Answers
Answer:
a). Center of the circle = (-2, 5)
b). Equation of the line ⇒ y = [tex]-\frac{4}{5}x+\frac{58}{5}[/tex]
Step-by-step explanation:
Equation of the circle is,
x² + 4x + y²- 10y + 20 = 30
a). [x² + 2(2)x + 4 - 4] + [y²- 2(5)y + 25] - 25 + 20 = 30
[x² + 2(2)x + 4] - 4 + [y² - 2(5)y + 25] - 25 + 20 = 30
(x + 2)² + (y - 5)²- 29 + 20 = 30
(x + 2)² + (y - 5)²- 9 = 30
(x + 2)² + (y - 5)² = 39
By comparing this equation with the standard equation of a circle,
Center of the circle is (-2, 5).
b). A point (2, 10) lies on this circle.
Slope of the line joining this point to the center (-2, 5),
[tex]m_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
= [tex]\frac{10-5}{2+2}[/tex]
= [tex]\frac{5}{4}[/tex]
Let the slope of the tangent which is perpendicular to this line is '[tex]m_{2}[/tex]'
Then by the property of perpendicular lines,
[tex]m_{1}\times m_{2}=-1[/tex]
[tex]\frac{5}{4}\times m_{2}=-1[/tex]
[tex]m_{2}=-\frac{4}{5}[/tex]
Now the equation of the line passing though (2, 10) having slope [tex]m_{2}=-\frac{4}{5}[/tex]
y - y' = [tex]m_{2}(x-x')[/tex]
y - 10 = [tex]-\frac{4}{5}(x-2)[/tex]
y - 10 = [tex]-\frac{4}{5}x+\frac{8}{5}[/tex]
y = [tex]-\frac{4}{5}x+\frac{8}{5}+10[/tex]
y = [tex]-\frac{4}{5}x+\frac{58}{5}[/tex]
Therefore, equation of the line will be, y = [tex]-\frac{4}{5}x+\frac{58}{5}[/tex]
Related Questions
I need help people please help me
Answers
Answer:
Each Cup has 3/8
Step-by-step explanation:
Divide
∠A and ∠B are complementary. If m∠B = 64° , what is the measure of ∠A?
26°
36°
11°
64°
Answers
Answer: 26
Step-by-step explanation:
Two Angles are Complementary when they add up to 90 degrees (a Right Angle). Then
∠A + ∠B = 90
∠A =90- ∠B
∠A = 26
Answer:
The measure of [tex]\angle A[/tex]:
[tex]\angle A = 26\textdegree[/tex]
Step-by-step explanation:
Since both [tex]\angle A[/tex] and [tex]\angle B[/tex] are complementary (Which they both add up to 90°), and you want to find the measure of
Measure of [tex]\angle A[/tex]: unknown
Measure of [tex]\angle B[/tex]: 64°
Finding the measure of [tex]\angle A[/tex]:
[tex]90 - 64 = 26[/tex]
[tex]\angle A = 26\textdegree[/tex]
So, the measure for [tex]\angle A[/tex] is [tex]26\textdegree[/tex].
part 1. Find the value of the trig function indicated, use the Pythagorean Theorem to find the 3rd side if you need it
Answers
Answer: [tex]\bold {1)\ \cos\ \theta}=\dfrac{\sqrt2}{2}\qquad 2)\ \tan \theta =\dfrac{1}{3}\qquad 3)\ \cos\ \theta=\dfrac{3\sqrt{13}}{13}\qquad 4)\ \cos\ \theta = \dfrac{2\sqrt5}{5}}[/tex]
Step-by-step explanation:
Pythagorean Theorem is: a² + b² = c², where "c" is the hypotenuse
[tex]1)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{2}{2\sqrt2}\quad =\large\boxed{\dfrac{\sqrt2}{2}}[/tex]
Note: 2² + 2² = hypotenuse² → hypotenuse = 2√2
[tex]2)\ \tan \theta=\dfrac{\text{side opposite to}\ \theta}{\text{side adjacent to}\ \theta}=\dfrac{2}{2\sqrt2}\quad =\dfrac{5}{15}\quad \rightarrow \large\boxed{\dfrac{1}{3}}[/tex]
Note: hypotenuse not needed for tan θ
[tex]3)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{3}{\sqrt{13}}\quad =\large\boxed{\dfrac{3\sqrt{13}}{13}}[/tex]
Note: 2² + 3² = hypotenuse² → hypotenuse = √13
[tex]4)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{4}{2\sqrt5}\quad =\large\boxed{\dfrac{2\sqrt5}{5}}[/tex]
Note: hypotenuse given in problem
Simultaneous equation
Answers
Answer:
x = 5, y = 9.
Step-by-step explanation:
8^x / 2^y = 64
3^4x * (1/9)^(y -1) = 81
From the first equation
2^3x / 2^y = 2^6
2^(3x-y) = 2^6
So 3x - y = 6 ..........(1)
From the second equation:
3^4x * 9^(-(y-1)) = 3^4
3^4x * 3^2(-(y-1)) = 3^4
3^(4x+ 2(1 - y)) = 3^4
So 4x + 2(1 - y) = 4
4x - 2y = 2
2x - y = 1 .............(2)
Subtract: (1) - (2):
x = 5.
and 2(5) - y = 1
so y = 9.
Solving the simultaneous equations we get x is 5 and y is 9 .
Simultaneous equations in algebra are those that concurrently involve two or more variables, such as x and y. Even though they are solved simultaneously, the equations are known as simultaneous equations. Just these equations alone have innumerable answers.
A system of equations, often known as an equation system, is a collection of finite equations for which common solutions are sought.
The two given equations can be simplified as:
[tex]8^x \div 2^y = 64\\\\or,\frac{2^{3x}}{2^y} =2^6\\\\or, 2^{3x-y}=2^6\\\\or, 3x-y = 6[/tex]
And :
[tex]3^{4x} \times (\frac{1}{9})^{y-1}=81\\\\or, 3^{4x} \times 3^{-2(y-1)}=3^4\\\\or, 3^{4x+2-2y}=3^4\\\\or, 4x-2y = 2\\\\or,2x-y=1[/tex]
Now we can solve the two simultaneous equations :
3x - y = 6 and 2x - y = 1
Subtracting the equations we get:
x = 5
and
y = 9
Solving the simultaneous equations we get the value of x as 5 and the value of y as 9 .
To learn more about simultaneous equations visit:
brainly.com/question/16763389
#SPJ1
Last year, there were “x” students in the Math Club, but this year, there was a 40% increase in membership. Represent this year’s membership in terms of “x”.
Answers
Answer:
(x)1.4=Y
Step-by-step explanation:
40% increase of memeber so ita 140% of X
the distance between (3,k) and ( 5,6) is 2root2 units then k
Answers
Answer:
Step-by-step explanation:
[tex]\sqrt{x} Distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\\\\\sqrt{(5-3)^{2}+(6-k)^{2}}=2\sqrt{2}\\\\\sqrt{(2)^{2}+[(6)^{2}-(2*6*k)+(k)^{2}]}=2\sqrt{2}\\\\\sqrt{4+[36-12k+k^{2}]}=2\sqrt{2}\\\\\sqrt{40-12k+k^{2}}=2\sqrt{2}\\[/tex]
Take square both side
[tex]40-12k+k^{2}=(2\sqrt{2})^{2}\\\\40-12k+k^{2}=4*2\\\\40-12k+k^{2}=8\\\\k^{2}-12k+40-8=0\\\\k^{2}-12k+32=0\\[/tex]
Factorize,
Sum = -12
Product = 32
Factors = -8 , -4
k² - 8k - 4k + (-8)*(-4) = 0
k(k - 8) - 4(k - 8) = 0
(k - 8)(k - 4) = 0
k = 8 or 4
The points are (3,k) and (5,6).
Given, distance = 2√2 units
Applying distance formula,
Distance = √(x2-x1)^2 + (y2-y1)^2
2√2 = √(x2-x1)^2 + (y2-y1)^2
Squaring both sides,
(2√2)^2 = [√(x2-x1)^2 + (y2-y1)^2]^2
8 = (x2-x1)^2 + (y2-y1)^2
8 = (5-3)^2 + (6-k)^2
8 = 2^2 + (6^2 - 2x6xk + k^2)
8 = 4 + 36 - 12k + k^2
8 = 40 - 12k + k^2
= k^2 - 12k + 32 = 0
On factorising,
=> k^2 - 4k - 8k + 32 = 0
=> k(k-4) -8(k-4) = 0
=> (k-4)(k-8) = 0
=> k-4 = 0 , k-8 = 0
=> k = 4 , k = 8
Can anyone help me ?????
Answers
Answer:
Step-by-step explanation:
The graph of a function and its inverse will always reflect through the line
y = x.
This is because a function has a specific set of coordiates, (x, y). That function's inverse has a set of coordinates that flips the x and y coordinates. For example, if a function has a set of coordinates (0, 1), (2, 3), (4, 5) then its inverse will have the coordinates (1, 0), (3, 2), (5, 4). If you plot the function's points and then the inverse's points in the same plane (meaning on the same graph) and connect the dots, you will see that the function and its inverse are reflections of each other through y = x. Below is an example of this. The dotted purplish line is the line y = x.
Which is equivalent to v10 3/4?
Answers
Answer:
d) [tex](\sqrt[8]{(10} )^{3 x}[/tex]
Step-by-step explanation:
Step(i):-
Given [tex](\sqrt{10} )^{\frac{3 x}{4} }[/tex]
we will use formula
[tex](a)^{m n} = (a^{m} )^{n}[/tex]
[tex](\sqrt{10} )^{\frac{3 x}{4} } =( (10)^{\frac{1}{2} } )^{\frac{3 x}{4} }[/tex]
= [tex]( (10)^{\frac{1}{2} X\frac{3 x}{4} } )[/tex]
= [tex]( (10)^{\frac{3 x}{8} } )[/tex]
= [tex]((10)^{\frac{1}{8} } )^{3x}[/tex]
Step(ii):-
we will apply [tex](a)^{\frac{1}{n} } = \sqrt[n]{a}[/tex]
= [tex](\sqrt[8]{(10} )^{3 x}[/tex]
Ian has 20 football cards, and Jason has 44 baseball cards. They agree to trade such that jason
gives Ian 2 baseball cards for every card Ian gives to Jason. After how many such trades will Ian
and Jason each have an equal number of cards?
Answers
Answer:
12 trades
Step-by-step explanation:
Let's call 'x' the number of trades they will do.
After each trade, the number of cards Ian has increase by 1 (he gives 1 but receives 2), and the number of cards Jason has decrease by 1 (he receives 1 but gives 2), so after x trades, the number of cards Ian has is 20 + x, and Jason has 44 - x.
To find the number of trades when they will have the same amount of cards, we have that:
20 + x = 44 - x
2x = 24
x = 12 trades
The number of trades will Ian and Jason each have an equal number of cards is 12 trades
The calculation is as follows;
Let's us assume the x' be the number of trades they will do.
20 + x = 44 - x
2x = 24
x = 12 trades
Learn more: brainly.com/question/16911495
what is 100,000 written as a power with a base of 10? ANSWER QUICK
Answers
Answer:
Its either 10 to the power of 6 or ten to the power of 5
Step-by-step explanation:
...
. Alexandro, o professor de Física, avisou aos alunos que a média bimestral seria calculada conforme o seguinte critério: Adicionam-se as notas obtidas no projeto, na prova e no trabalho em grupo e divide-se o resultado obtido por três. Laura é uma das alunas do professor Alexandre. As notas de Laura: Projeto: 5,0 Prova: 6,5 trabalho em grupo: 9,5. A) Por que o resultado deve ser dividido por 3?
Answers
Answer:
É necessário dividir por 3 para calcular a média simples das 3 notas.
Média = 7.
Step-by-step explanation:
O resultado deve ser dividido por três porque três notas com pesos iguais (projeto, prova e trabalho em grupo) foram somadas, portanto para calcular a média bimestral de Laura, a soma das três notas deve ser dividida por 3. A média de Laura é:
[tex]M=\frac{5,0+6,5+9,5}{3}\\ M=7[/tex]
PLS HELP will give brainliest
If a graph is symmetric with respect to the x-axis, then it cannot be symmetric with respect to the y-axis.
A. FALSE
B. TRUE
Answers
Answer:
False, it could be.
At the corner store near Billy’s
house, loose mixed nuts cost
$1.75 per 100 g. Write an
equation to represent the amount
of mixed nuts, n, he can buy if he
has d dollars. Then, use your
equation to determine how many
grams of mixed nuts Billy can buy
if he has $5.
Answers
Answer:
d = 0.0175n ---> required equation
Billy can buy 285.714 gram nut with $5
Step-by-step explanation:
cost of 100g loose nut = $1.75
dividing LHS and RHS by 100
cost of 100/100g loose nut = $1.75
Thus, cost of 1 gm loose nut = $0.0175
let the weight of loose nut be n gm
Multiplying LHS and RHS by n
cost of x g loose nut = $0.0175*n = $0.0175n
It is given that Billy spent d dollars to buy n gm nuts
thus,
d = 0.0175n ---> required equation
________________________________________________
He spent $5 to buy nuts
substituting value of d as 5 we have
0.0175n = 5
=>n = 5/0.0175 = 285.714
Thus, Billy can buy 285.714 gram nut with $5.
Which set of ordered pairs does not represent a function?
Answers
Answer:
it is the last one
Step-by-step explanation:
Since a function is based on a set of ordered pairs, where the first element in each pair is from the domain and the second is from the codomain. Also A function is a mapping from a set of inputs (the domain) to a set of possible outputs (the codomain).
The last one doesn't show the correct inputs and outputs
express 0.3°8° in form a/b where by b#0
Answers
Answer:
0.3° = 0.3π/180
8° = 2π/45
Multiplying both
0.3π/180×2π/45
3/10π/180 × 2π/45
You will get
π/300 × π/45
= π²/13500 where a = π² b= 13500
Hope this helps.
Which one of the following is discrete data?
Answers
Answer:
Number of people in a room
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Airborne Airlines Inc. has a $1,000 par value bond outstanding with 20 years to maturity. The bond carries an annual interest payment of $102 and is currently selling for $880. Airborne is in a 30 percent tax bracket. The firm wishes to know what the aftertax cost of a new bond issue is likely to be. The yield to maturity on the new issue will be the same as the yield to maturity on the old issue because the risk and maturity date will be similar.
a. Compute the yield to maturity on the old issue and use this as the yield for the new issue. (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)
b. Make the appropriate tax adjustment to determine the aftertax cost of debt. (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)
Answers
Answer:
(a) 11.64%
(b) 8.15%
Step-by-step explanation:
Airborne airlines has an annual interest of payment= $102
Principal payment= $1,000
Time to maturity= 20 years
Current price of the bond= $880
The formular for calculating the yield on maturity is
[ Annual interest payment+Principal payment-(price of the bond/number of years to maturity)] / 0.6(price of the bond) + 0.4(principal payment)
(a) [102+(1000-880)/20)]/ [0.6(880) + 0.4(1000)]
= [102+ (120/20)]/ [528+400]
= [102+6]/ 928
= 108/928
= 11.637%
= 11.64% ( to 2 decimal places)
(b) Kd= Yield(1-T)
Kd= 11.64(1-0.30)
Kd= 11.64×0.7
Kd= 8.145%
Kd= 8.15%( to 2 decimal places)
Hence the yield to maturity on the new issue is 11.64% and the aftertax cost of debt is 8.15%
I wiol mark you brainliest!!! Use the substitution method to solve the system of equations.
Answers
Answer: b. (6,27)
Step-by-step explanation:
y=5x- 3 x=6<---- put in the equation
y=5(6)-3 <------- mulitply 5 and 6
y=30-3 <---- subtracted
y= 27. <---- y value.
Answer being (6,27)
Hope it helps :)
Point D is located on the segment CE. IF CD = 24 and DE = x and CE - 5x, what is the measure of segment CE?
Answers
Answer:
30Step-by-step explanation:
If point D is located on the segment CE, then point C, D and E lies on the same line i.e they are collinear. Mathematically, CD+DE = CE
Given CD = 24 and DE = x and CE = 5x, on substituting this values in the equation we have;
[tex]24+x = 5x\\5x-x = 24\\4x = 24\\x = 24/4\\x = 6[/tex]
Since CE = 5x, CE = 5(6) = 30
The measure of segment CE is 30
Joey and Nolan are each solving the equation 13x - 42 = 18 - 7x.
Joey's first step was to rewrite the equation as 20x - 42 = 18 while Nolan's first step was to rewrite the
equation as 13x = 60 - 7x.
Who is correctly applying the addition property of equality in the first step of his work?
A. Only Joey
B. Only Nolan
C. Both Joey and Nolan
D. Neither Joey nor Nolan
Answers
Answer:
First step=13x+7x=18+42
Step-by-step explanation:
13x-42=18-7x
First step
It is to collect like terms of the equation
13x+7x=18+42
20x=60
x=60/20
x=3
What is the value of x?
Answers
Answer:
x = 20
Step-by-step explanation:
The angles are vertical angles and we know that vertical angles are equal
x+40 = 3x
Subtract x from each side
x+40-x = 3x-x
40 = 2x
Divide each side by 2
40/2 = 2x/2
20 =x
Answer:
The value of [tex]x[/tex]:
[tex]x = 20[/tex]
Step-by-step explanation:
-Since, one angle with the measure [tex]x + 40[/tex] and another angle with measure [tex]3x[/tex] are vertical angles, they equal each other. So, it will be written as:
[tex]x + 40 = 3x[/tex]
-After you have formed an equation, you switch the equation and you solve for the value of [tex]x[/tex]:
[tex]x + 40 = 3x[/tex]
[tex]x - x + 40 = 3x -x[/tex]
[tex]40 = 2x[/tex]
[tex]\frac{40}{2} = \frac{2x}{2}[/tex]
[tex]20 = x[/tex]
So, the final answer is [tex]20 = x[/tex] or [tex]x = 20[/tex] (They are both the same, you just switch them).
3a+2b=9 and 8x+6y=60
what is the value of 9a+6b
what is the value of 4x+3y
Answers
Answer:
The Value of 9a+6b is 27. and the value of 4x+3y is 30.
Explanation
1)
3a+2b=9
multiplying both by side by 3
or, 3×( 3a+2b)=3×9
Hence, 9a+6b=27
2)
8x+6y=60
Dividing both by side by 2
or, (8x+6y)/2 = 60/2
Hence, 4x+3y=30
pleaseeeeee right answer struggling
Answers
The right answer is of:
option C
please see the attached picture....
Hope it helps.....
Good luck on your assignment.....
in a wood there are 420 silver birch trees, 160 oak tees and 300 wild cherry trees. what is the percentage of the oak trees give your answer to 1 decimal place
Answers
Answer:
18.2%
Step-by-step explanation:
The total number of trees in the wood = 420 + 160 + 300
= 880 trees
∴ The percentage of the oak trees = [tex]\frac{160}{880} * \frac{100}{1}[/tex]
= [tex]\frac{2 * 100}{11}[/tex]%
= [tex]\frac{200}{11}[/tex]%
= 18.181818...%
In 1 decimal place = 18.2%
Hope this helps!!
Just the top half is what I need help with. I will give the the big
Answers
Answer:
Step-by-step explanation:
5.volume=8×7×6=336 mi³
6.r=16/2=8 yd
volume=4/3×π×8³=2048/3 π yd³
≈2144.7 yd³
7.r=2.5/2=1.25 in
v=πr²h=π×1.25²×5
volume of 150 cups=7.8125 π×150=1171.875 π in³≈3681.6 in³
8. statement not visible.
How do I post a picture
Answers
Answer:
Go to me. Click on your profile picture then click on your profile picture again to change it
If f(x) = 3x-2 and g(x) = 2x + 1 find (f-g)(x)
Answers
Answer:
x-3
Step-by-step explanation:
f(x) = 3x-2
g(x) = 2x + 1
(f-g)(x) = 3x-2 - (2x+1)
Distribute the minus sign
=3x-2-2x-1
Combine like terms
= 3x-2x-2-1
=x-3
Q, A fruit seller buys 10 apples for Rs. 45 each from wholesale market .He packs them in a fruit basket for 40 and sells them each for 20 bakets Rs. 600 .Is it loss or gain
Answers
Answer:
It is a gain.
Step-by-step explanation:
CLEAR STATEMENT:
Given that the fruit seller buys 10 apples for 45Rs each from wholesale market.
This implies her buys them for 10 × 45Rs = 450Rs.
UNCLEAR STATEMENT:
He packs them in a fruit basket for 40 and sells them each for 20 baskets Rs. 600.
ASSUMING:
What you are trying to say is that he bought baskets for 40Rs, and sold the apples for 600Rs.
Subtracting his expenses from this value, we have
600Rs - 450Rs - 40Rs = 110Rs
Since this amount is positive, we conclude that it is a gain of 110Rs.
Please answer correctly!!!!!! Will mark brainliest !!!!!!!!!!!
Answers
Answer:
see below
Step-by-step explanation:
g(x) = sqrt(x+3)
g(-6) = sqrt(-6+3) = sqrt(-3) not a real number not in domain
g(-3) = sqrt(-3+3) = sqrt(0) 0 in domain
g(3) = sqrt(3+3) = sqrt(6) in domain
Which of the following is an angle shown in the drawing?
Answers
Answer:
ABE
DBC
CBE
Step-by-step explanation:
They all have B as the middle one, and B is the vertex
I think
