find the lengths of the sides of the triangle pqr. p(5, 1, 4), q(3, 3, 3), r(3, −3, 0)
Answers
The lengths of the sides of triangle PQR are: PQ = 3, QR = 3√5, RP = 6.
In order to find the lengths of the sides of the triangle pqr with p(5, 1, 4), q(3, 3, 3), r(3, −3, 0), we can use the distance formula.
The distance formula for finding the distance between two points (x1, y1, z1) and (x2, y2, z2) in a 3-dimensional space is given by:
\($$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$$\)
The length of the side PQ is:
\($$\begin{aligned} PQ&=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2} \\ &=\sqrt{(3-5)^2+(3-1)^2+(3-4)^2} \\ &=\sqrt{4+4+1} \\ &=\sqrt{9} \\ &=3 \end{aligned}$$\)
The length of the side QR is:
\($$\begin{aligned} QR&=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2} \\ &=\sqrt{(3-3)^2+(3-(-3))^2+(3-0)^2} \\ &=\sqrt{36+9} \\ &=\sqrt{45} \\ &=3\sqrt{5} \end{aligned}$$\)
The length of the side RP is:
\($$\begin{aligned} RP&=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2} \\ &=\sqrt{(3-5)^2+(-3-1)^2+(0-4)^2} \\ &=\sqrt{4+16+16} \\ &=\sqrt{36} \\ &=6 \end{aligned}$$\)
Therefore, the lengths of the sides of triangle PQR are: PQ = 3, QR = 3√5, RP = 6.
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Related Questions
Help me with this question please!!
Answers
Answer:
∠1 = 19°∠2 = 76°Step-by-step explanation:
You want to know the measure of angle 1 given that angle 2 is four times angle 1, and their sum is 95°.
Angle sum theoremThe angle sum theorem tells you the whole is equal to the sum of the parts.
∠1 +∠2 = ∠WXZ
Using the given information, we can write ...
∠1 + (4×∠1) = 95°
5×∠1 = 95° . . . . . . . . collect terms
∠1 = 19° . . . . . . . . . divide by 5
Then angle 2 is ...
∠2 = 4×∠1 = 4×19°
∠2 = 76°
Which number
is two less than
one million?
Answers
Answer:
999,998
Step-by-step explanation:
Solve the right triangle for all unknown sides and angles. Round your answers to two decimal places.
B = 71
, b = 24
Answers
Angle A is 19 degrees.
Angle C is 90 degrees.
Side a is approximately 7.83.
Side c is approximately 34.50.
To solve the right triangle given that B = 71 degrees and b = 24, we can use the trigonometric ratios sine, cosine, and tangent.
Finding Angle A:
Angle A is the complementary angle to B in a right triangle, so we can calculate it using the equation:
A = 90 - B
Substituting the given value, we have:
A = 90 - 71
A = 19 degrees
Therefore, Angle A is 19 degrees.
Finding Angle C:
Since it is a right triangle, Angle C is always 90 degrees.
Therefore, Angle C is 90 degrees.
Finding Side a:
We can use the sine ratio to find the length of side a:
sin(A) = a / b
Rearranging the equation to solve for a, we have:
a = b * sin(A)
Substituting the given values, we have:
a = 24 * sin(19)
a ≈ 7.83
Therefore, the length of side a is approximately 7.83.
Finding Side c:
Using the Pythagorean theorem, we can find the length of side c:
c^2 = a^2 + b^2
Substituting the given values, we have:
c^2 = 7.83^2 + 24^2
c^2 ≈ 613.68 + 576
c^2 ≈ 1189.68
Taking the square root of both sides to solve for c, we have:
c ≈ √1189.68
c ≈ 34.50
Therefore, the length of side c is approximately 34.50.
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56 pens are packaged in 7 boxes how many are packed in 9? help plss
Answers
Answer:
7 boxes=56 pens
1 box = 56/7
9 boxes = (56/7)×9
=72
Ted can clear a football field of debris in 3 hours. Jacob can clear the same field in 2 hours. When they work together, the situation can be modeled by the equation, where t is the number of hours it would take to clear the field together.
1/3+1/2=1/t
How long will it take Ted and Jacob to clear the field together?
Answers
Ted can clear a football field in 3 hours, while Jacob can clear it in 2 hours. When they work together, the time it takes to clear the field can be determined by solving the equation 1/3 + 1/2 = 1/t.
Let's consider the equation 1/3 + 1/2 = 1/t, where t represents the number of hours it would take Ted and Jacob to clear the field together. To solve for t, we need to find a common denominator for the fractions on the left-hand side. The least common multiple (LCM) of 3 and 2 is 6.
By multiplying the first fraction by 2/2 and the second fraction by 3/3, we can rewrite the equation as (2/6) + (3/6) = 1/t. This simplifies to 5/6 = 1/t.
To isolate t, we can take the reciprocal of both sides, giving us t/1 = 6/5. Cross-multiplying, we find t = 6/5 = 1.2.
Therefore, it will take Ted and Jacob 1.2 hours (or 1 hour and 12 minutes) to clear the football field together.
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Find the two consecutive integers such that the sum of the larger and 23 less than the smaller is 50.
Answers
Answer: The two consecutive integers are 36 and 37.
Step-by-step explanation: Let's call the smaller integer "x".
According to the problem, the larger integer is the next consecutive integer, so we can call it "x + 1".
The problem tells us that the sum of the larger integer and 23 less than the smaller integer is 50. So we can set up the equation:
(x + 1) + (x - 23) = 50
Simplifying the equation, we get:
2x - 22 = 50
Adding 22 to both sides, we get:
2x = 72
Dividing both sides by 2, we get:
x = 36
So the smaller integer is 36. The next consecutive integer is 37.
Therefore, the two consecutive integers are 36 and 37.
help find the missing number for x
Answers
Answer:
41
Step-by-step explanation:
x² = 40²+9²
= 1600+81
= 1681
x= √1681 = 41
FIRST CORRECT ANSWER GETS BRAINLIEST 50 PTS \((2x-5)^{2} +3(2x-5)-18\)
Answers
Answer:
4x² -14x - 8
Step-by-step explanation:
(2x - 5)² + 3(2x-5) - 18
Expand brackets.
(2x-5)(2x-5) + 6x -15 - 18
2x(2x-5)-5(2x-5) + 6x - 33
4x² - 10x - 10x + 25 + 6x - 33
Combine like terms.
4x² -14x - 8
Answer:
4x^2 -14x -8
Step-by-step explanation:
( 2x-5)^2 + 3( 2x-5) -18
Foil
(2x-5)(2x-5) = 4x^2 -10x-10x +25 = 4x^2 -20x+25
Distribute
3( 2x-5) = 6x -15
( 2x-5)^2 + 3( 2x-5) -18
Replace with the foil and distribute
4x^2 -20x+25 +6x -15 - 18
Combine like terms
4x^2 -14x -8
The table how the quantity and unit price for the item Camillo bought. Total cot for bread:
$48. 75
Total cot for peanut butter:
$384
Total cot for jelly:
If he would have pent $986. 50 without better-buy unit price, how much money did he ave?
Answers
Using the addition and subtraction operations, we find out that the money left with Camillo is equal to $361.75.
It is given to us that -
The total cost for bread = $48.75
The total cost for peanut butter = $384
and, the total cost for jelly = $192
It is also given to us that Camillo has spent $986. 50.
We have to find out the money he has left.
Firstly, we have to find out the total costs spent by Camillo by adding the costs spent on bread, peanut butter, and jelly.
Total costs = $48.75 + $384 + $192 = $624.75
The total amount that Camillo had with him initially is given by $986. 50.
So, in order to find out the money that Camillo is left with, we have to subtract the total costs spent by Camillo from the initial total amount that Camillo had.
Thus, money left = $986. 50 - $624.75 = $361.75
Therefore using addition and subtraction operations, we find out that the money left with Camillo is equal to $361.75.
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Answer: Camillo had $361.75.
Step-by-step explanation:
I really need help with part a and b, please help. Incorrect answers will be downvoted, correct answers will be upvoted. 1. The army is interested in characterizing the acoustic signature of a helicopter. The following data show measurements of acoustic pressure (made dimensionless) for a two-bladed helicopter rotor through of a rotor revolution. The data points are equally spaced in time, and the period of the data collection is of a second. p=00.00040.0015 0.0028 0.0040 0.0048 0.0057 0.0071 0.0095 0.0134 0.0185 0.02420.0302 0.0364 0.0447 0.0577 0.0776 0.0955 0.0907 -0.0477 -0.0812 -0.0563 -0.0329 -0.0127 0.0032 0.0147 0.0221 0.0256 0.0255 0.0222 0.0170 0.0112 0.0064 0.0035 0.0023 0.0020 0.0019 0.0016 0.0009 0.0002 a) Find the real discrete Fourier transform for this data set. (b) Any term in the Fourier series can be written: ak Cos(kwt)+bk sin(kwt) =ck Cos(kwt+$k) ak Find the ck's and plot their amplitude on a bar graph vs. k to illustrate the relative size of each term in the series. Explain the significance of the plot
Answers
(a) The real discrete Fourier transform (DFT) is calculated for the given data set to analyze the helicopter's acoustic signature.
(b) To obtain the ck values and illustrate the relative size of each term in the Fourier series, we calculate the magnitude of each coefficient and plot their amplitudes on a bar graph against the corresponding frequency component, k.
To analyze the helicopter's acoustic signature, the real DFT is computed for the provided data set. The DFT transforms the time-domain measurements of acoustic pressure into the frequency domain, revealing the different frequencies present and their corresponding amplitudes. This analysis helps in understanding the spectral characteristics of the helicopter's acoustic signature and identifying prominent frequency components.
Using the Fourier series representation, the amplitudes (ck's) of the different frequency components in the Fourier series are determined. These amplitudes represent the relative sizes of each term in the series, indicating the contribution of each frequency component to the overall acoustic signature. By plotting the amplitudes on a bar graph, the relative strengths of different frequency components become visually apparent, enabling a clear comparison of their importance in characterizing the helicopter's acoustic signature.
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f(x)=x^4−2x^2+3
a) Find the intervals on which f is increasing or decreasing.
b) Find the local maximum and minimum values of f.
c) Find the intervals of concavity and the inflection points.
Answers
The derivative of the function f(x) is f'(x) = 4x^3 - 4x. The local maximum value is f(0) = 3 and the local minimum value is f(1) = 2. There is an inflection point at x = -1/√3 and another at x = 1/√3.
a) The derivative of the function f(x) is f'(x) = 4x^3 - 4x.To find the intervals where f(x) is increasing or decreasing, we need to determine the sign of the derivative in each interval. Setting f'(x) = 0, we get x = 0 and x = 1 as critical points. We then make a sign chart and test the sign of f'(x) in each interval:
Interval (-∞,0) : f'(x) < 0, so f(x) is decreasing.
Interval (0,1) : f'(x) > 0, so f(x) is increasing.
Interval (1,∞) : f'(x) < 0, so f(x) is decreasing.
b) To find the local maximum and minimum values of f(x), we need to examine the critical points and the endpoints of the intervals. We know that x=0 and x=1 are critical points. We can then evaluate the function at these points and the endpoints of the intervals:
f(-∞) = ∞
f(0) = 3
f(1) = 2
f(∞) = ∞
Therefore, the local maximum value is f(0) = 3 and the local minimum value is f(1) = 2.
c) The second derivative of the function f(x) is f''(x) = 12x^2 - 4. To find the intervals of concavity and the inflection points, we need to determine the sign of the second derivative in each interval. We make a sign chart and test the sign of f''(x) in each interval:
Interval (-∞, -1/√3) : f''(x) < 0, so f(x) is concave down.
Interval (-1/√3, 1/√3) : f''(x) > 0, so f(x) is concave up.
Interval (1/√3, ∞) : f''(x) < 0, so f(x) is concave down.
The inflection points are the points where the concavity changes. From the sign chart, we can see that there is an inflection point at x = -1/√3 and another at x = 1/√3.
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The occupancy rate of a motel is the percentage of rooms that are occupied on a particular night. The
histogram below summarizes the occupancy rates for a random sample of 100 nights for a motel.
0.35
0.30
0.25-
0.20-
0.15-
0.10-
0.05
0+
0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95
Motel Occupancy Rate
Based on the histogram, which of the following values could represent Q3?
Relative Frequency
(A) 0.24
(B) 0.63
(C) 0.67
(D) 0.71
(E) 0.75
Answers
For the given table, the third quartile is given by:
(D) 0.71.
What are the median and the quartiles of a data-set?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.The first quartile is the median of the first half of the data-set, which is the 25th percentile.The third quartile is the median of the second half of the data-set, which is the 75th percentile.Given a cumulative frequency table, the third quartile Q3 is the value when the sum of the frequencies is of 0.75.
From the frequency table, we have that:
A rate of 0.65 is the 30th percentile.A rate of 0.7 is the 57th percentile, as 0.3 + 0.27 = 0.57.A rate of 0.75 is the 80th percentile, as 0.57 + 0.23 = 0.8.Hence the 75th percentile is between 0.7 and 0.75, meaning that option D is correct.
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. When Ariana was 3 years old she was 32 inches tall. She grew at a rate of 2 inches per year. Write an equation to represent Adriana's height after each year. Identify your variables.
Answers
Answer:
A=32+2x
Step-by-step explanation:
A= Adriana's height
x= years since Adriana was 3 years old
A= 32+ 2x
Pretty please for a homie
Answers
_______
Y+4=-2x+8
Y=-2x+4
Complete the table of values for y=1/2x^3-2x+1
Answers
Table of values:
x y
-2 5
-1 3/2
0 1
1 1/2
2 1
We may solve for y by substituting the supplied values of x into the equation \(y=1/2x3-2x+1\) and completing Table of values .
For instance,\(y=1/2(-2)3-2(-2)+1\) Equals 5 when\(x=-2.\) The equivalent values of y for x=-1, 0, 1, and 2 are similarly found.
The ordered pairs (x,y) that fulfil the equation are displayed in the resultant table. These points allow us to graph the equation and see how the curve looks. In this instance, the equation describes a cubic function with two turning points at (-1,3/2) and (1,1/2), as well as a horizontal intercept at (0,1).
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-4x+5x combine like terms
Answers
Answer:
1x
Step-by-step explanation:
Answer:
-20x
Step-by-step explanation:
can anybody help me?
Answers
f(-2) = 2(-2)² - 8(-2) + 6 = 30
f(-1) = 2(-1)² - 8(-1) + 6 = 16
f(0) = 2(0)² - 8(0) + 6 = 6
f(1) = 2(1)² - 8(1) + 6 = 0
f(2) = 2(2)² - 8(2) + 6 = -2
I dont understand what postulate/theorem i need to use. can u help?
Answers
Answer:
I believe it is SAS
Step-by-step explanation:
You are unable to use AS S because donkeys do not belong in math
You are also unable to use AAA because triple A is good for your car, but not in math.
They give us an angle, so I am assuming it is ASA
i need help;-; Like 25 points or something
Answers
Answer:
28.26
Step-by-step explanation:
area of a circle formula:
\(\pi \times r^{2} \)
since we substitute pi for 3.14 it would be 3.14×(3)^2
3^2=9
9×3.14=28.26
Answer:
28.26
Step-by-step explanation:
hope this helps
The radius of a circle is 9 miles. What is the area of a sector bounded by a 60° arc?Give the exact answer in simplest form. ____ square miles. (pi, fraction,)
Answers
Given a figure of a circle:
As shown, the radius of the circle = r = 9 miles
The shown sector bounded by a 60-degree arc
We need to find the area of the shown sector
as we know the area of the circle =
\(\pi\cdot r^2\)The area of the sector represents 60/360 of the area of the circle
So, the area of the sector =
\(\frac{60}{360}\cdot\pi\cdot r^2=\frac{1}{6}\cdot3.1416\cdot9^2=42.4115\)so, the answer will be the area of the shown sector = 42.4115 square miles
We will write the area in terms of pi and fractions as follow:
\(\frac{1}{6}\cdot\pi\cdot9^2=\frac{27}{2}\pi\)So, the answer will be:
\(\frac{27}{2}\pi\)Every three years the population of one part of Brooklyn is recorded.
In 2014 there was a population of 10,500 people.
From 2014 to 2017 the population increased by 22%.
From 2017 to 2020 the population decreased by 10%.
What was the population of this area in 2020?
Answers
Answer:
11,529
Step-by-step explanation:
10500x22%=2310
10500+2310=12810
12810x10%=1281
12810-1281=11529
Answer:
Hello there!
Your question asks to find what was the size of the population in 2017
Answer: 6,721
In order to solve this problem, we're going to need to use the given information in the question in order to find the population in 2017.
Key information:
In 2010, population was 6500
In 2014, population increased by 10% from 2010
In 2017, population decreased by 6% from 2014.
With the information above, we can solve the problem.
We're going to start with 6500 as our starting population.
We know that the population increased by 10% in 2014, so we would multiply 6500 by 1.10.
Step-by-step explanation:
The gas tank in felizs car is 5/6 full each time he drives to or from work he uses 1/12 of a full tank of gas which equation represent the number of times feliz can drive to or from work with the gas in his tank answers are either 1/10 or 7 or 5/72 or 10
Answers
Answer:
the answer is \(\frac{5}{6}\)÷\(\frac{1}{12}=10\)
Step-by-step explanation:
which of the following expressions is the conjugate of a complex number with −5 as the real part and 4i as the imaginary part? (1 point) 5 4i 5 − 4i −5 − 4i −5 4i
Answers
The conjugate of a complex number with a real part of -5 and an imaginary part of 4i is represented by :
C) -5 - 4i.
The conjugate of a complex number with a real part of -5 and an imaginary part of 4i can be found by changing the sign of the imaginary part. In this case, the imaginary part is 4i, so the conjugate will have a negative sign for the imaginary part.
The conjugate of the complex number is given by -5 - 4i. This means that if we have a complex number of the form -5 + 4i, its conjugate will be -5 - 4i. The conjugate of a complex number is important in various mathematical operations, such as complex number multiplication and division, as it helps simplify the expressions and eliminate the imaginary parts when needed.
Among the given options, option C) -5 - 4i represents the conjugate of the complex number with a real part of -5 and an imaginary part of 4i.
The correct question should be :
Which of the following expressions represents the conjugate of a complex number with a real part of -5 and an imaginary part of 4i?
A) 5
B) 4i
C) -5 - 4i
D) -5 + 4i
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A box has volume 2.5m³.
Express this volume in cm³
Answers
Answer:
2.5 Cubic Meters =2500000 Cubic CentimetersStep-by-step explanation:
2.5 Cubic Meters =2500000 Cubic Centimeters
(1m³ = 1000000cm³)
F(x) = 6x+2, find f (x+3)
Answers
Answer:
6x+20
Step-by-step explanation:
F(x) = 6x+2
f(x+3) means replace x with x+3
F(x+3) = 6(x+3)+2
= 6x+18+2
= 6x+20
Answer:
A; F(x+3) = 6x^2 + 20x + 6
Step-by-step explanation:
To find it you just would multiply F(x) onto the other side. So it would look like this:
F(x+3) = 6x + 2 (x+3)
F(x+3) = 6x^2 + 2x + 18x + 6 *combine like terms getting you
F(x+3) = 6x^2 + 20x + 6
Hope this helped!!
I need help on this one too please and thank you
Answers
so it’s C because it needs to equal 90
A simulated game of chess is programmed between two computers. The game is supposed to be biased in favor of player B winning 4 out of 5 times. Which is the most suspicious set of outcomes of 30 games played between the two computers?AABABBBABBBBBBBBABBBABBBBBBBBAABBABBAABBBBBABBBBBBBBBBBBBABBABBABABABABBABABABABABABABABAAABBABBBABBBBBBBBABBBABBBBBBBBB
Answers
A simulation game attempts to copy various activities from real life in the form of a game for various purposes such as training, analysis, prediction, or entertainment.
How will outcome be decided?The most suspicious set of outcomes for a simulated game of chess that is supposed to be biased in favor of player B winning 4 out of 5 times would be if player B won all 30 games. This outcome would be highly unlikely if the game was truly random and the bias towards player B was accurate. Other suspicious outcomes could include player B winning 29 out of 30 games or player B winning 28 out of 30 games with a high margin of victory in each game.
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PLS HELP ME WITH THIS EQUATION! Find X
\({3}^{2}x - 32 = {2}^{2}x - 4x\)
Answers
Answer:
\(3x^{2} -32=2x^{2} -4x\\3x^{2} -2x^{2} +4x-32=0\\x^{2} +4x-32=0\\x^{2} -4x+8x-32=0\\x(x-4)+8(x-4)=0\\(x-4)(x+8)=0\\x-4=0 \ or\ x+8=0\\x=4\ or\ x=-8\)
Determine whether the ratios are equivalent.
28 : 32 and 7 : 8
Answers
Answer:
They are
Step-by-step explanation:
28:32 is equal to 7/8
Follow the steps to find the product of and 0.55.
Estimate the product of and 0.55.
1/4-
Convert the decimal 0.55 to a fraction.
V55/100
What is the product of the two numbers?
X 110/150 or 11/15
110/300 or 11/30
77/103
Answers
1) Estimate value of the product of 2/3 and 0.55 is, 2/3.
2) The fraction part is, 55 / 100
3) The product of the two numbers is, 11/30
We have to given that,
Estimate the product of 2/3 and 0.55.
And, Convert the decimal 0.55 to a fraction.
And, The product of the two numbers.
Now,
Estimate the product of 2/3 and 0.55,
So, we can round 0.55 to the nearest whole number, which is 1.
Then, multiply 2/3 by 1 to get an estimate of the product.
so, The correct answer is 2/3.
Now, we can convert the decimal 0.55 to a fraction,
= 0.55
= 55/100
= 11/20
Thus, The correct answer is, 55/100.
And, the product of 2/3 and 0.55,
= 2/3 x 55/100
= 110/300
= 11/30.
Hence, The correct answer is, 110/300 or 11/30
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