Which polar coordinates represent the point plotted on the graph? Select all that apply. (2 answers)
a. (-4, 90 degrees)
b. (4, 90 degrees)
c. (4, -90 degrees)
d. (-4, 270 degrees)
e. (-4, -270 degrees)
Answers
Answer: The correct options are (b) and (d).
Explanation:
It the polar form [tex]r^2=x^2+y^2[/tex], where
[tex]x=r\cos \theta,y=r\sin \theta[/tex]
The polar coordinate are in the form of [tex](r,\theta)[/tex].
From the given figure it is noticed that the value of r is 4 and [tex]\theta=\frac{\pi}{2}[/tex] or [tex]90^{\circ}[/tex] .
So the point is defined as [tex](4,90^{\circ})[/tex] and option b is correct.
The value,
[tex](r\cos \theta, r\sin \theta)=(0,4)[/tex]
Check the each option if we get the same value then that option is correct.
For option a.
[tex](r\cos \theta, r\sin \theta)=(-4\cos 90^{\circ} , -4\sin 90^{\circ})=(0,-4)[/tex]
Therefore option (a) is incorrect.
For option c.
[tex](r\cos \theta, r\sin \theta)=(4\cos (-90)^{\circ} , 4\sin (-90)^{\circ})=(0,-4)[/tex]
Therefore option (c) is incorrect.
For option d.
[tex](r\cos \theta, r\sin \theta)=(-4\cos (270)^{\circ} , -4\sin (270)^{\circ})\\(-4\cos (360-90)^{\circ} , -4\sin (360-90)^{\circ})=(0,4)[/tex]
Therefore option (d) is correct.
For option (e).
[tex](r\cos \theta, r\sin \theta)=(-4\cos (-270)^{\circ} , -4\sin (-270)^{\circ})\\(-4\cos (270)^{\circ} , 4\sin (270)^{\circ})=(0,-4)[/tex]
Therefore option (e) is incorrect.
Answer:
1. A
2. B, D
3. A, D, E
4. C
5. A
Step-by-step explanation:
Related Questions
Due tomorrow. Please help!!!!
Answers
[tex]d=\dfrac{a_{17}-a_{7}}{17-7}=\dfrac{81-41}{17-7}=\dfrac{40}{10}=4[/tex]
The first term of the sequence can be found from either of the given terms.
[tex]a_{7}=41=a_{1}+(7-1)d=a_{1}+24\\a_{1}=41-24=17[/tex]
The sum of 40 terms is
[tex]S_{40}=\dfrac{40}{2}(a_{1}+a_{40})=20(17+(17+39\cdot 4)=20\cdot 190=3800[/tex]
The sum of the first 40 terms is 3800.
You are painting a ceiling in a room. The room measures 30 feet by 40 feet. One gallon of paint costs $25 and covers 200 square feet. How much will it cost to paint the ceiling?
A. $6
B. $17.50
C. $150
D. $1,200
Answers
the area of the room=30*40------> 1200 ft²
1 gallon of paint cover----------------> 200 ft²
x---------------------------> 1200 ft²
x=1200/200------> x=6 gallons
1 gallon cost------------> $25
6 gallons-----------> x
x=6*25-----> x=$150
the answer is
the option C. $150
Answer:
C. $150
Step-by-step explanation:
we know that
the area of the room=30*40------> 1200 ft²
1 gallon of paint cover----------------> 200 ft²
x---------------------------> 1200 ft²
x=1200/200------> x=6 gallons
1 gallon cost------------> $25
6 gallons-----------> x
x=6*25-----> x=$150
the answer is
the option C. $150
A professor wants to arrange his books on a shelf. he has 30 books and only space on the shelf for 20 of them. how many different 20-book arrangements can he make using the 30 books? this is an example of a problem that can be solved using which method?
Answers
The number of possible arrangements is
[tex]P\left(30,20\right)=\frac{30!}{\left(30-20\right)!\times 20!}=30,045,015[/tex]
There are 30,045,015 possible 20-book arrangements.
Answer: Total arrangement are 30045015
Given problem will be solved with help of combination.
Step-by-step explanation:
When we find the arrangement in which the order does not matter then we use combination,
Here, we have to find the possible arrangement in which order does not matter,
Thus, we will use combination to find the answer.
Here the total number of books = 30
A self contains, the number of book = 20,
Hence, the total arrangement of 20 books out of 30 books
[tex]=^{30}C_{20}[/tex]
[tex]=\frac{30!}{20!(30-20)!}[/tex]
[tex]=\frac{30\times 29\times 28\times 27\times 26\times 25\times 24\times 23\times 22\times 21}{10!}[/tex]
[tex]=\frac{4.9557887\times 10^{12} }{3628800 }=30045015 [/tex]
Which of the following is equivalent to the midpoint between the points (8, -9) and (0, 5)?
(4, -2)
(4, 2)
(-2, 4)
(2, 4)
Answers
same to go for the y points
so the and is (4,-2)
Find the quotient of 569.7 divided by 10 to the 3 power
Answers
.....................
Daniel ate 0.55 of a candy bar. Which fraction represents the part of the candy bar that Daniel ate?
A. 10/22
B. 11/20
C. 2/5
D. 3/4
E. 11/40
Answers
Answer:
The answer is B 11/20
Step-by-step explanation:
To transform a decimal to a fraction you must do the following:
1. Multiply by an specific power of 10 until your decimal becomes a whole number. In this case 0.55 we multiply by 10 ^2 or 100 and we obtain 55.
2 Divide the decimal by this same power of 10 so that you do not change the original value. For example
0.55 *(100/100) = 55/100 As you see Im multiplying and dividing by 100 ( thats equivalent to 1 so it doesnt change the original number)
3 Simplify the fraction
To simplify your fraction you must find the Greatest Common Factor of 55 and 100. For doing this, you only perform a prime factorization. Divide 55 and 100 by the smallest common prime factor, besides 1. (For this case is 5) until you arrive to two number without common prime factors.
55/5 = 11
100/5 = 20
As 11 and 20 have no common prime factors it is the most simplified fraction
Erins water bottle holds 665 milliliters. Dylan is carrying two water bottles. Each one holds 0.35 liters. Who is carrying more water?
Answers
Dylan = 0.35 x 2 = 0.7 liters = 700 ml
Answer: Dylan is carrying more water.
Select the statement that is true. Answer Choices The sum of 0.12x2+0.3⎯⎯⎯ and 1.5x2−0.75 is 1.62x2+0.416 . -0.45x2+0.9 subtracted from 2.5x2−7.32 is -2.95x2+8.22 . The difference of 18.94x−0.4⎯⎯⎯ and -10.2x+4.5 is 8.74x−4.94⎯⎯⎯ . The product of 0.6⎯⎯⎯x+3.4 and -6x+5.7 is -4x2−16.6x+19.38 .
Answers
1]
(0.12x^2+0.3)+(1.5x^2-0.75)
=(0.12x^2+1.5x^2)+(0.3+0.75)
=1.62x+1.05
2]
(2.5x^2-7.32)-(-0.45x^2+0.9)
(2.5x^2+0.45x^2)+(-7.32-0.9)
2.95x^2-8.22
3](18.94x-0.4)-(-10.2x+4.5)
=(18.94x+10.2x)+(-0.4-4.5)
=29.14x-4.9
4] (x+3.4)(-6x+5.7)
=x(-6x+5.7)+3.4(-6x+5.7)
=-6x^2+5.7x-20.4x+19.38
=-6x^2-14.7x+19.38
Find the length of the side of a square with an area of 144inches squared.
a.48 in
b.12 in
c.206 in
d.288 in
Answers
Length = √144
Length = 12 in
Answer: 12 in
your answer is here..
given the area of the square is 144 in²
therefore side × side = 144 in²
==> side² = 144 in²
==> side = √144
==> side = 12 in
hence, the length of the side of the square is 12 in.
( b. 12 in )...final answer
cheers!!
Rectangle ABCD is shown below with line EF passing through the center:
If rectangle ABCD is dilated by a scale factor of five about the center of the rectangle to create rectangle A'B'C'D', dilated line E'F' will
A: be parallel to the original line
B: shift five units to the right
C: be perpendicular to the original line
D: lie on the same line as the original
Answers
D: lie on the same line as the original
Answer:
D lie on thesame line as the original
Step-by-step explanation:
I took the test and hurray! It was correct
the number of mosquito at the beginning of the summer was 4,000. the population of mosquito is expected to grow at a rate of 25% a month . how many mosquitoes will there be after 4 months
Answers
Using the formula for exponential growth and given an initial population of 4,000 mosquitoes with a 25% monthly growth rate, the mosquito population is expected to grow to approximately 9,766 after 4 months.
Explanation:The question involves calculating the growth of a mosquito population over a period, specifically after 4 months, given an initial population of 4,000 mosquitoes and a monthly growth rate of 25%. To find the population after 4 months, we use the formula for exponential growth:
P = P0 × (1 + r)n
where P is the population at the end, P0 is the initial population, r is the growth rate (expressed as a decimal), and n is the number of time periods.
Substituting the values, we get:
P = 4000 × (1 + 0.25)4
P = 4000 × (1.25)4
After calculating, we find that P = 9765.63. Thus, the population of mosquitoes after 4 months is expected to be approximately 9,766.
The mosquito population grows from 4,000 to approximately 9,766 over 4 months with a 25% monthly increase.
The initial number of mosquitoes is 4,000, and the population increases at a rate of 25% per month. To find the population after 4 months, we use the formula for compound interest:
P = P0 [tex](1 + r)^{t[/tex]
where:
P0 is the initial populationr is the growth ratet is the time in monthsGiven:
P0 = 4,000r = 25% or 0.25t = 4Substitute these values into the formula:
P = 4000 × (1 + 0.25)⁴
First, calculate (1 + 0.25):
1 + 0.25 = 1.25
Then, raise this to the power of 4:
(1.25)⁴ = 2.4414
Finally, multiply by the initial population:
P = 4000 × 2.4414 = 9765.6
Thus, the mosquito population after 4 months is approximately 9,766.
how do I solve this?
Answers
[2² * (√(3x⁵))² - 2² * (√y)²]
Now simplify. Placing a square root to the power of 2 just cancels each other out so you're left with:
[4(3x⁵) - 4y]
Simplify again for your answer:
12x⁵ - 4y
Anyone know this geometry question? Will give brainiest
Answers
If prices increase at a monthly rate of 1.1%, by what percentage do they increase in a year, What is the annual inflation rate
Answers
P0=$1
A=P(1+r)^(td)
A=1(1+0.011)^12
A=1(1.011)^12
A=$1.1403
Yearly increase will therefore be 14.03%. Hence the inflation per year is 14.03%
Final answer:
To find the annual inflation rate when prices increase at a monthly rate of 1.1%, you use the formula for compounding interest, resulting in an approximate annual rate of 13.97%.
Explanation:
If prices increase at a monthly rate of 1.1%, to calculate the annual inflation rate, you should consider the compounding effect over the year. The general formula for finding the total percentage increase over multiple periods when compounded at each period is:
(1 + rate)^number of periods - 1.
In this case, the monthly rate is 1.1%, or 0.011 when expressed as a decimal. The number of periods (months) in a year is 12. Plugging these values into the formula gives:
(1 + 0.011)^12 - 1,
which calculates to:
1.011^12 - 1 = 0.1397 or 13.97%.
So, the annual inflation rate when prices increase at a monthly rate of 1.1% is approximately 13.97%.
Urgent!!! What is the slope-intercept form of the equation of the line that passes through the points (2, 7) and (4, −1) ?
Answers
[tex] \frac{y2-y1}{x2-x1}[/tex]
[tex] \frac{-1 - 7}{4-2} = \frac{-8}{2} = -4[/tex]
Find the y-intercept of the line by multiplying the slope by the distance between x = 0 and a point. We'll use (2,7) to find the y-intercept.
0 - 2 = -2
-2(-4) + 7 = 15
The new point on the line is (0,15). Since x = 0, 15 is your y-intercept.
Plug in your slope and y-intercept into the equation:
[tex]y = mx + b[/tex]
Answer:
[tex]y = -4x + 15[/tex]
Best rentals charges a daily fee plus a mileage fee for renting its cars. barney was charged $81 for 3 days and 300 miles, while mary was charged $145 for 5 days and 600 miles. what does best rental charge per day and per mile?
Answers
x: rental charge per day
y: rental charge per mile
We write the system of equations:
3x + 300y = 81
5x + 600y = 145
Solving the system we have:
x = 17
y = 1/10
Answer:
rental charge per day = 17 $
rental charge per mile = 1/10 $
A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. if the smaller rim makes x revolutions per second, how many revolutions pe
Answers
1 revolution of a circle with the diameter of 28 inches = πd=28ππd=28π inches. Hence, x revolutions per second = 28πx28πx inches per second = 60∗28πx60∗28πx inches per minute.
Given that 60∗28πx=35πn60∗28πx=35πn --> n=60∗28πx35π=48xn=60∗28πx35π=48x.
Which of the following have been used to measure wealth in early societies?
Cows
Dogs
Grain
Land
Metals
Answers
The answer is cows, metals, land, and grains.
The first-serve percentage of a tennis player in a match is normally distributed with a standard deviation of 4.3%. If a sample of 15 random matches of the player is taken, the mean first-serve percentage is found to be 26.4%. What is the margin of error of the sample mean? please provide explination
Answers
[tex]E=z_{\alpha /2}\cdot \frac{\sigma }{\sqrt{n}}[/tex]
The value of z will be taken with the assumption that the significance level is 5%. So, α=0.025. Then [tex]z_{\alpha \:/2}=1.96[/tex].
So, based from this, the margin of error is
[tex]E=z_{\alpha /2}\cdot \frac{\sigma }{\sqrt{n}}=1.96\cdot \frac{0.043}{\sqrt{15}}=0.02[/tex]
The margin of error is about 2%.
Before a renovation, a movie theater had 111 seats. After the renovation, the theater has 154 seats. What is the approximate percentage increase of the number of seats in the theater? If necessary, round to the nearest tenth of a percent.
A. 28.1% B. 38.7% C. 43.3% D. 24.8%
Answers
(New number-Old number)/(Old number)×100
new number=154 seats
old number =111 seats
thus
Percentage increase is:
(154-111)/111×100
=38.7%
Answer: B. 38.7%
At Silver Gym, membership is $30 per month, and personal training sessions are $45 each. At Fit Factor, membership is $90 per month, and personal training sessions are $35 each. In one month, how many personal training sessions would Sarah have to buy to make the total cost at the two gyms equal?
Answers
To make the total monthly cost of Silver Gym and Fit Factor equal, Sarah would have to buy 6 personal training sessions in a single month.
Explanation:Solution:The question is asking to find out how many personal training sessions Sarah would need to take in a month for the cost at Silver Gym to equal the cost at Fit Factor.
To solve this, we need to create an equation. Let's represent the number of personal training sessions as x. For Silver Gym, the total cost in a month would be 30 + 45x, and for Fit Factor, it would be 90 + 35x.
Setting these two expressions equal to each other gives us the equation 30 + 45x = 90 + 35x.
Moving the variable terms to one side and the constants to the other side of the equation gives us 10x = 60.
We solve for x by dividing both sides of the equation by 10 to get x = 6.
This means that Sarah would need to take 6 personal training sessions for the total cost at the two gyms to be equal.
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30 POINTS!
The generic equation for the curve (shown in the picture) is y = mx +c.
A) True
B) False
Answers
Answer:
FALSE
Step-by-step explanation:
The correct equation would be y = mx + b
y --> y coordinate
m --> the slope
x --> x coordinate
b --> the y-intercept
Answer:
false!
Step-by-step explanation:
Y = mx + b is the generic form of a linear equation written in slope-intercept form.
If f(x) =3x-2, find f-1(x)
Answers
To find the inverse of a function, follow these steps: replace f(x) with y, interchange x and y, solve for y, and replace y with f-1(x). Applying these steps to the given function f(x) = 3x - 2 results in the inverse function f-1(x) = (x + 2)/3.
Explanation:To find the inverse of a function, we can follow these steps:
Replace the function notation f(x) with yInterchange x and y in the equationSolve the resulting equation for yReplace y with f-1(x)Let's apply these steps to the given function f(x) = 3x - 2:
Replace f(x) with y: y = 3x - 2Interchange x and y: x = 3y - 2Solve for y: x + 2 = 3yy = (x + 2)/3Replace y with f-1(x): f-1(x) = (x + 2)/3
Therefore, the inverse of the function f(x) = 3x - 2 is f-1(x) = (x + 2)/3.
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The inverse function of [tex]\( f(x) = 3x - 2 \)[/tex] is [tex]\( f^{-1}(x) = \frac{x + 2}{3} \).[/tex]
To find the inverse function [tex]\( f^{-1}(x) \)[/tex] for the given function [tex]\( f(x) = 3x - 2 \)[/tex], follow these steps:
Start with the original function:
[tex]\[ y = 3x - 2 \][/tex]
Swap y and x to find the inverse:
[tex]\[ x = 3y - 2 \][/tex]
Solve for y:
[tex]\[ x + 2 = 3y \][/tex]
[tex]\[ y = \frac{x + 2}{3} \][/tex]
Rewrite y as [tex]\( f^{-1}(x) \):[/tex]
[tex]\[ f^{-1}(x) = \frac{x + 2}{3} \][/tex]
So, the inverse function [tex]\( f^{-1}(x) \)[/tex] is:
[tex]\[f^{-1}(x) = \frac{x + 2}{3}\][/tex]
Complete Question:
If [tex]f(x) =3x-2[/tex], find [tex]f^{-1}(x)[/tex]
WHO LIKES PARABOLAS 3 MULTIPLE CHOICE
1. What is the vertex of the parabola? y−3=12(x+5)^2
2. The equation of a parabola is y=12x2+6x+23 .
What is the equation of the directrix?
y = 5.5
y = 4.5
y = 2
y = 0.5
3.The equation of a parabola is 132(y−2)2=x−1 .
What are the coordinates of the focus?
(−7, 2)
(1, 10)
(1, −6)
(9, 2)
Answers
[tex]y-3=12(x+5)^{2} \\ \\ y= 12(x+5)^{2}+3[/tex]
The vertex of the general parabolic equation:
[tex]y=a(x-h)^{2}+k [/tex]
lies at (h,k)
Comparing the given equation to general equation, we can write:
h = - 5
k = 3
So, the vertex of the given parabola will be (-5, 3)
Question 2) Equation of Directrix
The correct equation of the parabola is:
[tex]y= \frac{1}{2} x^{2} +6x+23 \\ \\ [/tex]
First we need to convert the equation to standard form as shown below:
[tex]y= \frac{1}{2}( x^{2} +12x)+23 \\ \\ y= \frac{1}{2}( x^{2} +12x+36)+23- \frac{1}{2}(36) \\ \\ y= \frac{1}{2}(x+6)^{2}+5 \\ \\ y-5= \frac{1}{2}(x+6)^{2} \\ \\ 2(y-5)=(x+6)^{2} \\ \\ 4( \frac{1}{2})(y-5)= (x+6)^{2}[/tex]
The directrix of the general parabola of the form:
[tex]4p(y-k)=(x-h)^{2} [/tex]
is y = k - p
Comparing equation of given parabola with general parabolic equation, we can write:
p =1/2
k = 5
So, equation of directirx will be:
y = 5 - 1/2 = 4.5
So, option B gives the correct answer.
Question 3) Focus of the parabola
The correct equation of the parabola is:
[tex] \frac{1}{32}(y-2)^{2}=x-1 \\ \\ (y-2)^{2}=32(x-1) \\ \\ (y-2)^{2}=4*8(x-1)[/tex]
Comparing this equation to the general parabolic equation, we can write:
p=8
h =1
k = 2
The focus of the parabola will be at (h+p,k) = (9,2)
So the focus of the parabola is at (9,2)
Thus, option D gives the correct answer.
The perimeter of a rectangle is 30 centimeters. The width of the rectangle is 6 centimeters. How long is the rectangle?
Answers
The equation of a circle is x2 − 4x + y2 + 8y − 29 = 0. what are the center and radius of the circle? enter your answers in the boxes.
Answers
[tex]\text{We have}\\\\x^2-4x+y^2+8y-29=0\\\\\text{use:(*)}(a\pm b)^2=a^2\pm2ab+b^2[/tex]
[tex]x^2-2x\cdot2+y^2+2y\cdot4=29\ \ \ |+2^2\ \ |+4^2\\\\\underbrace{x^2-2x\cdot2+2^2}_{(*)}+\underbrace{y^2+2y\cdot4+4^2}_{(*)}=29+2^2+4^2\\\\(x-2)^2+(y+4)^2=49[/tex]
[tex]\text{Answer: the center (2;-4), the radius}\ r=\sqrt{49}=7[/tex]
Final answer:
The center of the circle described by the equation x2 − 4x + y2 + 8y − 29 = 0 is (2, -4), and the radius is 7 units.
Explanation:
The equation of a circle given in the question is x2 − 4x + y2 + 8y − 29 = 0. To find the center and radius of the circle, we will complete the square for both x and y terms.
This involves adding and subtracting the squared half of the coefficients of x and y to complete the square:
(x2 - 4x + 4) - 4 + (y2 + 8y + 16) - 16 = 29 + 4 + 16
(x - 2)2 + (y + 4)2 = 49
This equation is now in standard circle form, which is (x - h)2 + (y - k)2 = r2, where (h, k) is the center and r is the radius.
The center of the circle is therefore at (2, -4) and the radius is √(49) = 7 units.
Chauncey has 42 coins, all dimes and quarters. the total value of all these coins is $5.70. how many dimes does he have?
Answers
32 dimes = $3.20
$3.20 + $2.50 = $5.70
To determine the number of dimes Chauncey has, you can use the system of equations stemming from the total number of coins and their total value. Following through with the calculations, it turns out that Chauncey has 32 dimes.
Explanation:The subject at hand revolves around the concept of linear equations. Given that Chauncey has 42 coins (all dimes and quarters) worth $5.70, you can use a system of equations to figure out the number of each type of coin.
First, let d be the number of dimes and q be the number of quarters. The total number of coins is 42, so the first equation is d + q = 42.Second, a dime is worth $0.10 and a quarter is worth $0.25. Since the total value of coins is $5.70, another equation you can form is 0.10d + 0.25q = 5.70.Having formed this system of two equations, you can solve it by multiplying the first equation by 0.10, which gives 0.10d + 0.10q = 4.2.Subtract this new equation from the second equation: 0.10d + 0.25q - 0.10d - 0.10q = 5.70 - 4.2. Simplify this to 0.15q = 1.5.Divide each side by 0.15, then q = 10. Substitute q = 10 into the first equation to solve for d. This gives d = 42 - 10 = 32.So, Chauncey has 32 dimes.
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In the data set below, what is the mean absolute deviation?4461526If the answer is a decimal, round it to the nearest tenth.mean absolute deviation (MAD):
Answers
If so, then the MAD is 1.43
To find the MAD, you first find the mean of the list. It is 4.
Then find the absolute difference of each number from the mean.
Those values are: 0,0,2,3,1,2,2
Now find the mean of those numbers and you have about: 1.43
M and n are integers such that 6 < m < n. what is the value of n ?
Answers
A barn is an atomic unit of area equal to 10–28 m2. what is the surface area of the earth expressed in units of barn? assume the earth is a sphere with a radius of km. (the surface area of a sphere is 4πr2.)
Answers
we know that
surface area of a sphere=4*pi*r²
for r=6380 km------->r=6380 x 10^3 m
surface area of of the earth=4*pi*(6380 x 10^3)²-----> 511506576035121,52 m²
if 1 barn is equal to-------------> 10^(-28) m²
x barn----------------------> 511506576035121,52 m²
x=511506576035121,5/(10^(-28))------> x=5.12 x 10^42 barn
the answer is5.12 x 10^42 barn