Answers
The hypotenuse (x) of the right triangle is 10 units
Finding the hypotenuse of the right triangleFrom the question, we have the following parameters that can be used in our computation:
The right triangle
The hypotenuse (x) of the right triangle can be calculated using the following sine equation
sin(30) = 5/x
Using the above as a guide, we have the following:
x = 5/sin(30)
Evaluate
x = 10
Hence, the hypotenuse of the right triangle is 10
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Related Questions
If the manager of a bottled water distributor wants to estimate, 95% confidence, the mean amount of water in a 1-gallon bottle to within ±0.006 gallons and also assumes that the standard deviation is 0.003 gallons, what sample size is needed?
If a light bulb manufacturing company wants to estimate, with 95% confidence, the mean life of compact fluorescent light bulbs to within ±250 hours and also assumes that the population standard deviation is 900 hours, how many compact fluorescent light bulbs need to be selected?
If the inspection division of a county weighs and measures department wants to estimate the mean amount of soft drink fill in 2-liter bottles to within ± 0.01 liter with 95% confidence and also assumes that the standard deviation is 0.08 liters, what sample size is needed?
An advertising executive wants to estimate the mean amount of time that consumers spend with digital media daily. From past studies, the standard deviation is estimated as 52 minutes. What sample size is needed if the executive wants to be 95% confident of being correct to within ±5 minutes?
Answers
n = (Z * σ / E)^2
where:
n = required sample size
Z = Z-value for the desired confidence level (for 95% confidence, Z ≈ 1.96)
σ = standard deviation
E = desired margin of error
Let's calculate the sample sizes for each scenario:
1. Bottled Water:
Z ≈ 1.96, σ = 0.003 gallons, E = 0.006 gallons
n = (1.96 * 0.003 / 0.006)^2 ≈ 384.16
Since we can't have a fraction of a sample, we round up to the nearest whole number. Therefore, a sample size of 385 bottles is needed.
2. Compact Fluorescent Light Bulbs:
Z ≈ 1.96, σ = 900 hours, E = 250 hours
n = (1.96 * 900 / 250)^2 ≈ 49.96
Again, rounding up to the nearest whole number, a sample size of 50 light bulbs is needed.
3. Soft Drink Fill:
Z ≈ 1.96, σ = 0.08 liters, E = 0.01 liters
n = (1.96 * 0.08 / 0.01)^2 ≈ 122.76
Rounding up, a sample size of 123 bottles is needed.
4. Digital Media Consumption:
Z ≈ 1.96, σ = 52 minutes, E = 5 minutes
n = (1.96 * 52 / 5)^2 ≈ 384.16
Rounding up, a sample size of 385 consumers is needed.
Please note that the sample sizes calculated here assume a simple random sampling method and certain assumptions about the population.
```
n = (Z^2 * σ^2) / E^2
```
where:
- Z is the z-score corresponding to the desired confidence level (in this case, 1.96 for 95% confidence)
- σ is the population standard deviation
- E is the desired margin of error
Substituting the given values, we get:
```
n = (1.96^2 * 52^2) / 5^2
n ≈ 385.07
```
Rounding up, we get a required sample size of 386.
Therefore, the advertising executive should sample at least 386 individuals to estimate the mean time that consumers spend with digital media with a margin of error of ±5 minutes and 95% confidence level.
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A
C
Intro
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4
3
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x
Suppose quadrilateral ABCD has been transformed by
Ty=x. What are the coordinates for the vertices of the
reflected quadrilateral A'B'C'D'?
A' =
B' =
C' =
D'=
Answers
The coordinates of the reflected quadrilateral A'B'C'D' are:
A' = (6, 4)
B' = (-3, 2)
C' = (-1, 23)
D' = (-x, 12)
To find the coordinates of the reflected quadrilateral A'B'C'D', we need to apply the transformation Ty = x to each vertex of the original quadrilateral ABCD. The transformation Ty = x reflects each point across the y-axis.
Given the coordinates of the original quadrilateral ABCD as:
A = (-6, 4)
B = (3, 2)
C = (+1, 23)
D = (x, 12)
Applying the transformation Ty = x to each vertex, we can determine the coordinates of the reflected quadrilateral A'B'C'D':
A' = (-(-6), 4) = (6, 4)
B' = (-3, 2)
C' = (-1, 23)
D' = (-x, 12)
The reflected quadrilateral A'B'C'D' thus has the following coordinates:
A' = (6, 4)
B' = (-3, 2)
C' = (-1, 23)
D' = (-x, 12)
Therefore, the x-coordinate for point D' will be represented as -x in the reflected quadrilateral.
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NO LINKS!! URGENT HELP PLEASE!!
29. A tree casts a shadow that is 12 feet long. If the tree is 20 feet tall, what is the angle of elevation of the sun? Draw a diagram to represent the situation. Round the answer to the nearest tenth.
30. In ΔABC, m∠A = 75°, m∠B = 50°, and c = 9. Draw ΔABC, then use the Law of Sines to find a. Round final answer to the nearest tenth.
Answers
Answer:
29. 59.06°
30. 10.6
Step-by-step explanation:
29.
By using the Tangent angle rule, we can find the angle of elevation,
We know that
Tan Angle = opposite/adjacent
Tan x=AB/BC
Tan x=20/12
Tan x=5/3
[tex]x=Tan^{- }(\frac{5}{3})[/tex]
x=59.06°
30.
The law of sine is a formula that can be used to find the lengths of the sides of a triangle, or to find the angles of a triangle, when two sides and the angle between them are known. The formula is:
a / sin(A) = b / sin(B) = c / sin(C)
Here taking
a / sin(A) = c / sin(C)
here A=75°, C=180-75-50=55° and c -9 and
we need to find a,
substituting value
a/Sin(75°)=9/Sin(55°)
a=9*Sin(75°)/Sin(55°)
a=10.61
Therefore, the value of a is 10.6
Answer:
Question 29: Angle of Elevation is -------> 59.0°Question 30: The length of side A in --------> △ABC is approximately 10.3Step-by-step explanation:Question 29: In this question, we can use the tangent function to solve the problem. We can set the Sun's elevation angle as theta (θ). Then we can get the equation:
tan (θ) = 20/12, and solve for θ
Solve the problem:We can draw a right triangle with the tree, the shadow, and the Sun.The tree's height is the opposite side, and the length of the shadow is the adjacent side.The angle of the sun's elevation is the angle between the ground and the line from the top of the tree to the sun.We can set the angle of elevation of the sun as theta (θ).We then get the equation tan (θ) = 20/12
We can solve for theta (θ) using the equationθ = arctan(5/3)
We can use a calculator to find that: Let the angle of elevation = θTan θ = opp/adj
Tan θ = 20/12
θ = Tan^-1 (20/12)
θ = 59.03624346 degrees
θ = 59.0 degrees
Draw the conclusion:Hence, the Angle of Elevation is -------> 59.0°
Question 30: △
m < C = 180 degrees - m<A - m<B
m<C = 180 degrees - 75 degrees - 50 degrees
Simplify:
m<C = 55 degrees
Apply the Law of Sines:
a/sin A = c/sin C
Substitute the values:
a/sin 75 degrees = 9/sin 55 degrees
Solve for A:
a = 9 * sin 75 degrees/sin 55 degrees
Calculate the value of A:a = 10.3
Draw a conclusion:Therefore, The length of side A in --------> △ABC is approximately 10.3
Hope this helps you!
Which equation best shows that 45 is a multiple of 15?
Choose 1 answer:
A45-15 = 30
B
45 x 3 = 15
48= 45 +3
45÷3= 15
Answers
The correct Option is D. 45÷3= 15 . The equation that best shows that 45 is a multiple of 15 is 45 ÷ 3 = 15.
A multiple is a product that results from multiplying two or more numbers.
A common multiple is a multiple that is common to two or more numbers.
A multiple of a number can be expressed as an integer multiple of the number.
If the result is a whole number, the first number is a multiple of the second.
An equation that shows 45 is a multiple of 15 is as follows: 45 ÷ 3 = 15.
A multiple is a number that can be divided by another number without leaving a remainder.
As a result, we divide 45 by 3 to find out whether 45 is a multiple of 15.
If the result is a whole number, 45 is a multiple of 15.
Here is the equation that shows this: 45 ÷ 3 = 15
Thus, we can conclude that the equation that best shows that 45 is a multiple of 15 is 45 ÷ 3 = 15.
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Function A is represented by the equation y= 6x-1.
Function B is a linear function that goes through the points shown in the
table.
x 13 4 6
y 0 10 15 25
Which statement correctly compares the rates of change of the two
functions?
A. The rate of change of function A is 6.
The rate of change of function B is 5.
B. The rate of change of function A is 6.
The rate of change of function B is 10.
C. The rate of change of function A is
-1.
The rate of change of function B is 5.
D. The rate of change of function A is
-1.
The rate of change of function B is 10.
Answers
The rates of change of the two functions that compare correctly is A. The rate of change of function A is 6, and the rate of change of function B is -10/9.
To compare the rates of change of the two functions, we can calculate the slope of each function. The slope represents the rate of change of a linear function.
For Function A, the equation is y = 6x - 1. The coefficient of x, which is 6, represents the slope. The rate of change of Function A is 6.
For Function B, we are given three points: (13, 0), (4, 10), and (6, 15). We can calculate the slope using the formula: slope = (change in y) / (change in x). Taking the first two points, we have: slope = (10 - 0) / (4 - 13) = 10 / (-9) = -10/9.
Comparing the rates of change, we have:
A. The rate of change of function A is 6.
The rate of change of function B is -10/9.
The correct option is A. The rate of change of function A is 6, and the rate of change of function B is -10/9.
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Find the area of the shaded portion if we know the outer circle has a diameter of 4 m and the inner circle has a diameter of 1.5 m.
A. 43.2 m2
B. 10.8 m2
C. 12.6 m2
D. 1.8 m2
Answers
Determine the range of the following graph:
Answers
Answer: [-2,7]
Step-by-step explanation: The range of a graph is just the range of minimum and maximum outputs of the y axis. The minimum y axis value is -2, while the maximum is 7. Putting your answer in brackets means that the endpoints (-2 and 7) are inclusive, which is the case since the dots are filled in. If the dots are hollow, the range does not include those endpoints and you would use parentheses instead.
which of the following is equivalent to x^2 -5x +6
Answers
Hello!
x² - 5x + 6
= (x² - 2x) + (-3x + 6)
= x(x - 2) - 3(x - 2)
= (x - 2)(x - 3)
Given f(x) = √6x and g(x)=
-9
=
Which value is in the domain of fᵒg?
-1
1
x - 6
Click on the correct answer.
6
7
Answers
The values in the domain of fᵒg are all real numbers.
Therefore, the correct answer is: x - 6.
To determine the domain of the composite function fᵒg, we need to find the values of x that are valid inputs for the composition.
The composite function fᵒg represents applying the function f to the output of the function g. In this case, g(x) is equal to -9.
So, we substitute -9 into the function f(x) = √6x:
f(g(x)) = f(-9) = √6(-9) = √(-54)
Since the square root of a negative number is not defined in the set of real numbers, the value √(-54) is undefined.
Therefore, -9 is not in the domain of fᵒg.
To find the values in the domain of fᵒg, we need to consider the values of x that make g(x) a valid input for f(x).
Since g(x) is a constant function equal to -9, it does not impose any restrictions on the domain of f(x).
The function f(x) = √6x is defined for all real numbers, as long as the expression inside the square root is non-negative.
So, any value of x would be in the domain of fᵒg.
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(5/8x+y^5)(y^5- 5/8x) write the expression as a polynomial
100 points for this
Answers
Answer:
y^10 + (5/8xy^5 - 5/8xy^6) - (25/64x^2)
Step-by-step explanation:
To simplify the given expression, we can expand it using the distributive property:
(5/8x + y^5)(y^5 - 5/8x)
Expanding the expression yields:
= (5/8x * y^5) + (5/8x * -5/8x) + (y^5 * y^5) + (y^5 * -5/8x)
= (5/8xy^5) - (25/64x^2) + y^10 - (5/8xy^6)
Combining like terms, we have:
= y^10 + (5/8xy^5 - 5/8xy^6) - (25/64x^2)
Hope this help! Have a good day!
(5/8x + y^5)(y^5 - 5/8x) = (5/8x) * (y^5) - (5/8x) * (5/8x) + (y^5) * (y^5) - (y^5) * (5/8x)
Simplifying further, we get:
(5/8)x*y^5 - (25/64)x^2 + y^10 - (5/8)x*y^5
Notice that the first and last terms cancel out, leaving us with:
y^10 - (25/64)x^2
Thus, the expanded expression can be simplified to the polynomial:
y^10 - (25/64)x^2
when 24/5and another number are added together the answer is 9. what is the number
Answers
The number we're looking for, which when added to 24/5 results in 9, is 21/5 or 4.2 in decimal form.
Let's solve the equation: 24/5 + x = 9, where x represents the unknown number we're trying to find.
To isolate x, we'll start by subtracting 24/5 from both sides of the equation:
x = 9 - 24/5
To add these two fractions, we need a common denominator. The denominator of 9 is 1, and the denominator of 24/5 is 5. To find a common denominator, we multiply 1 by 5:
x = (9 * 5)/5 - 24/5
This gives us:
x = 45/5 - 24/5
Now we can combine the fractions with the same denominator:
x = (45 - 24)/5
Simplifying the numerator:
x = 21/5
Therefore, the number we're looking for is 21/5. In decimal form, it can be written as 4.2.
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Please answer ASAP I will brainlist
Answers
Answer:
-x + 20(8) = 147 -x + 10(8) = 67
-x + 160 = 147 -x + 80 = 67
x = 13 x = 13
A. The system has exactly one solution. The solution is (13, 8).
B. All three colonies had a population of 8 thousand people in 2013.
John can ride his bide 4 miles in 30
minutes. At his current rate, what is the
distance, in miles, John can ride his
bike in 12 minutes?
Answers
The distance John can ride his bike in 12 minutes is approximately 1.6 miles.
To find out the distance John can ride his bike in 12 minutes, we can use the information given about his rate of riding.
We are told that John can ride his bike 4 miles in 30 minutes. This implies that his rate of riding is 4 miles per 30 minutes.
To calculate the distance John can ride in 12 minutes, we need to determine the proportion of time he is riding compared to the given rate.
We can set up a proportion to solve for the unknown distance:
(4 miles) / (30 minutes) = (x miles) / (12 minutes)
Cross-multiplying, we get:
30 minutes * x miles = 4 miles * 12 minutes
30x = 48
Now, we can solve for x by dividing both sides of the equation by 30:
x = 48 / 30
Simplifying the fraction, we have:
x = 8/5
So, John can ride his bike approximately 1.6 miles in 12 minutes, at his current rate.
Therefore, the distance John can ride his bike in 12 minutes is approximately 1.6 miles.
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HELP ME PLS I'LL MARK BRAINLIEST AND GIVE U 13 POINTS
Answers
Answer:
The answer is number 3
Y =-3/7X + 3
Step-by-step explanation:
Substitue with the value of the two points in all answers
The value of the left side must equal the value or the right side
For instance,
The two points are (0,3) & (7,0)
Substitue in the first answer with the point (0,3)
3 = - 3 (rejected)
Second answer
3 = 3 works for the point (0,3) then also Substitue with the other point (7,0)
0 = 6 (rejected)
The third answersub. With point (0,3).
3 = 3 it worksSub. With point (7,0)
0= - 3+3 0=0 it worksThen that's the right one
Solve b + 6 < 14.
Write your answer in set builder notation
Answers
b + 6 - 6 < 14 - 6
This simplifies to:
b < 8
Therefore, the solution to the inequality is the set of all numbers b that are less than 8.
In set builder notation, we can represent this solution as:
{ b | b < 8 }
What is the volume of the following triangular prism?
A. 380 m³
B. 398 m³
C. 351 m³
D. 327 m³
Answers
Answer:
C-351
Step-by-step explanation:
Find the length of an isosceles 90 degree triangle with the hypothenuse of 4 legs x
Answers
The length of the hypotenuse in the isosceles 90-degree triangle is √(2).
In an isosceles 90-degree triangle, two legs are equal in length, and the third side, known as the hypotenuse, is longer. Let's denote the length of the legs as x and the length of the hypotenuse as 4x.
According to the Pythagorean theorem, in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. In this case, we have:
[tex]x^2 + x^2 = (4x)^2.[/tex]
Simplifying the equation:
[tex]2x^2 = 16x^2.[/tex]
Dividing both sides of the equation by [tex]2x^2[/tex]:
[tex]1 = 8x^2.[/tex]
Dividing both sides of the equation by 8:
[tex]1/8 = x^2[/tex].
Taking the square root of both sides of the equation:
x = √(1/8).
Simplifying the square root:
x = √(1)/√(8),
x = 1/(√(2) * 2),
x = 1/(2√(2)).
Therefore, the length of each leg in the isosceles 90-degree triangle is 1/(2√(2)), and the length of the hypotenuse is 4 times the length of each leg, which is:
4 * (1/(2√(2))),
2/√(2).
To simplify the expression further, we can rationalize the denominator:
(2/√(2)) * (√(2)/√(2)),
2√(2)/2,
√(2).
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15. AB2+ BC2 = AC²
O A.
OB.
O C.
OD.
2 BDC = LADB
LBCA
DCB
2 BAC = LBAD
2 DBC = LBAC
multipl
Rese
Answers
Answer:
Step-by-step explanation:
The base of a triangle is 21 inches and the height is 12 inches. Which of these expressions correctly shows how to calculate the area of a triangle?
A. (21 × 12) × 2
B. (21 + 12) ÷ 2
C. (21 + 12) × 2
D. (21 × 12) ÷ 2
Answers
The correct expression to calculate the area of a triangle with a base of 21 inches and height of 12 inches is (21 × 12) ÷ 2.
Explanation:The subject of your question is Mathematics, specifically dealing with the topic of how to calculate the area of a triangle. The formula to calculate the area of a triangle is 1/2 multiplied by the base multiplied by the height. So, in your question where the base of the triangle is 21 inches and the height is 12 inches, the correct choice would be D. (21 × 12) ÷ 2 which applies the formula correctly.
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Question 11 of 26
Given the diagram below, what is cos(45)?
Triangle not drawn to scale
A. √2
O B.
√3
C. 3-√2
45⁰
OD.
Answers
Answer:
chemical reaction that releases heat energy to the surroundings is known as endothermis reaction
Bela's ice cream cone is 9 inches tall and 6 inches across. What volume of ice cream can fit within the cone? Show your work and draw a picture of the scenario. Type your answer as a number only. Round your answer to the nearest tenth. Volume = cubic inches
Answers
The volume of ice cream that can fit within the cone is 84.78 cubic inches.
To determine the volume of ice cream that can fit within the cone, we can consider the cone as a right circular cone with a height of 9 inches and a radius of 3 inches (half of the diameter, which is 6 inches).
The formula for the volume of a right circular cone is given by:
V = (1/3) * π * r^2 * h
where V represents the volume, π is a mathematical constant (approximately 3.14159), r is the radius, and h is the height.
Substituting the given values into the formula, we have:
V = (1/3) * 3.14159 * 3^2 * 9
= (1/3) * 3.14159 * 9 * 9
≈ 84.78 cubic inches
Therefore, the volume of ice cream that can fit within the cone is approximately 84.78 cubic inches.
To provide a visual representation, imagine a cone shape with a height of 9 inches and a diameter of 6 inches. The radius is half of the diameter, so it is 3 inches.
The ice cream fills the cone up to the top, creating a rounded triangular shape. The volume of the ice cream is equivalent to the volume of this cone shape.
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Note the complete question is
Bela's ice cream cone is 9 inches tall and 6 inches across. What volume of ice cream can fit within the cone? Show your work and draw a picture of the scenario.
Type your answer as a number only.
Round your answer to the nearest tenth. Volume = cubic inches
Juan, standing at one focus of a whispering gallery; is 20 ft from the nearest
wall. His friend is standing at the other focus, 80 ft away. How high is its elliptical
ceiling at the center?
Fill in the blank:
The elliptical ceiling is
ft high at the center.
Give your answer to the nearest whole ft (no decimal places).
Answers
The elliptical ceiling is approximately 30 ft high at the center.
To find the height of the elliptical ceiling at the center, we can use the properties of an ellipse.
In this case, the two foci of the ellipse represent the positions where Juan and his friend are standing.
The distance between the two foci is 80 ft, and Juan is 20 ft away from the nearest wall.
This means that the sum of the distances from any point on the ellipse to the two foci is constant and equal to 80 + 20 = 100 ft.
Since Juan is standing at one focus and the distance to the nearest wall is given, we can determine the distance from Juan to the farthest wall by subtracting the distance to the nearest wall from the sum of the distances.
Distance from Juan to the farthest wall = 100 ft - 20 ft = 80 ft.
The height of the elliptical ceiling at the center is equal to half of the distance between the nearest and farthest walls.
Height of elliptical ceiling = (80 ft - 20 ft) / 2 = 60 ft / 2 = 30 ft.
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if a=7 and b =2 what is 2ab
Answers
Answer: 28
Step-by-step explanation:
If [tex]a = 7[/tex] and [tex]b = 2[/tex], then [tex]2ab[/tex] can be worked out as follows:
[tex]\Large 2ab = 2 \times a \times b[/tex]
Substituting the values of [tex]a[/tex] and [tex]b[/tex], we get:
[tex]2 \times 7 \times 2 = 28[/tex]
Therefore, [tex]2ab[/tex] is equal to 28 when [tex]a = 7[/tex] and [tex]b = 2[/tex].
________________________________________________________
The answer is:
28Work/explanation:
To evaluate the expression [tex]\sf{2ab}[/tex], I begin by plugging in 7 for a and 2 for b:
[tex]\large\pmb{2(7)(2)}[/tex]
Simplify by multiplying.
[tex]\large\pmb{2*14}[/tex]
[tex]\large\pmb{28}[/tex]
Therefore, the answer is 28.What is the degree in leading coefficient of f(x) equals 3X -5
Answers
Answer:
1
Step-by-step explanation:
The degree of a polynomial is the exponent of the varieble x. So the exponent of x in that function is 1.
Please awnser asap I will brainlist
Answers
The result of the row operation on the matrix is given as follows:
[tex]\left[\begin{array}{cccc}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]
How to apply the row operation to the matrix?The matrix in this problem is defined as follows:
[tex]\left[\begin{array}{cccc}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]
The row operation is given as follows:
[tex]R_1 \rightarrow \frac{1}{2}R_1[/tex]
The first row of the matrix is given as follows:
[2 0 0 16]
The meaning of the operation is that every element of the first row of the matrix is divided by two.
Hence the resulting matrix is given as follows:
[tex]\left[\begin{array}{cccc}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]
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The diagram shows the curve y = √8x + 1 and the tangent at the point P(3, 5) on the curve. The tangent meets the y-axis at A. Find:
(i) The equation of the tangent at P.
(ii) The coordinates of A.
(iii) The equation of the normal at P.
Answers
The tangent and normal lines of the curve:
Case (i): y = (4 / 5) · x + 13 / 5
Case (ii): (x, y) = (0, 13 / 5)
Case (iii): y = - (5 / 4) · x + 35 / 4
How to determine the equations of the tangent and normal lines
In this problem we have the representation of a curve whose equations for tangent and normal lines must be found. Lines are expressions of the form:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variable.y - Dependent variable.Both tangent and normal lines are perpendicular, the relationship between the slopes of the two perpendicular lines is:
m · m' = - 1
Where:
m - Slope of the tangent line.m' - Slope of the normal line.The slope of the tangent line is found by evaluating the first derivative of the curve at intersection point.
Case (i) - First, determine the slope of the tangent line:
y = √(8 · x + 1)
y' = 4 / √(8 · x + 1)
y' = 4 / √25
y' = 4 / 5
Second, determine the intercept of the tangent line:
b = y - m · x
b = 5 - (4 / 5) · 3
b = 5 - 12 / 5
b = 13 / 5
Third, write the equation of the tangent line:
y = (4 / 5) · x + 13 / 5
Case (ii) - Find the coordinates of the intercept of the tangent line:
(x, y) = (0, 13 / 5)
Case (iii) - First, find the slope of the normal line:
m' = - 1 / (4 / 5)
m' = - 5 / 4
Second, determine the intercept of the normal line:
b = y - m' · x
b = 5 - (- 5 / 4) · 3
b = 5 + 15 / 4
b = 35 / 4
Third, write the equation of the normal line:
y = - (5 / 4) · x + 35 / 4
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Which measure gives the most accurate picture of the data's centre?
Answers
The mean is the measure that gives the most accurate picture of the data's center. It is an essential measure of central tendency that represents the arithmetic average of a dataset.
It is calculated by summing up all the values in the dataset and dividing the sum by the total number of values. The mean is suitable for datasets that have a normal or symmetrical distribution.
The mean is highly sensitive to outliers, which can significantly influence the average value. When outliers are present, it is appropriate to use other measures of central tendency such as the median or mode to obtain an accurate picture of the data's center.
The median is the middle value in a dataset arranged in ascending or descending order. It is not affected by outliers and is suitable for datasets with skewed distributions.
The mode is the most frequent value in the dataset. It is suitable for categorical data but can also be used for continuous data.
In summary, the mean is the most accurate measure of central tendency, but its accuracy can be improved by using the median or mode in datasets with outliers or skewed distributions.
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Select the correct answer. Which function represents the inverse function of the function f(x)=x^2 +5
Answers
Answer:
f^(-1)(x) = ±√(x - 5).
Step-by-step explanation:
Replace f(x) with y: y = x^2 + 5.
Swap the x and y variables: x = y^2 + 5.
Solve the equation for y. To do this, we'll rearrange the equation:
x - 5 = y^2.
Take the square root of both sides (considering both positive and negative square roots):
±√(x - 5) = y.
Swap y and x again to express the inverse function:
f^(-1)(x) = ±√(x - 5).
Angelica’s bouquet of a dozen roses contains 5 white roses. The rest of the roses are pink. What fraction of the bouquet is pink roses? There are 12 roses in a dozen.
StartFraction 5 Over 12 EndFraction
StartFraction 7 Over 12 EndFraction
StartFraction 5 Over 7 EndFraction
Answers
EXPLAINATION:
To find the fraction of the bouquet that is pink roses, we need to subtract the number of white roses from the total number of roses (12) and then express it as a fraction.
Number of pink roses = Total number of roses - Number of white roses
Number of pink roses = 12 - 5 = 7
Therefore, there are 7 pink roses in the bouquet.
The fraction of the bouquet that is pink roses is:
StartFraction 7 Over 12 EndFraction
So, the correct answer is StartFraction 7 Over 12 EndFraction.
Which ordered pair makes both inequalities true?
y < –x + 1
y > x
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 1) and (1, 0). Everything below and to the left of the line is shaded. The second dashed line has a positive slope and goes through (negative 1, negative 1) and (1, 1). Everything above and to the left of the line is shaded.
(–3, 5)
(–2, 2)
(–1, –3)
(0, –1)
Answers
The ordered pair that is a solution for both inequalities is (-2, 2).
Which ordered pair makes both inequalities true?Here we have the system of inequalities:
y < -x + 1
y > x
And we want to see which one of the given points makes both of them true.
To find that, just replace the values in both inequalities and see if both become true or not.
For example, for the first point:
(-3, 5)
We will get:
5 < -(-3) + 1 = 4
5 > -3
The first one is false, and the second one is true.
The correct option is the second point:
2 < -(-2) +1 = 3
2 > -2
Both are true.
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