P, Q, and R are three different points. PQ = 3x + 2, QR = x, RP = x + 2, and . List the angles of PQR in order from largest to smallest and justify your response.
The angles of triangle PQR are ordered from largest to smallest as <>R,
The question involves applying the principles of geometry to compare lengths of sides in a triangle, and thereby determine the relative magnitude of angles in triangle PQR. According to the triangle inequality theorem, the largest angle in a triangle is opposite the longest side, and the smallest angle is opposite the shortest side. Given that the side lengths are represented as PQ = 3x + 2, QR = x, and RP = x + 2, we can compare the expressions to conclude which side is longest and which is shortest, assuming all values of x are positive since they represent lengths.
Firstly, it is obvious that QR (x) is the shortest side since it is just x without any additional positive value. Secondly, between RP (x + 2) and PQ (3x + 2), PQ will always be longer than RP for all positive x because it has a larger coefficient in front of x. Hence, the angle opposite PQ (angle R) will be the largest angle, and the angle opposite QR (angle P) will be the smallest. The angle at Q will be between the other two angles in terms of their measurements since PQ is longer than RP but both are longer than QR.
To summarize, the angles of Triangle PQR ordered from largest to smallest are: ∠R, ∠Q, and ∠P.
How many cubic feet of dirt are there in a hole that is 3’ deep x 3’ wide x 3’ long? 0?
the volume of the hole would be 3*3*3 = 27 cubic feet.
however since it is a hole, there is nothing in it.
An object is thrown upward with an initial velocity of 32 feet per second. The objects height is modeled by the function h(t) = - 16t2 + 32t where t is the time of the at height, h(t). What is the maximum height of the object?
32 ft
60 ft
72 ft
104 ft
Opposite angles of a parallelogram are congruent.
a. True
b. False
A 30 inch board is to be cut into three pieces? a 30 inch board is to be cut into three pieces so that the second piece is 4 times as long as the first piece and the third piece is 5 times as long as the first piece. if x represents the length of the first piece, find the length of all three pieces.
First, we construct an equation based on the problem: x+(4x)+(5x)=30. Solving this gives us x=3 inches. Thus, the first piece is 3 inches, the second piece is 12 inches and the third piece is 15 inches.
Explanation:In this problem, a 30 inch board is being divided into three pieces. If the first piece is designated as x, then the second piece would be 4 times as long which is 4x, and the third piece would be 5 times as long which is 5x. If all these pieces add up to the total length of the board which is 30 inches so we can construct the equation: x+(4x)+(5x)=30.
To solve, we combine like terms to get 10x = 30. Divide both sides by 10 to isolate x, so x=3 inches. Thus, the first piece is 3 inches, the second piece is 4 times the first piece which is 12 inches, and the third piece is 5 times the first piece which is 15 inches.
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The expression sin 50 cos 40 + cos 50 sin 40 is equivalent to
The expression sin 50 cos 40 + cos 50 sin 40 is equivalent to 1.
Explanation:The expression sin 50 cos 40 + cos 50 sin 40 can be simplified using the trigonometric identity:
sin(a + b) = sin a cos b + cos a sin b
By applying this identity, we can rewrite the expression as:
sin(50 + 40) = sin 90 = 1Therefore, the expression sin 50 cos 40 + cos 50 sin 40 is equivalent to 1.
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using the graph of f(x)=log2x below approximate the value of y in the equation 2^2y=4
A rectangle that has an area of 357 square inches is 17 inches wide. How long is the rectangle?
What is the exact value of x in the exponential equation 15.5 + e10x = 85.5?
Given the arithmetic sequence A1, A2, A3, A4, 58,69,80,91
What is the Value of A21?
***PLEASE HELP******
An angle is 15 degrees less than twice its complement. find the angles
The population of greenville is currently 50,000 and declines at a rate of 1.2% every year. This models:
Exponential growth.
Exponential logarithm
Exponential decay
verify the identity
cosx/1+sinx + 1+sin/cosx = 2sec x
Which geometric series converges?
A. 2+0.2+0.02+0.002+...
B. 2+4+8+16+...
C. 2-20+200-2000+...
D. 2+2+2+2+...
Answer: The correct option is (A) 2 + 0.2 + 0.02 + 0.002 + . . .
Step-by-step explanation: We are given to select the correct geometric series that converges.
We know that
a geometric series converges if the modulus of its common ratio is less than 1.
Option (A) : 2 + 0.2 + 0.02 + 0.002 + . . .
Here, first term, a= 2 and the common ratio is given by
[tex]r=\dfrac{0.2}{2}=\dfrac{0.02}{0.2}=\dfrac{0.002}{0.02}=~.~.~.~=0.1\\\\\Rightarrow |r|=|0.1|=0.1<1[/tex]
So, this geometric series will converge.
Option (A) is correct.
Option (B) : 2 + 4 + 8 + 16 + . . .
Here, first term, a= 2 and the common ratio is given by
[tex]r=\dfrac{4}{2}=\dfrac{8}{4}=\dfrac{16}{8}=~.~.~.~=2\\\\\Rightarrow |r|=|2|=2>1.[/tex]
So, this geometric series will not converge.
Option (B) is incorrect.
Option (C) : 2 - 20 + 200 - 2000 + . . .
Here, first term, a= 2 and the common ratio is given by
[tex]r=\dfrac{-20}{2}=\dfrac{200}{-20}=\dfrac{-2000}{200}=~.~.~.~=-10\\\\\Rightarrow |r|=|-10|=10>1.[/tex]
So, this geometric series will not converge.
Option (C) is incorrect.
Option (D) : 2 +2 + 2 + 2 + . . .
Here, first term, a= 2 and the common ratio is given by
[tex]r=\dfrac{2}{2}=\dfrac{2}{2}=\dfrac{2}{2}=~.~.~.~=1\\\\\Rightarrow |r|=|1|=1.[/tex]
So, this geometric series will not converge.
Option (D) is incorrect.
Thus, the correct option is (A).
The geometric series that converges is 2+0.2+0.02+0.002+ ...:
Thus, option (A) is correct.
In a geometric series, the terms are multiplied by a constant ratio to obtain the next term.
If the absolute value of the common ratio is less than 1, the series converges.
A. 2 + 0.2 + 0.02 + 0.002 + ...:
In this series, the common ratio is 0.1 (each term is divided by 10).
Since the absolute value of the common ratio is less than 1, this series converges.
B. 2 + 4 + 8 + 16 + ...:
In this series, the common ratio is 2 (each term is multiplied by 2).
Since the common ratio is greater than 1, this series diverges.
C. 2 - 20 + 200 - 2000 + ...:
In this series, the terms alternate in sign, but the absolute value of the common ratio is 10.
Since the absolute value of the common ratio is greater than 1, this series diverges.
D. 2 + 2 + 2 + 2 + ...:
In this series, the common ratio is 1 (each term is the same).
Since the common ratio is equal to 1, this series neither converges nor diverges. It is a divergent series.
Therefore, the geometric series that converges is 2 + 0.2 + 0.02 + 0.002 + ...
Thus, option (A) is correct.
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PLEASE HELP precal!
Is the following relation a function? x y −1 −2 2 3 3 1 6 −2
Answer:
Yes, the relation is a function.
Step-by-step explanation:
We have been given the table
x y
-1 -2
2 3
3 1
6 -2
We know that a relation is a function if every x value has a unique y value.
For the given relation all the x values have a single and unique y values. For example -1 has value -2, 2 has a value 3, 3 has a value 1 and 6 has a value -2.
Thus, the given relation is a function.
PLEASE HELP!!!!! The velocity of sound in air is given by the equation , where v is the velocity in meters per second and t is the temperature in degrees Celsius. Find the temperature when the velocity is 329 meters per second by graphing the equation. Round the answer to the nearest degree. Show your work.
The equation of velocity of sound in air is v = 20 √(273 + t). In this problem, we need to find the temperature when the velocity is 329 meters/s. You need to measure the time it takes a sound to travel a measured distance in order to measure its speed in air.
Given:
Velocity of sound in air equation = v = 20 √(273 + t)
Velocity = 329 m/s
To solve:
V = 20 √(273 + t)
329 = 20 * sqrt(273 + t)
16.45 = sqrt(273 + t)
273 + t = 16.45^2
t- 16.45^2-273
t = -2.4 degrees Celsius
So, the temperature when the velocity is 329 meters per second is -2.4 degrees Celsius.
Susie divided a9-pound bag of apples into 5 equal piled. How many pounds of apples are in each piles?
divide the total weight by the number of piles
9/5 = 1.8 pounds per pile
A certain drug dosage calls for 25 mg per kg per day and is divided into two doses (1 every 12 hours). if a person weighs 80 pounds, how much of the drug should be administered each time?
The required amount of drug for each time a day is given as 425 mg.
What is a Measurement unit?A measurement unit is a unit to measure certain quantities.
For example, the mass can be measured in kilograms, length can be measured in meter and time can be measured in seconds.
To find the measurement of a new quantity known units can be used in operation. As to find the unit for speed we use m/s as a unit, where, m is the unit of distance and s is the unit of time.
Given that,
The weight of the person is 80 pounds.
The amount of dose of drug per day is 25 mg/kg
Then, the amount of drug for each time a day is 12.5 mg/kg.
The weight of the person in kilogram can be calculated as follows,
1 pound = 0.45 kg
Then, 80 pounds = 0.45 × 80
= 34 kg
Now, the amount of drug to be taken each time is 34 × 12.5 = 425mg.
Hence, the amount of drug that should be administered to the person each time is 425 mg.
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Eloise started to solve a radical equation in this way: Square root of negative 2x plus 1 − 3 = x Square root of negative 2x plus 1 − 3 + 3 = x + 3 Square root of negative 2x plus 1 = x + 3 Square root of negative 2x plus 1 − 1 = x + 3 − 1 Square root of negative 2 x = x + 2 (Square root of negative 2 x)2 = (x − 4)2 −2x = x2 − 8x + 16 −2x + 2x = x2 + 8x + 16 + 2x 0 = x2 + 10x + 16 0 = (x + 2)(x + 8) x + 2 = 0 x + 8 = 0 x + 2 − 2 = 0 − 2 x + 8 − 8 = 0 − 8 x = −2 x = −8 Both solutions are extraneous because they don't satisfy the original equation. What error did Eloise make?
Please see attached image for the choices and proper formatting of the problem.
What she did:
[tex] \sqrt{-2x + 1 } - 1 = x + 3 - 1 \sqrt{-2x} = x + 2[/tex]
What she should have done:
[tex]( \sqrt{-2x + 1} ^{2} = (x + 3)^2 -2x + 1 = (x + 3)^2 -2x + 1 - 1 = (x + 3)^2 - 1 -2x = (x +3)^2 - 1[/tex]
The error that Eloise made in solving the radical equation was that she subtracted 1 before squaring both sides.
To add, the equation where at least one variable expression is fixed inside a radical, usually a square root is called a radical equation.
Answer:
We need to subtract 1 after squaring both sides
Step-by-step explanation:
Step1: [tex]\sqrt{-2x+1} -3 = x \\[/tex]
adding 3 both sides
[tex]\sqrt{-2x+1} =3 + x \\[/tex]
we need to square here first and then we need to subtract
and this is the error which Eloise make in solving it .
According to a recent survey, the salaries of assistant professors have a mean of $41,750 and a standard deviation of $7000 . assuming that the salaries of assistant professors follow a normal distribution, find the proportion of assistant professors who earn more than $48,000 . round your answer to at least four decimal places.
Using the z score formula and the z table, we find that approximately 18.67% of assistant professors earn more than $48,000 given a mean salary of $41,750 and a standard deviation of $7000.
Explanation:The question is asking for the proportion of assistant professors who earn more than $48,000 based on a normal distribution of salaries with a mean of $41,750 and a standard deviation of $7,000. To find this, we first need to calculate the z score, which is the number of standard deviations a data point is from the mean. The z score can be calculated using the formula z = (X - μ) / σ, where X is the data point, μ is the mean, and σ is the standard deviation.
Substituting the given values, we get z = (48,000 - 41,750) / 7,000 = 0.8929. Looking up this z value in the z table, we find that the proportion for z = 0.89 is 0.8133. This is the proportion of salaries that are below $48,000. Thus, to find the proportion of salaries above $48,000, we subtract this value from 1, giving us 1 - 0.8133 = 0.1867 or 18.67% when expressed as a percentage. So, approximately 18.67% of assistant professors earn more than $48,000.
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In a big garden 60% of the trees are coconut trees,25%of the number of coconut trees are mango trees and 20% of the number ofof mango trees are apple trees. if the number of apple trees are 1500 then the number of trees in the garden is?
Angle C is an inscribed angle of circle P. Angle C measures (3x + 5)° and arc AB measures (16x)°. Find x.
Final answer:
By applying the theorem that an inscribed angle is half the measure of its intercepted arc, we can solve the given equation to find that the value of x is 1.
Explanation:
The problem involves the relationship between an inscribed angle and its intercepted arc in a circle, which is a fundamental concept in circle geometry. According to the theorem that states an inscribed angle is half the measure of its intercepted arc, we can set up an equation to find the variable x.
Given that angle C measures (3x + 5)° and arc AB measures (16x)°, the relationship between them can be expressed as:
Angle C = ½ × measure of arc AB
(3x + 5)° = ½ × (16x)°
Solving this equation for x gives:
3x + 5 = 8x
5 = 5x
x = 1
Therefore, the value of x is 1.
If a triangle has a height of 14 inches and a base of 9 inches what's the area
PLEASE HELP.
Widget wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x.
The company also discovered that it cost $23 to produce 2 widgets, $103 to produce 4 widgets, and $631 to produce 10 widgets.
Find the total cost of producing 6 widgets.
Answer:
The total cost of producing 6 widgets is $231.
Step-by-step explanation:
Given : Widget wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x.
To find : The total cost of producing 6 widgets.
Solution :
Cost is given by [tex]c (x) = ax^2 + bx + d[/tex]
Cost $23 to produce 2 widgets,[tex]c(2) = a(2)^2 + b(2) + d[/tex]
[tex]23= 4a+2b+d[/tex] .........[1]
Cost $103 to produce 4 widgets,[tex]c(4) = a(4)^2 + b(4) + d[/tex]
[tex]103= 16a+4b+d[/tex] ............[2]
Cost $631 to produce 10 widgets.,[tex]c(10) = a(10)^2 + b(10) + d[/tex]
[tex]631= 100a+10b+d[/tex] ...........[3]
Now, we solve equation [1], [2] and [3]
Subtract equation [2]-[1] and [3]-[2]
[2]-[1] → [tex]12a+2b=80[/tex] ........[4]
[3]-[2] → [tex]84a+6b=528[/tex] .......[5]
Solving equation [4] and [5] by elimination method,
Multiply equation [4] by 3 and subtract from [5]
[tex]84a+6b-3(12a+2b)=528-3(80)[/tex]
[tex]84a+6b-36a-6b=528-240[/tex]
[tex]48a=288[/tex]
[tex]a=6[/tex]
Put in equation [4]
[tex]12(6)+2b=80[/tex]
[tex]72+2b=80[/tex]
[tex]2b=8[/tex]
[tex]b=4[/tex]
Substitute the value of a and b in [1] to get d
[tex]23= 4a+2b+d[/tex]
[tex]23= 4(6)+2(4)+d[/tex]
[tex]23= 24+8+d[/tex]
[tex]23= 32+d[/tex]
[tex]d=-9[/tex]
Substitute a=6,b=4,d=-9 in the cost equation,
The required equation form is [tex]c(x) = 6x^2 + 4x-9[/tex]
The total cost of producing 6 widgets.
Put x=6
[tex]c(6) = 6(6)^2 + 4(6)-9[/tex]
[tex]c(6) = 216+15[/tex]
[tex]c(6) =231[/tex]
Therefore, The total cost of producing 6 widgets is $231.
Lala is on a bycyle trip every 4 days he bikes 230km if lala keeps this same pace for 16 days how many kilometers will he bike
A simple random sample of 1350 registered voters shows that 58% favor Candidate A over Candidate B. Which is the 99% confidence interval for the percent of the population of all registered voters who prefer Candidate A over Candidate B.
Final answer:
The 99% confidence interval for the percentage of registered voters who prefer Candidate A is between 54.6% and 61.4%.
Explanation:
To calculate the 99% confidence interval for the percentage of the population of registered voters who prefer Candidate A over Candidate B, you can use the formula for the confidence interval of a proportion:
The sample proportion (p') is given as 58%, which is 0.58 in decimal form. The size of the sample (n) is 1350.
To calculate the confidence interval, we also need the z-value for the 99% confidence level. The z-value for a 99% confidence level is approximately 2.576 (you can find this value in a standard z-table).
The formula for the margin of error (EBP) is:
EBP = z * sqrt((p'*(1-p'))/n)
Plugging the values into the formula:
EBP = 2.576 * sqrt((0.58*(1-0.58))/1350)
EBP ≈ 0.034
The confidence interval for the true binomial population proportion is given by:
(p' - EBP, p' + EBP)
Therefore, the 99% confidence interval is:
(0.58 - 0.034, 0.58 + 0.034)
(0.546, 0.614)
Interpreting this, we can say with 99% confidence that the true percentage of all registered voters who prefer Candidate A over Candidate B is between 54.6% and 61.4%.
Final answer:
To calculate the 99% confidence interval for the percent of registered voters who prefer Candidate A, we can use the formula CI = p ± Z * √(p*(1-p)/n). Plugging in the values, we find the 99% confidence interval is between 54.6% and 61.4%.
Explanation:
To calculate the 99% confidence interval for the percent of the population of all registered voters who prefer Candidate A over Candidate B, we can use the formula:
CI = p ± Z * √(p*(1-p)/n)
Where:
p = sample proportion
Z = Z-value for the desired confidence level
n = sample size
In this case, the sample proportion is 0.58, the sample size is 1350, and the Z-value for a 99% confidence level is approximately 2.58.
Plugging in these values, we get:
CI = 0.58 ± 2.58 * √(0.58*(1-0.58)/1350)
Simplifying the equation gives us the 99% confidence interval for the percent of registered voters who prefer Candidate A: between 0.546 and 0.614, or 54.6% and 61.4%.
The product of a positive number and 14 more than seven times the number is 105. Find the two numbers. first number =______ and second number =_________
Answer:
can you explain it in more depth please
Step-by-step explanation:
Find the value of x for which l || m
The value of x for which l is parallel to m would be; 31.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
First angle 105 is the vertical opposite angle with the other angle.
The angles are corresponding angles which are equal when the lines are parallel.
Therefore,
3x - 18 + 105 = 180
3x + 87 = 180
3x = 180 - 87
3x = 93
x = 93/3
x = 31
Hence, the value of x for which l is parallel to m would be; 31.
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Tamara earns $8 an hour at her job working 25 hours per week. If 25% of her paycheck goes to taxes, what is Tamaras monthly cash flow? (Asssume this is her only source of income and that there are 4 pays per month)