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What is the measure of angle R?
A) 17 degrees
B) 25 degrees
C) 34 degrees
D) 65 degrees
Answers
The measure of angle R is approximately 91.8 degrees.
How to find the value angle R?We can use the law of cosines to solve for angle R in triangle PQR, since we know the lengths of two sides and the included angle:
\(c^2 = a^2 + b^2 - 2ab cos(C)\)
where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides.
In this case, we want to solve for angle R, so we'll use c = PR = 36, a = PQ = 20, and b = QR. We can find QR using the Pythagorean theorem, since triangle PQR is a right triangle with right angle at Q:
\(QR^2 = PR^2 - PQ^2\)
\(QR^2 = 36^2 - 20^2\)
\(QR^2 = 776\)
\(QR = \sqrt(776) = 28\sqrt(2)\)
Now we can use the law of cosines to solve for angle R:
\(c^2 = a^2 + b^2 - 2ab cos(C)\)
\(36^2 = 20^2 + (28sqrt(2))^2 - 2(20)(28sqrt(2)) cos(R)\)
\(1296 = 400 + 784 - 1120\sqrt(2) cos(R)\)
\(cos(R) = (400 + 784 - 1296)/(1120\sqrt(2))\)
cos(R) = -0.0271
R = arccos(-0.0271)
R = 91.8 degrees (rounded to one decimal place)
Therefore, the measure of angle R is approximately 91.8 degrees.
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Related Questions
\( {4}^{3} \)
evaluate this expression
Answers
Answer:
64
Step-by-step explanation:
Answer:
64
Step-by-step explanation:
4^3
= 4 * 4 * 4
= 16 * 4
= 64
If a line is tangent to a circle, then it is ___________ to the radius drawn to the point of tangency.
Answers
If a radius is drawn to the point of tangency of a tangent line, then the radius is basically perpendicular to the tangent line.
Given that the radius is drawn to the point of tangency of a tangent line.
We are required to fill the blank with the appropriate word.
Radius is basically the line segment which joins the center to any point on the circumference of the circle.
Tangent line is basically a line which is drawn from an outside point on the circumference of the circle.
When the radius is drawn to the point of tangency of a tangent line, then the radius is perpendicular to the tangent line.
Hence if a radius is drawn to the point of tangency of a tangent line, then the radius is perpendicular to the tangent line.
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Hexagon DEFGHI is translated on the coordinate plane below to create hexagon D′E′F′G′H′I′: Hexagon DEFGHI and Hexagon D prime E prime F prime G prime H prime I prime on the coordinate plane with ordered pairs at D 2, 5, at E 5, 5, at F 6, 3, at G 5, 1, at H 2, 1, at I 1, 3, at D prime negative 6, negative 2, at E prime negative 3, negative 2, at F prime negative 2, negative 4, at G prime negative 3, negative 6, at H prime negative 6, negative 6, at I prime negative 7, negative 4
Answers
Answer: To find the image of a figure under a translation, you need to apply the same translation to every point in the figure.
In this case, the image of hexagon DEFGHI is hexagon D′E′F′G′H′I′. To find the image of each point, you can apply the translation that maps point D to point D′.
For example, to find the image of point E under the translation, you can apply the same translation that maps point D to point D′:
Point D is located at (2, 5).
Point D′ is located at (-6, -2).
The translation that maps point D to point D′ is a translation 6 units to the left and 2 units down.
To find the image of point E under this translation, you can apply the same translation to point E:
Point E is located at (5, 5).
The image of point E is located at (5 - 6, 5 - 2) = (-1, 3).
You can follow the same process to find the images of the other points under the translation.
Alternatively, you can use the coordinates of point D and point D′ to find the translation vector that describes the translation. The translation vector is a displacement that describes the change in position of a point under the translation.
In this case, the translation vector is given by the displacement from point D to point D′:
Point D is located at (2, 5).
Point D′ is located at (-6, -2).
The translation vector is given by the displacement (-6 - 2, -2 - 5) = (-8, -7).
To find the image of any point under the translation, you can add the translation vector to the coordinates of the point. For example, to find the image of point E under the translation, you can add the translation vector to the coordinates of point E:
Point E is located at (5, 5).
The translation vector is (-8, -7).
The image of point E is located at (5 - 8, 5 - 7) = (-3, -2).
You can follow the same process to find the images of the other points under the translation.
Step-by-step explanation:
An arithmetic sequence is given below.
16, 13, 10, 7, ...
Which is the explicit formula for the nth term an?
Answers
The answer is
a (n) = -3n +22
Answer:
Nth term: -3n+19
Step-by-step explanation:
You can see the sequence is decreasing by 3 each time so the Nth term is -3n.
The 0 term would therefore be 19 so the formula would be -3n+19.
work this out 8.26 + 2 =
a. 4.13
b.5.13
c.5.20
Answers
Answer:
10.26
Step-by-step explanation:
This is the answer because:
1) 8 + 2 = 10
2) Now, just add .26 to 10 which is 10.26
Hope this helps! :D
What type of job is usually paid off of commission?
1. Teacher
2. Car salesman
3. Computer technician
4. Doctor
Answers
Correct Answer: car salesman
what is the x normally stand for?
Answers
Answer:
The letter "x" is often used in algebra to mean an unknown value. It is often called a "variable".
Example:
In x + 5 = 12, x is a variable, but we can work out its value if we try!
A group of five friends are long-distance runners who will be running in an upcoming marathon. To prepare for the marathon, each of the friends recorded the number of miles they ran each week for 12 weeks. The results of the friends' training are shown in the data set provided below. Which of the friends was the most consistent with the number of miles run each week during the training? Hint: You should not need to compute the standard deviation for each friend.
Answers
The most consistent friend with the number of miles run each week during the training is given as follows:
Caleb.
How to obtain the mean and the standard deviation of a data-set?The mean of a data-set is given by the sum of all values in the data-set, divided by the cardinality of the data-set, which is the number of values in the data-set.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the cardinality of the data-set.Looking at each value, we have that Caleb's values are quite close to each other, hence the sum of the differences squared is the smallest, and thus he has the lowest standard deviation.
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pleaseee somebody tell me the answer.
Answers
Answer:
aprx. 50.24 inches
Step-by-step explanation:
I hope this helps! :)
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Which fractions are equal to 0.6
1 over 6,60 over 100,1 over 60,6 over 10
Answers
What should be the third row in the following series of shapes
Answers
Answer:
The answer is number 2
pls answer
worth 25 points!!!!!
Answers
Answer:
\( \sf \: c \: = \: 28.3\)
Step-by-step explanation:
To find the circumference of a circle .
We have to use the formula,
Where, C = \( 2 \pi r \)
\( \pi \) = 3.142
\( r \) = 4.5m
So,
C = 2 × 3.142 × 4.5
C = 28.278 ≈ 28.3
Answer: 28.3
Step-by-step explanation:
C=2\(\pi r\)
=2\(\pi\)(4.5)
=28.3 m
Simplify (-18^2)^3.
18^-6
-18^5
1/18^6
-18^6
Answers
-18^6
Step-by-step explanation:
Which of the following are true about a line in Geometry?
a line can be measured
a line does not have to be straight
a line is named using 3 points (3 letters)
O a line has an arrow on both sides indicating that it goes forever in both directions
a line has an arrow on one side indicating that it goes forever in only that
direction
Submit Answer
Answers
Answer:
a line has arrow on both sides indicating that it goes forever in both directions.
The mapping diagram represents a relation where x represents the independent variable and y represents the dependent variable.
Is the relation a function? Explain.
O Yes, because for each input there is exactly one output
Yes, because for each output there is exactly one input
O No, because for each input there is not exactly one output
O No, because for each output there is not exactly one input
Answers
To verify if the relation is a function, it must be verified if from each value of x only one arrow departs.
When does a relation represents a function?A relation represents a function when each input value is mapped to a single output value.
In mapping notation, with the arrows, it must be verified if there is no input from which more than one arrow departs.
Missing Information
The problem is incomplete, hence the general procedure to verify if the relation is a function was presented.
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HELLPPP PLSSS!! i need help help help
Answers
Answer:25.50
Step-by-step explanation:
Because .50 is in the hundreths, and it rounds up to that because it is above 5.
If 14 bags of mulch cost $51.10, how much would 35 bags Cost round answer to the nearest cent
Answers
Answer:
127.80
Step-by-step explanation:
14 ÷ 51.10 = 3.65
3.65 × 35 = 127.75
127.75 = 127.80 (rounded off)
Consider the function represented by the table.
For which x is f(x)=-3?
0-7
0 4
X
-7
-3
2
4
f(x)
-3
5
-4
-8
04
05
Answers
Answer:
B. -4
Step-by-step explanation:
Just took the test on Edge it is correct.
Considering the table given, it is found that the value of x for which f(x) = -3 is of x = -7.
What is the table representing the function?The table is a set of points (x, f(x)), hence from it we get that it has these following points:
f(-7) = -3;f(-3) = 5;f(2) = -4;f(4) = -8;Hence, the value of x for which f(x) = -3 is of x = -7.
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I need to know how how to do these please.
Answers
The scatter plot shows negative correlation because as the plotted values of x increase, the values of y generally decrease.
What is negative correlation?When two variables are said to have negative correlation, it means that they move in the opposite direction from each other. When one variable is increasing, the other variable is decreasing.
The values of x and y in order of x are:
x 3 4 5 6 7 8 9
y 6 7 5 4 3 4 2
As shown above, when x increases, y generally decreases and when x decreases, y generally increases. This is therefore a negative correlation relationship.
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explain 3 factors that should be considered in the construction of index numbers
Answers
1. selection of index number: during the construction of index number it is to be kept in mind that the selection of the index number should be correct accordingly.
2. selection of formula: while the construction of index numbers it is compulsory to select the correct formula for the given question.
3. selection of price: selection of prices should be done accordingly while constructing the index numbers.`
construction of index number is also available in two parts:
1. simple
2. weighted
1. simple: the simple method is classified into simple aggregative and simple relative.
2. weighted: the weighted method is classified into a weighted aggregative and weighted average.
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Ghana van company invested P45 700 for two years at a rate of 12%per annum compounded for quarter year. Work out the compound interest over the two years
Answers
\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$45700\\ r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &2 \end{cases}\)
\(A = 45700\left(1+\frac{0.12}{4}\right)^{4\cdot 2}\implies A=45700(1.03)^8 \implies A \approx 57891.39 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{earned interest}}{57891.39~~ - ~~45700} ~~ \approx ~~ \text{\LARGE 12191.39}\)
help me please i really need it I need solution.
Answers
Answer:
Step-by-step explanation:
1. To figure this out, you need to first convert the percentage to a decimal. To do this, you move the decimal two places back. 75.0% -> 0.75
40 * 0.75 = 30 students are present, because 75% of 40 is 30
40 - 30 = 10 students are absent, because 30 students are present.
2. To figure this out, you must do the same thing you did for number 1 above. It would look like this: 80% -> .80
250 * 0.8 = 200 euros - not sure if that's what it is but that is what I'm going with - is what she spent, because 80% of 250 is 200
250 - 200 = 50 is what she saved.
The diameter of a circle is 8cm. Find its circumference to the nearest tenth.
Answers
Answer:
\(C = 25.1 \text{ cm}\)
Step-by-step explanation:
We can find the circumference of the circle by plugging the given radius value 8 cm into the formula:
\(C = \pi d\)
Note: This formula can also be written as \(C = 2\pi r\) because \(2r = d\).
↓ plugging in the given radius
\(C = 8\pi \text{ cm}\)
↓ rounding to the nearest tenth
\(\boxed{C = 25.1 \text{ cm}}\)
Find the 87th term in the following
arithmetic sequence:
-2, 6, 14, 22, ...
Hint: Write a formula to help you.
1st term + common difference (desired term - 1)
Answers
Answer:
first term (a)=-2
common difference (d)=8
Now,
87th term=a+(n-1)d
=-2+(87-1)×8
=-2+86×8
=-2+688
=686
The selling price of an item is 495$. It is marked down by 20%, but this sale price is still marked up from the cost of 360$. Find the markup from cost to sale price.
Answers
Answer:
396
Step-by-step explanation:
The solution is $ 36
The markup from the cost price to the sale price is $ 36
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the markup from the cost to the sale price be = A
Now , the equation will be
Let the initial selling price of an item be = $ 495
Now , it is marked down by 20 %
So ,
The new selling price after marked down = initial selling price of an item -
( 20 / 100 ) initial selling price of an item
Substituting the values in the equation , we get
The new selling price after marked down = 495 - ( 20/100 ) x 495
The new selling price after marked down = 495 - ( 0.2 x 495 )
The new selling price after marked down = 495 - 99
The new selling price after marked down = $ 396
The new selling price is marked up from the cost price of = $ 360
So , the equation will be
The markup from the cost to the sale price = new selling price after marked down - marked up from the cost price
Substituting the values in the equation , we get
The markup from the cost to the sale price = 396 - 360
The markup from the cost to the sale price = $ 36
Therefore , the value of A is $ 36
Hence , the markup from the cost price to the sale price is $ 36
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Solve for x
A) 9
B) 11
C) 5
D)-4
Answers
LOLLL HELO HELP PLS PLS PLS
Answers
Answer: C
2 1/6 x 1 1/3 = 26/9 which = 2 8/9
Solving a distance, rate, time problem using a system of linear
A motorboat travels 124 kilometers in 4 hours going upstream. It travels 180 kilometers going downstream in the same amount of time. What is the rate of the
boat in still water and what is the rate of the current?
Answers
Answer:
boat: 38 km/hcurrent: 7 km/hStep-by-step explanation:
Let b and c represent the rates of the boat and current, respectively. The speed upstream is ...
speed = distance/time
b -c = (124 km)/(4 h) = 31 km/h
And the speed downstream is ...
b +c = (180 km)/(4 h) = 45 km/h
Adding the two equations gives ...
2b = 76
b = 38
From the first equation, ...
c = b -31 = 38 -31 = 7
The rate of the boat in still water is 38 km/h; the rate of the current is 7 km/h.
What is the equation of the line in slope intercept form?
Answers
Answer:
y = x + 60
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = (20, 80) and (x₂, y₂ ) = (40, 100) ← 2 points on the line
m = \(\frac{100-80}{40-20}\) = \(\frac{20}{20}\) = 1
the line crosses the y- axis at (0, 60 ) ⇒ c = 60
y = x + 60 ← equation of line
Pls help me pls dont answer if you dont know
Answers
Answer:
the answer is 147
Step-by-step explanation:
first you do 3.5cm times 84cm which is 294cm
then you do 294cm divided by 2 which is 147cm
the reason why you divide by 2 is because parallelograms like the triangle can be also halved into 2 separate triangles!!
hope this helped <3