaller range indicates less variability, suggesting more consistent warm temperatures. Therefore, the higher median and smaller range are strong indicators that, on average, the temperatures in Orlando are warmer.
Why other options are incorrect:
Option a is incorrect because the Interquartile Range (IQR) represents the middle 50% of the data. While a greater IQR indicates a larger spread in the middle 50% of the temperatures, it doesn't necessarily mean the average temperature is higher.
Option c is incorrect while Tampa Bay having the highest temperature might indicate that it reached the highest peak temperature, this single data point does not provide enough information about the overall average or consistency of warm temperatures. The highest temperature alone doesn't guarantee that the city is warmer on average.
Option d is incorrect because a larger range indicates a wider spread of temperatures, which could mean more variability. This does not necessarily mean that any given day will be warm; it could also mean that there are very low temperatures included in that range.
The complete question is
Dominick is planning to take a vacation to either Orlando or Tampa Bay. He wants to go to the city that is warmer, on average. The box plot shows the temperatures from the previous year during the time that Dominick will take his vacation:
Which city should Dominick visit, and why?
a. He should visit Orlando. It has a greater IQR.
b. He should visit Orlando. The median is higher and the range is smaller, so the temperature is higher on average.
c. He should visit Tampa Bay. The highest temperature occurred there.
d. He should visit Tampa Bay. The range is very large, so there is a better chance that any given day will be warm.
the base of a side of a ramp is 3 meters, and the height is 0.6 meters. what is the area of the triangular side of the ramp in square meters
area = base x height divided by 2
3*0.6 = 1.8/2=0.9 square meters
HELP! 20 POINTS!!! Graph the system of inequalities on your paper. Please provide only one ordered pair (x, y) that will work for both system of inequalities.
To earn full credit you must prove your answer by substituting the (x, y) order pair into both inequalities. Show all work for each inequality.
y < 4x + 3
y > -3x - 3
WILL GIVE A BRAINLIEST IF UR 100% CORRECT PLEASE HELP!!
On which of the following lines does the point (8, 41) lie?
a.
y=5x+1
b.
y=3x-2
c.
y=-x-7
d.
y=4x-5
where does the line y = 3x + 5 cross the y-axis
WILL GIVE A BRAINLIEST IF YOURE RIGHT PLEASE HELP ASAP!!
Find the greatest possible error for each measurement.
18.9 m
a.
0.01 m
b.
0.5 m
c.
9.45 m
d.
0.05 m
the greatest possible error for meters is 1/2 the increments
since 18.9 is to the tenths place
1/2 x 1/10 = 0.05
so greatest possible error for 18.9 is 0.05m
In the diagram below, is an altitude of DEF. What is the length of ? If necessary, round your answer to two decimal places.
I need it asap!!!! Plz help 20 POINTS USED PLZ PLZ ASAP
What integer is closest to 13/3 divided by 2/11
Please give ur answer as a simplest fraction not a mixed number
Thanks
What is the measure of JL
A: 84 degrees
B: 42 degrees
C: 96 degrees
D: 168 degrees
The measure of arc JL is 168.
Option D is the correct answer.
What is the arc length of a circle?
The arc length of a circle is the distance between two points on the curve of the circle.
We have,
The angle subtended by the minor arc on the circle is half of the arc length.
So,
∠JKL = 84°
The length of arc JL.
= 2 x 84
= 168
Thus,
The length of arc JL is 168.
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A conjecture becomes a theorem after it has been proven true by logic.
True or False
True, A conjecture becomes a theorem after it has been proven true by logic.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The sentence is,
''A conjecture becomes a theorem after it has been proven true by logic.''
Now, We know that;
Conjectures are unproven claims.
Hence, Once someone proves a conjecture, it is called a theorem.
Thus, A conjecture becomes a theorem after it has been proven true by logic.
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On the evening news, the meteorologist states that there is a 70% chance that it will rain the next morning. Select all the statements that are true.
YOU CAN PICK MORE THAN ONE
A. It is neither unlikely nor likely that it will rain the next day.
B. It is certain that it will rain the next day.
C. It is likely that it will not rain the next day.
D. It is unlikely that it will rain the next day.
E. It is unlikely that it will not rain the next day.
F. It is likely that it will rain the next day.
Answer:
E. It is unlikely that it will not rain the next day.
F. It is likely that it will rain the next day.
2p2+3p-4 less -2p2-3p+4
Answer:
[tex]4p^{2}+6p-8[/tex]
Step-by-step explanation:
Being a subtraction of polynomials, the second polynomial will change the signs of its terms and then the algebraic sum is done.
[tex]2p^{2} -3p-4 - (-2p^{2} -3p+4)[/tex]
changing the signs
[tex]2p^{2} -3p-4 +2p^{2}+3p-4[/tex]
performing indicated operations
[tex]4p^{2}+6p-8[/tex]
At an airport, its costs $7 to park for up to one hour and $5 per hour for each additional hour. Let x represent the number of hours parked. Write a function that models the cost, C(x), of parking x hours, where x is an integer greater than 1.
A: C(x)=5x+12
B: C(x)=5(x+1)+7
C: C(x)=5(x-1)+7
D: C(x)=5x+7
the answer would be C
because it is taking the total hours ( x) and subtracting 1 ( the first hour that cost $7
and then multiplying x by the $5 per minute and then adding the $7 for the first hour
Choose the correct description of the graph of the compound inequality: 3x + 2 > 5 and 3x less than or equal to 9 A:number line with an open circle on 1, shading to the left, and a closed circle on 3, shading to the right B:number line with a closed circle on 1, shading to the left, and an open circle on 3, shading to the right C:number line with a closed circle on 1, an open circle on 3, and shading in between D:number line with an open circle on 1, a closed circle on 3, and shading in between
Answer:
Step-by-step explanation:
D
Give an example of a compound inequality that has no solution
An example of a compound inequality that has no solution:
x >5 and x < -4.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
What is Number Line?In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.
|____|____|____|____|____|____|____|____|____|____|
-5 -4 -3 -2 -1 0 1 2 3 4 5
Here is an example of a compound inequality that has no solution:
x >5 and x < -4.
x may be both higher than 5 and less than -4.
Here it is not possible that x can be both lower than -4 and larger than 5.
Hence, these inequalities have no solution.
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I need help answering number 8 please
What is the value of SM
9/15 = 12/x =
x = 180/9 = 20
answer is 20
A rectangular area is to be fenced in with 600 feet of chicken wire. find the maximum area that can be enclosed.
The maximum area that can be enclosed is 22500 feet²
A rectangle is a quadrilateral in which opposite sides are equal and parallel to each other.
Let x represent the length and y represent the width. Hence:
perimeter = 2(length + width)
600 = 2(x + y)
300 = x + y
y = 300 - x
The area of a rectangle (A) = length * width
A = x * (300 - x)
A = 300x - x²
The maximum area is at dA/dx = 0, hence:
dA/dx = 300 - 2x
300 - 2x = 0
2x = 300
x = 150 feet
y = 300 - x = 300 - 150 = 150 feet
The maximum area = x * y = 150 * 150 = 22500 feet²
The maximum area that can be enclosed is 22500 feet²
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What is the inverse of 2x-6y=1