Answer:
12
Step-by-step explanation:
2 is 40 percent of 5
12 is 40 percent of 30
Answer:
15 people would be running out of 30
Step-by-step explanation:
30/2
Rewrite the following equation in logarithmic form.
e^a=95/73
The logarithmic form of e^a = 95/73 is [tex]loge_{\frac{95}{73} }[/tex] = a
What is natural logarithm?natural logarithm can be referred to as the power to which the base ‘e’ that has to be raised to obtain a number called its log number. Here e is the exponential function. It was initially discovered in the 17th century by John Napier, who discovered and conceptualized the theory of logarithms. Before looking into the key difference between ln and log, let’s understand the definition of log and ln.
if e^a = 95/73
means that the natural logarithm of 95/73 is the number a
so that we have
a = [tex]loge_{\frac{95}{73} }[/tex]
In conclusion the logarithmic form of the expression is a = [tex]loge_{\frac{95}{73} }[/tex]
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Write a story that can be represented by the equation y=x+1/5x
please help 20pt
We might write [tex]y=x+\frac{1}{5} x[/tex] if the entire amount of money is y and the first week's deposit is x.
What is equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
When are given an x and y equation that is [tex]y=x+\frac{1}{5} x[/tex] , and the further discussion can be defined as follows:
We must now imagine a condition that can be represented by the above equation.
Let's calculate the place money in piggy bank over two weeks in a row.
In the first week, I deposit a [tex]\frac{1}{5}[/tex] of a particular amount of money, and the next week, I deposit a quarter of such previous week's investment.
We must now determine the entire amount of money that I have deposited.
We might write [tex]y=x+\frac{1}{5} x[/tex] if the entire amount of money is y and the first week's deposit is x.
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in huffman encoding if all the letters have the same frequency then they have equal code lengths. true or false g
If all the letters have the same frequency then they have may or may not be equal codes.
What is Huffman encoding?
A lossless data compression algorithm is Huffman coding. Input characters are given variable-length codes, the lengths of which are determined by the frequency of the matching characters.
The variable-length codes (bit sequences) assigned to input characters are Prefix Codes, which indicates that no other character will have a code that is the prefix of the code assigned to that character. This is how Huffman Coding ensures that the produced bitstream cannot contain any ambiguities during decoding.
Let's use a counter example to better grasp prefix codes. Assume that the four characters a, b, c, and d have the variable length codes 00, 01, 0 and 1, respectively. Because the code assigned to c is the prefix of the codes assigned to a and b, this coding causes uncertainty. If the bit stream being compressed is 0001, the decompressed output might be "cccd," "ccb," "acd," or "ab."
In huffman coding, if two nodes have the same frequency, they are considered to be identical for compression reasons, therefore you can select either one and gain an equal amount of compression.
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12. A hot air balloon is flying at an altitude of 1,000 ft. The pilot wants to increase the altitude of
the balloon at 5° angle over the next 500 ft. What will be the balloon's change in altitude?
(sin 5° -0.0872; cos 5º = 0.9962; tan 5° = 0.0875)
A. 25.8 ft
B 43.7 ft
C. 231.4 ft
D. 498 ft
Balloon's altitude = 43.7ft as
change in altitude/500 = tan 5°
change in altitude = .0875*500
=43.7ft
4. Write the equation of a line that is perpendicular to y= 3/7x-1 and goes through the point (3,-3).
Answer:
y+3 = -7/3(x-3)
y = -7/3x + 4
Tell whether $x$ and $y$ show a positive, negative, or no correlation. Ten dots on a coordinate plane. From left to right, the points generally start lower and move higher on the graph. The points are. Ordered pair negative 3 comma negative 2. Ordered pair negative 2 comma negative 2. Ordered pair negative 1.5 comma negative 1. Ordered pair negative 1 comma 0. Ordered pair negative 0.5 comma 1. Ordered pair 0.5 comma negative 1. Ordered pair 0.5 comma 2. Ordered pair 1 comma 1. Ordered pair 1.5 comma 2. Ordered pair 1.5 comma 3. $x$ and $y$ show correlation.
The variables x and y show a positive correlation
How to determine the correlation shown by the variable?From the question, we have the following parameters that can be used in our computation:
Variables = x and yNumber of dots on a coordinate plane = 10The points start from left to right (and moves from lower to higher)The ordered pairs are (-3, -2).(-2, -2), (-1.5, -1), (-1, 0), (-0.5, 1), (0.5, -1), (0.5, 2), (1, 1), (1.5, 2), (1.5, 3)Next, we plot the graphs of the points using a graphing calculator
See attachment for the graph
From the graph, we can see that the points are approximately linear
And the points show a linear pattern with a positive slope
This means that the correlation is positive
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a piece of wire 10 m long is cut into two pieces. one piece is bent into a square and the other is bent into an equilateral triangle. how should the wire be cut so that the total area enclosed is
The triangle should have 4.35 metres of wire, which means the square should have 6.978 meters
Let "x" is the cutting distance from one end of the wire.
Then, area of square would be ,
Area = (x/4)²
The side of equilateral triangle would be,
L=(10-x)/3
height would be (10-x)/3*√(3)/2
=> (10-x)√(3)/6
So, the area of triangle is
Area of triangle= ((10-x)/3)² ×√(3)/4
=> (10-x)² ×√(3)/36
So, the total area is ,
A = (x/4) + (10 - x)²/36√3
Differentiating Area w.r.t x
dA/dx=x/8-2 ×√(3)/36(10-x)
=> x/8+20× √(3)/36-2 × √(3)/36x
Putting the expression equal to 0,
x/8+20× √(3)/36-2 × √(3)/36x = 0
=> x(1/8+ √(3)/18
=> 10√(3)/18
x*0.22122 = 0.96225
x=4.35
Substituting the value of x
This corresponds to minimum area which is:
A(4.35)=(4.35/4)^2+(10-4.35)^2 × √(3)/36=1.183+1.536
=> 2.719m²
Thus , the minimum area is 2.71 square meters when x=4.35 m. As a result, the wire should be cut such that the dimension of the square is formed by the piece having a length of 4.35 m, and the equilateral triangle is formed by the piece having a length 5.65 m.
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extrapolation is the use of the regression line to estimate a mean of y-values for an x-value that is far outside the x-range of data.
Extrapolation is the use of the regression line to estimate a mean of y-values for an x-value that is far outside the x-range of data.
What is extrapolation?
A statistical technique called extrapolation aims to understand the unknown data from the known data. It uses historical data to attempt to predict future data. For instance, using the current population size and growth rate to project the size of a population in a few years.
Predicting hypothetical values outside of a specific data set is the goal of extrapolation.
Contrary to interpolation, which typically focuses on estimating past values, extrapolation is used to predict unknown future values due to its predictive nature.
Hence, extrapolation is the use of the regression line to estimate a mean of y-values for an x-value that is far outside the x-range of data.
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find the gradient vector field of f. f(x, y) = xe3xy
The gradient vector field of function f(x,y) is given as follows:
grad(f(x,y)) = (1 + 3xy)e^(3xy) i + 3x²e^(3xy) j.
How to obtain the gradient vector field of a function?
Suppose that we have a function defined as follows:
f(x,y).
The gradient function is defined considering the partial derivatives of function f(x,y), as follows:
grad(f(x,y)) = fx(x,y) i + fy(x,y) j.
In which:
fx(x,y) is the partial derivative of f relative to variable x.fy(x,y) is the partial derivative of f relative to variable y.The function in this problem is defined as follows:
f(x,y) = xe^(3xy).
Applying the product rule, the partial derivative relative to x is given as follows:
fx(x,y) = e^(3xy) + 3xye^(3xy) = (1 + 3xy)e^(3xy).
Applying the chain rule, the partial derivative relative to y is given as follows:
fy(x,y) = 3x²e^(3xy).
Hence the gradient vector field of the function is defined as follows:
grad(f(x,y)) = (1 + 3xy)e^(3xy) i + 3x²e^(3xy) j.
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Find the value of a for which v = [6 -10 4 a] is in the set H = span
The value of a for which v is a linear combination is given as follows:
a = -8.
How to obtain the value of a?
A vector generated by adding two or more vectors (with various orientations) and multiplying by scalar values is known as a linear combination of two or more vectors.
v will be a linear combination of the set H if it can be obtained as the solution of a system of equations from the set H.
From the vectors, the system is defined as follows:
-x = -1.
2x - y = 4.
5x + 4y - 3z = -6.
-x + 3y - z = a.
From the first equation, the value of x is obtained as follows:
-x = -1
x = 1.
From the second equation, the value of y is obtained as follows:
2x - y = 4
2 - y = 4
y = 2 - 4
y = -2.
From the third equation, the value of z is obtained as follows:
5x + 4y - 3z = -6.
5 - 8 - 3z = -6
3z = 3
z = 1.
Then the value of a needed for the linear combination is of:
a = -x + 3y - z
a = -1 - 6 - 1
a = -8.
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A primary credit card holder's card has an APR of 11.99%. The current monthly balance, before interest, is $6,299.59. The cardholder makes a
payment of $350 the first 11 months and then pays off the balance at the end of the 12th month. How much more did the credit card holder pay over the 12 months versus paying the balance in full before the end of the first month?
A. 123.02
B $562.73
C $211.04
D $559.56
The credit card holder paid an additional D. $559.56 over the 12 months versus paying the balance in full before the end of the first month.
How is the additional payment determined?The additional payment made by the credit card holder results from paying installments instead of clearing the balance in the first month.
Installment plans attract finance charges at an annual percentage rate (APR), which increases the total amount paid.
Therefore, the additional payment is the difference between the total installment payments and the credit card balance at the beginning of the first month.
N (# of periods) = 12 months
I/Y (Interest per year) = 11.99%
PV (Present Value) = $6,299.59
PMT (Periodic Payment) = $-350
Results:
FV = $3,009.15
Sum of all periodic payments = $3,850 ($350 x 11)
Total Interest = $559.57
The total amount paid over the 12 months = $6,859.15 ($3,009.15 + $3,850)
The total amount paid in full in the first month = $6,299.59
Additional payment made via installments = $559.56 ($6,859.15 - $6,299.59)
Thus, for making installment payments, the credit card holder incurred the additional cost of Option D.
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What are some benefits of representing data sets using frequency distributions What are some benefits of using graphs of frequency distributions? What are some benefits of representing data sets using frequency distributions? Organizing the data into frequency distribution can make patterns within the data more evident: Organizing the data into frequency distribution makes it possible to graph quantitative data_ It is easier t0 determine the minimum and maximum values of a data set when has been arranged into a frequency distribution. What are some benefits of using graphs of frequency distributions? It can be easier t0 determine the class boundaries by looking at a graph of the frequency distribution_ Graphing a frequency distribution makes possible to determine the relative frequencies of each of the classes_ It can be easier to identify patterns of a data set by looking at a graph of the frequency distribution_ Graphing frequency distribution makes it possible to find the total number of observations.
That's so the 4th 1 option is correct organizing their data into a frequency distribution and the 2nd option C.
Frequency distributions are visual displays that organise and present frequency counts so that the information can be interpreted more easily. Frequency distributions can show absolute frequencies or relative frequencies, such as proportions or percentages. It is easier to identify patterns of our data set by looking at a graph of the frequency distribution. So here is both the points which are given in the caution. So the first point option is correct organizing the data into a frequency distribution can make patterns within the data more evident And the 2nd point option C. is correct. It is easier to identify patterns of our data set by looking at a graph of the frequency distribution.
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apparently i’m supposed to solve for x? please someone explain this i’m stuck
Answer:
solve for N cause that is the only variable
Step-by-step explanation:
When a constant force acts upon an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with mass 2kg, the acceleration of the object is 26 m/s^2 If the same force acts upon another object whose mass is 13kg, what is this object's acceleration?
A ∝ 1/M
A = K/M
A is the acceleration and M is the mass of the object.
The object's acceleration for an object of mass 13 kg is 4 m/s²
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 8 is an equation.
We have,
When a constant force acts upon an object, the acceleration of the object varies inversely with its mass.
This means,
A ∝ 1/M
A is the acceleration and M is the mass of the object.
Now,
A = K/M
26 = K / 2
K = 26 x 2
k = 52
Now,
M = 13
A = K/M
A = 52/13
A = 4 m/s²
Thus,
The object's acceleration for an object of mass 13 kg is 4 m/s²
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Sergio says the triangle DEF was dilated by a scale factor of 5/2. Simone says triangle DEF was dilated by a scale factor of 3/2.
write an explicit rule for the nth term of
7, 9, 13, 21, 37
man how?
Answer:
as per the question the nth term is 7,9,13,21,37,69.
Step-by-step explanation:
By looking at the consecutive numbers We can understand, the difference of consecutive terms of given series: 7, 9, 13, 21, 37,… forms a G.P.: 2, 4, 8, 16, 32, …. And more.
So when we subtract the first term from the second term we get:
9−7=2 and after doing the same for the following numbers we get: -
13−9=4
21−13=8
37−21=16
Let the nth term be x,
x−37=32 and now solve this equation to get the nth term∴x=32+37
=69
hence the next term is 69
Letting × represent the number of messages over 500, and y the total monthly charges, write equations representing the charges for plans A and B.
Then graph the equations for plans A and B on the same coordinate grid.
The system of equations representing the charges for plans A and B include the following:
y = 0.2x - 50
y = 0.3x - 105
A graph of the system of equations for plans A and B are shown in the image attached below.
How to write the system of equations representing the charges?In order to write the system of equations representing the charges, we would have to calculate the slope of the line based on the data points described above for each plans.
Mathematically, the slope of a straight line can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (66 - 50)/(580 - 500)
Slope, m = 16/80
Slope, m = 0.2
At point (500, 50), a linear equation for plan A can be calculated by using the point-slope form:
y - y₁ = m(x - x₁)
Where:
x and y are the points.m represents the slope.c represents the y-intercept.Substituting the given points into the point-slope form formula, we have;
y - 50 = 0.2(x - 500)
y - 50 = 0.2x - 100
y = 0.2x - 100 + 50
y = 0.2x - 50.
For plan B, the slope is as follows;
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (69 - 45)/(580 - 500)
Slope, m = 24/80
Slope, m = 0.3
At point (500, 45), a linear equation for plan B can be calculated by using the point-slope form:
y - y₁ = m(x - x₁)
y - 45 = 0.3(x - 500)
y - 45 = 0.3x - 150
y = 0.3x - 150 + 45
y = 0.3x - 105.
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Complete Question:
Three cell phone plans, A, B, and C, each have a different flat monthly rate for the first 500 text messages and a different constant rate for every additional message over 500. These tables show the monthly charges for plans A and B when different numbers of messages are sent. Plan A Cell Phone Charges
Phone plans A and B each have a different flat monthly rate for the first 500 text messages and a different constant rate for every additional message over 500.
Plan A charges $50 monthly for 500 text messages and $66 monthly for 580 text messages.
Plan B charges $45 monthly for 500 text messages and $69 monthly for 580 text messages.
Letting x represent the number of messages over 500, and y the total monthly charges, write equations representing the charges for plans A and B. Then graph the equations for plans A and B on the same coordinate grid.
a pair of 6-sided dice is thrown. someone tells you that both the dice are showing an even number. with this information, what is the probability of the total (when you sum up the dice) being equal to 8?
As per the given dice, the probability of the total being equal to 8 is 1/9 or 11.11%.
Probability:
In statistics, probability refers the possibility of the particular event.
Given,
Here we need to find the probability of the total (when you sum up the dice) being equal to 8.
In order to calculate this probability, we must first calculate all the possible combinations of two six-sided dice that add up to 8.
Hence both the dice are showing an even number, the possible combinations are (2, 6), (4, 4), and (6, 2). the total number of possible combinations for two six-sided dice is 36 (6 x 6).
So, the probability of the total being equal to 8 is 3/36 or 1/9 or 11.11%.
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|9x| ≥ 27 what are the solutions of this inequality
Answer:
x ≤ -3 or x ≥ 3
Step-by-step explanation:
Answer:
To solve this inequality, you can start by isolating the absolute value term on one side of the inequality. To do this, you can subtract 9x from both sides, which gives you:
|9x| - 9x ≥ 27 - 9x
|9x| - 9x ≥ -9x
Next, you can apply the properties of absolute values to simplify the expression. The absolute value of a number is always positive, so the absolute value of any expression will be equal to the expression itself if it is positive, and equal to the negative of the expression if it is negative.
Since the inequality is "greater than or equal to," you need to consider both cases.
If 9x is positive:
9x - 9x ≥ -9x
0 ≥ -9x
x ≤ 0
If 9x is negative:
-9x - 9x ≥ -9x
-18x ≥ -9x
-9x ≥ 0
x ≤ 0
In both cases, the solution is x ≤ 0. This means that any value of x that is less than or equal to 0 will satisfy the inequality.
To write this solution in interval notation, you can use the notation [0,∞) to represent all values of x that are greater than or equal to 0. Alternatively, you can use the notation (-∞,0] to represent all values of x that are less than or equal to 0.
Step-by-step explanation:
Please answer the question below:
Answer:
Given, x²+y²+4X −2y= −1
⇒x²+4x+y²=−1
⇒(x²+4x+4)+(y² −2y+1) =−1+4+1
⇒(x+2)²+(y−1) = 2²
Clearly, = (−2,1)
Radius = 2
The radius of the circle is 2. Therefore, A) is the answer
How to find the radius of the circle using the equation?
The standard form of the equation of a circle is
(x-a)² + (y-b)² = r²
where (a, b) is the center and r is the radius
Given the equation of the circle as x² + y² + 4x - 2y = -1
Factorize the equation using the completing square:
x² + y² + 4x - 2y = -1
x² + 4x + (2)² + y² - 2y + (-1)² = -1 + (2)² + (-1)²
(x+2)² + (y-1)² = -1 + 4 + 1
(x+2)² + (y-1)² = 4
(x+2)² + (y-1)² = 2²
Comparing this equation with (x-a)² + (y-b)² = r²:
r = 2
Thus, the radius of the circle is 2
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Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options.
The steps that she could use to solve the quadratic equation is determined as 2(x² + 6x + 9) = 18 + 3.
How to solve the equation by quadratic equation?x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem.
The Following is the determination of the quadratic equation's solution;
2x² + 12x - 3 = 0
2x² + 12x = 3
multiply across by two
x² + 6x = ³/₂
Add the two sides of the equation after squarely multiplying the coefficient of x by half.
(x + 3)² = ³/₂ + 3² + 6x + 9 =
9 + ³/₂ (x² + 6x + 9)
= 18 + 3
Thus, the steps that she could use to solve the quadratic equation is determined as 2(x² + 6x + 9) = 18 + 3.
The complete question is : Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Check all that apply.
2(x2 + 6x + 9) = 3 + 18
2(x2 + 6x) = –3
2(x2 + =6x) = 3
x + 3 = 21/2
2(x2 + 6x + 9) = –3 + 9
(x + 3)2 = 6/2
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for a two-factor study with 2 levels of factor a, 2 levels of factor b, and a separate sample of 10 participants in each treatment condition, the two means for level a1 are 4 and 1, and the two means for level a2 are 3 and 2. for these data, what is the value of ss between treatments?
As per the two factor study, the value of s is 60.
Two factor study
In math, two factor study defined as an experimental design in which data is collected for all possible combinations of the levels of the two factors of interest.
Given,
Here we have that for a two-factor study with 2 levels of factor a, 2 levels of factor b, and a separate sample of 10 participants in each treatment condition, the two means for level a1 are 4 and 1, and the two means for level a2 are 3 and 2.
And we need to find the value of s between treatments.
As per the given question, we have identified that the values,
Number of participants = 10
And we also know that, level a1 are 4 and 1, and the two means for level a2 are 3 and 2.
So, based on the two factor method, the value of s calculated as,
Here we have to multiple factors first,
=> 3 x 2 = 6
And then multiply that by n = 10,
=> 6 x 10 = 60
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Help please! Two angles are complementary. One is three times the measure of the other. What are the measures if each angle?
Answer: 22.5 and 67.5
Step-by-step explanation:
A complementary angle means that two angles add up to 90°
If one angle is 3 times the other,
let x be the value of the other angle.
The bigger angle would be 3x.
Therefore,
3x+x=90°
4x=90°
x=22.5
22.5 is the measure of the smaller angle
and 22.5x3=67.5 would be the other (larger) angle.
Answer:
22.5 degrees and 67.5 degrees
Step-by-step explanation:
3x + x = 90
4x=90
x=90/4
x=22.5
other angle is 3x which is 67.5
the price of an book is $10. to buy the book. Rosie must also pay 6% sales tax. Rosie wants to know the total price of the book including sales tax.
Turn a percent into a decimal by moving the decimal point two to the left.
10 x 6% = 10 x .06
10 x .06 = .60
Sales tax: 60 cents
Total price: $10.60
2) At a concert, 35% of the audience members were teenagers. If the number of audiences at the concert was 1800, what was the number of teenager members?
Answer:
630
Step-by-step explanation:
35% of 1800 = 0.35 × 1800 = 630
does the injection and surjection have to come from the same function for there to exist a bijection
No, the injection and surjection do not have to come from the same function for there to exist a bijection between the two sets.
A bijection is a mathematical function that establishes a one-to-one correspondence between two sets, known as the domain and codomain. This means that for every element in the domain, there is exactly one element in the codomain, and vice versa. A bijection is both an injection and a surjection, meaning that it is both injective and surjective. Injective means that each element in the domain is mapped to a unique element in the codomain, while surjective means that every element in the codomain is mapped to at least one element in the domain. Therefore, a bijection establishes a perfect match between the two sets, where each element of one set is paired up with a unique element of the other set.
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A pilot flies in a straight path for 1 h 30 min. She then makes a course correction, heading 10 degrees to the right of her original course, and flies 2 h in the new direction. If she maintains a constant speed of 670 mi/h, how far is she from her starting position?
On solving the provided question, we got to know that - distance she covered from her starting position is 2731 miles
What is equation?If two things are equal, an equation declares it. A "=" equals sign will appear in the format: 7 + 2 = 10 − 1 What is on the left (7 + 2) equals what is on the right (10 1), according to that equation. The statement "this equals that" is analogous to an equation.
The flight's first leg is 1020 miles long and lasts (1.5 hours) at 680 mph. We'll refer to this as our triangle's side B.
The second leg of the journey is 1360 miles (2 hours x 680 mph) long. We'll refer to this as the triangle's side C.
The law of cosines allows us to determine the triangle's side a's length.A is a 170° angle between the two sides whose lengths we are aware of. (180° - 10° = 170°).
[tex]a^2 = b^2 + c^2 - (2)*(a)*(b)*cos(A)[/tex]
[tex]a^2 = (1020 miles)^2 + (1360 miles)^2 - (2)*(1020 miles)(1360 miles)*cos(170)\\ a^2 = 1040400 miles^2 + 1849600 miles^2 - (2774400 miles2)*cos(170)\\ cos(170) = -0.9848\\ a^2 = 2890000 miles^2 + 2732251 miles^2 = 5622250.6 miles^2\\ a = (5622250.6 miles^2)^{\frac{1}{2} } = 2371 miles[/tex]
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This design began from the construction of a regular hexagon.
Select all true statements about quadrilateral JKLO.
1.) When JKLO is reflected across segment OA, JKLO is taken to HGLO. So, quadrilateral JKLO is congruent to quadrilateral HGLO.
2.) When JKLO is reflected across segment OJ, JKLO is taken to JIHO. So, quadrilateral JKLO is congruent to quadrilateral JIHO.
3.) When JKLO is reflected in any way, it will not produce another congruent quadrilateral in this figure. However, there is a way to translate JKLO to take it to another quadrilateral in this figure.
4.) When JKLO is reflected across segment OI, JKLO is taken to JIHO. So, quadrilateral JKLO is congruent to quadrilateral JIHO.
5.) When JKLO is reflected across segment OL, JKLO is taken to HGLO. So, quadrilateral JKLO is congruent to quadrilateral HGLO.
The true statements regarding the construction are statement 2) and statement 5)
What is construction?"Construction" in Geometry means to draw shapes, angles or lines accurately. These constructions use only compass, straightedge (i.e. ruler) and a pencil.
Given that, A design began from the construction of a regular hexagon.
The true statements made on the construction is;
2) When JKLO is reflected across segment OJ, JKLO is taken to JIHO. So, quadrilateral JKLO is congruent to quadrilateral JIHO.
5) When JKLO is reflected across segment OL, JKLO is taken to HGLO. So, quadrilateral JKLO is congruent to quadrilateral HGLO.
Hence, The true statements regarding the construction are statement 2) and statement 5)
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BRAINLIEST TO BEST SOLUTION! The question is attached. THANK YOU FOR YOUR HELP!
Answer: not sure on this problem too
Step-by-step explanation:
sorry, can't really help!
The area of the circle is 66.50cm²
How to calculate the area of the circle?A circle is an object in which all distances are equal from the center.
In a circle, the length of the two tangents are equal.
From the figure, BP=CP
Also, the angles between a tangent and a radius is = 90⁰
⇒<OCP=90⁰
<PCB=<PBC=(180-60)/2 = 120/2 = 60⁰
Using cosine rule,
p²=b²+c²-2bccosP
p²=8²+8²-2*8*8*cos60
p²=64+64-128*0.5
p²=128-64
p²=64
Take the square root of both sides to get
p=√64=8
Note that CB=8 .....................(given)
Cx=8/2=4cm
Using trigonometric ratio
CosC = Adjacent/Hypotenuse
Cos30 = 4/CO
CO = 4/cos30
CO = 4/0.8660
CO = 4.6cm
CO = radius (r)
Area of circle = пr²
Area = 22/7 * 4.6 * 4.6
Area = 66.50 cm²
In conclusion, the area of the circle is 66.50cm²
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Quadrilateral STUV is similar to quadrilateral WXYZ. Find the measure of side XY.
Figures are not drawn to scale.
Answer:
11.4
Step-by-step explanation:
Given these quadrilaterals are similar, all we have to do is divide 21 (ST) by 5.7 (WX). That should give us 3.6842105263, which is the scale factor. To find the length of XY, we have to divide UT (the side similar to XY) by the scale factor. UT = 42, and 42/3.6842105263 = 11.4
Answer:
11.4
Step-by-step explanation: