The angular measure L is : 47°
What are angles?Angles are formed when two lines meet.
Analysis:
Firstly, we calculate for m using cosine rule.
[tex]m^{2}[/tex] = [tex]510^{2}[/tex] + [tex]820^{2}[/tex] -2(510)(820) cos 20
[tex]m^{2}[/tex] = 260100 + 672400 -83600(0.9396)
[tex]m^{2}[/tex] = 146618.56
m = [tex]\sqrt{146618.56}[/tex] = 382.9cm
using sine rule to find ∠L
382.9/sin20 = 820/sinL
sinL = 820sin20/382.9
sinL = 820(0.342)/382.9
sinL = 0.732
L = sin inverse of 0.732 = 47°
In conclusion, ∠L is 47°
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The length of a rectangle is four times the width. The perimeter of the rectangle is 45 inches. Write a system of equations that represents this problem. What is the area of the rectangle
Step-by-step explanation:
2×length + 2×width = 45
length = 4×width
now, we are using the second equation (a variable identity) in the first equation
2×4×width + 2×width = 45
8×width + 2×width = 45
10×width = 45
width = 45/10 = 4.5 in
length = 4×width = 4×4.5 = 18 in
the area of the rectangle is
length × width = 18 × 4.5 = 81 in²
determine whether sec x -tanxsinx=cosx is a possible identity
[tex]\text{L.H.S}\\\\\sec x - \tan x \sin x\\\\\\=\dfrac{1}{\cos x}- \dfrac{\sin x }{ \cos x } \cdot \sin x\\\\\\=\dfrac 1{\cos x} - \dfrac{\sin^2 x}{\cos x}\\\\\\=\dfrac{1- \sin^2 x}{\cos x}\\\\\\=\dfrac{\cos^2 x}{\cos x}~~~~~~~~~~~~~;[\sin^2 x + \cos^2 x = 1]\\\\\\=\cos x\\\\\\=\text{R.H.S}\\\\\text{Since both sides are equal, the given equation is an identity.}[/tex]
What is the standard deviation of the data? Round to the nearest whole number.
65
75
100
130
Rounded to the nearest whole number, the standard deviation of the data is 29.
How do we calculate the standard deviation of data?The following notations and formulas will be used in these calculations:
Mean = (sum of the values) / n
Variance = ((Σ(x - mean)^2) / (n - 1)
Standard deviation = Variance^0.5
Where:
n = number of values = 4
x = each value
Therefore, we have:
Mean = (65 + 75 + 100 + 130) / 4 = 92.50
Variance = ((65-92.5-)^2 + (75-92.50)^2 + (100-92.50)^2 + (130-92.50)^2) / (4-1) = 2,525 / 3 = 841.666666666667
Standard deviation = Variance^0.50 = 841.666666666667^0.5 = 29.011491975882
Rounding to the nearest whole number, we have:
Standard deviation = 29
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Answer:
The answer is C. 100
Step-by-step explanation:
The lengths of the diagonals of a parallelogram are 10 feet and 16 feet. If one side of the parallelogram measures 4 feet, to the nearest hundredth of a degree, find the measure of the acute angle formed by the intersection of the diagonals.
Answer: 24.15
Step-by-step explanation:
a boat leaves at 4:25 a.m. and returns to port at 10:55a.m. How long was the boat out?
Answer:
6 hours 30 minutes
Step-by-step explanation:
10 subtract 4 is 6
55 subtract 25 is 30
ΔDEF rotates 90° clockwise about point A to create ΔD 'E 'F. Therefore, which equation must be true?
The equation that must be true about the rotation is that m∠EAE ' = m∠FAF.
How to explain the rotation?Rotation is a type of transformation in which the shape of the original object is preserved and the angle of rotation is constant for all the parts of the body.
In this case, ΔDEF rotates 90° clockwise about point A to create ΔD 'E 'F, m∠EAE ' = m∠FAF.
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Indicate in standard form the equation of the line passing through the given points, writing the answer in the equation box below.
M(0,6), N(6,0)
The slope of the line is [tex]\frac{6-0}{0-6}=-1[/tex]. so in point-slope form, the equation of the line is [tex]y=-x+6[/tex].
In standard form, this is [tex]\boxed{x+y=6}[/tex]
PLEASE HELP ASAP CANT MOVE ON
What is the scale factor of LaTeX: \triangle ABC\:to\:\triangle DEC? Be sure to simplify your answer!
answers:
2/7
10/21
3/14
5/14
Answer:
[tex]\frac{2}{7}[/tex]
Step-by-step explanation:
Triangle ABC is similar to triangle DEC, because all angles in one triangle are equal to angles in the other triangle.
That means that corresponding sides have the same ratio. Side AB and side DE are corresponding sides. Since there are no unknowns we can calculate the ratio (scale factor).
Since we are looking for scale factor of triangle DEC to triangle ABC, we put side AB (which is in triangle ABC) in the numerator.
[tex]\text{scale factor} = \frac{\text{AB}}{\text{DE}} = \frac{6}{21} = \frac{2}{7}[/tex]
I've marked corresponding sides and angles in the attached picture.
In a city park, three walking paths form triangle ABC. The length AB is 800 meters, the length BC is 900 meters, and the length AC is 850 meters. Which angle of this triangle has the greatest measure?
Answer:
Step-by-step explanation:
angle c
The angle of the triangle with the greatest measure is ∠A
What is a triangle?A triangle is a polygon with three sides and three angles.
Analysis:
For the triangle, ABC the angle facing the side with the greatest measure is the angle with the greatest measure. From the given information side BC is the side with the greatest measure and the angle facing it is ∠A.
In conclusion, the angle with the greatest measure is ∠A
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Which polar coordinates represent the same point as the rectangular coordinate (1,-3)?
The ANSWERS are (sqrt{10} , 288.4°) and (-sqrt{10} , 108.4°) ----- PLEASE EXPLAIN THANK YOU!!!
A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the objects. The polar coordinate of the coordinate (1, -3) is (√10, 288.435).
What are coordinates?A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.
The polar coordinate of the coordinate (1, -3) are,
r = √(x² + y²) = √[(1)²+(-3)²] = √10
θ = tan⁻¹(-3/1) = -71.565 = 288.435
Hence, The polar coordinate of the coordinate (1, -3) is (√10, 288.435).
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14 What are the solutions to the equation 3(x − 4)² = 27?
(1) 1 and 7
(3) 4 ± √24
(2) −1 and -7
(4) − 4 ± √24
Answer:
(1) 1 and 7
Step-by-step explanation:
Hello!
We can solve by isolating the variable.
Solve3(x - 4)² = 27There are two solutions, 1 and 7.
The answer is option 1: x = 7, x = 1.
solve 2(4x-3) = 5(2x-5)
Answer:
x = 19/2 or 9.5
Step-by-step explanation:
Hello!
We can distribute the parenthesis and solve.
Solve2(4x - 3) = 5(2x - 5)2(4x) - 2(3) = 5(2x) - 5(5)8x - 6 = 10x - 25Move all x terms to one side and integer terms to the other
8x - 6 = 10x - 25-6 + 25 = 10x - 8x19 = 2xx = 19/2x = 9.5In triangle ABC, m∠A=47∘ and m∠B=70∘. What is the measure of angle C?
Answer:
63
Step-by-step explanation:
Answer:
63
Step-by-step explanation:
To see why no one noticed time dilation until the twentieth century, consider the time dilation of a clock in an automobile moving past you at 30m / s (about 67mph for reference). What happens when you try to compute gamma for this problem? Write out the steps you take.
(PLLS)!!!
When we try to compute gamma, for this problem, the value of gamma is 1
To answer the question, we need to know what time dilation is.
What is time dilation?Time dilation is a phenomenon in special relativity in which there is an elongation of time due to the motion of an object.
Now, the time is given by t = γt₀ where
γ = gamma = 1/√[1 - (v/c)²] where v = speed of object c = speed of light and t₀ = proper timeThe value of gammaSince we need to compute gamma when the speed of the automobile moving past you is 30 m/s.
Given that
v = 30 m/s and c = 3 × 10⁸ m/sSubstiting these into γ, we have
γ = 1/√[1 - (v/c)²]
γ = 1/√[1 - (30 m/s/3 × 10⁸ m/s)²]
γ = 1/√[1 - (1/1 × 10⁷)²]
γ = 1/√[1 - (1 × 10⁻⁷)²]
γ = 1/√[1 - (1 × 10⁻¹⁴)]
γ = 1/√[1 - 0.00000000000001]
γ = 1/√0.99999999999999
γ = 1/1
γ = 1
So, when we try to compute gamma, the value of gamma is 1
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The midpoint of AB = ([?], [])
M = (x¹+x², ¹2²)
PLS HELP I WILL MARK BRAINLIEST
Answer:
[tex]\sf M=\left(-\dfrac{1}{2},0\right)[/tex]
Step-by-step explanation:
Let (x₁, y₁) = Point A = (-2, 1)
Let (x₂, y₂) = Point B = (1, -1)
[tex]\sf Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
[tex]\implies \sf Midpoint=\left(\dfrac{-2+1}{2},\dfrac{1+(-1)}{2}\right)[/tex]
[tex]\implies \sf Midpoint=\left(-\dfrac{1}{2},0\right)[/tex]
Question 17 of 25
Which is a correct expansion of (3x+2)(3x² + 4)?
OA. 3x 3x² + 3x • 4+2·3x²+2 • 4
OB. 3x. 3x² + 3x• 4+2·3x+2·4
O C. 3x. 3x²+2·3x² + 3x².4+2·4
Answer:
A is the answers for the question
Step-by-step explanation:
please mark me as brainlest
A chandelier is suspended from the ceiling by two chains. one chain is 46cm long and forms an angle of 60o with the ceiling. the other chain 64cm long. what angle does the longer chain make with the ceiling?
The angle the longer chain makes with the ceiling is 38.5°
The two chains and ceiling form a triangle and with two sides and an angle, we use the sine rule to find the other angle
What is the sine rule?The sine rule states in any triangle with sides a, b, c and angles A, B and C, repsectively, we have that
a/sinA = b/sinB = c/sinC
Since one chain is 46cm long and forms an angle of 60° with the ceiling. the other chain 64cm long. So, we find the other angle.
So, a/sinA = b/sinB where
a = 46 cm, b = 64 cmA = other angleB = 60°The value of the other angleMaking A subject of the formula, we have
A = sin⁻¹(asinB/b)
So, substituting the values of the variables into the equation, we have
A = sin⁻¹(asinB/b)
A = sin⁻¹(46 cm × sin60/64 cm)
A = sin⁻¹(46 cm × 0.8660/64 cm)
A = sin⁻¹(39.84 cm/64 cm)
A = sin⁻¹(0.6225)
A = 38.49°
A ≅ 38.5°
So, the angle the longer chain makes with the ceiling is 38.5°
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what is the formula for the nth term of the sequence (1x3),(2x4),(3x5)
Answer:
nth term = n(n + 2)
Step-by-step explanation:
Note that the first number in each parentheses is the sequence number n of the term. This value of n is then multiplied by (n + 2) - for example 3 x 5
( 3 x (3+2)).
So the nth term = n(n + 2).
This is an example of a Quadratic Sequence.
Abrianna sold 20, 23, 18, 4, 17, 21, 15, and 56 boxes of cookies after different football games. Which data value(s) are outliers? Select all that apply.
The data value that is an outlier in the data for boxes of cookies is: E. 56.
How to Determine Outliers in a Data?The simple rule is that values lower than Q1 - 1.5 × IQR and values greater than Q3 + 1.5 × IQR are outliers of a data distribution.
Given the data, 20, 23, 18, 4, 17, 21, 15, 56, find the Q1, Q3, and IQR of the data distribution:
First Quartile (Q1) = 15.5
Third Quartile (Q3) = 22.5
Interquartile Range (IQR) = 22.5 - 15.5 = 7
Q1 - 1.5 × IQR = 15.5 - 1.5 × 7 = 5
Q3 + 1.5 × IQR = 33
None of the values are lower than 5.
However, the only value that is greater than 33 is 56.
The outlier in the data is: E. 56.
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Which of the following represents y > 2x - 3?
Answer: Choice A
The two characteristics here are:
The boundary line is a dashed line. This visually indicates to the reader "points on the boundary do NOT count as solutions". Think of the boundary as an electric fence you cannot touch, but can get closer and closer to. We aren't including boundary points directly because of the lack of "or equal to". The shading is above the boundary, due to the "greater than" sign. This only works if we have y isolated.The graph of choice B is [tex]y \le 2x-3[/tex] since we have a solid line and shading below the solid line. This time points on the boundary are part of the solution set.
A new pizza restaurant uses paid advertisement to increase pizza sales on Mondays. The table below is a record of the restaurant’s sales each Monday for the first quarter (13 weeks) of the paid advertisement.
Part A: Create a scatter plot to represent the data in the table. Then, draw the line of best fit, going through the points representing weeks 5 and 13. Be sure to label each axis, as well as to include the proper titles for the scatter plot.
Part B: Use the total sales for weeks 5 and 13 to write an equation for the line of best fit. In your final answer, include all of your calculations.
Part C: In terms of the slope of the equation for the lines of best, fit explain whether or not you think the paid advertisement is responsible for the restaurant's increase or decrease in pizza sales during the first quarter. Use complete senteneces in your answer.
Part D: Assuming that the pizza restaurant wishes to continue the paid advertisement for an additional quater, use the equation for the line of best fit to predict the restaurant's sales for the Monday of the 20th week.
A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.
What is a line of best fit?A line of best fit is also referred to as a trendline and it can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any correlation between a data.
Part B.By critically observing the graph (see attachment) which models the data in the given table, we can infer and logically deduce that an equation for the line of best fit is given by:
y = 22.214x + 291.27
Part C.Since the slope of the equation for the line of best fit is positive, the paid advertisement is responsible for the restaurant's increase in pizza sales during the first quarter.
Part D.Next, we would predict the restaurant's sales for the Monday of the 20th week as follows:
y = 22.214x + 291.27
y = 22.214(20) + 291.27
y = 444.28 + 291.27
y = $735.55.
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A water sprinkler sends water out in a circular pattern. How many feet away from the sprinkler can it spread water if the area formed by the watering pattern is452.16 square feet? Use 3.14 for .
We need radius
Let that be r
πr²=452.163.14r²=452.16r²=144r=√144r=12ftAnswer:
12 feet
Step-by-step explanation:
It asks how many feet away from the sprinkler can water be spread. Therefore, in this scenario, we require the radius.
Area of a circle :
Area (circle) = πr²
Solving :
⇒ 452.16 = 3.14 × r²
⇒ r² = 452.16 ÷ 3.14
⇒ r = √144
⇒ r = 12 feet
please help me out :(
Answer:
The correct answer is B.
Step-by-step explanation:
Pay per month depends on hours of training, so hours of training is the domain, and pay per month is the range.
Alisha buys 200 books costing £3 each.
She sells 2/5 of the books at £8 each.
Alisha then reduces the price of the remaining books by a quarter.
She then sells some of the remaining books.
Alisha makes £490 profit.
Work out how many books Alisha did not sell?
The number of books Alisha did not sell after making a profit of £490 is 45 books
How to find how many book she sell base on the profit?
She buys 200 books costing £3 each.
Therefore,
cost = 3 × 200 = £600
Hence,
She sells 2/5 of the books at £8 each.
total amount = 2 / 5 of 200 × 8
total amount = 80 × 8
total amount = £640
Alisha then reduces the price of the remaining books by a quarter.
She then sells some of the remaining books.
Therefore,
the remaining book = 120
She sold some of the remaining books.
profit = selling price - cost price
490 = selling price - 600
selling price = 490 + 600
selling price = £1090
Therefore,
the cost of the remaining book she sold = 1090 - 640 = £450
Hence,
let
x = number of book sold
6(x) = 450
x = 450 / 6
x = 75
The number book she did not sell = 120 - 75 = 45
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1. the prices for 6 different jerseys are
$98, $85, $34, $79, $85, and $92.
what is the outlier in the data set?
Answer:
Step-by-step explanation:
8
25% of 80 help nowww
80 * 25 /100 = 20 .........
Answer:
20
Step-by-step explanation:
25% of 80
to turn 25% into a decimal, 25 / 100 = 0.25
multiply 80 by 0.25, 80 x 0.25 = 20
If a plumber chargers a call out fee of $85 plus $72 per hour how much would it cost for 3 hours?
Show working out pls
Answer:
$301
Step-by-step explanation:
Charge for 1 hour = $ 72
To find the cost for 3 hours, multiply hourly rate ($72) by 3
Charge for 3 hours = 72 * 3 = $ 216
Now, to find the total cost, add the charge for 3 hours and the fixed rate.
Total cost = fixed rate + charge for 3 hours
= 85 + 216
= $ 301
HELP!!!! THIS IS A MATRIX PROBLEM (WILL GIVE BRAINLIEST)
If T= 23 -38
17 -6
What is -10(T)
Answer:
hope you can understand
Write the slope intercept form of each equation of the line. Use a fraction for slope if needed.
Parallel to y=−x+5, through (2, 4)
Answer:
y=-x+6
Step-by-step explanation:
Start by graphing y=-x+5. Then mark the point (2,4) for easier reference. A parallel line just has the same slope, so if you make another line with the same slope, and change the y-intercept until the line goes through (2,4), you will have the answer.
whats equlvlent to 3√6
Answer:
Important: 3
6
looks like a fraction, but it is actually an improper fraction.
There is an infinity number of equivalent fractions to 3
6
.
To find an equivalent fraction to 3
6
, or to any other fraction, you just need to multiply (or divide, if the fraction is not yet reduced), both the numerator and the denominator of the given fraction by any non-zero natural number. For example:
By dividing the original fraction by 3, we get:
3 ÷ 3
6 ÷ 3
= 1
2
By multiplying the original fraction by 2, we get:
3 × 2
6 × 2
= 6
12
Step-by-step explanation: