5. If R(2.2) and S(5.4) i. Calculate the magnitude of RS ii. Express RS in the form (K,D), where K is the magnitude and Q the bearing.
Answer:
We have:
R = (2, 2)
S = (5, 4)
RS is the segment that connects R with S.
So RS is just the distance between R and S.
Remember that the distance between two points (a, b) and (c, d) is given by:
[tex]distance = \sqrt{(a - c)^2 + (b - d)^2}[/tex]
Then the distance between S and R is
[tex]distance = \sqrt{(5 - 2)^2 + (4 - 2)^2} = \sqrt{3^2 + 2^2} = \sqrt{13}[/tex]
Then:
RS = √13
ii) Now we want to express RS in the form (K, Q)
where K is the magnitude (we already know that it is √13) and Q is the bearing, which is measured with respect to the horizontal axis.
To interpret the bearing, let's look at the image below:
We can use the relation:
Tan(θ) = (opposite cathetus)/(adjacent cathetus)
where the opposite cathetus is just the difference between the y-values:
Opposite cathetus = 4 - 2 = 2
And the adjacent cathetus is the difference between the x-values:
Adjacent cathetus = 5 - 2 = 3
Then we have:
Tan(θ) = 2/3
If we apply the inverse tangent equation to both sides, we get:
Atan(tan(θ)) = Atan(2/3)
θ = Atan(2/3) = 33.69°
The bearing is 33.69°
then:
RS = (√13, 33.69°)
Question: Consider the graph of f(x) = 5^x + 1. Explain how to find the average rate of
change between x = 0 and x = 4. What is the average rate of change?
Answer:
156
Step-by-step explanation:
Given that,
[tex]f(x)=5^x+1[/tex]
We need to find the average rate of change between x = 0 and x = 4. It can be calculated as follows :
[tex]r=\dfrac{f(4)-f(0)}{4-0}\\\\=\dfrac{5^4+1-(5^0+1)}{4-0}\\\\=156[/tex]
So, the average rate of change between x = 0 and x = 4 is 156.
What is the solution of the equation, n + 12 = 12?
n = ______
Which value is equal to 1/2 ?Select all that apply.
Please help fast fast !! Will give brainliest
Answer:
The Answer to your problem is A i'm pretty sure mark me brainliest plss and a thanks heart !!
77 out of 100 people Prefer sunny days what percentage of people prefer sunny days
Answer:
77% prefer sunny days because 77/100 is equivalent to 77%
if two lines are parallel and one has a slope of 1/6, what is the slope of the other line?
please help me please
Answer:
x=17
Step-by-step explanation:
5^2+3^2=x^2 (get the square of 5,3,and x)
25+9=2x (add)
34=2x (now divide)
17=x there's your answer hope i helped :)
If 90 people were at a game and one-sixth bought programs for $1.50 each,
how much did they spend on programs all together?
Answer:
I'm pretty sure they spent $22.50
Step-by-step explanation:
do (1÷6)×(90) then multiply 15 and 1.50
What is the scale factor from ∆ABC to ∆DEF?
Answer:
D
Step-by-step explanation:
6*8 = 48
4*8 = 32
A test has multiple choice questions with 3 choices for each answer; only one answer is correct for each question. Suppose a student guesses the answer to each question. Assuming the guesses are independent, find the probability that the student will guess correctly when answering two questions.
Answer:
a
Step-by-step explanation:
10
1
board/home
Solving Linear Equations. Tutorial Level
Four times the sum “n plus 10" is 34. What is the
value of n?
Multiply (n + 10) by 4.
4(x + 10) = 34
ESSICA
2
n+
2
= 34
DONE
00
P750
Answer:
-1.5 or -1 1/2
Step-by-step explanation:
I can only guess what is actually asked for. a lot of things went wrong when copying this problem description in here.
the basic question I understand is to solve the equation of
4(n + 10) = 34
=>
n + 10 = 34/4 = 8.5 or 8 1/2
n = 8.5 - 10 = -1.5 or -1 1/2
i need help with this?
i’m so confused
Answer:
See below
Step-by-step explanation:
In #4, the angles are vertical because the angles are congruent to each other. Therefore, you would set up the equation x+8=120 where x=112.
In #5, the angles are complementary because their sum is 90°. Therefore, you would set up the equation 43+x+3=90 where x=44.
In #6, the angles are supplementary because their sum is 180°. Therefore, you would set up the equation 76+2x+4=180 where x=50.
Please help me with this (work out 10% of 13kg)
Answer:
1.3kg
Step-by-step explanation:
Answer:
its 1.3kg
Step-by-step explanation:
to work out 10% of anything just divide it by 10.
e.g 13kg÷10=1.3kg
Which domain would make the list of ordered pairs a function? {(-2, 5), (3, -1), (_, 4), (_, -9), (5, 6)}
Hope this help!!!
Have a nice day!!!
The required domain would make the list of the ordered pairs are-4 and 5.
Given that,
Which domain would make the list of ordered pairs a function, {(-2, 5), (3, -1), (_, 4), (_, -9), (5, 6)} is to be determined.
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
The domain of the function follows the pattern of increasing the number by unit with the alternate sign change,
So the domain of function after 3 is given as -4 and 5.
Thus, the required domain would make the list of the ordered pairs are -4 and 5.
learn more about function here:
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The figures below are congruent. Which series of transformations
maps figure ABCD onto EFGH?
A
F. rotation followed by a translation
G. rotation followed by a dilation
H. reflection followed by a translation
I. reflection followed by
9514 1404 393
Answer:
H. reflection, translation
Step-by-step explanation:
The order of vertices ABCD is clockwise. The order of vertices EFGH is counterclockwise, so a reflection must be involved.
The orientation direction of GH is nearly vertical. The corresponding direction of CD is up to the left. A reflection can make the directions be the same, but the reflection that gets the orientation correct may not put the figure in the correct location.
So, we choose the transformations ...
H. reflection followed by translation
Which graph has a slope of 4/5?
Answer:
I think its the last option i think option D the one one the bottom
Step-by-step explanation:
If helps mark as brainllest
What is the surface area of the rectangular prism shown below?
A: 159
B: 294
C: 318
D: 378
(All squared)
List 2 different ways to name angle 2 shown below.
Let U be the set of all books, N the set of all novels, and H be the set of all hardcover books. Describe, in words, the following sets:
Given:
U be the set of all books, N the set of all novels, and H be the set of all hardcover books.
To find:
The description for the sets [tex]N\cap H[/tex] and [tex]H'[/tex] in words.
Solution:
We have,
U = The set of all books
N = The set of all novels
H = The set of all hardcover books.
We know that [tex]N\cap H[/tex] means common elements of set N and set H.
Therefore, [tex]N\cap H[/tex] is set of all books that are both novels and hardcover books.
We know that [tex]H'[/tex] is the set of elements of universal set except the elements of set H.
Therefore, [tex]H'[/tex] is the set of all books that are not hardcover books.
What is the length of the hypotenuse of the triangle below?
45°
h
5V2
45°
90°
52
The length of the hypotenuse of the triangle whose other two sides are of the length 5√2 units is given by: Option B: 10 units.
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
For this case, consider the figure attached below.
Then, we are given the facts that:
Triangle ABC is a right angled triangle with right angle at vertex BThe lengths of non-hypotenuse sides AB and BC are 5√2 unitsThe length of the hypotenuse AC, denoted by h is to be found.Using the Pythagoras theorem, we get:
[tex]|AC|^2 = |AB|^2 + |BC|^2\\\\h^2 = (5\sqrt{2})^2 + (5\sqrt{2})^2 \\\\h^2 = 2(5\sqrt{2}))^2[/tex]
Taking root, we get:
[tex]h = \sqrt{2 (5\sqrt{2})^2}[/tex] (only positive root since h is denoting length, which is a non-negative quantity).
Thus, we get:
[tex]h = \sqrt{2 (5\sqrt{2})^2} = \sqrt{(5\sqrt{2})^2} \times \sqrt{2} = (5\sqrt{2}) \times \sqrt{2} = 5 \times (\sqrt{2})^2 = 5 \times 2 \\\\h= 10 \: \rm units[/tex]
(square cancelled the square root).
Thus, the length of the hypotenuse of the triangle whose other two sides are of the length 5√2 units is given by: Option B: 10 units.
Learn more about Pythagoras theorem here:
https://brainly.com/question/12105522
Answer:
10 units.
Step-by-step explanation:
just took the quiz
Can Snap say your somewhere when your not with someone????
Answer:
In my choice yes, it helped me I mean snap showed me where I am.
Step-by-step explanation:
if you want to know how then just be online and turn on location
Answer:
if it says that your somewhere when you're not with someone or did not allow snap to know your location someone other than you may access to your account somehow.
id advise you to put extra security for your safety and your account.
Step-by-step explanation:
solve the system of equations y=x-7 y=x^2-9x+18
9514 1404 393
Answer:
(x, y) = (5, -2)
Step-by-step explanation:
Equating expressions for y, we have ...
x^2 -9x +18 = x -7
x^2 -10x +25 = 0 . . . . . add 7-x to both sides
(x -5)^2 = 0 . . . . . . . . factor
The value of x that makes the factor(s) zero is x=5. The corresponding value of y is ...
y = x -7 = 5 -7 = -2
The solution is (x, y) = (5, -2).
The scores and their final grade for a statistics student are given. What is the student’s weighted mean score?
Homework
Quiz
Quiz
Project
Final Exam
Score
86
81
96
99
89
Percent of final grade
20
15
15
25
25
Answer:
a) final exam: 90.2 B b) percent of final grade: 20 F
Step-by-step explanation:
calculator: a)86+81+96+99+89=451/5=90.2
b) 20+15+15+25+25=100/5=20
The weighted mean of a distribution is the sum of the product of the data elements of the distribution by the proportion of each element.
The weighted mean score of the students is 90.75
To calculate the weighted mean score, we simply multiply the score of each student by the percentage grade.
So, we have:
[tex]Mean = 86 \times 20\% + 81 \times 15\% + 96 \times 15\% + 99 \times 25\% + 89 \times 25\%[/tex]
This gives:
[tex]Mean = 17.20 + 12.15 + 14.40 + 24.75 + 22.25[/tex]
[tex]Mean = 90.75[/tex]
Hence, the weighted mean score of the students is 90.75
Read more about weighted mean at:
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You have one each of $0.05, $0.10, $0.25, $1.00 and $2.00 coins in your wallet. How many different sums of money could you form by reaching into your wallet and pulling out some coins?
Answer:
The correct answer is - 26 sums for pulling few coins.
Step-by-step explanation:
Given:
coins in the wallet = 5 ($0.05, $0.10, $0.25, $1.00 and $2.00)
Different sums of money = ?
Formula: Different combination of items can be calculated with the help of a formula of combination that is -
nCr = n! / ((n – r)! r!)
where, n = total number of items
r = number of item in a set
solution:
In this question number of set is not given only few mention so the sets could be 2 coins, 3 coins, 4 coins and 5 coins.
a. for set of 2 coins
= 5! / ((5 – 2)! 2!)
= 20/2
= 10 combination of sums
b. for the set of 3 coins
= 5! / ((5 – 3)! 3!)
= 10
C. for 4
= 5! / ((5 – 4)! !)
= 5
d. for 5 coins
only 1 sum
thus, the total types of different sums = 10+10+5+1
= 26.
what's the formula of finding an area of a room?
Answer:
For a square or rectangular room you will need the length and width
Then you multiply I.e length x width gives Area
bye :-)
Explain how u got the answer!
Answer: 525
Step-by-step explanation:
1000 dogs in 2013 and 4500 dogs in 2016
15 percent in animal shelters
(4500-1000)x0.15 = 525
The circumference of a circle is 47 in. Find its diameter, in inches.
[tex]{ \bf{ \underbrace{Given :}}}[/tex]
Circumference of the circle = 47 inch.
[tex]{ \bf{ \underbrace{To\:find:}}}[/tex]
The diameter of the circle.
[tex]{ \bf{ \underbrace{Solution :}}}[/tex]
[tex]\sf\orange{The\:diameter\:of\:the\:circle\:is\:15\:inch.}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\blue{Step-by-step\:explanation}}{\blue{:}}}}}[/tex]
We know that,
[tex]\sf\purple{Circumference\:of\:a\:circle \:=\:2πr }[/tex]
[tex]\longrightarrow{\blue{}}[/tex] 47 in = 2 π [tex]r[/tex]
[tex]\longrightarrow{\blue{}}[/tex] [tex]r[/tex] = [tex]\frac{47 \times 7}{2 \times 22}[/tex] in
[tex]\longrightarrow{\blue{}}[/tex] [tex]r[/tex] = [tex]\frac{329}{44}[/tex] in
[tex]\longrightarrow{\blue{}}[/tex] [tex]r[/tex] = 7.477 in
Now,
[tex]\sf\pink{Diameter\: of \:the \:circle\: =\: 2 \:r }[/tex]
= 2 x 7.477 in
= 14.954 in
= 15 in ( round to nearest whole number )
Therefore, the diameter of the circle is 15 inch.
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35}}}}}[/tex]
The diameter of the circle is approximately 14.97 inches.
We have,
To find the diameter of a circle given its circumference, we can use the formula:
Circumference = π * Diameter
Given the circumference of the circle is 47 inches, we can rearrange the formula to solve for the diameter:
Diameter = Circumference / π
Substituting the given circumference into the formula:
Diameter = 47 / π
Calculating the value:
Diameter ≈ 14.97 inches
Therefore,
The diameter of the circle is approximately 14.97 inches.
Learn more about Circle here:
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Evaluate:
2n=1(3n + 2) = [?]
Answer:
n = -2
Step-by-step explanation:
2n = 3n + 2
-n = 2
n = -2
Suppose that there are 25 students in a class, each either a freshman, a sophomore, or a junior. How many students must be in the same cohort
Answer:
at least 9 students in each cohort.
Step-by-step explanation:
Given that :
In a class, there are 25 students and each of them is either a sophomore, a freshman or a junior. We have to determine the number students in the same cohort.
Let us suppose there are equal number of students in each of the cohort.
Now let us assume that the number of the students in each cohort be 8, i.e. each as a freshman, a junior or a sophomore. Therefore, the total number in the all the cohorts will be 24 students only.
Thus, we can say that there are at least [tex]9[/tex] freshman, at least [tex]9[/tex] sophomore or at least [tex]9[/tex] junior in each of the cohort.
. What is this number?
It is a 3-digit whole number. It is an odd number. It is divisible by 5 and less than 400. When you get the sum of each digits is equal to 17.
Step-by-step explanation:
when it is divided by 5 we easily know the last digit is 0 or 5
it os odd it can't divided to 2
the some of each digit is 17
so the answer will be 170
170÷5=34
170<400
1+7+0=17 true
485÷5=97
4+8+5=17
but 485>17 false
