Answers
9514 1404 393
Answer:
y = -4/3x +23/2
Step-by-step explanation:
The tangent of interest is perpendicular to the radius at the given point on the circle. To find the perpendicular, it helps to know the slope of the radius segment. To find that, we need the center of the circle.
The center of the circle can be found by completing the square for each variable.
(x^2 -2x) +(y^2 +4y) = 20
(x^2 -2x +1) +(y^2 +4y +4) = 20 +1 +4
(x -1)^2 +(y +2)^2 = 25
Comparing this equation to the standard form equation for a circle, we can find the center.
(x -h)^2 +(y -k)^2 = r^2 . . . . . . . circle of radius r centered at (h, k)
The center of circle P is (1, -2).
__
The slope m' of the line segment between (1, -2) and (5, 1) is given by ...
m' = (y2 -y1)/(x2 -x1)
m' = (1 -(-2))/(5 -1) = 3/4
The slope m of the perpendicular line is the opposite reciprocal of this, so is ...
m = -1/m' = -1/(3/4) = -4/3
The y-intercept of the desired line can be found from ...
b = y -mx . . . . . . . for m=-4/3 and (x, y) = (5, 1)
b = 1 -(-4/3)(5) = 23/3
Then the equation of tangent line AB is ...
y = mx +b
y = -4/3x +23/3
Related Questions
Area = ???????????????
Answers
Answer:
x^2+10x+21
Step-by-step explanation:
Blue box: x*x=x^2
Green box: x*3=3x
Purple box: 7*x=7x
Orange box: 7*3=21
x^2+(3x+7x)+21
Combine like term
A: x^2+10x+21
3.
At time t = 0 years, a forest preserve has a population of 1500
deer. If the rate of growth of the population is modeled by
R(t) = 2000e0.231 deer per year, what is the population at time
t=3.
Answers
The population of deer at time t=3 years is approximately 4128 deer.
What is an exponential function?An exponential function is a mathematical function of the form [tex]f(x) = a^x[/tex], where a is a positive constant called the base, and x is the input variable. The exponent x represents the power to which the base a is raised.
The rate of growth of the deer population is given by the function [tex]R(t) = 2000e^{(0.231t)}[/tex], where t is the time in years since t=0.
To find the population at time t=3, we need to evaluate R(3) using the given function:
[tex]R(3) = 2000e^{(0.231\times 3)[/tex]
[tex]R(3) = 2000e^{0.693}[/tex]
R(3) ≈ 4127.72
Therefore, the population of deer at time t=3 years is approximately 4128 deer.
To know more about an exponential function follow
https://brainly.com/question/30135888
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Find the acceleration. I don’t understand this, please help
Answers
Answer:
At t = 9, Whitney's acceleration will be -0.2 miles per minute.
Step-by-step explanation:
Remember that the acceleration is the derivative of velocity.
Since we want to find Whitney's acceleration at t = 9 and we are given the velocity function, we can simply find the derivative of the point at t = 9. In other words, a(9) = v'(9).
For the interval (7, 11), we simply have a line. So Whitney's acceleration at t = 9 will be equivalent to the slope of that line.
We have the two points (7, 0.8) and (11, 0). So, the slope between them is:
[tex]\displaystyle m=\frac{0-0.8}{11-7}=\frac{-0.8}{4}=-\frac{1}{5}[/tex]
So, a(t) = v'(t) = -0.2 ∀t ∈ {t | 7 < t < 11}. Then at t = 9, Whitney's acceleration will be -0.2 miles per minute.
The Miller family likes to petal along the north River. 1. They paddled the same distance each day throughout the course of three days, traveling a total of 14 miles. How many miles do they travel each day?
Two. If the millers went half their daily distance each day, but extend their trip to twice as many days, how far would they travel?
Answers
Answer:
The Millers paddled 4,666 miles each day. If they reduced their daily distance by half, extending their trip to twice as many days, the distance traveled by the Millers would have been the same.
Step-by-step explanation:
Given that the Miller family likes to paddle along the river, and they paddled the same distance each day throughout the course of three days, traveling a total of 14 miles, to determine how many miles did they travel each day the following calculation must be performed :
14/3 = X
4.666 = X
Thus, the Millers paddled 4,666 miles each day.
In turn, if the Millers went half their daily distance each day, but extend their trip to twice as many days, to determine how far would they travel, the following calculation must be performed:
4.666 / 2 x 6 = X
2.333 x 6 = 13.9999
Thus, the distance traveled by the Millers would have been the same.
P(A)=0.45, P(A∩B)=0.15 and P(B\A)=0.25 what is the value of P(A\B)
0.45
0.25
0.35
None of the above
Answers
Answer:
0.35? That is correct?
Please help!
The distance between two tall buildings is 480ft. While standing on the roof of the shorter building, an inquisitive geometry student measures the angle of descent to the base of the taller building to be 48 degrees. She also measures the angle of elevation to the top of the taller building to be 25degrees. How tall is the shorter building? How tall is the taller building?
Answers
Answer:
450ft
Step-by-step explanation:
In the picture
Use △GHJ, where A, B, and C are midpoints of the sides.
When AB = 3x+8 and GJ = 2x+24, what is AB?
Answers
please help me and don't put sum bs answer or a link
Answers
Answer:
Both X and Y are equal to 15 multiply by the square root of 2.....(i just do not know how to type the symbol on my keyboard)
Step-by-step explanation:
So for X:
X=30 sin 45
=15 multiply by the square root of 2
For Y:
Y=30 cos 45
=15 multiply by the square root of 2
But you could also use theorem of Pythagoras
ASAP I need help 10 points
Answers
Answer:
$80.66 and $48
Step-by-step explanation:
1.
Find the total cost of your outfit. 49+25=$74
Find 9% of 74 by doing 0.09x74, which is 6.66. This means that the sales tax is $6.66. 74+6.66=$80.66.
2.
Find 25% of 64 by doing 0.25x64=16. 64-16=$48.
6 months ago, Juan used his credit card for a transaction of 128 dollars. The bank charges a rate of interest
of 50% per month compounded monthly
How much does Juan owe to the bank today?
Answers
The compound interest implies that Juan owes $163.52 today
How to determine the amount Juan owes?The given variables can be represented as:
Loan amount P = $128Rate of interest, R = 50%Time to pay back the loan, t = 6 months i.e. 0.5 yearThe amount from a compound interest can be calculated using:
A = P(1 + r/n)^nt
Also from the question, we have
n = 12
This is so because the loan is compounded 12 times in a year as a result of being compounded monthly
So, we have
A = P(1 + r/n)^nt
A = 128 * (1 + (50%/12))^(0.5*12)
Evaluate
A = 163.52
Hence, the amount owed is $163.52
Read more about compound interest at:
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Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator
4 : 2.4
Answers
Answer:
4:2.4 = 4/2.4
= 40/24 = 5/3 = 1 1/3
find the perimeter of the figure below.
PLEASE GIVE A EXPLANATION
Answers
Answer:
Perimeter of the figure = 198.54 feet
Step-by-step explanation:
Given figure comprises a rectangle and two semicircles.
Perimeters of two semicircle = 2πr
Here 'r' = Radius of the circle
Perimeter of two semicircles at the sides of the rectangle = [tex]2\pi (\frac{25}{2})[/tex]
= 25π feet
= 78.54 feet
Length of side AB = Length of side CD = 60 feet
Perimeter of the given figure = 2(60) + 78.54
= 198.54 feet
Linear function last one
Answers
Answer:
y=1/2x
Step-by-step explanation:
y=-x would go the other way so cross that one
y=2x would go up really quickly so cross that one
y=0.001x would be more like a horizontal line so cross that one
y = 1/2 is correct
PLEASE HELP!!! ILL GIVE BRAINLIEST !! Which is the correct answer ? 100 POINTS !! EXPLAIN.
Answers
Answer:
the correct answer would be B
Answer:
B
Step-by-step explanation:
I just did this problem
Mrs. Hampton’s class is studying the feeding habits of captive turtles in the community. Which of these samples represents the best random sample for the study?
A.
some turtles at the local reptile zoo and some turtles kept as pets
B.
all the turtles found in science classrooms at the school
C.
every other turtle the class finds in the pond behind their school
D.
every third turtle that appears on the beach near the lake
Answers
Answer:
A
Step-by-step explanation:
I just took the test
:>
Answer:
I hope this helps
Step-by-step explanation:
What type of fraction is 26 1/3?
Answers
It is known as a mixed fraction.
Martin buys a car for $15,000. The value of the car depreciates by 7% each year. What is the value of his car 5 years after he purchased it? Round to the nearest dollar. can somone help asap?
Answers
Answer:
5250
Step-by-step explanation:
you multiply 7 times 5 then it gives you 35 then you
Help please and explain
Answers
Answer:
Volume of a cone = 50 in³
Step-by-step explanation:
diameter = 5 in
radius = 2.5 in
height = 8 in
Volume of cone = [tex]\frac{\pi r^2h}{3}[/tex]
V = (3 × 2.5 × 2.5 × 8)/3
V = 150/3
V = 50 in³
PLEASE HELP, ITS URGENT I WILL GIVE BRAINLY...
Shopping for school supplies, you recently spent $22 to purchase a notebook, a box of pencils, and a package of pens. The box of pencils costs $2 less than the notebook. The package of pens costs 3 times as much as the box of pencils. Choose a variable. Define the variable. Write and solve an algebraic equation to find the cost of each item you purchased. Please show work for Notebook and Box of Pencils and Package of pens. And an equation. (I WILL GIVE POINTS AND BRAINLY PLEASE HELPPPPPPP)
Answers
Answer:
Cost of the box of pencils = x = $4
Cost of the notebook = x+2 = 4+2 = $6
Cost of package of pens = 3x = 3(4) = $12
Step-by-step explanation:
Let the cost of the box of pencils = x
Cost of the notebook = 2 more than the pencils cost = x+2
Cost of package of pens = 3 times the pencils cost = 3x
The total was $22, so we can say:
(x)+(x+2)+(3x) = 22
5x=22-2
x=20/5
x=$4
Cost of the box of pencils = x = $4
Cost of the notebook = x+2 = 4+2 = $6
Cost of package of pens = 3x = 3(4) = $12
Find the volume of the tank with a radius of 2 m and height of 5 m
Answers
Answer:
20.943951023932 m^3
Step-by-step explanation:
v=1/3pi(r)^2h
v=1/3pi(2)^2(5)
v=20.943951023932 m^3
Answer:
62.8
Step-by-step explanation:
2 × 2 × 3.14 × 5 = 62.8
Which of the following situation illustrates combination
Answers
This Inflatable Crayon has a diameter of 8 in a length of 40 inches and is topped with a cone shaped tip with a height of 12 inches Round your answer to the nearest tenth of an inch.
Answers
Answer:
Assuming you want to know the volume,
volume = 2210.6 in³
Step-by-step explanation:
radius = diameter/2 = 8/2 = 4 in
area of base = πr² = (3.14)(4²) = 50.24 in²
volume of tube portion = base area x height = 50.24 x 40 = 2009.6 in³
cone volume = 1/3bh = 1/3(50.24)(12) = 200.96 in³
total volume = 2009.6 + 200.96 = 2210.56 in³
Use this list to find the range: 53, 66, 68, 68, 75, 75, 75, 79, 82
(This is from Edginuity btw)
Answers
Answer:
29
Step-by-step explanation:
Answer:
29
Step-by-step explanation:
Range =Largest - smallest
82 - 53=
29
Emily bought 4 cheeseburgers for $6 each and then spent $18 on a new shirt. She paid for the cheeseburgers and shirt with her debit card. The change to Emily's bank account can be found using the expression below:
4(-6) + (-18)
Which of the integers below shows the change in balance to Emily's bank account?
28
-42
-64
6
Answers
Help me but i am gonna know the answer cause i know it
Answers
Answer:
D. 12
Step-by-step explanation:
93/3 = 31
155/5 = 31
248/8 = 31
In every case, you see that the number of pages is 31 times the number of hours.
For 372 pages, the number of hours is 372/31 = 12
Check: 372/12 = 31
Answer: D. 12
The bakery shop purchased 7 2/10 pounds of sugar and 7 5/10 pounds of flour. How much sugar and flour did they purchase in all?
Answers
Answer:
Sugar = 1-2/5 pounds, Flour = 3-1/2 pounds
Together = 5-9/10 pounds
Step-by-step explanation:
sugar = 7(2/10)
flour = 7(5/10)
sugar + flour = 7(2/10) + 7(5/10)
sugar = 14/10 or 1-2/5 pounds
flour = 35/10 or 3-1/2 pounds
Can someone please help me find the answer?
Answers
Answer:
149.84
Step-by-step explanation:
Pleaseee helppp!!! I’m not sure
Answers
It’s A, 8(7+8+16)
Hope this helps!
solve the system algebraically (using elimation or substitution method)
4x + 5y = 2
x + 2y = -1
Answers
Answer:
Equation form: x=3, y=-2
Point Form: (3,-2)
Step-by-step explanation:
Find the missing angle measure in each triangle 29, 88, x || Hurry :)
Answers
Answer:
63
Step-by-step explanation
180-29-88=63
