Determine whether the following equation defines y as a function of x: x^2 + y^2 = 169. How was this solved? Where does the 2 (pictured) come from?
Answers
Answer:
Step-by-step explanation:
Assuming you can follow how the equation was solved for y, the 2 comes from the "±" in front of the square root. That means that there is a positive and a negative result when you plug in a number for x. For example, if we were asked to solve
[tex]x^2=4[/tex]
we would take the square root of both sides, giving us
x = ±2
This is because a positive 2 squared gives us a positive 4, and a negative 2 squared also gives us a positive 4. There will ALWAYS be 2 solutions when you take a square root of a number, both the positive (principle) and negative roots.
Related Questions
Let f(x)=x+8 and g(x)=x^2-7x-9 find f(g(-1))
Answers
Answer:
First, we need to evaluate g(-1):
g(-1) = (-1)^2 - 7(-1) - 9
= 1 + 7 - 9
= -1
Now, we can plug in g(-1) into f(x):
f(g(-1)) = f(-1)
= -1 + 8
= 7
Therefore, f(g(-1)) = 7.
We have:
g(x) = x^2 - 7x - 9
So:
g(-1) = (-1)^2 - 7(-1) - 9
= 1 + 7 - 9
= -1
Now that we have g(-1) = -1, we can use it as the input for the function f:
f(x) = x + 8
f(g(-1)) = f(-1) = -1 + 8 = 7
Therefore, f(g(-1)) = 7.
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Translate and solve: 5 less than m is at most 70.
Write your solution in interval notation
Answers
The interval notation for the inequality statement "5 less than m is at most 70" is (-∞, 75].
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
The statement given is - 5 less than m is at most 70.
The given sentence can be translated into a mathematical inequality as -
m - 5 ≤ 70
To solve for m, we can add 5 to both sides of the inequality -
m - 5 + 5 ≤ 70 + 5
m ≤ 75
Therefore, m is less than or equal to 75.
In interval notation, we can represent this solution as -
(-∞, 75]
Therefore, the interval value is (-∞, 75].
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Given: trap. SPQR with SP || QR ; MN is the median of the trap. m∠QRS = 120 ; m∠QPS = 135 ; SP = PQ = 12. Find: MN.
Answers
Answer:
From the information given, we can draw the following diagram:
S ------- P
/ \ / \
/ \ QR / \
/ \ / / \
/ Q \
R-----------------P
MN
Here, SP || QR, so we have ∠QSP = ∠PQR and ∠SPQ = ∠QRP.
Since m∠QRS = 120, we have m∠QRP = 360 - m∠QRS = 360 - 120 = 240.
Since m∠QPS = 135 and ∠QSP = ∠PQR, we have m∠PQR = 360 - m∠QPS = 360 - 135 = 225.
Let x = MN. Since MN is the median of the trapezoid, we have MP = NR = x.
Now, consider the triangles SPQ and RPQ. We have:
tan(∠SPQ) = x/12 (using the tangent ratio in triangle SPQ)
tan(∠RPQ) = x/12 (using the tangent ratio in triangle RPQ)
Since ∠SPQ = ∠RPQ (as they are corresponding angles), we have:
x/12 = x/12
x = 12
Therefore, MN = x = 12.
b. Let f:x=3x² +1 and g: x=x-5
Find
i. fog(x)
ii. go f(x)
iii. (ƒ o g)−¹(x)
Answers
i. To find fog(x), we need to first apply g to x and then apply f to the result.
g(x) = x - 5
So,
fog(x) = f(g(x)) = f(x - 5)
= 3(x - 5)² + 1
= 3(x² - 10x + 25) + 1
= 3x² - 30x + 76
Therefore, fog(x) = 3x² - 30x + 76.
ii. To find gof(x), we need to first apply f to x and then apply g to the result.
f(x) = 3x² + 1
So,
gof(x) = g(f(x)) = g(3x² + 1)
= 3x² + 1 - 5
= 3x² - 4
Therefore, gof(x) = 3x² - 4.
iii. We want to find the inverse of the composite function f o g.
Let y = fog(x) = f(g(x)) = f(x - 5) = 3(x - 5)² + 1
To find the inverse of f o g, we need to solve for x in terms of y.
3(x - 5)² + 1 = y
3(x - 5)² = y - 1
(x - 5)² = (y - 1) / 3
x - 5 = ±√((y - 1) / 3)
x = 5 ±√((y - 1) / 3)
Therefore, the inverse of f o g is:
(ƒ o g)−¹(x) = 5 ±√((x - 1) / 3)
HELPP ! , Use substitution to solve each system of equations , find x and y and do checks
Answers
Y=6
Explanation:
5x - Y = 9
5x - 2x = 9 (Substituting 2x for Y)
3x = 9
x = 3
Now that we have found the value of x, we can use it to find y by substituting it into either of the original equations:
Y = 2x
Y = 2(3)
Y = 6
how do scatter graphs work
Answers
The scatter graph is used to show correlation between variables
How do scatter graphs work A scatter graph, also known as a scatter plot or scatter chart, is a type of data visualization tool that uses coordinates to display the values of two variables for a set of data.
In a scatter graph, each point on the graph represents a single data point, with one variable plotted on the x-axis and the other variable plotted on the y-axis.
The position of each point is determined by the values of the two variables for that data point.
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The number of animals in a population at the start of year t is Pt
The number of animals at the start of year 1 is 400
Given that
Pt + 1 = 1.01Pt
work out the number of animals at the start of year 3
Answers
Therefore, the number of animals at the start of year 3 is approximately 408.04.
What is equation?An equation is a mathematical statement that shows the equality of two expressions, usually with an equal sign "=" in between them. An equation can contain variables, constants, and operators. The variables are represented by letters and can take on different values, while constants are fixed values that do not change. Operators include mathematical symbols like plus, minus, multiplication, and division, as well as exponents and logarithms.
Here,
We are given that the population at the start of year 1 (P1) is 400. Using the recurrence relation Pt + 1 = 1.01Pt, we can find the population at the start of year 2 (P2) and year 3 (P3) as follows:
P2 = 1.01 * P1 = 1.01 * 400 = 404
P3 = 1.01 * P2 = 1.01 * 404 = 408.04
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22.
Number of Cookies
YA
72
60
48
36
24
12
Origin O
Bake Sale
2 4 6 8 10 12 X
Packages
a) k = 6
c) k = 1/6
e) none (not proportional)
Identify the constant of proportionality.
b) k = 12
d) k=1/12
Answers
Since the ratio of Y to X is not constant for different values of X, the relationship between Y and X is not proportional, and there is no constant of proportionality.
What is proportion?Proportion is a mathematical concept that expresses the relationship between two or more quantities that are related to each other in a consistent way. A proportion can be expressed as an equation in which two ratios are set equal to each other, and it states that the ratios of two quantities are always the same. In other words, if we know that two quantities are proportional, we can use this relationship to find one quantity given the other.
Here,
Based on the given table, we can see that the number of cookies (Y) is directly proportional to the number of packages (X). Thus, we can write:
Y = kX
where k is the constant of proportionality.
a) When k = 6, we can find the value of Y for different values of X as follows:
When X = 12, Y = kX = 6(12) = 72
When X = 10, Y = kX = 6(10) = 60
When X = 8, Y = kX = 6(8) = 48
When X = 6, Y = kX = 6(6) = 36
When X = 4, Y = kX = 6(4) = 24
When X = 2, Y = kX = 6(2) = 12
Thus, the constant of proportionality is k = 6.
b) When k = 12, we can find the value of Y for different values of X as follows:
When X = 12, Y = kX = 12(12) = 144
When X = 10, Y = kX = 12(10) = 120
When X = 8, Y = kX = 12(8) = 96
When X = 6, Y = kX = 12(6) = 72
When X = 4, Y = kX = 12(4) = 48
When X = 2, Y = kX = 12(2) = 24
Thus, the constant of proportionality is k = 12.
c) When k = 1/6, we can find the value of Y for different values of X as follows:
When X = 12, Y = kX = (1/6)(12) = 2
When X = 10, Y = kX = (1/6)(10) = 5/3
When X = 8, Y = kX = (1/6)(8) = 4/3
When X = 6, Y = kX = (1/6)(6) = 1
When X = 4, Y = kX = (1/6)(4) = 2/3
When X = 2, Y = kX = (1/6)(2) = 1/3
Thus, the constant of proportionality is k = 1/6.
e) Since the ratio of Y to X is not constant for different values of X, the relationship between Y and X is not proportional, and there is no constant of proportionality.
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50x212 with steps like
212
x 50
Answers
1 )Use the algorithm method.
5 0
× 2 1 2
1
100
500
1
10000
10600
2) Therefore,50×212=10600
10600
What is the approximate (use 3.14 for pi) volume of this cylinder?
(Diameter is 10 in and height is 12.2 in)
A)383.1 cubic inches
B)957.7 cubic inches
C)122cubic inches
D)3830.8 cubic inches
Answers
Answer: B
V=957.7 cubic inches
Step-by-step explanation:
V=Hxpixr^2
V=12.2x3.14x5^2 r=5 because it is half of the diamter, which is 10.
V=12.2x3.14x25
V=957.7 cubic inches
Anybody answer!!!!, I'm trying to do my IXL. Have to get it to 90!!
What kind of transformation converts the graph of f(x)=x–1 into the graph of g(x)=9x–9?
Horizontal Shrink
Horizontal Stretch
Vertical Shrink
Vertical Stretch
Answers
The transformation that converts the graph of f(x) = x - 1 into the graph of g(x) = 9x - 9 is a vertical stretch by a factor of 9, followed by a vertical shift downwards by 8 units.
What are some instances of graphs?
Some instances of graphs include line graphs, bar graphs, scatter plots, pie charts, and histograms, which are visual representations of data or mathematical functions.
To see this, we can rewrite g(x) as:
g(x) = 9(x - 1) = 9x - 9
This shows that g(x) is a vertical stretch of f(x) by a factor of 9, which means that every y-value of g(x) is 9 times the corresponding y-value of f(x). The horizontal axis remains the same.
Next, we can see that g(x) is shifted downward by 8 units compared to f(x). This is because g(x) has a y-intercept of -9, while f(x) has a y-intercept of -1. This means that every y-value of g(x) is 8 units less than the corresponding y-value of f(x).
Therefore, the transformation that converts the graph of f(x) = x - 1 into the graph of g(x) = 9x - 9 is a vertical stretch by a factor of 9, followed by a vertical shift downwards by 8 units.
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A city currently has 138 streetlights. As part of a urban renewal program, the city council has decided to install 2 additional streetlights at the end of each week for the next 52 weeks.
How many streetlights will the city have at the end of 30 weeks?
streetlights
Answers
Answer:
The number of additional streetlights installed every week is 2, and this will continue for 52 weeks. Therefore, the total number of streetlights added during this period will be:
2 streetlights/week x 52 weeks = 104 streetlights
If the city currently has 138 streetlights, then after 30 weeks, the total number of streetlights will be:
138 streetlights + 2 streetlights/week x 30 weeks = 198 streetlights
Therefore, the city will have 198 streetlights at the end of 30 weeks.
Step-by-step explanation:
1. The problem states that the city currently has 138 streetlights.
2. The city council has decided to install 2 additional streetlights at the end of each week for the next 52 weeks. This means that every week, the city will add 2 streetlights to its total.
3. To find out how many streetlights will be added in total over the 52-week period, we can multiply the number of additional streetlights per week (2) by the number of weeks (52):
2 streetlights/week x 52 weeks = 104 streetlights
Therefore, over the 52-week period, the city will add 104 streetlights.
4. To find out how many streetlights the city will have at the end of 30 weeks, we need to calculate how many additional streetlights will be added during this time period. Since the city is adding 2 streetlights per week, we can multiply 2 by the number of weeks (30):
2 streetlights/week x 30 weeks = 60 streetlights
This means that over the course of 30 weeks, the city will add 60 streetlights.
5. To find out the total number of streetlights at the end of 30 weeks, we need to add the current number of streetlights to the number of streetlights added during the 30-week period. Therefore, we can add 138 (the current number of streetlights) and 60 (the number of streetlights added during the 30-week period):
138 streetlights + 60 streetlights = 198 streetlights
Therefore, the city will have 198 streetlights at the end of 30 weeks.
Find the area of the triangle, round to the nearest tenths if necessary. *Hint: You will need to use Pythagorean Theorem to find the base of the triangle
Answers
Answer:
(c) 42.9 ft²
Step-by-step explanation:
You want the area of the right triangle with hypotenuse 17.3 ft and long side 16.5 ft.
Pythagorean theoremThe Pythagorean theorem tells you the relationship between the side lengths is ...
c² = a² +b²
The missing side, b, can be found as ...
b² = c² -a²
b = √(c² -a²) = √(17.3² -16.5²) = √27.04 = 5.2
AreaThe area of the triangle is ...
A = 1/2bh
A = 1/2(16.5 ft)(5.2 ft) = 42.9 ft²
The area of the triangle is 42.9 square feet.
Help with math problems
Answers
The value of the expressions are 1. Distributive property: -3 √3 (2 + √6) = -6 √3 - 9 √2. [2] (-2 √3 + 2)(√3 - 5) = 12 √3 - 16. [3] (-2 -3 √5)(5 - √5) = -15 √5 + 5.
What is distributive property?The distributive property in algebra says that the sum or difference of the products of the number and each term in the sum or difference is equal to the product or difference of the number and each phrase in the sum or difference. To put it another way, a(b + c) = ab + ac and a(b - c) = ab - ac are true for any value of a, b, and c. The distributive property is frequently employed in parenthetical expansion and algebraic simplification.
1. Distributive property:
-3 √3 (2 + √6)
= -6 √3 - 3 √3 √6
= -6 √3 - 3 √18
= -6 √3 - 9 √2
2. Multiplying:
(-2 √3 + 2)(√3 - 5)
= -2 √3 (√3) + 2 (√3) - 10 + 10 √3
= -2 (3) - 10 + 12 √3
= 12 √3 - 16
3. Multiplying:
(-2 -3 √5)(5 - √5)
= -2 (5) - 3 √5 (5) + 2 √5 + 15
= -10 - 15 √5 + 2 √5 + 15
= -15 √5 + 5
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=2x-1
7) through: (-4,-4), parallel to y=-
3
=2x-4
9) through: (-4,-4), parallel to y =
11) through: (5,-2), perp. to y =
y=²x-5
13) through: (-2, 5), perp. to y = x + 2
8) through: (1, 0), parallel to y = 2x - 1
5
10) through: (5, 5), perp. to y = --
y = ²√x + 4
12) through: (3,-2), perp. to y = -
14) through: (-4, 0), perp. to y = -
Answers
The equation of the lines parallel or perpendicular to another line and that pass through a point are listed below:
Case 7: y = (7 / 4) · x + 3
Case 8: y = 2 · x + 1
Case 9: y = (3 / 2) · x + 2
Case 10: y = (6 / 5) · x - 1
Case 11: y = - (2 / 5) · x
Case 12: y = - (5 / 2) · x - 19 / 2
Case 13: y = - x + 3
Case 14: y = - (5 / 4) · x - 5
How to derive the equation of a line
In this problem we have eight cases of line equations parallel or perpendicular to a line and that pass through a point. The equation of a line is an expression of the form:
y = m · x + b
Where:
x - Independent variable.y - Dependent variable.m - Slopeb - InterceptThere are the following relationships between two lines:
Two lines are parallel when they have the same slope.Two lines are perpendicular when the product of their slopes is equal to - 1.Now we proceed to determine the line equations:
Case 7
Slope
m = 7 / 4
m' = 7 / 4
Intercept
b = y - m · x
b = - 4 - (7 / 4) · (- 4)
b = - 4 + 7
b = 3
Equation of the line
y = (7 / 4) · x + 3
Case 8
Slope
m = 2
m' = 2
Intercept
b = 1 - 2 · 0
b = 1
Equation of the line
y = 2 · x + 1
Case 9
Slope
m = 3 / 2
m' = 3 / 2
Intercept
b = - 4 - (3 / 2) · (- 4)
b = - 4 + 6
b = 2
Equation of the line
y = (3 / 2) · x + 2
Case 10
Slope
m = - 5 / 6
m' = 6 / 5
Intercept
b = 5 - (6 / 5) · 5
b = 5 - 6
b = - 1
Equation of the line
y = (6 / 5) · x - 1
Case 11
Slope
m = 5 / 2
m' = - 2 / 5
Intercept
b = - 2 - (- 2 / 5) · 5
b = 0
Equation of the line
y = - (2 / 5) · x
Case 12
Slope
m = 2 / 5
m' = - 5 / 2
Intercept
b = - 2 + (- 5 / 2) · 3
b = - 2 - 15 / 2
b = - 4 / 2 - 15 / 2
b = - 19 / 2
Equation of the line
y = - (5 / 2) · x - 19 / 2
Case 13
Slope
m = 1
m' = - 1
Intercept
b = 5 - (- 1) · (- 2)
b = 3
Equation of the line
y = - x + 3
Case 14
Slope
m = 4 / 5
m' = - 5 / 4
Intercept
b = 0 - (- 5 / 4) · (- 4)
b = 0 - 5
b = - 5
Equation of the line
y = - (5 / 4) · x - 5
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A spinner has three sections which are coloured black, red and yellow. Lincoln spun the spinner 100 times in total.
The frequency of spins that landed on red was
35.
The ratio of the frequency of black to the frequency of red was 2: 7.
What is the estimated probability of the spinner landing on yellow?
Give your answer as a decimal.
Answers
Let's use the ratio of black to red frequency to find the frequency of black spins:
Black frequency : Red frequency = 2 : 7
Let x be the frequency of red spins. Then, the frequency of black spins is 2/7 of x, or:
Black frequency = (2/7)x
The total frequency of all three colors is 100, so we can write:
Black frequency + Red frequency + Yellow frequency = 100
Substituting the values we have:
(2/7)x + x + Yellow frequency = 100
Simplifying and solving for x, we get:
(9/7)x = 100 - Yellow frequency
x ≈ 45.22 - (7/9)Yellow frequency
We know that the total number of spins is 100, so we can write:
Black frequency + Red frequency + Yellow frequency = 100
(2/7)x + x + Yellow frequency = 100
Substituting the value we have for x, we get:
(2/7)(45.22 - (7/9)Yellow frequency) + 45.22 - (7/9)Yellow frequency + Yellow frequency = 100
Simplifying and solving for Yellow frequency, we get:
Yellow frequency ≈ 21.08
Therefore, the estimated probability of the spinner landing on yellow is 21.08/100, or approximately 0.2108 as a decimal.
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PLEASE HELP WILL GIVE BRAINLISET WORHT 30 POINTS !!
Answers
The mapping of the functions h(x) = |x|/2, f(x) = 2x + 8, and f(x) = x² - 5x + 2 is defined at;
1). -2, f(-2) = 1
2). 6, f(6) = 20
3). 2, f(2) = -4
What is a functionA function is a rule that defines a relationship between one variable. It is the mapping whose codomain is the set of real numbers
For x = -2;
h(-2) = |-2|/2
h(x) = 2/2 {absolute value of -2 is 2 units}
h(x) = 1
for x = 6;
f(6) = 2(6) + 8
f(6) = 12 + 8
f(6) = 20
for x = 2;
f(2) = (2)² - 5(2) + 2
f(2) = 4 - 10 + 2
f(2) = -4
Therefore, the mapping of the functions h(x) = |x|/2, f(x) = 2x + 8, and f(x) = x² - 5x + 2 is defined at;
1). -2, f(-2) = 1
2). 6, f(6) = 20
3). 2, f(2) = -4
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Please Help! 50 Points!!! This composite figure is created by placing a sector of a circle on a triangle. What is the area of this composite figure? Use 3.14 for . Round to the nearest hundredth. Show your work
Answers
The Japanese automobile company Lexus has established a reputation for quality control. Recents statistics indicate that a newly purchased Lexus ES 300 will have:
0 defects with probability 0.12
1 defect with probability 0.18
2 defects with probability 0.25
3 defects with probability 0.20
4 defects with probability 0.15
5 defects with probability 0.10
If you purchase a new Lexus ES 300, find:
a) the probability that it will have 2 or fewer defects.
b) the probability that it will have 4 or more defects.
c) the probability that it will have between 1 and 3 (all inclusive) defects.
d) the expected number of defects
Answers
a) The probability that it will have 2 or fewer defects is: 0.55 = 55%.
b) The probability it will have 4 or more defects is: 0.25 = 25%.
c) The probability it will have between 1 and 3 defects is: 0.63 = 63%.
d) The expected number of defects is: 2.38.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
For this problem, we are given the frequencies, hence we must identify the outcomes and then add their frequencies.
The probability that it will have 2 or fewer defects is obtained as follows:
P(X = 0) + P(X = 1) + P(X = 2) = 0.12 + 0.18 + 0.25 = 0.55.
The probability it will have 4 or more defects is obtained as follows:
P(X = 4) + P(X = 5) = 0.15 + 0.10 = 0.25.
The probability it will have between 1 and 3 defects is obtained as follows:
P(X = 1) + P(X = 2) + P(X = 3) = 0.18 + 0.25 + 0.20 = 0.63.
The expected value is given by the sum of each value multiplied by it's respective probability, hence:
E(X) = 0 x 0.12 + 1 x 0.18 + 2 x 0.25 + 3 x 0.20 + 4 x 0.15 + 5 x 0.1
E(X) = 2.38.
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need to Graph y≥13x−3.
Answers
The dοtted line is the line y=13x3, and the shaded area is abοve it.
what the slοpe οf the line?As is well knοwn, the equatiοn fοr a straight line is y = mx + c. Where 'c' is the y-axis intercept and 'm' is the slοpe οn the y-axis. The fοrmula fοr a hοrizοntal line is y = 3.
In οrder tο graph the inequality y≥13x−3, we can first plοt the line y=13x3
(which has a slοpe οf 13 and a y-intercept οf -3) as a dοtted line.
Since the inequality is y≥13x−3, we must shade the area abοve the line.
The dοtted line is the line y=13x3, and the shaded area is abοve it.
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3n + 2n + 7 + 3n = 7solve for n
Answers
Answer: 0
Step-by-step explanation:
1. Bring the Variables to one side and the constants to the other (3n + 2n + 3n = 7 - 7)
2. Solve ( 8n = 0, n = 0/8, n = 0)
HELP ASAP!
Your boss hands you a memo with a summary of the monthly data. The number of imports is shown as f(x), and the number of exports is shown as g(x). Use the data in the table below, representing both functions, to explain to your boss the solution to the system of equations and what that solution represents. Use complete sentences.
Month f(x) = No. of imports g(x) = No. of exports
January (1) 3 1
February (2) 4 3
March (3) 5 5
April (4) 6 7
Answers
The system of equations modeling the number of imports and the number of exports is given as follows:
f(x) = x + 3.g(x) = 2x + 1.The solution f(x) = g(x) represents the month at which the number of imports and the number of exports was the same.
How to model the system of equations?The system of equations is modeled by linear functions in slope-intercept form, as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the initial amount.Hence the equations are given as follows:
f(x) = x + 3 -> initial amount of 3 is increased by one each month.g(x) = 2x + 1 -> initial amount of 1 is increased by two each month.More can be learned about linear functions at https://brainly.com/question/24808124
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the question is in the picture attached
Answers
A line of best fit, also known as a regression line, is a straight line that best represents the relationship between two variables in a scatter plot. The association between the variables is strong.
How do you know strong association using line of best fit?To determine whether there is a strong association between the two variables, you need to examine the pattern of the data points in relation to the line of best fit.
If the data points are tightly clustered around the line of best fit, this indicates a strong association between the two variables. On the other hand, if the data points are more spread out and do not follow a clear pattern, this suggests a weak association.
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A circular hot spring has a diameter of 110 meers. Over time, the diameter of the spring decreases by 3 meters. By how many square meters does the area of he hot spring decrease?
Answers
The area οf the hοt spring decreases by apprοximately 540.24 square meters.
What is area οf a circle?The area οf a circle is fοund οut using the fοrmula. Area = πr²
Given that, r = d/2 = 110/2 = 55 meters
The οriginal area οf the hοt spring can be calculated as:
[tex]A = \pi r^2 = \pi(55)^2 = 9,525.69[/tex] square meters (rοunded tο twο decimal places)
After the diameter οf the hοt spring decreases by 3 meters, its new diameter is 110 - 3 = 107 meters. Therefοre, its new radius is:
r' = d'/2 = 107/2 = 53.5 meters
The new area οf the hοt spring can be calculated as:
[tex]A' = \pi r'² = \pi(53.5)² = 8,985.45[/tex] square meters (rοunded tο twο decimal places)
The decrease in the area οf the hοt spring is the difference between the οriginal area and the new area:
ΔA = A - A' = 9,525.69 - 8,985.45 = 540.24 square meters (rοunded tο twο decimal places)
Therefοre, the area οf the hοt spring decreases by apprοximately 540.24 square meters.
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I WILL GIVE BRAINLIEST AND 5 STARS
Triangle ABC is similar to triangle DEF.
What is the length of AC?
Answers
Answer:
a
Step-by-step explanation:
16÷4 is 4 and 12÷4 is 3. I matched up the angles.
After calc, the lenght of AC segment is 3 cm. Alternative A
Similarity of trianglesThe similarity of triangles property has a way of calculating how much an unknown segment of the triangle is worth through measures of available equivalent segments of the two triangles and matching angles.
Let's see calc[tex]\begin{array}{l}\raisebox{8pt}{$\sf \dfrac{AC}{BC}=\dfrac{DF}{EF}$}\\\raisebox{8pt}{$\sf \dfrac{AC}{4}=\dfrac{\red{\diagup\!\!\!\!\!\!12}^{\div4}}{\red{\diagup\!\!\!\!\!\!16}^{\div4}}$}\\\raisebox{8pt}{$\sf \dfrac{AC}{\red{\diagup\!\!\!\!4}}=\dfrac{3}{\red{\diagup\!\!\!\!4}}$}\\\bf\therefore AC=3\end{array}[/tex]
Found the length of segment AC, which is 3cm
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Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the curves x=√y, x=0, and y=4 about the x-axis.
Answers
The volume generated by rotating the region bounded by the curves [tex]$x = \sqrt{y}$[/tex], [tex]$x = 0$[/tex], and [tex]$y = 4$[/tex] about the x-axis using the method of cylindrical shells is [tex]$4\pi$[/tex] cubic units.
What is the formula for the volume of the cylinder?The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.
According to given information :To find the volume generated by rotating the region bounded by the curves [tex]$x = \sqrt{y}$[/tex], [tex]$x = 0$[/tex], and [tex]$y = 4$[/tex] about the x-axis using the method of cylindrical shells, we need to follow these steps:
Sketch the region and the axis of rotation. The region bounded by the curves [tex]$x = \sqrt{y}$[/tex], [tex]$x = 0$[/tex], and [tex]$y = 4$[/tex] is a quarter-circle with radius 2 centered at the origin. The axis of rotation is the x-axis.
Choose a vertical strip with width $\Delta x$ that runs parallel to the y-axis and intersects the region. The height of this strip is given by the equation $y = 4 - x^2$.
Imagine rotating this strip around the x-axis to form a cylindrical shell with thickness [tex]$\Delta x$[/tex], height [tex]$4 - x^2$[/tex], and radius [tex]$x$[/tex].
The volume of this cylindrical shell is given by the formula [tex]$V = 2\pi x(4-x^2)\Delta x$[/tex].
To find the total volume of the solid, we need to add up the volumes of all the cylindrical shells. This can be done by taking the limit as the width of the strips $\Delta x$ approaches zero and summing up the volumes of the resulting shells. This gives us the integral:
[tex]$V = \int_{0}^{2} 2\pi x(4-x^2) dx$[/tex]
We can simplify this integral by expanding the expression inside the parentheses, which gives us:
[tex]$V = \int_{0}^{2} 8\pi x - 2\pi x^3 dx$[/tex]
We can then integrate each term separately to get:
[tex]$V = [4\pi x^2 - \frac{1}{2}\pi x^4]_{0}^{2}$[/tex]
[tex]$V = (4\pi \cdot 2^2 - \frac{1}{2}\pi \cdot 2^4) - (4\pi \cdot 0^2 - \frac{1}{2}\pi \cdot 0^4)$[/tex]
[tex]$V = 8\pi - 4\pi = 4\pi$[/tex]
Therefore, the volume generated by rotating the region bounded by the curves [tex]$x = \sqrt{y}$[/tex], [tex]$x = 0$[/tex], and [tex]$y = 4$[/tex] about the x-axis using the method of cylindrical shells is [tex]$4\pi$[/tex] cubic units.
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Martin has a spinner that is divided into four sections labeled A, B, C, and D. He spins the spinner twice. PLEASE ANSWER BOTH RIGHT HELP EASY THANK UU
Question 1
Part A
Drag the letter pairs into the boxes to correctly complete the table and show the sample space of Martin's experiment.
Question 2
Part B
If Martin repeats this experiment 400 times, how many times should he expect to spin C and then A?
Enter the correct answer in the box.
Answers
the answers B
Two boats are headed to a lighthouse from
opposite directions. From point A, the crew
of boat A (red boat) measures the angle of
elevation to the top of the lighthouse as 45°.
On the other hand, from point B, the crew
of boat B (green boat) measures the angle
of elevation to the top of the lighthouse as
30°. The lighthouse is at a height of 300 ft
above the water.
A
45°
L
300 FT
30
a) How far is boat A from the
lighthouse? (the horizontal distance)
b) How far is boat B from the
lighthouse? (the horizontal distance)
c) And hence, find the total horizontal
distance between the two boats.
Answers
Hypotenuse equals opposite/tan(45°) = 300/1 = 300 feet. Boat A is therefore 300 feet horizontally away from the lighthouse.
what is distance ?The numerical measurement of distance is the separation between two objects or points. Typically, it is expressed in terms of metres, kilometres, miles, or feet. Distances can be calculated either along a simple path (the Euclidean distance) or along a more complicated one (such as a curved surface or a circuitous route). Distance is a crucial notion that is used to define the separation between things, the length of a route or path, and the displacement of an object through time in many disciplines, including physics, mathematics, geography, and engineering.
given
We may utilise trigonometry and create some equations based on the provided angles and distances to solve this problem.
a) We can use the tangent function to calculate the separation between boat A and the lighthouse:
opposite/hypotenuse = tan(45°)
where the hypotenuse is the distance between boat A and the lighthouse, the other side is the lighthouse's height (i.e., the horizontal distance we want to find). By calculating the hypotenuse, we obtain:
Hypotenuse equals opposite/tan(45°) = 300/1 = 300 feet. Boat A is therefore 300 feet horizontally away from the lighthouse.
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help with this example, I'm from Kazakhstan, sorry, help in any way you can
Answers
The inequalities are factorized to;
1. x > 5 and x > -1
x > 2 and x > -6
2. x < 2
x < -4 and x < 2
3. x > 7
x> 1 and x> 3
How to solve the inequalitiesFrom the information given, we have the inequalities;
(x - 5)(x + 1)> 0
expand the bracket, we get;
x² + x - 5x - 5> 0
x(x + 1) - 5(x + 1) > 0
x > 5 and x > -1
2. x-2/x + 3 < 0
cross multiply the values
x - 2< 0
make 'x' the subject
x < 2
3. x -7/x + 4 > 0
cross multiply the values
x - 7> 0
make 'x' the subject
x > 7
x² + 4x - 12 > 0
x² + 6x - 2x - 12> 0
Factorize
x(x + 6) - 2(x + 6)> 0
x > 2 and x > -6
x² - 2x - 8< 0
x² -2x + 4x - 8 < 0
Factorize
x(x - 2) + 4(x -2 )< 0
x < -4 and x < 2
x² - 4x + 3 > 0
x² - 3x - x + 3> 0
factorize
x(x - 3) - 1(x - 3)> 0
x> 1 and x> 3
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Four hundred fifty-nine
Answers
Answer:
459..
hope you understand