Answer:
They are in conflict.
Step-by-step explanation:
for statement (a) we have child gunshot deaths doubling every year. So if it was 1 death in 1950, it is 2 in 1951, 4 in 1952, 8 in 1953, 16 in 1954. That would make the deaths in 1994 = (deaths in 1950) x 2 x 2 x 2 x 2 ... with 44 factors of 2. That number is over a trillion.
for statement (b) we have child gunshot deaths doubling over a period of 44 years, which might even be true
HELP PLEASE 80 POINTS!!! GOD BLESS WILL GIVE BRAINLIEST
PICTURE BELOW
Answer:
x ≥ -3 3/4
Step-by-step explanation:
-1/3x + 1/2 ≥ -3/4
1/3x ≥ -5/4
x ≥ -3 3/4
Compute the Laplace transforms, F(s), of the functions f(t) below f(t) - e8 sin 5 t F(s) =
f(t) - eSt sinh 7t F(s) = f(t)-7t cosh 5t F(s)= (t) = 9t sin ut . Fu(s)
To compute the Laplace transform of a function, we use the integral definition , F(s) = L{f(t)} = ∫ f(t) e^(-st) dt.
What is integral definition ?
The integral definition of the Laplace transform is a mathematical method used to find the Laplace transform of a function. It is defined as,
F(s) = L{f(t)} = ∫ f(t) e^(-st) dt , Where F(s) is the Laplace transform of the function f(t), s is a complex variable known as the frequency domain variable, and t is the time domain variable.
Given the functions f(t) provided ,
f(t) = e^(-8t)sin(5t)
F(s) = L{e^(-8t)sin(5t)} = ∫ e^(-8t)sin(5t) e^(-st) dt = (5/(s+8+5i))(e^(-8-s)) - (5/(s+8-5i))(e^(-8-s))
f(t) = e^(-st)sinh(7t)
F(s) = L{e^(-st)sinh(7t)} = ∫ e^(-st)sinh(7t) e^(-st) dt = (7/(s^2+49))(e^(-s-7i)) - (7/(s^2+49))(e^(-s+7i))
f(t) = -7t cosh(5t)
F(s) = L{-7t cosh(5t)} = ∫ -7t cosh(5t) e^(-st) dt = (-7/s^2)(e^(-s-5)) - (7/s^2)(e^(-s+5))
f(t) = 9t sin(ut)
F(s) = L{9t sin(ut)} = ∫ 9t sin(ut) e^(-st) dt = (9/(s^2 + u^2))(e^(-su)) - (9/(s^2 + u^2))(e^(su))
Note that in all cases, we should check if the integral converges, and that the limits of integration are appropriate.
To compute the Laplace transform of a function, we use the integral definition , F(s) = L{f(t)} = ∫ f(t) e^(-st) dt.
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Victoria is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Victoria will earn $40 every time one of her songs is played in a commercial and she will earn $140 every time one of her songs is played in a movie. Victoria earned a total of $560 in royalties on 9 commercials and movies. Graphically solve a system of equations in order to determine the number of commercials,
x
,
x, and the number of movies,
y
,
y, on which Victoria's songs were played.
A graph of each function is shown in the image attached below.
The number of commercials (x) is equal to 7 commercials while the number of movies (y) is equal to 2 movies.
How to write and solve the system of equations graphically?In order to graphically solve the system of equations, we would write two (2) equations that models the situation by assigning variables to the number of commercials and number of movies respectively, and then translate the word problem into algebraic equation as follows:
Let the variable V represent the number of commercials.Let the variable y represent the number of movies.Since Victoria would earn $40 every time one of her songs is played in a commercial and $140 every time one of her songs is played in a movie, an equation which models it is;
40x + 140y = 560
Additionally, Victoria earned a total of $560 in royalties on 9 commercials and movies;
x + y = 9
Next, we would use an online graphing calculator to plot the above system of equations with a point of intersection at (7, 2) as shown in the image attached below.
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58
n 8: Notes
potes
Name
2.
JuliAN A.
A plant's height is proportional to
the number of days since it was
purchased. On Day 6, it was 3 inches
tall.
1.
Add more points to the graph to
represent the plant's height on
other days.
Height of a Plant (in.)
1
5
(63)
5
10
Days Since Purchased
Should the origin, (0, 0), be included in this relationship?
Why or why not?
The height define how long the attribute is and the width specify about the breadth of the attributes.
What is height?Height is defined in mathematics as the vertical distance separating an object's top from its base. On occasion, it is referred to as "altitude". In coordinate geometry, an object's height is calculated along the y-axis and is referred to as height.height, altitude, elevation mean vertical distance either between the top and bottom of something or between a base and something above it. height refers to something measured vertically whether high or low.Height is measure of vertical distance, either vertical extent (how "tall" something or someone is) or vertical position (how "high" a point is). For example, "The height of that building is 50 m" or "The height of an airplane in-flight is about 10,000 m".Height is a common body measurement typically measured in feet (ft) + inches (in) in the United States and centimeters (cm) elsewhere. These are length measurements, so the SI unit would be meters. Keep in mind that x feet + y inches is commonly denoted as x' y“.
Given:
Arty's height is 63 inches.
Suppose Julian's height is x inches.
As Arty's height is 3 inches less than 1.5 times Julian's height.
⇒ 1.5x - 3 = 63
1.5x = 63 + 3
1.5x = 66
x = 44
Hence, the Julian's height is 44 inches.
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Pedro and Bella are reading the same book for their language-arts class. On Saturday, Pedro starts the day at page 20 and reads at an average rate of 25 pages per hour. Bella starts reading at the same time, but she starts at page 60 and reads at an average rate of 18 pages per hour.
Answer: If Pedro starts reading at page 20 and reads at an average rate of 25 pages per hour, and Bella starts reading at the same time but starts at page 60 and reads at an average rate of 18 pages per hour,
We can use the formula: distance = rate x time
To find out when they will meet we need to find out when they are on the same page.
let's say t be the time in hours, Pedro will be reading t25 pages, and Bella will be reading t18 pages.
So we can write the equation: 20+t25 = 60+t18
Solving this equation we get t = 2
So, they will meet after 2 hours.
Pedro will be on page 20+225 = 70, and Bella will be on page 60+218 = 96
So they will meet at page 70 when Pedro reaches that page after 2 hours of reading, which means Bella will have read 26 pages more than Pedro on that point.
Step-by-step explanation:
A triangle has side measures of 15,15 and 15 . Choose the term that describes the triangle .
1 . Right 2. Equilateral 3. Scalene 4. Isosceles
Answer:
Equilateral Triangle
Step-by-step explanation:
Answer:
Equilateral
Step-by-step explanation:
The Answer to this given question is a Equilateral
Reason : The sides of an equilateral triangle are congruent, which means that all sides are of equal length.
140-100
Need help with this maths
40
.
.
.
.
.
.
.
.
.
.
.
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.
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........
Researchers routinely chose an alpha level of 0.05 for testing their hypotheses. What are some experiments for which you might want a lower alpha level (e.g., 0.01)? What are some situations you might accept a higher level (e.g., 0.1)?
Researchers frequently select a level of significance of 0.05. The reason for this is that if we chose a lower threshold of significance, we will have less room to reject the null hypothesis and so a higher likelihood of making a type 2 error.
On the other hand, if the degree of significance is higher, more type 1 errors are made, leading us to reject the hypothesis even though it is correct. Therefore, 0.05 is a balanced level that is neither significantly greater nor significantly smaller. The health care and nutrition-related industries are mostly included in some of the studies where we require a lower level of importance. This type of industry has a higher error rate, which causes more fatalities and negative side effects.
We can use a higher level of relevance in a variety of circumstances, such as the entertainment and marketing-related industries. The reason for this is that even if there are more potential for error, it won't harm the person; instead, it just affects the information, which we can assess using common sense.
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A man crosses a distance of 48 meters while going round a quadrilateral field twice. What will be the cost of fencing the field at the cost $1.75 per meter?
A man crosses a distance of 48 meters while going round a quadrilateral field twice. For 24 m cost of fencing the field is $42.
What is perimeter?The circumference of an object is known as its perimeter. For instance, your home has a yard that is enclosed. The length of the fence is the perimeter. The length of your fence is 200 feet if the yard is 50 feet by 50 feet. P = length + breadth + length + breadth is the equation for a rectangle's perimeter. Add the lengths of the four corners of a rectangle to find its perimeter. You can quickly locate all four sides if you only know the width and height (two sides are each equal to the height and the other two sides are equal to the width). Add the outcomes after dividing the height and breadth by two.Perimeter of the field is the total lengths of its boundary = 48/2 m = 24 m
For 1 m, cost of fencing the field = $1.75
Therefore, for 24 m cost of fencing the field = $(1.75 × 24) = $42
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Which equation could be used to find the missing side of the triangle shown?
10 m
am
5 m
O a² +52
10²
O 5² + 10² a²
O2 (5) +2 (10) = 2a
O a² + 10² 5²
=
O a² + 10² 5² =25 + 100 =2a ,2a=125 , a=\sqrt{125} , a=11.18 m
Therefore, the missing side (a) is 11.18 m.
Calculate the missing side (a) of the triangle
We are trying to find the missing side (a) of the triangle shown in the diagram.
To do this, we will use the Pythagorean Theorem, which states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the longest side.
The two shorter sides of the triangle are 5 m and 10 m.
We will use the Pythagorean Theorem to calculate the missing side (a).
First, we need to square the lengths of the two shorter sides:
5² = 25
10² = 100
Next, we add the squares of the two shorter sides together:
25 + 100 = 125
Finally, we take the square root of the sum to find the length of the missing side:
√125 = 11.18 m
Therefore, the missing side (a) is 11.18 m.
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a pair of dice are rolled. (a) what is the probability space s? (b) determine the probability of each of the following events: i. the sum of the rolls is even. ii. the first roll is equal to the second. iii. the first roll is larger than the second.
a)The probability Space, S = {(1,1) (1,2) (1,3) (1,4) (1,5) (1,6), (2, 1) (2, 2) (2,3) (2,5) (2,4),(2,6), (3,1) (3,2) ,(3,3), (3,4) (3,5)(3,6), (4,1) (4,2) (4,3) (4,4) (4,5) (4,6), (5,1) (5,2) (5,3) (5,4) (5,5) (5,6),(6,1) (6,2) (6,3) (6,4) (6,5) (6,4), (6,5),(6,6)}
b) i) Probability that the sum of the rolls is even, P(A) = 0.5
ii)Probability that first roll is equal to the second, P(B) 0.166
iii) Probability that the first roll is larger than the second, P(C) = 0.4166.
We have a pair of dice are rolled, then the Sample space is same as probability space.
a) The probability space , S is a non-empty set contains all possible outcomes. The probability space is written as
S = {(1,1) (1,2) (1,3) (1,4) (1,5) (1,6), (2, 1) (2, 2) (2,3) (2,5) (2,4),(2,6), (3,1) (3,2) ,(3,3), (3,4) (3,5)(3,6), (4,1) (4,2) (4,3) (4,4) (4,5) (4,6), (5,1) (5,2) (5,3) (5,4) (5,5) (5,6),(6,1) (6,2) (6,3) (6,4) (6,5) (6,4), (6,5),(6,6)}
b) Total possible outcomes from rolling = 36
Let us consider the events,
A : sum of the rolls is even
B : first roll is equal to the second
C : first roll is larger than the second.
Now, favourable outcomes for event A = 18
i) Probability (Sum is even), P( A) = 18/36
= 0.5
Favourable outcomes for event B = 6 = { (1,1),(2,2),(3,3),(4,4), (4,1) (4,2) (4,3), (5,5),(6,6)}
ii) So, Probability that first roll is equal to the second, P(B) = 6/36 = 0.166
Favourable outcomes for event C = 15 = { (2,1),(3,2),(3,1),(4,1),(5,1) (5,2) (5,3) (5,4),(6,1) (6,2) (6,3) (6,4) (6,5) (6,4), (6,5)}
iii) So, probability that the first roll is larger than the second, P(C) = 15/36
= 0.4166.
Hence, we get all required probabilities.
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The probability of P(Sum is even)=0.5, P(the first roll is equal to the second)=[tex]\frac{1}{6}[/tex], P(the first roll is larger than the second)=0.4167.
A pair of dice are rolled
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur.
The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favourable outcomes and the total number of outcomes.a) Sample space,
[tex]$$\begin{aligned}S= & \left\{\begin{array}{l}(1,1)(1,2)(1,3)(1,4)(1,5)(1,6) \\(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)\end{array}\right. \\& (3,1)(3,2)(3,3)(3,4)(3,5)(3,6) \\& (4,1)(4,2)(4,3)(4,4)(4,5)(4,6) \\& (5,1)(5,2)(5,3)(5,4)(5,5)(5,6) \\& (6,1)(6,2)(6,3)(6,4)(6,5)(6,2)\}\end{aligned}$$[/tex]
(b).
(i).The probability of each of the following events
Probability of event to happen
P(E) = Number of favourable outcomes/Total Number of outcomes⇒P(Sum is even)=[tex]\frac{18}{36} =\frac{1}{2}[/tex]=0.5
⇒P(Sum is even)=0.5
(ii). P(the first roll is equal to the second)=[tex]\frac{6}{36} =\frac{1}{6}[/tex]
⇒P(the first roll is equal to the second)=[tex]\frac{1}{6}[/tex]
(iii). P(the first roll is larger than the second)=[tex]\frac{15}{36}=0.4167[/tex]
⇒P(the first roll is larger than the second)=0.4167
Therefore, the P(Sum is even)=0.5, P(the first roll is equal to the second)=[tex]\frac{1}{6}[/tex], P(the first roll is larger than the second)=0.4167.
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area of a trapezoid using decomposition pleas help wanted begs!
The area for the trapezoid is 35 square inches. Last option
How to solve for the trapezoidThe formula for the decomposition method of finding trapezoid is given as: ( x + y ) / h
The variables are given as
x = 3
y = 4
h = 5
we would have to fix the values into the formula in order to get the area of the trapezoid
Hence we would have
( 3 + 4) * 5
7 * 5
= 35 square units
Hence the area of the trapezoid by decomposition is given as 35 square units.
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Find dy/dx of i)x, ii)xy, iii) y^2, iv) x^2y
Answer: i) dy/dx of x = 1
ii) dy/dx of xy = y
iii) dy/dx of y = 2y
iv) dy/dx of xy = 2xy
Step-by-step explanation:
Drag each object to show whether cost is proportional to area in the situation represented.
Since the points on this graph represent a relationship between x- and y-values, a statement about the relationship which is true include the following: A, it cannot be proportional because the straight line through the points does not go through the origin.
What is a proportional relationship?In Mathematics, the graph of any proportional relationship between two (2) variables is always characterized by a straight line with the data points starting from the origin (0, 0) and passes through other unique data points on the cartesian coordinate.
By critically observing the graph which shows a relationship between the x-values and y-values, we can logically deduce that it does not start from the origin (0, 0) and as such, it does not represent a proportional relationship.
In this context, we can reasonably infer and logically conclude that cost is not proportional to area in the situation represented by this graph.
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what number can divide 153 and 48. 50 points will.amrk as brainliest
Answer:
3
Step-by-step explanation:
3 can divide both 153 and 48
4/7 = 12/g 21 15 24 3
Answer:
4/7 = 12/g cannot be true, as the numbers on the right side of the equation are not related to the numbers on the left side of the equation and cannot be used to solve for the variable "g".
The correct way to solve for the variable in an equation like this is by cross-multiplying and simplifying the equation.
4/7 = 12/g
multiply both sides by 7g
4*g = 12
Divide both sides by 4
g = 3
So in this case the value of g is 3, but the given numbers 21 15 24 3 are not related to this equation.
Step-by-step explanation:
Answer:12/21
Step-by-step explanation:
cross-multiply 4/7 = 12/g so 4g = 84 . 4 x3 =12 7x3=21 So the answer is 12/21.
59) When scrap iron in a boat is thrown overboard in a swimming pool, the pool level
A) rises.
B) falls.
C) remains unchanged.
As rain drop and sink through the rock, it often solvates some of the iron. It conveys that iron along with it as it continues to seep through the rock and soil.
When the rainwater becomes groundwater or dart into freshwater sources like lakes and rivers, it may become the part of the local water supply.
Municipal water systems that get their water from these sources can end up with high levels of iron in their water, and the riddle they have set up to remove bacteria and other harmful contaminants may not always riddle it out.
Wells that portray water from aquifers with high iron content may contain high iron concentrations as well.
Iron in water generally takes two types of ferrous iron, which is soluble in water, and next one is ferric iron, which is insoluble.
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2/25
two fractions
I need help please this is too hard and can you tell me the answer please
Two equivalent fractions to 2/25 are given as follows:
4/50 and 8/100.
What are equivalent fractions?A fraction is a numerical representation of the division of the two terms x and y, as follows:
Fraction = x/y.
The terms are classified as follows:
The top term x is the numerator of the fraction.The bottom term y is the denominator of the fraction.Two fractions are called equivalent when the ratio between their numerators and denominators is the same.
The fraction in this problem is defined as follows:
2/25.
To obtain an equivalent fraction, we multiply both the numerator and denominator by the same constant, hence:
Multiplying by 2: 2/25 = 4/50.Multiplying by 4: 2/25 = 8/100.Missing InformationThe problem asks for two equivalent fractions to 2/25.
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rkKeys 34 134 134 Your development company recently purchased 12.5 acres of land. According to local regulations, each housing lot must be at least 54, 450 square feet. In a of the purchased land must be left undeveloped. What is the maximum number of housing lots that you can develop on the land? A C 10 11 D. 13 18 A ; for Review & Tools a O Contrast 은 * Clear Highlights ? Help (H) n Text To Speech « Prev TAO Software 3.4.0-sprint140 © 2013-2023 by Open Assessment Technolo DOLL 3 $ 4 % 5 € ∞♪ g y h u k b m
Price divided by size is the formula for calculating the price per square foot (in square feet). For instance, if a 2,000-square-foot property is being sold for $300,000, the price per square foot would be $150 if you took the overall price and divided it by the size.
What do you mean by rectangular area?
A rectangle's sides determine its area. In essence, the length and breadth of the rectangle multiplied together gives the area of the rectangle.A shape called a quadrilateral has two opposing sides that are equal and parallel. It is a four-sided polygon with four 90-degree angles. Rectangles have a two-dimensional form.The area of a rectangle is the region contained by its four sides or boundaries.This is how the whole process occurs in a company which recently purchased 12,5 acres of the given land.To know more about rectangular area here
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Write a mixed number for t so that 2 3/4 X is more than 2 3/4
Answer: it will be improper
Step-by-step explanation:11/4
Answer:11/4
Step-by-step explanation:it is improper.
The methods of statistics follow a process. Place the processes in the correct order:
Identify the research objective, Perform interference, Describe the data, Collect the data needed to Answer Research question
The order for the process of Statistcal Method will be Identify the research objective, Collect the data needed to Answer the Research question, Describe the data, and Perform Inference.
For any statistics method, we first must have an objective as to why are we conducting that research. Hence the first process has to be Identifying the research objective.
For any statistical method, samples need to be drawn to conduct statistic tests. This essentially requires data to work with. Hence, Collecting the data needed to Answer the Research question must be the next step.
After data is collected, numerous tests are possible to be performed on any set of data but to select the most appropriate statistic, we need to first understand the nature, range, and limitations of the data. Hence, the net step should be to describe the data.
The last step out of the available step would be to perform the inference since this is the only other step possible from the ones mentioned.
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Two angles are complementary to each other. One angle measures 18°, and the other angle measures (8x − 28)°. Determine the value of x.
Answer:
Step-by-step explanation
since they are complementary their angles should add up to 90.
18+(8x-28)=90
you solve from there
add common values
8x-10+90
add 10 to both sides
8x=100
divide by 8
x=12.5
The answer is:
x = 12.5Work/explanation:
Since we're given both angles, we can set up an equation and find x.
The sum of two complementary angles is 90°.
Now, set up the equation:
[tex]\sf{8x-28+18=90}[/tex]
[tex]\sf{8x-10=90}[/tex]
Add 10 on each side
[tex]\sf{8x=100}[/tex]
Divide each side by 8
[tex]\sf{x=12.5}[/tex]
Hence, x = 12.5In the figure above, segment BC is 4 units long, segment CD is 8 units long, and segment DE is 6 units
long. What is the length of segment AC?
6 is the length of segment AC in right-angled triangle .
What is a right-angle triangle, exactly?
A right-angled triangle is a particular kind of triangle in which one of the angles is 90 degrees. The combined angles of the other two are 90 degrees.
Perpendicular and the triangle's base make up the sides that the right angle is formed from. The hypotenuse, or third side, is the longest of the three. It is also known as the hypotenuse.
let length of AC is x
BC + CD = AC + DE
4 + 8 = X + 6
12 = X + 6
X = 6
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The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 7 to 4 . If there were 8657 total votes, how many yes votes were there?
Answer:
5509 yes votes
Step-by-step explanation:
We will start by adding together our ratio, so we know how many voters there were in a total ratio, so we can divide our total number of people by it, and then multiply it by the number of people who said yes (7 people).
Our ratio was 7:4, so adding those two numbers together gives us 11. Then, dividing 8657 by 11 gives us:
8657 / 11 = 787
Now, we will multiply 787 by 7, since that was the number of people who said yes:
787 * 7 = 5509
So, there were 5509 yes votes.
Hope this helped!
please need help asap!!!!!!!!!!!!!! please answer 28, and 29
The length of the midsegment of 28. is 17 units and 29. is 27 units.
What is midsegment?A line drawn by joining the midpoints of any two of the triangle's sides is known as the midsegment. All three sides of a triangle can be divided in half, with the midpoint being the point that is equally spaced from either vertex, regardless of whether the triangle is a right triangle, isosceles triangle, or sometimes an equilateral triangle.
If the slope and sides are same then we can cut the midsegment ad paste it such that it becomes an rectangle.
28. Now the length of the rectangle = n + 12 + n + 12 = 4n + 6 + 2n - 2
⇒ 2n + 24 = 6n +4
⇒ 20 = 4n
⇒ n = 20/4
⇒ n = 5
Length of midsegment = 5 + 12
= 17 units
29. Now the length of the rectangle = 2n+ 11 + 2n+ 11 = 5n - 2 + n + 8
⇒ 4n + 22 = 6n + 6
⇒ 16 = 2n
⇒ n = 16/2
⇒ n = 8
Length of midsegment = 2(8) + 11
= 27 units
Thus, he length of the midsegment of 28. is 17 units and 29. is 27 units.
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Please answer Asap. Math algebra 2
Answer:
Domain: [0, ∞)
Range: [√5, ∞)
Step-by-step explanation:
Find the domain by finding where the piecewise is defined. The piecewise range is the set of values that correspond with the domain.
Domain: [0, ∞)
Range: [√5, ∞)
hope that helps...
140,100,71.4, ,36.44 what is the missing number
The required missing number is 51.02
What is a geometric progression?Any progression in which the ratio of adjacent terms is fixed is a Geometric Progression. The general form of representation of a geometric sequence is a, ar, ar2, ar3, ar4, ar5, .....
Given here the numbers 140,100,71.4, ,36.44
clearly 140/100=100/71.4=1.4
Thus the given set of numbers form a geometric progression with common ratio 1.4
Therefore the complete set of numbers are 140,100,71.4,51.02,36.44
Hence, the required numbers is 51.02
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The population of a town increased from 3600 in 2007 to 4700 in 2011. Find the absolute and relative (percent) increase.
1100 Absolute is a 30.55% increment relative percent
To find an Increment percentage in population we need the Number of increases in population.
4700- 3600 = 1100
That is absolutely increased number.
For relative increment, we need to find the Percentage -
Increment Percentage = (value / total value) * 100%so the population in 2007 was 3600
so percentage = 1100/3600*100
=> 30.55%
SO Relative increase = 30.55%
Here we can see that percent is the way to analyze the change, Increment/decrease in terms of 100 as it multiple the fractional changes in quantity by 100 to make it out of 100. So percentage simply means out of 100.
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What is the fewest number of regions that three lines can separate a plane into? Describe the configuration of lines that gives you this many regions.
As long as they are not all on the same line, three points can define a plane in a three-dimensional space.
How many different numbers of regions can three lines divide a plane into?Intersecting Space with Planes A plane just divides space into two distinct regions. Space is divided into a maximum of four sections by two planes. Space can only be divided into eight sections by three planes.
One line has the ability to split a plane into two regions; two non-parallel lines have the ability to divide a plane into four regions; three non-parallel lines have the ability to divide a plane into seven regions; and so on.
Four unique, nonintersecting zones can be created by selecting three separate points on a circle and connecting each pair of them with a chord.
Three points can define a plane in a three-dimensional space as long as they are not all on the same line.
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One line can divide a plane into two regions, two non-parallel lines can divide a plane into 4 regions and three non-parallel lines can divide into 7 regions.
What is the maximum number of regions can divide a plane?The maximum number Ln of regions in the plane that can be defined by n straight lines in the plane is: Ln=n(n+1)2+1. This sequence is A000124 in the On-Line Encyclopedia of Integer SequenceOne line can divide a plane into two regions, two non-parallel lines can divide a plane into 4 regions and three non-parallel lines can divide into 7 regionsIf three planes meet pairwise in three parallel lines they create 7 regions. A plane not parallel to these lines doubles the number of regions, a plane parallel to them creates at four more regions. Thus all triples of planes meet in one pointAn infinite number of regions can be formed in a circle by the number of chords of the circle. How many regions can be formed by a circle and two chords? There are two options for a circle and two chords, depending on whether the chords intersect or not.
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Find the indicated side of the
triangle.
7
a
b
45°
a = [?]
Enter
Answer:
[tex]a=7[/tex]
Step-by-step explanation:
The legs of an isosceles right triangle are congruent.
The Pythagorean Theorem may be used to calculate the length of side a: [tex]a^{2}[/tex] = 72 + [tex]b^{2}[/tex] = 49 + [tex]b^{2}[/tex]. When we solve for a, we obtain a = (49 + [tex]b^{2}[/tex]). As a result, the length of side an equals the square root of 49 multiplied by the square of side b.
What is Pythagorean Theorem?The Pythagorean Theorem is a mathematical equation that asserts that the square of the length of the hypotenuse (the side opposite the right angle) in a right triangle is equal to the sum of the squares of the other two sides. The Pythagorean Theorem is stated in equation form as [tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex], where a and b are the lengths of the triangle's legs (the two sides that meet at a right angle) and c is the length of the hypotenuse.
In the given question,
a = 7 * sin(45°)
= 7 * 0.707
= 4.949
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