Answers
Choice B) [tex]9.9 \angle \underline{76.10^{\circ}}[/tex]
============================================
Explanation:
The given vectors in polar form are
(17,60)
(8,220)
by polar form I mean (r,theta) where
r = magnitude
theta = angle
Convert the polar form (r,theta) = (17,60) to component form
x = r*cos(theta)
x = 17*cos(60)
x = 8.5
y = r*sin(theta)
y = 17*sin(60)
y = 14.72243186
The component form of the first vector is (x,y) = (8.5, 14.72243186)
Do the same for the second vector
x = r*cos(theta)
x = 8*cos(220)
x = -6.1283555
y = r*sin(theta)
y = 8*sin(220)
y = -5.1423009
The component form of the second vector is (x,y) = (-6.1283555, -5.1423009)
Now we add the vectors. Add up the corresponding components
(8.5, 14.72243186)+(-6.1283555, -5.1423009)
(8.5+(-6.1283555) , 14.72243186+(-5.1423009))
(2.3716445, 9.58013096)
So,
(x,y) = (2.3716445, 9.58013096)
is the component form of the resultant vector. Its the vector we get after adding the two original vectors
The last step is to convert this back to polar form
r = sqrt(x^2+y^2)
r = sqrt(2.3716445^2+9.58013096^2)
r = 9.869326564
which is roughly 9.9
theta = arctan(y/x)
theta = arctan(9.58013096/2.3716445)
theta = 76.09548164
which rounds to 76.10
So we end up with (r,theta) = (9.9, 76.10) pointing to choice B as the answer
Related Questions
A trapezoid has bases that measure 10 centimeters and 14 centimeters and a height that measures 8 centimeters. What is the area?
Answers
Hope this helped!
Brainliest Plz?
Use the angle sum identity to find the exact value of cos 105
Answers
Sue can sew a precut dress in 3 hours. helen can sew the same dress in 2 hours. if they work together, how long will it take them to complete sewing that dress? round to one decimal place.
Answers
The LCD is 2*3*t.
If you multiply everything by the LCD, you can clear your fractions.
6t (1/3) + 6t (1/2) = 6t (1/t)
2t + 3t = 6
5t = 6
5t/5 = 6/5
Answer:
Which is: t = 1.2 hrs.
Final answer:
Sue and Helen can sew a dress in 1.2 hours when working together.
Explanation:
Calculating Time to Sew a Dress Together
Sue and Helen are working together to sew a dress and we need to calculate the total time it will take them to complete the sewing when working simultaneously. Sue can sew a precut dress in 3 hours, which means Sue's rate is 1 dress per 3 hours, or
1/3 dress per hour. Helen can sew the same dress in 2 hours, which means Helen's rate is 1 dress per 2 hours, or
1/2 dress per hour. Working together, their combined rate is the sum of their individual rates:
Total rate = 1/3 + 1/2
This results in a combined rate of 5/6 dresses per hour when we find a common denominator and add the fractions. To find the time it takes them to sew one dress together, we take the reciprocal of their combined rate:
Time = 1 / (5/6) hours
This simplifies to 6/5 hours.
Therefore, Sue and Helen will take 1.2 hours to complete the dress when working together.
Find the complement of an angle whose measure is 74 degrees. Show all work.
Answers
angle = 16°
Explanation:
Complementary angles are angles that add up to 90°
Assume that the angle that we are looking for is x.
Based on the definition of the complementary angles, the equation will be as follows:
x + 74 = 90
Now, we will simply solve for x as follows:
x = 90 - 74
x = 16°
Hope this helps :)
Answer:
16⁰
Step-by-step explanation:
Angle = 74⁰
Complement = 90 - 74 = 16⁰
The Truth About Antibacterial Soap
According to Discovery Fit & Health, about 75 percent of liquid soaps claim to be antibacterial. While this kind of soap sounds like a good idea, it is really not more effective than regular soap. Soap in general works by binding with dirt and grime and bacteria. This binding action allows the particles to be washed away easily. Antibacterial soap really does no more than regular soap. In fact, to be more effective than regular soap, antibacterial soap should stay on your skin for about two minutes to do what it claims it can do. Most people do not wash their hands that long. In addition, antibacterial soap may do harm. First it kills both beneficial and harmful bacteria. Second, scientists believe bacteria may become resistant to antibacterial agents over time, especially if they are not used correctly. Finally, antibacterial soap does nothing to viruses. Most of the time, we get sick from viruses, not bacteria. In sum, antibacterial soap does not live up to the hype. You are better off just using regular soap.
Works Cited
Is Antibacterial Soap Any Better than Regular Soap?
http://health.howstuffworks.com/skin-care/cleansing/myths/question692.htm
How is "The Truth About Antibacterial Soap" organized?
Fact by fact
Cause and effect
Chronological order
Problem-solution
its actually language arts not math sorry
Answers
it is organized in chronological order
Answer:
chronlogical order
the other answer for the other question is they dont wash their hand long enough
the point (0,0) is a solution to which of these inequalities?
a.y+7< 2x + 6
b.y- 7< 2x - 6
c.y -6< 2x - 7
d.y + 7< 2x -6
Answers
the apex answer to it D. y – 7 < 2x – 6
Answer: The correct option is (B) [tex]y-7<2x-6.[/tex]
Step-by-step explanation: We are given to select the inequalities that has the point (0, 0) as a solution.
Option (A):
The given inequality is
[tex]y+7<2x+6.[/tex]
At the point (0, 0), we have
[tex]L.H.S.=y+7=0+7=7,\\\\R.H.S.=2x+6=2\times0+6=6.[/tex]
Since 7 > 6, so the point (0, 0) is not a solution to this inequality.
This option is NOT correct.
Option (B):
The given inequality is
[tex]y-7<2x-6.[/tex]
At the point (0, 0), we have
[tex]L.H.S.=y-7=0-7=-7,\\\\R.H.S.=2x-6=2\times0-6=-6.[/tex]
Since -7 < - 6, so the point (0, 0) is a solution to this inequality.
This option is correct.
Option (C):
The given inequality is
[tex]y-6<2x-7.[/tex]
At the point (0, 0), we have
[tex]L.H.S.=y-6=0-6=-6,\\\\R.H.S.=2x-7=2\times0-7=-7.[/tex]
Since -6 > - 7, so the point (0, 0) is not a solution to this inequality.
This option is NOT correct.
Option (D):
The given inequality is
[tex]y+7<2x-6.[/tex]
At the point (0, 0), we have
[tex]L.H.S.=y+7=0+7=7,\\\\R.H.S.=2x-6=2\times0-6=-6.[/tex]
Since 7 > - 6, so the point (0, 0) is not a solution to this inequality.
This option is NOT correct.
Thus, the point (0, 0) is a solution to the inequality [tex]y-7<2x-6.[/tex]
Option (B) is correct.
What is measure of angle C? Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
Answers
What is the value of x?
Answers
Firstly, the sum of all angles in a triangle is equal to 180.
Secondly, supplementary angles are two angles that form a straight line. In other words, the two lines sum up to 180 degrees.
Looking at your figure and the rules written above, you can then assume that the measure of angle x is equal to the sum of the two angles given inside the triangle.
53 + 45 = 98
Angle x is 98 degrees
Please help asap! Match the graph with the correct equation.
Answers
What is true about the solutions of a quadratic equation when the radicand in the quadratic formula is negative? No real solutions Two identical rational solutions Two different rational solutions Two irrational solutions
Answers
no real solutions. <<<< answer.
To confirm this, the question is saying what is the square root of (say) - 5?
There is no answer in the real number system.
Answer:
If the radicand in the quadratic formula is negative then no real solutions possible.
Step-by-step explanation:
Given that when the radicand in the quadratic formula is negative then we have to find the true statement about the solution of quadratic equation.
Radicand of quadratic formula i.e the discriminant of quadratic formula.
[tex]D=b^2-4ac[/tex]
which comes in the solution under the root.
The solution of general quadratic equation is
[tex]x=\frac{-b\pm \sqrt D}{2a}[/tex]
As discriminant is negative then we can not find any real root for the given equation.
Hence, option 1 is correct.
No real solutions possible.
The cost of 16 notebooks at store J is $24. The notebooks at store J are all the same price. The cost of notebooks at store J are all the same price. The cost of store K is shown on the graph below.
Which store has the least expensive cost per notebook and how much?
Answers
[tex]\bf \stackrel{Store~J}{\begin{array}{ccll} books&cost\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 16&24\\ 10&x \end{array}}\implies \cfrac{16}{10}=\cfrac{24}{x}\implies x=\cfrac{10\cdot 24}{16}\implies x=15[/tex]
so, that much at Store J.
now, look at the graph, notice the point when x = 10, y = 8, so at Store K, is 8 bucks for 10 books.
which is cheaper? well, surely you'd know that.
How the bloody hell do I answer these? Please explain how you did it.
1. In the xy plane, line m passes through the points (a,0) and (0,2a), where a>1. What is the slope of line m?
a)-2 b)-1/2 c)2 d)-2a e)2a
2. First, 3 is subtracted from x and the square root of the difference is taken. Then, 5 is added to the result, giving a final result of 9. What is the value of x?
a)3 b)4 c)5 d)16 e)19
3. If S is the set of positive that are multiples of 7, and if T is the set of positive integers that are multiples of 13, how many integers are in the intersection of S and T?
a)none b)one c)seven d)thirteen e)more than thirteen
4. A florist buys roses at $0.50 each and sells them for $1.00 each. If there are no other expenses, how many roses must be sold in order to make a profit of $3.00?
a)100 b)150 c)200 d)300 e)600
Answers
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
where (a,0) is x1, y1 and (0,2a) is x2, y2. try to see if you can do it now (:
2. take a number x, then step by step do whatever the question asks for example "First, 3 is subtracted from x" so you know the first thing you need to do is x-3, then go on and you'll get an equation which you can use to solve for x, try it!
3. make a set, S, which has multiples of 7. then make a set, T, which has multiples of 13.
now the intersection of S and T is a set having all elements of S, also found in T (basically the numbers that are common to both). try doing it now!
for fourth, this requires a profit formula(that I do not know), must be explained in your book, try going over it, I'm sure you'll find it there!
Which of the following numbers is irrational?
negative 15 over 4, negative 7 over 9, square root of 4, π
negative 15 over 4
negative 7 over 9
square root of 4
π,
Answers
For instance, the first few digits of the square root of two is written as 1.414213562373095... The digits keep going and cannot be expressed as a fraction. But think of 0.33333... That can easily be written as one-third. The distinguishing feature is that there’s no pattern in the digits for the square root of two.
The first two options are integer fractions. We rule those out immediately. The square root of four is tempting, but realize that it is just equal to two. We come to π (pi).
Arguably the most famous irrational number is π, which starts off as 3.14159265358979... Here, there is again no pattern and the digits extend forever. This meets our definition of our irrational.
The rational numbers are -15/4, -7/9, and √4, the irrational number is π.
What is an irrational number?It is defined as the numbers in all real numbers which cannot be represented as rational numbers, in other words, the irrational number cannot be expressed in the form of p/q form.
A rational number is a sort of real number that has the form p/q and does not equal zero.
It is given that:
It is given that the numbers are:
-15/4
-7/9
√4
π
As we know, the number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
The rational number can be written in the form of p/q
Where q cannot be zero.
-15/4 - It is a rational number.
-7/9 - It is a rational number.
√4 = 2 - It is a rational number.
π - Pi is an irrational number.
Thus, the rational numbers are -15/4, -7/9, and √4, the irrational number is π.
Learn more about the irrational number here:
brainly.com/question/17450097
#SPJ2
What is the y intercept of the line given by the equation y= 8x + 75
Answers
Answer: (0,8)
Step-by-step explanation:
here you go
What is the incorrect thing to do if you cause damage to an unattended vehicle?
Make every effort to find the owner of the vehicle
Contact your insurance company
Leave a note for the owner with your name, address, and vehicle plate number
Leave the scene immediately without notifying anyone
Answers
In the event of damaging an unattended vehicle, the incorrect thing to do is to leave the scene immediately without notifying anyone or attempting to find the owner. Correct actions include trying to find the owner, leaving a note with your contact details, and notifying your insurance.
Explanation:If you damage an unattended vehicle, the incorrect action to take is to leave the scene immediately without notifying anyone. Legally and ethically, you should make every effort to find the owner of the vehicle. If the owner cannot be found, it's good practice to leave a note with your name, contact information, and relevant details about the incident. Notifying your insurance company is also an important part of this process.
Learn more about Accountability after Property Damage here:https://brainly.com/question/32789245
#SPJ6
A car travels at an average speed of 40 miles per hour for the first 100 miles of a 200-mile trip, and at an average speed of 50 miles per hour for the final 100 miles. what is the car's average speed for the entire 200-mile trip?
Answers
Time needed for the first 100 miles
= 100 ÷ 40 = 2.5 hours
Time needed for the second 100 miles
= 100 ÷ 50 = 2 hours
Total time = 2.5 + 2 = 4.5 hours
Average speed = 200 ÷ 4.5 hours = 44.4 miles per hour
If, triangle MNO congruent triangle PQR which of the following can you NOT conclude as being true?
A. ray MN congruent ray PR
B. angle M congruent angle P
C. ray NO congruent ray QR
D. angle N congruent angle Q,
Answers
Heyo! ;D
So, we can conclude that based on the information given above, the only one we cannot conclude on being true would be Option A) Ray MN ≅ Ray PR
I WILL GIVE BRAINLIEST!!! I BEG SOMEBODY TO HELP ME PLS!!!
What is the slope of this line?
A) -1/4
B) 1/4
C) -4
D) 4
Answers
Since the line slopes downward (to the right), you know the sign of the slope is negative.
Only selection C is a viable choice. (It also happens to be right, since the line drops 4 units for each horizontal unit.)
find the simplified form of (-7.4)^0?
A.-1
B.-7.4
C.0
D.1
Answers
Final answer:
Any non-zero number raised to the power of 0 is 1, so the simplified form of (-7.4)⁰ is 1 that is option D is correct.
Explanation:
The simplified form of (-7.4)⁰ is determined by one of the fundamental rules of exponents, which states that any non-zero number raised to the power of 0 is 1. This means that regardless of what the base number is, as long as it is not zero, if the exponent is 0, the result will always be 1. It is important to note that 0^0 is an indeterminate form and is not covered by this rule. Therefore, the simplified form of (-7.4)⁰ is:
D. 1
PLEASE HELP ASAP!!! 51 PTS
Answers
y-1=-1/4(x+5)
x+5=-4y+4
x+5-5=-4y+4-5
x=-4y-1
I hope this helps!!!!!!!!!!
The sector of a circle with a diameter of 20 inches has a central angle measure of 36°. What is the area of the sector?
40π in²
10π in²
2π in²
π in²
plz explain what you did to get the answer so that i vcan understand and do it alone in the future
Answers
radius = 20/2 = 10
Area of sector:
πr²(x/360) = x is the central angle in degrees.
π(10)²(36/360)
10π in²
Hope this helps :)
If sound travels approximately 1 km in 3 s, and the lightning is striking 10 km from your house, how much time passes between a flash of lightning and the sound of thunder?
Answers
3 seconds * 10 kilometers = 30 seconds
please help i have 2 questions thank you
Answers
Here is your answer:
Since the second question is already solved ill solve the first on:
The proper answer to this question is option D "17.2".
Here is how:
Formula for area:
b*w*h
3*7=21
21-3.7=17.2
Your answer is D.
If you need anymore help feel free to ask me!
Hope this helps!
Find the vertex of y = x2 + 14x − 40 by completing the square.
Answers
x =(14+√36)/2=7+3= 10.000
or:
x =(14-√36)/2=7-3= 4.000
A number cube is rolled 450 times. The number 3 comes up 67 times. What is the theoretical probability of rolling a three,
Answers
We know that:
Experimental probability = number of positive results / number of experiments
So the Experimental probability = 67 / 450
Suppose you buy a CD for $300 that earns 3% APR and is compounded quarterly. The CD matures in 3 years. How much will this CD be worth at maturity?
A. $328.14
B. $309.12
C. $309.10
D. $303.01
help?,
Answers
For which pair of function is (g*f)(a)=|a|-2
1. f(a)=a^2-4 and g(a)= sqaureroot a
2. f(a)= 1/2a-1 and g(a)=2a-2
3. f(a)=5+a^2 and g(a) = sqaureroot (a-5)-2
4.f(a) =3 -3a and g(a)=4a-5
Answers
... selection 3 is appropriate.
Answer:
The correct pair is 3
Step-by-step explanation:
1.
[tex]f(a)=a^{2}-4 , g(a)=\sqrt{a} \\gof(a)=g(a^{2} -4)\\=\sqrt{a^{2}-4 } \neq |a|-2[/tex]
2.
[tex]f(a)=\frac{1}{2\cdot a-1}, g(a)=2\cdot a -2\\gof(a)=g(\frac{1}{2\cdot a-1} )\\=\frac{2}{2\cdot a-1}-2\\=\frac{4-2\cdot a}{2\cdot a-1}\neq|a|-2[/tex]
3.
[tex]f(a)=5+a^{2} , g(a)=\sqrt{a-5} -2\\gof(a)=g(5+a^{2} )\\=\sqrt{5+a^{2}-5 } -2\\=\sqrt{a^{2} } -2\\=|a|-2[/tex]
4.
[tex]f(a)=3-3\cdot a , g(a)=4\cdot a-5\\gof(a)=g(3-3\cdot a )\\=4(3-3\cdot a)-5\\=7-12\cdot a\neq|a|-2[/tex]
Hence, the Option 3 is correct
What is the value of x?
Answers
40/8 =5
x = 5
hope this helps
helpppppppppppppppppppppp
Answers
So we have to:
y = sin (x + 90)
We evaluate x = 0
y = sin (0 + 90)
y = 1
Answer:
y = sin (x + 90)
Option A
Express 1.21212121.... as a fraction
Answers
To solve such questions we will have to observe the fact that this is a repeating decimal number with the repeating figures being 2 and 1 as 21.
Thus, we can represent 1.21212121... as [tex] 1.\overline{21} [/tex]
Let us represent the original number 1.21212121... by the letter "a". Thus,
a=1.21212121...=[tex] 1.\overline{21} [/tex]
Therefore,[tex] a=1.\overline{21} [/tex]..................(equation 1)
Let us now multiply (equation 1) by 100 to get:
[tex] 100a=100\times 1.212121...=121.\overline{21} [/tex].....(equation 2)
Now, when we subtract (equation 2) from (equation 1), we will get:
[tex] 100a-a=121.\overline{21}-1.\overline{21} [/tex]
[tex] 99a=120 [/tex]
[tex] \therefore a=\frac{120}{99} [/tex]
Thus the given number 1.21212121... can be represented as a fraction as [tex] \frac{120}{9} [/tex].