Answers
Answer:
The correct answer will be option b
Step-by-step explanation:
We know that x = rcos( θ ), and y = rsin( θ ), so let's rewrite this polar equation.
r = 4( x / r ) + 2( y / r ),
r = 4x / r + 2y / r,
r = 4x + 2y / r,
r / 1 = 4x + 2y / r ( Cross - Multiply )
4x + 2y = r²
We also know that r² = x² + y², so let's substitute.
x² + y² = 4x + 2y,
x² - 4x - 2y + y² = 0,
Circle Equation : ( x - 2 )² + ( y - 1 )² = ( √5 )²,
Solution : ( x - 2 )² + ( y - 1 )² = 5
Related Questions
7.619 by 10^-3
7.254 by 10^2
Answers
Answer:
0.007619
0.07254
Step-by-step explanation:
1)7.619*10^-3
0.007619
2)7.254*10^2
0.07254
Explanation:
7.619*10^-3
The number here is 7.619 and the number written in scientific notation has minus 3 as its exponent.
.007.619
So the distance between the first decimal point and the second decimal is only three numbers.
Since it is exponent is minus three.
Another way to get the answer.
[tex]7.619 \times 10 {}^{ - 3} = \frac{7619}{1000} \times \frac{1}{1000} = \frac{7619}{1000000} = 0.007619 [/tex]
This applies to the second one too.
Hope this helps ;) ❤❤❤
How many solutions does the following equation have ?
−3x+9−2x=−12−5x
Answers
[tex]\text{Solve for x:}\\\\-3x+9-2x=-12-5x\\\\\text{Combine like terms}\\\\-5x+9=-12-5x\\\\\text{Add 5x to both sides}\\\\9=-12\\\\\text{Since that's not valid, there would be no solutions}\\\\\boxed{\text{No solutions}}[/tex]
Please answer this correctly without making mistakes
Answers
Answer:
[tex]\large \boxed{\mathrm{4/5 \ cups}}[/tex]
Step-by-step explanation:
Subtract 1/10 from 9/10 to find out how much is left.
9/10 - 1/10
8/10 = 4/5
Answer:
4/5 cupsStep-by-step explanation:
[tex]Volume\:of \: syrup \:in \:cup\:from\:jug = \frac{9}{10}\\\\ She \:took\: \frac{1}{10} from \:the\:cup\:into\:the \:jug \\\\Volume \:of syrup\:in\:cup=?\\\\\frac{9}{10} -\frac{1}{10} \\\\= \frac{4}{5} cups[/tex]
You have $2,000 on a credit card that charges a 16% interest rate. If you want to pay off the credit card in 5 years, how much will you need to pay each month (assuming you don't charge anything new to the card)?
Answers
9514 1404 393
Answer:
$48.64
Step-by-step explanation:
The monthly payment amount is given by the amortization formula ...
A = P(r/n)/(1 -(1 +r/n)^(-nt))
where P is the loan amount, r is the annual interest rate compounded n times per year for t years.
Here, you have P=2000, r=0.16, n=12 (months per year), t=5 (years), so the payment is ...
A = $2000(0.16/12)/(1 -(1 +0.16/12)^(-12·5)) = $320/(12(0.54828942))
A ≈ $48.636 ≈ $48.64
You will need to pay $48.64 each month to pay off the charge in 5 years.
Your friend Stacy has given you the following algebraic expression: "Subtract 20
times a number n from twice the cube of the number. What is the expression that your
friend is saying?
Answers
Answer:
Expression = 2n³ - 20n
Step-by-step explanation:
Find:
Expression
Computation:
Assume given number is 'n'
Cube of number = n³
Twice of cube = 2n³
Subtract number = 20n
Expression = 2n³ - 20n
Solving Equations by Dividing 2) 9x= -135 Solve for x. 0 -144 O 126 O 15 0 -15
Answers
Explanation:
9x = -135
Divide by 9 on both sides
X = -15
It is -15 since 135 is negative
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\boxed{\mathsf{9x = -135}}[/tex]
[tex]\huge\boxed{\text{DIVIDE 9 to BOTH SIDES}}[/tex]
[tex]\huge\boxed{\mathsf{\dfrac{9x}{9}= \dfrac{-135}{9}}}[/tex]
[tex]\huge\boxed{\mathsf{\bullet \ CANCEL: \dfrac{9}{9}\ because\ it \ gives\ you\ 1}}[/tex]
[tex]\huge\boxed{\bullet\ \mathsf{KEEP: \dfrac{-135}{9}\ because\ it\ helps\ solve \ for}}\\\huge\boxed{\mathsf{the\ x-value}}[/tex]
[tex]\huge\boxed{\mathsf{x = \dfrac{-135}{9}}}\\\\\huge\boxed{\mathsf{\dfrac{-135}{9}= x}}}[/tex]
[tex]\huge\boxed{Simplify \ it\uparrow}[/tex]
[tex]\huge\boxed{\mathsf{x = \bf -15}}[/tex]
[tex]\huge\boxed{\textsf{Therefore, your answer is: Option D. -15 }}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]
Please give me the answer ASAP The average of 5 numbers is 7. If one of the five numbers is removed, the average of the four remaining numbers is 6. What is the value of the number that was removed Show Your Work
Answers
Answer:
The removed number is 11.
Step-by-step explanation:
Given that the average of 5 numbers is 7. So you have to find the total values of 5 numbers :
[tex]let \: x = total \: values[/tex]
[tex] \frac{x}{5} = 7[/tex]
[tex]x = 7 \times 5[/tex]
[tex]x = 35[/tex]
Assuming that the total values of 5 numbers is 35. Next, we have to find the removed number :
[tex]let \: y = removed \: number[/tex]
[tex] \frac{35 - y}{4} = 6[/tex]
[tex]35 - y = 6 \times 4[/tex]
[tex]35 - y = 24[/tex]
[tex]35 - 24 = y[/tex]
[tex]y = 11[/tex]
Okay, let's slightly generalize this
Average of [tex]n[/tex] numbers is [tex]a[/tex]
and then [tex]r[/tex] numbers are removed, and you're asked to find the sum of these [tex]r[/tex] numbers.
Solution:
If average of [tex]n[/tex] numbers is [tex]a[/tex] then the sum of all these numbers is [tex]n\cdot a[/tex]
Now we remove [tex]r[/tex] numbers, so we're left with [tex](n-r)[/tex] numbers. and their. average will be [tex]{\text{sum of these } (n-r) \text{ numbers} \over (n-r)}[/tex] let's call this new average [tex] a^{\prime}[/tex]
For simplicity, say, sum of these [tex]r[/tex] numbers, which are removed is denoted by [tex]x[/tex] .
so the new average is [tex]\frac{\text{Sum of } n \text{ numbers} - x}{n-r}=a^{\prime}[/tex]
or, [tex] \frac{n\cdot a -x}{n-r}=a^{\prime}[/tex]
Simplify the equation, and solve for [tex]x[/tex] to get,
[tex] x= n\cdot a -a^{\prime}(n-r)=n(a-a^{\prime})+ra^{\prime}[/tex]
Hope you understand it :)
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. (If the quantity diverges, enter DIVERGES.) an = 1/sqrt(n)
Answers
This sequence converges to 0.
Proof: Recall that
[tex]\displaystyle\lim_{n\to\infty}\frac1{\sqrt n}=0[/tex]
is to say that for any given [tex]\varepsilon>0[/tex], there is some [tex]N[/tex] for which [tex]\left|\frac1{\sqrt n}-0\right|=\frac1{\sqrt n}<\varepsilon[/tex] for all [tex]n>N[/tex].
Let [tex]N=\left\lceil\frac1{\varepsilon^2}\right\rceil[/tex]. Then
[tex]n>\left\lceil\dfrac1{\varepsilon^2}\right\rceil\ge\dfrac1{\varepsilon^2}[/tex]
[tex]\implies\dfrac1n<\varepsilon^2[/tex]
[tex]\implies\dfrac1{\sqrt n}<\varepsilon[/tex]
as required.
4. Two unbiased coins are tossed. Calculate the probability that
(a) Two heads are obtained.
(b) One head and one tail is obtained.
Answers
(a) P(2 heads) = 1/4
(b) P(1 head and 1 tail) = 2/4 = 1/2
Find the distance between the points. Give an exact answer and an approximation to three decimal places.
(3.1,0.3) and (2.7. - 4.9)
The exact distance is
(Simplify your answer. Type an exact ans
Answers
Answer: sqrt(27.2) =approx 5.215
Step-by-step explanation:
The distance between 2 points can be calculated using Phitagor theorem
L= sqrt( (x1-x2)²+(y1-y2)²)
Where x1, y1 are the coordinates of the first point and x2, y2 are the coordinates of the 2-nd point.
L=sqrt((3.1-2.7)²+(0.3-(-4.9))²)= sqrt(0.4²+5.2²)=sqrt(27.2) - this is exact answer.
sqrt(27.2)=5.21536...=approx 5.215
Review the example argument and reasoning below. Identify the form (inductive or deductive) of reasoning and the type (example, analogy, causal correlation, syllogism, sign, or causal generalization) of reasoning Raul uses to justify his argument. Then, apply the three tests of argumentative reasoning (quantity, quality, & opposition) to test this argument.
Raul believes that if someone’s eyes shift to the left when they are responding to a question it is evidence that they are lying. While interviewing Michael, Raul notices Michael's eyes shifting to the left frequently when answering questions. Later, Raul tells a coworker that Michael was not hired because Raul believed Michael had lied about his previous experience during the interview.
Answers
Answer:
inductive - . Inductive reasoning makes broad generalizations from specific observations.
casual correlation
quality ( i think)
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
i just did it
HELP
PLSFind all the missing elements:
Answers
Answer:
a = 6.7 , c = 2.0
Step-by-step explanation:
For side aTo find the missing side a we use the sine rule
[tex] \frac{ |b| }{ \sin(B) } = \frac{ |a| }{ \sin(A) } [/tex]From the question
B = 58°
b = 6
A = 109°
Substituting the values into the above formula we have
[tex] \frac{6}{ \sin(58) } = \frac{ |a| }{ \sin(109) } [/tex][tex] |a| \sin(58) = 6\sin(109) [/tex]Divide both sides by sin 58°
[tex] |a| = \frac{6 \sin(108) }{ \sin(58) } [/tex]a = 6.728791
a = 6.7 to the nearest tenthFor side cTo find side c we use the sine rule
That's
[tex] \frac{ |b| }{ \sin(B) } = \frac{ |c| }{ \sin(C) } [/tex]C = 13°
[tex] \frac{6}{ \sin(58) } = \frac{ |c| }{ \sin(13) } [/tex][tex] |c| \sin(58) = 6 \sin(13) [/tex]Divide both sides by sin 58°
[tex] |c| = \frac{6 \sin(13) }{ \sin(58) } [/tex]c = 1.591544
c = 2.0 to the nearest tenthHope this helps you
Answer:
B=58 a=6.7 c=1.6
Step-by-step explanation:
It was right on Acellus
Sorry I cant give a better explanation but this unit is killing me.
Question 2b only! Evaluate using the definition of the definite integral(that means using the limit of a Riemann sum
Answers
Answer:
Hello,
Step-by-step explanation:
We divide the interval [a b] in n equal parts.
[tex]\Delta x=\dfrac{b-a}{n} \\\\x_i=a+\Delta x *i \ for\ i=1\ to\ n\\\\y_i=x_i^2=(a+\Delta x *i)^2=a^2+(\Delta x *i)^2+2*a*\Delta x *i\\\\\\Area\ of\ i^{th} \ rectangle=R(x_i)=\Delta x * y_i\\[/tex]
[tex]\displaystyle \sum_{i=1}^{n} R(x_i)=\dfrac{b-a}{n}*\sum_{i=1}^{n}\ (a^2 +(\dfrac{b-a}{n})^2*i^2+2*a*\dfrac{b-a}{n}*i)\\[/tex]
[tex]=(b-a)^2*a^2+(\dfrac{b-a}{n})^3*\dfrac{n(n+1)(2n+1)}{6} +2*a*(\dfrac{b-a}{n})^2*\dfrac{n (n+1)} {2} \\\\\displaystyle \int\limits^a_b {x^2} \, dx = \lim_{n \to \infty} \sum_{i=1}^{n} R(x_i)\\\\=(b-a)*a^2+\dfrac{(b-a)^3 }{3} +a(b-a)^2\\\\=a^2b-a^3+\dfrac{1}{3} (b^3-3ab^2+3a^2b-a^3)+a^3+ab^2-2a^2b\\\\=\dfrac{b^3}{3}-ab^2+ab^2+a^2b+a^2b-2a^2b-\dfrac{a^3}{3} \\\\\\\boxed{\int\limits^a_b {x^2} \, dx =\dfrac{b^3}{3} -\dfrac{a^3}{3}}\\[/tex]
PLEASE HELP ASAP THANKS IN ADVANCE
Answers
Answer:
the answer to the question is "C"
3x7-12-2=7?
I have no clue please help...
Answers
Answer:
X = 28/3, or 9 1/3 or 9.3
Step-by-step explanation:
Answer:
Step-by-step explanation:
3. The length of a rectangle is 4 inches more than its width. The area of the rectangle is equal to 5 inches more than 2 times the perimeter. Find the length and width of the rectangle.
Answers
Length: sqrt13 + 4
Width: sqrt13
Step-by-step explanation:
Denote the width as x, then the length is x+4. The area of the rectangle will be x(x+4), and the perimeter will then be 4x +8. Hence, you can write the equation x(x+4) - 5 = 4x+8. Solving, you get x = sqrt13.
PLEASE HELP IM SO LOST
1. Ted is working on his financial plan and lists all of his income and expenses in the spreadsheet below.
А
B
Net Pay
$5,000
2
Interest on Deposits $0
3 Income from Investments $225
4 Rent
$3,000
5 Utilities
$250
6 Satellite Dish
$175
7 Cell Phone Plan
$135
8 Car Payment
$385
9 Groceries
$200
10 Insurance
$380
11 Recreation
$400
What is Ted's net cash flow?
2. Tamara earns $8 an hour at her job working 25 hours per week. If her net pay is 78% of her paycheck
and she has no other sources of income, what is Tamara's monthly cash inflow? (Assume there are 4
pays per month.)
Answers
Answer: 1) $300 2) $624
Step-by-step explanation:
[tex]\begin{array}{l||l|l}\underline{\quad \text{Item}\qquad \qquad \qquad \qquad}&\underline{\text{Income} }&\underline{\text{Expense}}\\\text{Net Pay}&5000&\\\text{Interest on Deposits}&0&\\\text{Income from Investments}&225&\\\text{Rent}&&3000\\\text{Utilities}&&250\\\text{Satellite Dish}&&175\\\text{Cell Phone Plan}&&135\\\text{Car Payment}&&385\\\text{Groceries}&&200\\\text{Insurance}&&380\\\underline{\text{Recreation}\qquad \qquad \qquad}&\underline{\qquad \quad }&\underline{400\qquad}\\\end{array}[/tex]
TOTALS 5225 4925
Net Cash Flow = Income - Expenses
= 5225 - 4925
= 300
*************************************************************************************
[tex]\dfrac{25\ hours}{week}\times \dfrac{\$8}{hour}\times 4\ weeks\times 78\%\\\\\\=25\times \$8 \times 0.78\\\\= \$624[/tex]
A car dealer's markup on every car they sell is 20%. For what price did the dealership buy a car that they sold for $18,600?
Answers
Answer:
buying price = $15,500
Step-by-step explanation:
selling price 20% more than the buying price
let the buying price be 100% then;
selling price = 120%
120% = $18,600
100% = ?
(100 × 18600) ÷ 120
= $15,500
Write all the factors of 32
Matj
Answer
Answers
1 * 32
2 * 16
4 * 8
1, 2, 4, 8, 16, and 32
Answer: 1, 2, 4, 8, 16, and 32.
Step-by-step explanation:
Factors are what we can multiply to get the number.
Factors of 32:
1 x 32=32
2 x 16=32
4 x 8=32
Therefore, the factors of 32 are 1, 2, 4, 8, 16, and 32.
Complete the point-slope equation of the line through (2,3)(7,4). Use exact numbers. y-4=
Please help me, I would really appreciate it!
Answers
Answer:
The answer is
[tex]y - 4 = \frac{1}{5} (x - 7)[/tex]Step-by-step explanation:
To find the equation of a line given two points first find the slope and use the formula
[tex] y - y_{1} = m(x - x_{1})[/tex]Where m is the slope
To find the slope we use the formula
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]The slope of the line using points
(2,3)(7,4) is
[tex]m = \frac{4 - 3}{7 - 2} = \frac{1}{5} [/tex]Equation of the line using point (7,4) and slope 1/5 is
[tex]y - 4 = \frac{1}{5} (x - 7)[/tex]Hope this helps you
Answer:
y-4=1/5(x-3)
Step-by-step explanation:
We plug in the x's and the y's and find the slope with:
[tex](y-y_{1} )/ x-x_{1})=m[/tex]
I need help plotting this on number line
Answers
Answer:
Step-by-step explanation:
If I get paid $100 a week but my car cost $4, 990 how long will I have to save to officially buy my car?
Answers
Answer:
50 weeks.
Step-by-step explanation:
Did the math like u should've
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!
1. How can a matrix be used to solve a system of equations? Demonstrate by solving the following system. Show your work. In other words, use a problem of system of equations problem as an example.
Answers
Answer:
Step-by-step explanation:
Assuming the system is solvable in the first place, create an augmented matrix of coefficients from the equations. Then put the matrix into reduced row echelon form.
Example is attached.
"Demonstrate by solving the following system."
You need to provide the system of equations.
Yooo I just had MAD diarrhea D:
Answers
Find the solution of the system of equations.
2x – 10y = -28
-10x + 10y = -20
GbA
Answers
Answer:
(6, 4 )
Step-by-step explanation:
Given the 2 equations
2x - 10y = - 28 → (1)
- 10x + 10y = - 20 → (2)
Adding (1) and (2) term by term eliminates the term in y, that is
- 8x = - 48 ( divide both sides by - 8 )
x = 6
Substitute x = 6 into either of the 2 equations and evaluate for y
Substituting into (1)
2(6) - 10y = - 28
12 - 10y = - 28 ( subtract 12 from both sides )
- 10y = - 40 ( divide both sides by - 10 )
y = 4
Solution is (6, 4 )
convert 407 in base 8 to decimal
Answers
[tex]4\cdot8^2+0\cdot8^1+7\cdot8^0=256+7=263[/tex]
[tex]407_8=263_{10}[/tex]
Suppose that Y1, Y2,..., Yn denote a random sample of size n from a Poisson distribution with mean λ. Consider λˆ 1 = (Y1 + Y2)/2 and λˆ 2 = Y . Derive the efficiency of λˆ 1 relative to λˆ 2.
Answers
Answer:
The answer is "[tex]\bold{\frac{2}{n}}[/tex]".
Step-by-step explanation:
considering [tex]Y_1, Y_2,........, Y_n[/tex] signify a random Poisson distribution of the sample size of n which means is λ.
[tex]E(Y_i)= \lambda \ \ \ \ \ and \ \ \ \ \ Var(Y_i)= \lambda[/tex]
Let assume that,
[tex]\hat \lambda_i = \frac{Y_1+Y_2}{2}[/tex]
multiply the above value by Var on both sides:
[tex]Var (\hat \lambda_1 )= Var(\frac{Y_1+Y_2}{2} )[/tex]
[tex]=\frac{1}{4}(Var (Y_1)+Var (Y_2))\\\\=\frac{1}{4}(\lambda+\lambda)\\\\=\frac{1}{4}( 2\lambda)\\\\=\frac{\lambda}{2}\\[/tex]
now consider [tex]\hat \lambda_2[/tex] = [tex]\bar Y[/tex]
[tex]Var (\hat \lambda_2 )= Var(\bar Y )[/tex]
[tex]=Var \{ \frac{\sum Y_i}{n}\}[/tex]
[tex]=\frac{1}{n^2}\{\sum_{i}^{}Var(Y_i)\}\\\\=\frac{1}{n^2}\{ n \lambda \}\\\\=\frac{\lambda }{n}\\[/tex]
For calculating the efficiency divides the [tex]\hat \lambda_1 \ \ \ and \ \ \ \hat \lambda_2[/tex] value:
Formula:
[tex]\bold{Efficiency = \frac{Var(\lambda_2)}{Var(\lambda_1)}}[/tex]
[tex]=\frac{\frac{\lambda}{n}}{\frac{\lambda}{2}}\\\\= \frac{\lambda}{n} \times \frac {2} {\lambda}\\\\ \boxed{= \frac{2}{n}}[/tex]
Decide all proper subsets of A { 8 ,7 ,6 ,5 ,4 ,3 ,2 ,1} = A 1- { 4 ,3 ,2 ,1} 2- { } 3- { 9 ,8 ,7 } 4- { 11 ,2} 5- { 5 }
Answers
Answer:
A, E
Step-by-step explanation:
There should be 2^8-1 proper subsets of A. Its every one besides { }
What is the domain of f(x)=2/5x+6
Answers
Answer:
Look at that picture
Step-by-step explanation:
Please Help Me!!! (WORTH 60 POINTS) Will Give Extra points out
Answers
O C.
Step-by-step explanation:
To find a missing side length, use Pythagorean Theorem:
a^2 + b^2 = c^2 where a = 5 b = x and c = 6
5^2 + x^2 = 6^2
25 + x^2 = 36
x^2 = 36 - 25
x^2 = 11
x = 3.3
The value of x is sqrt rt 11
Answer:
√11 cm
Step-by-step explanation:
Pythagorean Thereom
a^2 + b^2= c^2
x^2 +5^2=6^2
x^2 + 25 = 36
subtract 25 from both sides
x^2=11
do the square root
x = √11