Convert the given rectangularcoordinates into polarcoordinates.(-5, -2) = (5.4, [?])Round your answer to the nearest tenth.Report theta in radians
![Convert The Given Rectangularcoordinates Into Polarcoordinates.(-5, -2) = (5.4, [?])Round Your Answer](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/sL2V9I7WssY04g4fv31uDq43DSUdxBEr.jpeg)
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Use the next relationships to convert rectangular coordinates to polar coordinates:
[tex]\begin{gathered} (x,y)=(r,\theta) \\ \\ r^2=x^2+y^2 \\ \\ tan\theta=\frac{y}{x} \end{gathered}[/tex]For the given rectangular coordinates:
[tex]\begin{gathered} (-5,-2) \\ x=-5 \\ y=-2 \\ \\ tan\theta=\frac{-2}{-5}=\frac{2}{5} \\ \\ \theta=\tan^{-1}(\frac{2}{5}) \\ \\ \theta=0.4 \end{gathered}[/tex]Then, the polar coordinates are (5.4, 0.4)Related Questions
Solve 2x^2-23=y when x=1
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The value of y in the expression [tex]2x^{2} - 23=y[/tex] is -21.
Given System of Equations are:
[tex]2x^{2} - 23=y[/tex] .....(1)
[tex]x=1[/tex] ..........(2)
Now substituting x = 1 in in equation (1)
[tex]2x^{2} - 23 = y\\ y = 2x^{2} - 23\\ y = 2 x 1^{2} - 23\\ y = 2 x 1 - 23\\ y = 1 - 23\\ y = -21[/tex]
Hence, the value of y in the expression [tex]2x^{2} - 23=y[/tex] is -21.
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Raymond invested $2,000 in an account that earns an 8% annual interest rate. Find a balance of his account after 4 years compounded the following ways round your answers to the nearest cent.
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The rule of the compounded interest is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]A is the new value
P is the initial value
r is the rate in decimal
n is the period
t is the time
He invested $2000
P = 2000
The account earns an 8% annual interest
r = 8% = 8/100 = 0.08
The balance is for 4 years
t = 4
For no 1 it is annual, then
n = 1
Substitute these values in the rule above
[tex]\begin{gathered} A=2000(1+\frac{0.08}{1})^{(1\times4)} \\ A=2000(1.08)^4 \\ A=2720.97792 \end{gathered}[/tex]Round it to the nearest cent means 2 d.p
[tex]A=2720.98[/tex]The balance is $2720.98
2. Semi-annual means
n = 2
So we will substitute n by 2
[tex]\begin{gathered} A=2000(1+\frac{0.08}{2})^{(2\times4)} \\ A=2000(1.04)^8 \\ A=2737.138101 \end{gathered}[/tex]Round it to the nearest cent
[tex]A=2737.14[/tex]The balance is $2737.14 in semi-annual
3. Quarterly means
n = 4
So we will substitute n by 4
[tex]\begin{gathered} A=2000(1+\frac{0.08}{4})^{(4\times4)} \\ A=2000(1.02)^{16} \\ A=2745.57141 \end{gathered}[/tex]Round it to the nearest cents
[tex]A=2745.57[/tex]The balance is $2745.57 quarterly
4. Monthly means
n = 12
Substitute n by 12
[tex]\begin{gathered} A=2000(1+\frac{0.08}{12})^{(12\times4)} \\ A=2000(1.006666667)^{48} \\ A=2751.332201 \end{gathered}[/tex]Round it to the nearest cent
[tex]A=2751.33[/tex]The balance is $2751.33 monthly
Here are 4 triangles that have each been transformed by adifferent transformation. Which transformation is not a rigidtransformation?
Answers
Rigid transformation is a geometric transformation of a Euclidean space that preserves the Euclidean distance between every pair of points. The rigid transformations include rotations, translations and reflections
Option A is a translation then is rigid
Option B is a rotation then is rigid
Option C is a reflection then is rigid
Option D is a dilation and translation then is not rigid because the dilation is not a rigid transformation because the size of the objects is different
then right o
+ 308 - 126 =450 what number can make the equation true
Answers
answer: the number is 268
5,624 ÷ 72 using estimation
Answers
=====================================================
Explanation:
5624 is close to 5600
72 is close to 70
Therefore, 5624 ÷ 72 is close to 5600 ÷ 70 = 80
Think of it like saying 56 ÷ 7 = 8 but then we add the zeros onto each to get what is shown above.
--------
Use your calculator to find that
5624 ÷ 72 = 78.111 approximately
which isn't too far from the estimate value of 80. Our estimate is an over-estimate.
Answer: 80
Step-by-step explanation:
First change the equation to the nearest tenth,
5620 divided by 70
Now, break up the 70 into ( 10 * 7 )
So first do 5620 divided by 10
5620 divided by 10 = 562
Now if we round to the nearest tenth again we get 560
Now we can divide 560 by 7
Which comes out to 80
What is the solution to the given inequality?½-½ x ²-1/O x₂ -1O xs-1O x ≥ 3O x≤ 3IntroSolve the inequality.1---X24Apply properties:AddMultiplySubtractDivideTo start over:ResetDone
Answers
Answer:
x ≤ 3
Explanation:
The given inequality is
[tex]\frac{1}{2}-\frac{1}{4}x\ge-\frac{1}{4}[/tex]To solve the inequality, we first need to subtract 1/2 from both sides
[tex]\begin{gathered} \frac{1}{2}-\frac{1}{4}x-\frac{1}{2}\ge-\frac{1}{4}-\frac{1}{2} \\ \\ -\frac{1}{4}x\ge-\frac{3}{4} \end{gathered}[/tex]Then, multiply both sides by -4. Since -4 is a negative number, the symbol of the inequality changes, so
[tex]\begin{gathered} (-4)(-\frac{1}{4}x)\leq(-4)(-\frac{3}{4}) \\ \\ x\leq3 \end{gathered}[/tex]Therefore, the answer is
x ≤ 3
Evaluate the following expression:
2/7 +3/7 = //
In the space below, enter the value of the numerator in your
answer. Do not include the division sign or the denominator.
For example, if the answer was, you would enter the
number 1 in the space below.
Answers
Answer:
[tex]\frac{2}{7}+\frac{3}{7}=\frac{5\\}{7}[/tex]
but if you want only the numerator it is 5
decimal form: 0.714
Write a division problem with a quotient greater than 20 less than 25? What do you guys think?
Answers
Answer:
hmmm, how about 242 divided by 11? the answer is 22 r0
Step-by-step explanation:
your sister is looking for a way to increase the amount she is earning on her savings account. what should she do?
Answers
The thing that she can do to increase the savings is A. Deposit money into her savings account each month.
What should she do?Your information is incomplete and the complete question is written below. Savings accounts offer interest based on the balance. Therefore, you can boost the interest you receive on a savings account by making a deposit each month. By doing so, you will increase the account's total balance and, consequently, the interest rate.
The alternate selections are incorrect since doing so will result in a decrease in the amount of money in the savings account and a reduced rate of interest. Instead, use the money to open a checking account.
Note that the complete question is attached.
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Your sister is looking for a way to increase the amount of interest she is earning on her savings account. What should she do?
A. Deposit money into her savings account each month
B. Use the money from her savings account to open a checking account instead
C. Switch to a savings account with a lower interest rate
D. Make monthly withdrawals from her savings account
Some fabric shrinks when it is washed.
A piece of fabric is washed twice.
After the first wash, the area of the fabric is 75% of the area of the original piece of fabric.
After the second wash, the area of the fabric is 90% of the area of the fabric after the first
wash.
After these two washes, the area of the fabric is 2700 cm².
Calculate the area of the original piece of fabric.
Answers
After performing some mathematical operations, we know that the original area of the fabric is 4,000 cm².
What are mathematical operations?In mathematics, an operation is a function that converts zero or more input values into a discrete output value.The number of operands in the operation determines how complex it is.The four mathematical operations are functions that convert inputs that are numerical into outputs that are numerical (i.e., another number).These are addition, subtraction, multiplication, and division.So, the original area of fabric is:
The area after two washes is 2700 cm² which is 90% of the area after the 1st wash.Then:
x/100 × 90 = 270090x = 270000x = 270000/90x = 3000 cm²The area after 1st wash is 3000 cm².
Which is 75% of the original area.Then:
x/100 × 75 = 300075x = 300000x = 300000/75x = 4,000 cm²Therefore, after performing some mathematical operations, we know that the original area of the fabric is 4,000 cm².
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Find the area of the shaded portion in the square. Show all work for full credit.
(Hint: Assume the central point of the arc is the corresponding corner.)
Answers
Non shadow part (white one) seems to be 1/4 of a circumference
So we need to find area of square minus area of 1/4 of the circumference
Square area = L^2 = 6^2 = 36
Circumference Area = (πr^2)/4 = (π*6^2)/4 = 28.27
Area of the shaded portion = 36 - 28.27 = 7.72
In three days Carter drove 2196 miles in 36 hours behind the wheel. The first day he averaged 64 mph, the second day 62 mph, and the third day 58 mph. If he drove 4 more hours on the third day than on the first day, then how many hours did he drive each day? I have x=z+4 and that's all, I need the other two equations please helpp.
Answers
Answer:
first day=10 hours, second day=12 hours, third day=14 hours
Step-by-step explanation:
64+62+58=
126+58=184
o=day 1. t=day 2. th=day 3
o+t+th=36
o+4=th
64o+62t+58th=2196
(o+t+th=36)*58
58o+58t+58th=2088
64o+62t+58th=2196
-(58o+58t+58th)=2088
6o+4t=108
o+t+th=36
o+t+o+4=36 ==> th=o+4
2o+t+4=36
2o+t=32
(2o+t=32)*3
6o+4t=108
-(6o+3t=96)
t=108-96
t=12
2o+12=32 ==> 2o+t=32
2o=20
o=10
o+4=th
10+4=14
th=14
o=10, t=12, th=14
Solve 2 - x= -7. O A. x=9 X B. X= 5 C. x= -9 D. x= -5
Answers
2 - x = - 7
Adding x at both sides of the equal signe, we get:
2 - x + x = - 7 + x
2 = -7 + x
Adding 7 at both sides:
2 + 7 = -7 + x + 7
9 = x
Theater Tickets. The El Portal Center for the Arts in North Hollywood, California, holds a maximum of 400 people. The two balconies hold 94 and 91 people each; the rest of the seats are at the stage level. Solving the equation x + 94 + 91 = 400 will give you the number of seats on the stage level.
Answers
So first of all we have to solve this equation:
[tex]x+94+91=400[/tex]We can perform the operation 94+91=185 so we get:
[tex]x+185=400[/tex]And we can substract 185 from both sides of the equation:
[tex]\begin{gathered} x+185-185=400-185 \\ x=215 \end{gathered}[/tex]Then the answer to part a is 215.
Now that we have the number of seats on the stage level we can find the max amount of money the theater can bring in. This will be given by the total number of seats in the stage level multiplied by the cost per ticket for these seats plus the total number of seats in balconies (185) multiplied by the cost per ticket for these seats. Then we get:
[tex]215\cdot30+185\cdot25=11075[/tex]Then the max amount of money the theater can bring in for a show and answer to part b is $11075.
Vladimir is looking to retire in 10 years. He has a plan to put $25,000 into an investment today that earns interest at a fixed amount per year. What would be a reasonable domain and range for a function modeling the total amount of the investment, including interest?explain your answer
Answers
If Vladimir is looking to retire in 10 years and he has planned to put $25,000 into an investment from today itself, that earns interest at a fixed amount per year, considering the rate of interest to be (R%) per annum, the domain and range for a function modeling the total amount of the investment, including interest are as follows:
Domain [X = {0 ≤ years ≤ 10}]
Range (total amount), [Y = {$25,000 ≤ Y ≤ 25,000( 1 + 10R)}]
As per the question statement, Vladimir is looking to retire in 10 years and he has planned to put $25,000 into an investment from today itself, that earns interest at a fixed amount per year, and since there is no information about the rate of interest of that investment, we are considering the rate of interest to be (R%) per annum.
We are required to determine the domain and range for a function modeling the total amount of the investment, including interest using the question statement mentioned data and our assumptions.
Since the starting principal amount, say P is $25,000, given,
Time of investment, say T is 10 years, also given,
And considering the interest rate per year to be R (%),
Then after 10 years, the total amount Vladimir has is [25000( 1 + xR)].
Where, the Domain (No. of years ) is [X = {0 ≤ years ≤ 10}]
And Range (total amount), [Y = {$25,000 ≤ Y ≤ 25,000( 1 + 10R)}]
Domain of a Function: In mathematics, the domain of a function is the set or group of inputs that is accepted by the function.Range of a Function: In mathematics, the range of a function is the set or group of outputs produced by the function using values from its domain.To learn more about Domain and Range of a Function, click on the link below.
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Michael has eight bags of mulch how many trees can he mulch if each tree requires 2/3 bags of mulch.a) 16/3, b) 3/4, c) 12, d)16
Answers
12 (option C)
Explanation:1 tree requires 2/3 bags of mulch
Let the number of trees for 8 bags of mulch = y
1 tree = 2/3 bags
y = 8 bags
Cross multiply:
8(1) = y(2/3)
[tex]\begin{gathered} 8\text{ = }\frac{2y}{3} \\ Mu\text{ltiply both sides by 3:} \\ 8(3)\text{ = 2y} \\ 24\text{ = 2y} \end{gathered}[/tex][tex]\begin{gathered} \text{Divide both sides by 2:} \\ \frac{24}{2\text{ }}=\frac{2y}{2} \\ y\text{ = 12 } \end{gathered}[/tex]Hence, 8 bags of mulch require 12 trees (option C)
help meeeeeeeeee pleaseee
Answers
Answer:
solid photo
Step-by-step explanation:
PLS HELP ME, I NEED HELP
Answers
Answer: A
Step-by-step explanation:
Substitute y for 0, and then find x, which is 3x<-10. divide by three, and you get x<-3.33 and A is the only one with the right x coordinate and going to the left.
Help plss
The deadline is tomorrow
Answers
The inverse and domain of the inverse of the function are attached below.
Inverse of a FunctionIn mathematics, an inverse is a function that serves to “undo” another function. That is, if y produces y, then putting y into the inverse of produces the output x. A function y that has an inverse is called invertible and the inverse is denoted by inverse of y.
The inverse of the given function is
[tex]y = (x+2)^2, y-^1(x) = \sqrt{x} - 2, -\sqrt{x} - 2[/tex]
The domain of the function is
[tex]domain= [0, \infty)[/tex]
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Find the whole. 500% of what number is 3,650
Answers
To find 500% of a number, you have to multiply that number by 500 and then divide by 100. Calling x to the unknown number, the situation is:
[tex]x\cdot\frac{500}{100}=3650[/tex]Solving for x,
[tex]\begin{gathered} x\cdot5=3650 \\ x=\frac{3650}{5} \\ x=730 \end{gathered}[/tex]500% of 730 is 3650
the 90% confidence interval
Answers
Answer:
With a 90 percent confidence interval, you have a 10 percent chance of being wrong.--
Step-by-step explanation:
think it helps
have a nice night
Which order pair represents point B in the graph (0, 2)(1, 0)(1, 2)(2, 1)
Answers
Notice that the point B is located two units away from the origin on the x-axis, and its one unit up fro the origin on the y-axis, thus, the point B is the ordered pair (2,1)
3. A taxi ride in a large city costs $3.50 plus $6 for each mile traveled. Write an equation to represent this
situation where d is the distance traveled.
If Brandon traveled 7.5 miles by taxi, how much was the cost, C, of his taxi ride?
Which equation represents this situation and the cost of Brandon's taxi ride?
Answers
The cost of Brandon's taxi ride is $ 4.8.
A taxi ride in a large city costs $3.50 plus $6 for each mile traveled .The 3 mile cab ride includes a basic charge as well as the cost for the distance covered.If Brandon traveled 7.5 miles by taxi, how much was the cost, C, of his taxi.
For a 6 mile trip, the cost is $4.80 which means that :
The cost of 3 miles is $4.80−$3.00=$1.80
Therefore the cost for 1 mile is $1.80÷3=$0.60
The basic fee for hiring the cab is $3.00−$1.80=$1.20
So the total cost, c for a trip of d miles will be shown below:
c=0.6d+1.2
Check:
If d=3
c=0.6(3)+1.2=3
If d=6
c=0.6(6)+1.2= 4.8
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Which of the following is the average rate of change over the interval [-5, 10] for the function g(x) = log2 (x+6)-3
A.4/5
B.5/4
C.4/15
D.15/4
Answers
It's answer is option(C) i.e, 4/15
What is Average rate of change?
The average rate of function f over the interval a≤x≤b is given by ,
(f(b) - f(a)) / (b - a)
It is the average amount by which the function changed per unit throughout that time period.
In this question the equation is given,
g(x) = log2 (x+6)-3
Solve this eq. by putting the values [-5, 10],
let, interval [-5, 10] = [a, b]
Then solve for g(a) and g(b), we know g(a) = g(-5),
g(-5) = log₂(-5+6) - 3
= log₂1 - 3
= 0 - 3
g(-5) = -3
Now, for g(b) = g(10)
g(10) = log₂(10+ 6) - 3
= log₂16 - 3
= 4 - 3
g(10) = 1
Now put these values in average rate formula,
Average rate = (g(b) - g(a)) / (b - a)
= (1 - (-3)) / (10 - (-5))
= (1 + 3) / (10 + 5)
= 4 / 15
Therefore, the average rate is 4/15 i.e, option(C)
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Answer: C. 4/15. I took the test and got it right.
Step-by-step explanation:
Just number 3.
Tuesday-Friday please I can do the total hours
Answers
The total hours for the week is 32 hrs 55 mins.
Mon total hours = ( 12:00 - 8:30) + ( 17:35 - 12: 35)hrs
= 3 hrs 30 mins + 5 hrs
= 8hrs 30mins
Tue total hours = ( 12:15 - 8:25) + ( 17:30 - 13: 00)hrs
= 3hrs 50mins + 4hrs 30mins
= 8hrs 20mins
Wed total hours = ( 12:45- 8:28) + ( 16:25 - 13: 15)hrs
= 4 hrs 17 mins + 3hrs 10 mins
= 7hrs 27mins
Thu total hours = ( 01:08- 8:15) + ( 17:42 - 13: 45)hrs
= 4hrs 53mins + 3hrs 57 mins
=8hrs 50mins
Fri total hours = ( 12:30- 8:50) + ( 17:08 - 13: 00)hrs
=3hrs 40mins + 4hrs 8 mins
=7 hrs 48 mins
Therefore total work hours = 32 hrs 55 mins
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A store purchased a piece of artwork then marked up the price 350% before selling to customers. If the artwork was sold for $52.50, what was its original price?
Answers
a ski slope can be modelled by the equation of the tangent to the curve y=-0.12x^2+12 at the point where x=30
Answers
Answer:
y= -96
Step-by-step explanation:
y= -0.12x^2 +12
y= -0.12x 30^2+12
y= -96
I think the question isn't complete so I'm pretty sure I'm wrong but this is what I got :)
How much would you need to deposit in an account now in order to have $2000 in the account in 15 years? Assume the account earns 3% simple interest. Round your answer to the nearest cent.
Answers
2000e^(15•.03
find an equation of the line containing the two given points.Express your answer in the indicated form. points (1,2) and (3,10):standard form
Answers
Equation of the line
There are several forms to express the equation of a line.
The equation of the line in slope-intercept form is:
y=mx+b
Being m the slope and b the y-intercept.
The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:
[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]The standard form of a line is:
Ax + By = C
We are given two points (1,2) and (3,10). The point-point equation is adequate according to the data we are provided.
[tex]\begin{gathered} \displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ \text{Substituting:} \\ \displaystyle y-2=\frac{10-2}{3-1}(x-1) \end{gathered}[/tex]Operating:
[tex]\begin{gathered} y-2=\frac{8}{2}(x-1)=4(x-1) \\ \\ \text{Operating:} \\ y-2=4x-4 \end{gathered}[/tex]Subtracting 4x and adding 2:
y - 4x = -4 + 2 = -2
Rearranging:
-4x + y = -2
This is the required equation in standard form
Write each percent as a fraction and a decimal 72% , 25% , 500%, 5%, 307%, 165% plss help
Answers
Answer:72%, 72/100, and .72
25%, 25/100, and .25
500% 5/1, and 5.0
5%, 5/100, and .05
307%, 307/100, and 3.07
165%, 165/100, and 1.65
Step-by-step explanation:
