Round 7.19 to the nearest tenth
Answer:
7.2
Step-by-step explanation:
The 1 looks at the number to the right of it. If the number to the right is 5 or more, the 1 moves up to a 2. Hope this helps!
Find the range of the data below.(Help asappp please)
The sum of the measures of the angles of a triangle is 180. The sum of the measures of
the second and third angles is five times the measure of the first angle. The third angle
is 26 more than the second. Let x, y, and z represent the measures of the first, second,
and third angles, respectively. Find the measures of the three angles.
The measures οf the three angIes are x = 51.43 degrees, y = 92.85 degrees, and z = 118.85 degrees.
What is Iinear equatiοn?A Iinear equatiοn is a mathematicaI equatiοn that describes a straight Iine in a twο-dimensiοnaI pIane.
We can use the infοrmatiοn given in the prοbIem tο fοrm a system οf three equatiοns with three variabIes. Let x, y, and z represent the measures οf the first, secοnd, and third angIes, respectiveIy.
Frοm the first piece οf infοrmatiοn, we knοw that: x + y + z = 180
Frοm the secοnd piece οf infοrmatiοn, we knοw that: y + z = 5x
Frοm the third piece οf infοrmatiοn, we knοw that: z = y + 26
We can substitute the third equatiοn intο the secοnd equatiοn tο eIiminate z:
y + (y + 26) = 5x
2y + 26 = 5x
2y = 5x - 26
y = (5x - 26)/2
We can substitute this expressiοn fοr y intο the first equatiοn tο eIiminate y and z:
x + (5x - 26)/2 + (5x - 26)/2 + 26 = 180
2x + 5x - 26 + 26 = 360
7x = 360
x = 51.43
We can substitute this vaIue οf x back intο the expressiοn fοr y tο find y:
y = (5x - 26)/2
y = (5(51.43) - 26)/2
y = 92.85
FinaIIy, we can use the equatiοn z = y + 26 tο find z:
z = y + 26
z = 92.85 + 26
z = 118.85
Therefοre, the measures οf the three angIes are x = 51.43 degrees, y = 92.85 degrees, and z = 118.85 degrees.
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-5 + x-2 = 3x + 10 - x Which of the following statements correctly describe the solution(s) of the equation above? Select all that apply. • The equation has only one solution. • The equation has no solutions. F The equation has infinitely many solutions. ) The equation's only solution is x = - 17. • The equation is solved by all numbers less than 17.
The equation's only solution is x = -17.
Simplifying the left-hand side of the equation:
-5 + x - 2 = -7 + x
Simplifying the right-hand side of the equation:
3x + 10 - x = 2x + 10
Substituting into the original equation, we get:
-7 + x = 2x + 10
Subtracting x from both sides, we get:
-7 = x + 10
Subtracting 10 from both sides, we get:
-17 = x
So the only solution to the equation is x = -17. Therefore, the correct statement about the solution(s) of the equation is:
• The equation's only solution is x = -17.
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a package contains 6 blue, 4 red, and 5 yellow gumballs. You randomly choose a gumball from the bag, and you do not replace it. Then you randomly choose another gumball. What is the propobility of both gumballs not being red?
The probability of both gumballs not being red is 11/21.
What is the probability?
The probability of the first gumball not being red is:
P(first gumball not red) = P(blue) + P(yellow)
= (6/15) + (5/15)
= 11/15
After removing the first gumball, there are 14 gumballs left in the bag. The probability of the second gumball not being red depends on what color the first gumball was.
Case 1: The first gumball was blue
If the first gumball was blue, there are 5 blue, 4 red, and 5 yellow gumballs left in the bag. The probability of the second gumball not being red is:
P(second gumball not red | first gumball was blue) = P(blue or yellow)
= P(blue) + P(yellow)
= (5/14) + (5/14)
= 5/7
Case 2: The first gumball was yellow
If the first gumball was yellow, there are 6 blue, 4 red, and 4 yellow gumballs left in the bag. The probability of the second gumball not being red is:
P(second gumball not red | first gumball was yellow) = P(blue or yellow)
= P(blue) + P(yellow)
= (6/14) + (4/14)
= 5/7
The probability of both gumballs not being red is the product of the probabilities of each event:
P(both gumballs not red) = P(first gumball not red) * P(second gumball not red | first gumball not red)
P(both gumballs not red) = (11/15) * (5/7)
P(both gumballs not red) = 55/105
P(both gumballs not red) = 11/21
Therefore, the probability of both gumballs not being red is 11/21.
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During a workout Felicia swims 15 laps in a pool where each lap is 50 yards. Then she walks 30 feet to an indoor track where she runs 5 laps around an indoor track that is 600 feet long. How many miles does she swim, walk, and run?
Felicia swims 0.43 miles, walks 0.0057 miles and runs 0.57 miles. The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
The four fundamental operations, often known as "arithmetic operations," are said to adequately describe all real numbers. The mathematical operations following division, multiplication, addition, and subtraction are quotient, product, sum, and difference.
We are given that she swims 15 laps in a pool where each lap is 50 yards.
By using arithmetic operations, we get
Total yards = 15 * 50 = 750 yard
We know that 1 mile = 1760 yards
So,
750 yards = 0.43 miles
She walks 30 feet.
We know that 1 mile = 5280 feet
So,
30 feet = 0.0057 miles
She runs 5 laps around an indoor track that is 600 feet long.
So, total feet she ran = 5 * 600 = 3000 feet
We know that 1 mile = 5280 feet
So,
3000 feet = 0.57 miles
Hence, she swims 0.43 miles, walks 0.0057 miles and runs 0.57 miles.
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100 POINTS PLEASEE HELPPP BRAINLIEST
Answer:
C
.........................
Answer: the answer is A
Step-by-step explanation: The process of nuclear fusion is the union of two light atomic nuclei into one heavier one while releasing enormous quantities of energy.
A sphere has a surface area of 60 square feet. Which choice is the best approximation of its radius? Use 3.14 to approximate pi.\
Answer:
Step-by-step explanation:
The surface area of a sphere is given by the formula:
S = 4πr^2
where S is the surface area and r is the radius of the sphere.
We are given that the surface area of the sphere is 60 square feet. Using the formula above, we can solve for the radius:
60 = 4πr^2
Dividing both sides by 4π, we get:
15/π = r^2
Taking the square root of both sides, we get:
r = sqrt(15/π)
Using 3.14 as an approximation for π, we can evaluate this expression:
r ≈ sqrt(15/3.14)
r ≈ 2.20
Therefore, the best approximation for the radius of the sphere is 2.20 feet.
Answer:
Radius is 2.18
Step-by-step explanation:
;)
A turtle and a snail are 300 feet apart when they start moving toward
each other. The turtle walks 5 feet per minute, and the snail crawls 1
foot per minute.
Answer:
Step-by-step explanation:
It will take 50 minutes for the turtle and snail to meet.
because they are all moving at feet per minute we can create a formula
total feet = (turtle feet per minute) + (snail feet per minute)
300 = 5m +1m
combine like terms
300 = 6m
divide both sides by 6
50=m
Answer:
See below.
Step-by-step explanation:
Let's denote the distance the turtle walks by x. Then the distance the snail crawls would be 300 − x.
We can now set up an equation to represent the situation. Since distance = rate × time, we have
x/5 = (300 - x)/1
Solving for x, we get
x = 250
So the turtle walks 250 feet before meeting the snail, and the snail crawls the remaining 50 feet.
To find the time it takes for them to meet, we can use either of the two distances and its corresponding rate:
time = distance/rate
For example, using the turtle's distance
time = 250/5 = 50 minutes
Therefore, it takes 50 minutes for the turtle and the snail to meet.
A group of 125 students went on a field trip to a museum. Mr. Shan asked a random sample of 50 students which exhibit was their favorite. Ten students favored the insect exhibit, 15 students favored the space exhibit, and 25 students favored the dinosaur exhibit. Based on the survey results, which inferences about the entire group of 125 students are true? Select TWO correct answers. 1.One-fifth of students favored the insect exhibit. 2.The dinosaur exhibit is most favored. 3.The insect exhibit is favored more than the space exhibit. 4.Only 24% of students favored the space exhibit. 5.Fifty students favored the dinosaur exhibit.
Answer:1 and 2
Step-by-step explanation:
so, they asked 50 students and then that was later broke down to smaller groups.
10,15,25
so, for every 10 students will be one. 1 vote= 10 students.
also, the dinosaur had the greatest number of votes so that explains answer 2.
determine what type of transformation is represented
The type of transformation represented in the figure is the translation transformation i.e. (c) none of these
Identifying the type of transformation representedGiven the triangles ABC and A'B'C'
The transformation between the triangles is translation
The translation transformation is a type of transformation that moves an object without changing its size, shape, or orientation.
This transformation involves sliding an object in a particular direction by a certain distance, either horizontally or vertically.
In this case, the direction is horizontally and vertically
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Question 8 Suppose the graph of rectangle ABCD shows the scale drawing for a safety fence that Kenny is setting up around a construction area. Each unit on the graph represents 25 feet. After studying the scale drawing, Kenny decides to build a fence that encloses a larger area. If Kenny dilates rectangle ABCD by a scale factor of 2.5, and fencing costs $5.25 per foot, how much will he spend on fencing?
Kenny will spend $4,593.75 on fencing the dilated rectangle.
What is rectangle ?
A rectangle is a quadrilateral with four right angles (90-degree angles) and opposite sides of equal length. It is a type of parallelogram in which both pairs of opposite sides are parallel and congruent (of equal length). The opposite sides of a rectangle are also perpendicular (form a right angle) to each other. The area of a rectangle is equal to the product of its length and width, while its perimeter is equal to the sum of the lengths of all its sides. Rectangles are commonly used in geometry, architecture, engineering, and many other fields.
According to the question:
Since each unit on the graph represents 25 feet, the dimensions of the original rectangle ABCD are:
AB = 4 units, which represents 4 x 25 = 100 feet
BC = 3 units, which represents 3 x 25 = 75 feet
Therefore, the perimeter of ABCD is 2(AB + BC) = 2(100 + 75) = 350 feet.
When dilating by a scale factor of 2.5, each dimension of ABCD will be multiplied by 2.5. Therefore, the dimensions of the dilated rectangle A'B'C'D' are:
A'B' = AB x 2.5 = 100 x 2.5 = 250 feet
B'C' = BC x 2.5 = 75 x 2.5 = 187.5 feet
The perimeter of A'B'C'D' is 2(A'B' + B'C') = 2(250 + 187.5) = 875 feet.
Therefore, Kenny will need to fence a perimeter of 875 feet. At a cost of $5.25 per foot, the total cost of fencing will be:
875 feet x $5.25/foot = $4,593.75
Therefore, Kenny will spend $4,593.75 on fencing the dilated rectangle.
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Lara grows apples in her orchard and sells them at the weekly farmer's market. Each week, she sells the apples for a different price and records the number of apples sold. The scatter plict below
shows the price of one apple and the number of apples that were sold. A line of best fit for these data points, the equation y=-z+32, is also shown on the plot
Apples Number of Apples Sold
Identify the nonlinear equation.
Responses
A y = 3x - 7y = 3 x - 7
B y = xy = x
C y = 3y = 3
D y = x2
PLS HELP
Answer:y=0.5
Step-by-step explanation:Comme tu peux le voir, y est égal à au tiers de 3, se qui équivaut à 1. Si 2x=y, cela signifie que x=y/2, soit 0,5
y =
Volume of Oxygen (liters)
+
10
M(0, 1)
Point M is a minimum value of the function. What is the equation of a cosine function, using radians, that gives the
volume as a function of time?
Enter your numbers in the boxes to complete the equation.
ANSWER FAST PLEASEEE
Y = 5 cos(0.3185x) + 10 is the volume of oxygen as a function of time can be modeled by this cosine function.
What is cosine function ?
The cosine function is a mathematical function that relates the ratio of the sides of a right triangle. In a right triangle, the cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. In trigonometry, the cosine function is defined as the ratio of the adjacent side to the hypotenuse in a right triangle. The cosine function is periodic, meaning it repeats itself at regular intervals, and has a range of values between -1 and 1. It is commonly used in mathematics, physics, and engineering to model periodic phenomena such as sound waves, electromagnetic waves, and oscillations.
According to the question:
To find the equation of the cosine function, we need to identify the amplitude, period, phase shift, and vertical shift of the function based on the given information.
Since point M is the minimum value of the function, the vertical shift is 10. This means that the equation of the function is of the form:
Y = A cos(Bx - C) + D
where D = 10.
To find the amplitude, we need to find the distance between the maximum and minimum values of the function. Since the graph of a cosine function oscillates between its maximum and minimum values, the amplitude is half the distance between these values.
From the graph, we can see that the maximum value of the function is 20, so the distance between the maximum and minimum values is:
20 - M = 20 - 10 = 10
Therefore, the amplitude is:
A = 10/2 = 5
To find the period, we need to find the distance between two consecutive peaks or troughs of the function. From the graph, we can see that the distance between two consecutive peaks is approximately 6.28 units. This means that the period is:
P = 6.28
To find the phase shift, we need to find the horizontal shift of the function from its standard form. Since the minimum value of the function occurs at x = 0, the phase shift is:
C =
Therefore, the equation of the cosine function is:
Y = 5 cos((2π/P)x - C) + D
Y = 5 cos((2π/6.28)x) + 10
Simplifying,
Y = 5 cos(0.3185x) + 10
So, the volume of oxygen as a function of time can be modeled by this cosine function.
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Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answer:
1x
Step-by-step explanation:
Firstly lets expand the brackets for the equation
(x - 7 )2 = 36
If we multiply what's in the brackets by 2 we get this:
2x - 14 = 36
Add 14 to both sides:
2x = 50
Divide both sides by 2:
x = 25
Answer = 1x (Only possible solution
Answer:
The two solutions to the given equation are x = 13 and x = 1.
Step-by-step explanation:
To solve the given equation (x - 7)² = 36, begin by square rooting both sides:
[tex]\implies \sqrt{(x-7)^2}=\sqrt{36}[/tex]
[tex]\implies x-7=\pm6[/tex]
Now add 7 to both sides of the equation:
[tex]\implies x-7+7=\pm6+7[/tex]
[tex]\implies x=7\pm6[/tex]
Therefore, the two solutions are:
[tex]\implies x=7+6=13[/tex]
[tex]\implies x=7-6=1[/tex]
Write 4/8 in lowest terms
Answer:
4/8 in lowest terms is 1/2.
Step-by-step explanation:
Answer: 1/2
4/8 is equivalent to 1/2
Which of the following is equivalent to 0=2x^(2)-16x-18 when completing the square?
Answer:
X=-1 or 9
Step-by-step explanation:
using the quadratic formula:
[tex]X=\frac{-b+-\sqrt{b^{2} -4ac} }{2a}[/tex]
X=-1
X=9
please help !!!!
Consider the table, equation,
and graph. Which of them represents a proportional relationship?
The graph represents a proportional relationship.
What is proportional relationship?
A proportional relationship is a relationship between two variables where their ratio remains constant. This means that as one variable increases or decreases, the other variable changes proportionally in order to maintain a constant ratio. In other words, the two variables are directly proportional to each other. This relationship can be represented by a straight line passing through the origin on a graph. Proportional relationships are commonly used in various fields such as physics, finance, and engineering to analyze and predict outcomes.
Explaining the table, equation and graph to know which represents a proportional relationship :
The relationship between the values in the given table is not proportional. If it was a proportional relationship, then the ratio of y to x would be constant. However, in this case, the ratios are not equal. For example, the ratio of y to x for the first row is 3.6/3 = 1.2, but the ratio of y to x for the second row is 6/5 = 1.2, and the ratio of y to x for the third row is 7.2/8 = 0.9. Therefore, the ratios are not equal and the relationship is not proportional.
The equation y=2x+5 does not represent a proportional relationship. In a proportional relationship, there is a constant ratio between the two variables. However, in this equation, the ratio between y and x is not constant, but rather it increases as x increases.
The graph represents a proportional relationship as the ratio between y and x is constant.
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Select all the true statements, if each interior angle measure of a regular polygon is (2x
+ 20)°.
All the true statements, if each interior angle measure of a regular polygon is (2x + 20)° include the following:
A. If x = 60, then the regular polygon is a nonagon.
C. If x = 77, then the regular polygon is a 60-gon.
D. If x = 65, then the regular polygon is a dodecagon.
D. If x = 44, then the regular polygon is a pentagon.
How to calculate the number of sides?In Geometry, the measure of each interior angle of a regular polygon can be calculated by using this mathematical expression:
Interior angle = [180 × (n - 2)]/n
Where:
n represents the number of sides of a regular polygon.
When x = 60, the number of sides of the regular polygon is given by:
(2x + 20)° = [180 × (n - 2)]/n
(2(60) + 20)° = [180 × (n - 2)]/n
140 = [180 × (n - 2)]/n
140n = 180n - 360
360 = 40n
n = 9 sides.
When x = 77, the number of sides of the regular polygon is given by:
(2x + 20)° = [180 × (n - 2)]/n
(2(77) + 20)° = [180 × (n - 2)]/n
174 = [180 × (n - 2)]/n
174n = 180n - 360
360 = 6n
n = 60 sides.
When x = 65, the number of sides of the regular polygon is given by:
(2x + 20)° = [180 × (n - 2)]/n
(2(65) + 20)° = [180 × (n - 2)]/n
150 = [180 × (n - 2)]/n
150n = 180n - 360
360 = 30n
n = 12 sides.
When x = 41, the number of sides of the regular polygon is given by:
(2x + 20)° = [180 × (n - 2)]/n
(2(41) + 20)° = [180 × (n - 2)]/n
102 = [180 × (n - 2)]/n
102n = 180n - 360
360 = 78n
n = 4.6 sides.
When x = 44, the number of sides of the regular polygon is given by:
(2x + 20)° = [180 × (n - 2)]/n
(2(44) + 20)° = [180 × (n - 2)]/n
108 = [180 × (n - 2)]/n
108n = 180n - 360
360 = 72n
n = 5 sides.
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Rose has made this scale drawing of her house. If her house actually 56 feet wide, then scale of her drawing is
If her hοuse actually 56 feet wide, then scale οf her drawing is scale = 56 feet / (drawing width)
What is the slοpe?The slοpe is a mathematical cοncept that refers tο the steepness οf a line. It is cοmmοnly denοted by the letter "m" and can be calculated using the fοrmula:
slοpe (m) = (change in y) / (change in x)
Withοut having the actual measurements οf the drawing, we cannοt determine the scale.
Tο find the scale οf a drawing, yοu need tο knοw the actual measurements οf the οbject being drawn as well as the cοrrespοnding measurements in the drawing. Fοr example, if yοu knοw that the actual width οf Rοse's hοuse is 56 feet and the width οf the hοuse in the drawing is 8 inches, yοu can determine the scale by using the fοllοwing fοrmula:
scale = actual width/drawing width
Using this fοrmula with the given infοrmatiοn, we get:
scale = 56 feet / (drawing width)
Therefοre, we dο nοt have the drawing width, we cannοt calculate the scale.
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Can anyone show how to solve these two questions. Thank you!
according the given question the exact value of given expression is [tex]$\cos\frac{x}{2} = -\sqrt{\frac{1}{2(1 - \left(-\frac{160}{81}\right)^2)}} = -\sqrt{\frac{81^2}{2(81^2 - 160^2)}} = \boxed{-\frac{81\sqrt{239}}{319}}$[/tex]
First, we need to find [tex]$\sin x$[/tex] using the identity[tex]$\cos^2x + \sin^2x = 1$:$\sin^2x = 1 - \cos^2x = 1 - \left(-\frac{4}{5}\right)^2 = \frac{9}{25}$[/tex]
Since [tex]$\frac{\pi}{2} < x < \pi$[/tex], we know that [tex]$\frac{\pi}{4} < \frac{x}{2} < \frac{\pi}{2}$[/tex]. Therefore, we can use the
identity [tex]$\tan\frac{x}{2} = \frac{\sin x}{1 + \cos x}$[/tex]:
[tex]$\tan\frac{x}{2} = \frac{\sqrt{\frac{9}{25}}}{1 - \frac{4}{5}} = \frac{\frac{3}{5}}{\frac{1}{5}} = \boxed{3}$[/tex]
[tex]If $\tan x = \frac{40}{9}$ and $\pi < x < \frac{3\pi}{2}$, find $\cos\frac{x}{2}$.[/tex]
First, we need to find [tex]$\sin x$[/tex] using the identity [tex]$\tan^2x + 1 = \sec^2x$[/tex]:
[tex]$\sin x = \frac{\tan x}{\sec x} = \frac{\frac{40}{9}}{-\frac{9}{40}} = -\frac{160}{81}$[/tex]
[tex]Since $\pi < x < \frac{3\pi}{2}$, we know that $\frac{\pi}{2} < \frac{x}{2} < \frac{3\pi}{4}$[/tex]. Therefore, we can use the identity [tex]$\cos\frac{x}{2} = \pm\sqrt{\frac{1 + \cos x}{2}}$[/tex]:
[tex]$\cos\frac{x}{2} = -\sqrt{\frac{1 + \cos x}{2}} = -\sqrt{\frac{1 + \frac{\cos^2x}{\sin^2x}}{2}} = -\sqrt{\frac{\sin^2x + \cos^2x}{2\sin^2x}} = -\sqrt{\frac{1}{2(1 - \sin^2x)}}$[/tex]
Plugging in [tex]$\sin x = -\frac{160}{81}$[/tex] , we get:
[tex]$\cos\frac{x}{2} = -\sqrt{\frac{1}{2(1 - \left(-\frac{160}{81}\right)^2)}} = -\sqrt{\frac{81^2}{2(81^2 - 160^2)}} = \boxed{-\frac{81\sqrt{239}}{319}}$[/tex]
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im confused can anyone help me on this question?
Answer:
7
Step-by-step explanation:
if you add 7 4's you get 28.
4+4=8+4=12+4=16+4=20+4=24+4=28
now if you count all the single 4's then you will get 7
Your sister has R375 000 and wants to retire. She expects to live for another 25 years, and she also expects to earn 8% on her invested funds. How much could she withdraw at the beginning of each of the next 25 years, and end up with zero in the account?
Answer:
Step-by-step explanation:
Your sister can use the formula for calculating the present value of an annuity to determine how much she can withdraw each year.
The formula for the present value of an annuity is:
PV = Payment x (1 - (1 + r)^-n) / r
Where:
- PV is the present value of the annuity
- Payment is the amount of each withdrawal
- r is the annual interest rate
- n is the number of periods (in this case, 25 years)
We can rearrange this formula to solve for Payment:
Payment = PV x r / (1 - (1 + r)^-n)
We know that your sister has R375 000 to start with, and she wants to end up with zero in 25 years. So, her present value (PV) is R375 000, and we can assume her future value (FV) is zero.
Using the future value formula, we can calculate the interest rate she needs to earn in order to end up with zero in 25 years:
FV = PV x (1 + r)^n
0 = 375000 x (1 + r)^25
(1 + r)^25 = 1
1 + r = (1)^1/25
r = 0
This means that your sister needs to withdraw all of her money over the 25 years in order to end up with zero at the end.
Her withdrawal each year would be:
Payment = PV x r / (1 - (1 + r)^-n)
Payment = 375000 x 0.08 / (1 - (1 + 0.08)^-25)
Payment = R34,028.82 per year
Your sister can withdraw R34,028.82 at the beginning of each year for the next 25 years, and she will end up with zero at the end, assuming she earns an 8% return on her invested funds.
If
sin
�
=
4
29
sinθ=
29
4
and angle
�
θ is in Quadrant I, what is the exact value of
tan
2
�
tan2θ in simplest radical form?
The exact value of tan(2θ) in simplest radical form is 58√(793) / 48 which has been calculated through Pythagorean theorem.
What is Pythagorean?The Pythagorean Theorem can be used to find the correct angled triangle's missing length. The triangle contains three sides: the hypotenuse, this same opposite, which will always be the longest, and the adjacent side, which really doesn't touch the hypotenuse. The Pythagorean equation is: a² + b² = c².
We know that sin(θ) = 29/4 and that θ is in Quadrant I, which means that all three trigonometric functions (sine, cosine, and tangent) are positive in this quadrant.
Using the identity:
tan(2θ) = 2tan(θ) / (1 - tan²(θ))
We can find the value of tan(2θ) by first finding tan(θ) and then using it to calculate tan(2θ).
To find tan(θ), we can use the Pythagorean identity:
sin²(θ) + cos²(θ) = 1
cos²(θ) = 1 - sin²(θ)
cos(θ) = ± √(1 - sin²(θ))
Since θ is in Quadrant I, we know that cos(θ) is positive, so we take the positive square root:
cos(θ) = √(1 - (29/4)²) = √(793) / 4
Now we can find tan(θ) as:
tan(θ) = sin(θ) / cos(θ) = (29/4) / (√(793) / 4) = 29 / √(793)
Substituting this into the formula for tan(2θ), we get:
tan(2θ) = 2tan(θ) / (1 - tan²(θ))
tan(2θ) = 2(29 / √(793)) / (1 - (29 / √(793))²)
tan(2θ) = 2(29 / √(793)) / (1 - 841/793)
tan(2θ) = 58√(793) / 48
Therefore, the exact value of tan(2θ) in simplest radical form is 58√(793) / 48.
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can someone help me please.
step by step please
here is the picture
For the given function f(x) = ⁿ√p(x), The Domain depends on the value of n and The Domain is all real numbers if n is ODD.
What is the definition of a function?
In mathematics, a function is a relation between a set of inputs (also known as the domain) and a set of possible outputs (also known as the range) with the property that each input is associated with exactly one output.
In other words, a function takes an input value, performs a specific operation or set of operations on it, and produces an output value. It can be represented by a rule, formula, or graph that relates each input to its corresponding output.
Now,
The domain of the function f(x) = ⁿ√p(x) depends on the value of n.
If n is odd, then the function is defined for all real numbers, and the domain is all real numbers.
If n is even, then the function is defined only for non-negative real numbers, and the domain is all non-negative real numbers.
Therefore, the statement "The Domain is all real numbers" is not always true for the function f(x) = ⁿ√p(x). The correct statements are:
The Domain depends on the value of nThe Domain is all real numbers if n is ODDTo know more about functions visit the link
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can you solve this question?
y'=?
The differentiation of the variable y is equal to [tex]\frac{1}{2} ( \frac{y^{2}-4x^{3}-4xy^{2} }{2x^{2} y+2y^{3}-xy } )[/tex] for the differential equation.
Given equation: [tex](x^{2} +y^{2} )^{2} = 2xy^{2}[/tex]
differentiate with respect to x
2 [tex](x^{2} + y^{2})[/tex] [ [tex]2x+2y.\frac{dy}{dx}[/tex] ] =[ (1).[tex]y^{2}[/tex] + [tex]x (2y) + \frac{dy}{dx}[/tex] ]
4 [tex](x^{2} + y^{2})[/tex] [ [tex]x+y \frac{dy}{dx}[/tex] ] = [tex]y^{2}[/tex] + [tex]2xy \frac{dy}{dx}[/tex]
4( [tex]x^{3} + x^{2} y \frac{dy}{dx} + xy^{2} + y^{3} \frac{dy}{dx}[/tex] ) = [tex]y^{2}[/tex] + [tex]2xy \frac{dy}{dx}[/tex]
[tex]4x^{3} +4 x^{2} y \frac{dy}{dx} +4 xy^{2} +4 y^{3} \frac{dy}{dx}[/tex] = [tex]y^{2}[/tex] + [tex]2xy \frac{dy}{dx}[/tex]
[tex]4x^{2}y \frac{dy}{dx}[/tex] + [tex]4y^{3}[/tex] [tex]\frac{dy}{dx}[/tex] - [tex]2xy\frac{dy}{dx}[/tex] = [tex]y^{2} - 4x^{3} - 4xy^{2}[/tex]
[tex](4x^{2}y + 4y^{3} - 2xy )[/tex] [tex]\frac{dy}{dx}[/tex] = [tex]y^{2} - 4x^{3} - 4xy^{2}[/tex]
[tex]\frac{dy}{dx}[/tex] = [tex]y^{2} - 4x^{3} - 4xy^{2}[/tex] / [tex](4x^{2}y + 4y^{3} - 2xy )[/tex]
[tex]\frac{dy}{dx}[/tex] = [tex]\frac{1}{2} ( \frac{y^{2}-4x^{3}-4xy^{2} }{2x^{2} y+2y^{3}-xy } )[/tex]
Hence solved. The differentiation for the given differential equation is done using the technique of implicit differentiation. The differentiation of the variable y is equal to [tex]\frac{1}{2} ( \frac{y^{2}-4x^{3}-4xy^{2} }{2x^{2} y+2y^{3}-xy } )[/tex] for the differential equation.
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Jim worked 45 hours this week. He earns time and a half for overtime. He is paid $12.59 per/hour, how much will he earn this week?
Answer: 566.55 US dollars
Step-by-step explanation: i think, please give 5 stars
The point (7,8) in the coordinates plane represents a ratio. Adela claims that you can find an equivalent ratio by adding the same number to both coordinates of the point. Is Adela correct?
Answer:
It depends on the context of the problem and the interpretation of the ratio represented by the point (7, 8).
If we interpret the point (7, 8) as representing the ratio 7:8, then Adela's claim is incorrect. Adding the same number to both coordinates of the point would change the value of the ratio. For example, adding 1 to both coordinates would give the point (8, 9), which represents the ratio 8:9, which is not equivalent to 7:8.
However, if we interpret the point (7, 8) as representing a different type of ratio, such as the ratio of the distances from the point to two fixed points or the ratio of the areas of two shapes, then it may be possible to find an equivalent ratio by adding the same number to both coordinates of the point. In this case, Adela's claim could be correct.
Without more information about the context and interpretation of the ratio represented by the point (7, 8), it is difficult to determine the correctness of Adela's claim.
Given that f( x ) = x^2 − 6x − 27 g(x)=x-9 find (f-g) (x) and express the result as a polynomial in simplest form.
The difference between f and g can be written as:
(f - g)(x) = x² - 7x - 18
How to express the difference between the polynomials?Here we have two polynomials given by:
f(x) = x² - 6x - 27
g(x) = x - 9
We want to find an expression for:
(f - g)(x)
This difference can be written as:
f(x) - g(x)
Now replacing the polynomials, we will get:
x² - 6x - 27 - (x - 9)
Now we can simplify this to get.
x² - 7x - 18
That is the simplest form.
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