Answer:
The equation of the circle is given by:
(x-a)^2+(y-b)^2=r^2
where:
(a,b) is the center of the circle
given that the center of our circle is (2,3) with the radius of 5, the equation will be:
(x+2)^2+(y+3)^2=5^2
expanding the above we get:
x^2+4x+4+y^2+6y+9=25
this can be simplified to be:
x^2+4x+y^2+6y=25-13
x^2+y^2+4x+6y=12
Answer:
[tex]\sf\longrightarrow \boxed{\sf x^2+y^2-4x-6y-12=0}[/tex]
Step-by-step explanation:
Here we are given the radius of circle as 5cm and the centre of the circle is (2,3) . We need to find the equation of the circle. Here we can yse the Standard equation of circle to find the equation .
Standard equation of circle :-
[tex]\sf\implies \green{ (x - h )^2+(y-k)^2 = r^2 }[/tex]
where (h,k) is the centre and r is radius .Substitute the respective values ,
[tex]\sf\longrightarrow ( x - 2 )^2 + ( y - 3)^2 = 5^2 [/tex]
Simplify the whole square ,
[tex]\sf\longrightarrow x^2 + 4 -4x + y^2+9-6y = 25[/tex]
Rearrange and add the constants ,
[tex]\sf\longrightarrow x^2 + y^2 -4x -6y +13 = 25 [/tex]
Subtract 25 on both sides ,
[tex]\sf\longrightarrow x^2 +y^2-4x-6y+13-25=0[/tex]
Simplify ,
[tex]\sf\longrightarrow \boxed{\blue{\sf x^2+y^2-4x-6y-12=0}}[/tex]
I NEEDDDD D HELPPPPP!!!
Answer:
70 degrees
Step-by-step explanation:
there are multiple ways, as all the trigonometric functions are related.
let's try it this way :
consider the missing side to be the radius of a circle.
then 41 would be the cos value of the angle (multiplied by that radius, of course).
so, let's calculate the missing side per Pythagoras
c² = a² + b² = 113² + 41² = 12769 + 1681 = 14450
c = 120.21
and now
41 = cos(?) × 120.21
cos(?) = 41/120.21 = 0.341...
? = 70.0576... ≈ 70 degrees
Answer:
70°
Step-by-step explanation:
tangent θ = (opposite side / adjacent side)
tangent θ = (113 / 41)
θ = arctan (113 / 41)
θ = 70.0576°
*Note: "arctan" is the same as "inverse tangent"
**Note: "soh-cah-toa" (and "cho-sha-cao" for sec, csc, & cot) is an easy mnemonic device to remember the trig functions (sin, cos, & tan) and their relations to the sides of a given angle.
Which represents the inverse of the function f(x) = 4x?
h(x) = x + 4
h(x) = x-4
h(x) = 3/4x
h(x) = 1/4x
Answer:
Let the inverse of f(x) be h(x):
[tex]{ \tt{h(x) = \frac{1}{4x} }}[/tex]
Which is the correct form of the partial fraction decomposition for the expression StartFraction 4 x cubed + 3 x squared Over (x + 1) squared (x squared + 7) squared EndFraction?
Given:
The expression is:
[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}[/tex]
To find:
The correct form of the partial fraction decomposition for the given expression.
Solution:
We have,
[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}[/tex]
By partial fraction decomposition, it can be written as:
[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{A}{x+1}+\dfrac{B}{(x+1)^2}+\dfrac{Cx+D}{x^2+7}[/tex] ...(i)
[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{(x+1)^2(Cx+D)+(x+1)(x^2+7)A+(x^2+7)B}{(x+1)^2(x^2+7)}[/tex]
[tex]4x^3+3x^2=(x+1)^2(Cx+D)+(x+1)(x^2+7)A+(x^2+7)B[/tex]
[tex]4x^3+3x^2=x^3A+x^3C+x^2A+x^2B+2x^2C+x^2D+7xA+xC+2xD+7A+7B+D[/tex]
[tex]4x^3+3x^2=x^3(A+C)+x^2(A+B+2C+D)+x(7A+C+2D)+7A+7B+D[/tex]
On comparing both sides, we get
[tex]A+C=4[/tex]
[tex]A+B+2C+D=3[/tex]
[tex]7A+C+2D=0[/tex]
[tex]7A+7B+D=0[/tex]
On solving these equations, we get
[tex]A=\dfrac{23}{32},B=-\dfrac{1}{8},C=\dfrac{105}{32},D=-\dfrac{133}{32}[/tex]
Substituting these values in (i), we get
[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{\dfrac{23}{32}}{x+1}+\dfrac{-\dfrac{1}{8}}{(x+1)^2}+\dfrac{\dfrac{105}{32}x-\dfrac{133}{32}}{x^2+7}[/tex]
Therefore, the required partial fraction decomposition is:
[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{\dfrac{23}{32}}{x+1}+\dfrac{-\dfrac{1}{8}}{(x+1)^2}+\dfrac{\dfrac{105}{32}x-\dfrac{133}{32}}{x^2+7}[/tex]
Answer:
A on Edg
Step-by-step explanation:
got it right
On an electricity bill of $40.80, Mrs.
Miller pays only $38.76 because she pays
before a certain date. What percent
discount is Mrs. Miller allowed?
Answer:
100%_$40.80
? × _$38.76
Step-by-step explanation:
100%×$38.76÷$40.80=95%
Answer:
40.80
Step-by-step explanation:
Please help me with this
Answer:
A
Step-by-step explanation:
first answer gets marked brainliest!!!
Answer:
in neighbourhood q the total number of people in the nine families I higher than that in neighbourhood s because of we add up the number of people in the families in neighbourhood q we get a total of 35 yet we have a total of only 27 people in the nine families in neighbourhood s
hope that helps ❤
Travis makes and sells fishing lures. He
has 56 fishing lures that he is putting into
boxes. Each box can hold 5 fishing lures.
How many boxes can Travis fill
completely?
James is 8 years old. Last year, his father was 4 times as old as he was. In how many years' time will their combined age be 51?
Last year He was 7 years old.
His father is 4 times the age 7 x 4 = 28
Last year his dad was 28, so this year he is 29.
Combined age this year = 29 + 8 = 37
51 - 37 = 14 years
14/ 2 people = 7 years
8 + 7 = 15
29 + 7 = 36
15 + 36 = 51
It will take 7 years.
Solve the inequality 4 is greater than n over -4
Answer:
4 > [tex]-\frac{n}{4}[/tex]
-16 > n
Step-by-step explanation:
Greater than would mean that the "arrow" is not facing the number. It would mean it is larger than the other number. Also, you have to construct the other part of the inequality which would be [tex]-\frac{n}{4}[/tex].
4×4 > [tex]-\frac{n}{4}[/tex]×4
16 > -n
-16 > n
How to find the area of this figure pls?
Kara Danvers (Supergirl) has always relied on her strength to win fights. But what happens when she meets an alien just as strong? Her sister is training her to be a more technical fighter so that Supergirl can meet any challenge. The data below record the significant strikes during randomly selected training sessions 6 months apart. Is Kara showing improvement in her fighting?
Strikes (pre): 29 32 44 34 19
Strikes (post): 51 45 68 92 64
Write the Hypotheses:
H_0:_______________, the mean difference in ___________ between ____________ and ______________ is _______________
H_a:_______________, the mean difference in ___________ between ____________ and ______________ is _______________
Answer:
H0 : The mean difference in strikes between pre and post strike is equal to 0
H1 : The mean difference in strikes between pre and post strike is not equal to 0
Step-by-step explanation:
The scenario described abibe meets the condition for a paired (dependent) sample t test as the same subject is involved in both the pre and post strike data. Therefore measurement from the strike(pre) must be paired with measurement from the strike(post) data.
For a paired test involving a single subject ; The mean difference in the two sample is 0 ; that is both are the same while the alternative negates the null by claiming that the mean difference is not equal to zero.
If $10,500 is borrowed for 5 years at an annual simple interest rate of 1.73%, how much interest will be paid if the entire loan is paid off at the end of the fifth year? Enter the answer in dollars and cents, and round to the nearest cent, if needed. Do not include the dollar sign. For example, if the answer is $0.61, only the number 0.61 should be entered.
Answer:
Step-by-step explanation:
So, yearly $2100 is paid, plus the 1.73% interest, so 1.73% interest is $2136.33every year interest stacks on itself so youll take 1.73% of the year 1 total with interest.
Year 1 total: $2136.33
Year 2 total:$2173.29
Year 3 total:$2210.89
Year 4 total:$2249.14
Year 5 total:$2288.05
Total Paid After 5 years:$11057.70
Year 1 total interest:$36.33
Year 2 total interest:$36.96Year 3 total interest:$37.60Year 4 total interest:$38.25Year 5 total interest:$38.91
Total Interest paid after 5 years:$188.05
Point P is the incenter of DEF. Point P is the point of concurrency of the angle bisector. Find PV
Answer:
12
Step-by-step explanation:
because line FB divides triangle f v w into two equal halves therefore line WP is equal to line PV which is equal to 12
The required value of the PV is 12 in triangle DEF where p is the incenter.
Point P is the incenter of ΔDEF. Point P is the point of concurrency of the angle bisector. PV to be determined.
The incenter of a triangle is the intersection point of the internal angle bisectors of the triangle. In additional expressions, it can be clarified as the point where the internal angle bisectors of the triangle and perpendicular distance from this point to any of the sides of triangle is the same.
Since in triangle FGH, P is the incenter and PW, PV,PX is perpendicular distance to the sides HF, GF and GH respectively.
From image,
PW = 12
So by the property of incenter, perpendicular distance from this point to any of the sides of triangle is the same.
PW = PV
PV = 12
Thus, the required value of the PV is 12 in triangle DEF where p is the incenter.
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You just decided to open a savings account and went to the bank and made an initial deposit. You decide to save another set amount each month. Without any interest being paid, the equation =20+50
represents the amount of money,
y
, in your savings account after
m
months. Select what the slope and y-intercept represent in this problem.
(Choose 2)
Answer:
Options (1) and (4)
Step-by-step explanation:
Given equation for the deposit in the saving account is,
y = 20x + 50
Here, y = Amount of money in the account
20 = money added in the account every month
50 = Initial deposit
By comparing this equation with the slope-intercept form of the equation of a line,
y = mx + b
Here, slope m = money added in the account every month
And b = y-intercept
Therefore, Options (1) and (4) will be the answer.
What is the answer I need help ASAP be truthful
Answer:
your closest number should be A
Answer:
A.√99
Step-by-step explanation:
10^2 = 100
Or vise versa √100 = 10
The closest number to 100 is 99
So √99 is closest to 10
Plot each angle on the unit circle below. You will need to draw additional radius segments
○ 0, 30, 60, 90, 120, 135, 150, 180, 210, 225, 240, 270, 300, 315, 330
Determine the radian measure for each angle
Determine the Sin, Cos, Tan for each angle
Use 0 as an example
Upload your completed circle in the dropbox provided.
Solution :
Trigonometric angles :
The trigonometric angles are defined as the angles that are obtained by the ratios of trigonometric functions. It shows the relationship between the sides of the triangle and the angles between them. These values of the trigonometric angles ranges from 0 to 36 degrees.
Below attached shown are the angles on a unit circle which shows the angles for each value of sin, cos and tan, and also the radian measure for each of the angles.
4cos^4(x) – 5cos^2(x) + 1 = 0 from [0, 2π)
please show steps!!
Answer:
x = 0, π/3, 2π/3, π, 4π/3, 5π/3
Step-by-step explanation:
4cos^4(x) – 5cos^2(x) + 1 = 0
(4cos^2(x) - 1)(cos^2(x) - 1) = 0
When 4cos^2(x) - 1 = 0
cos^2(x) = 1/4
cos x = +/-1/2
so x = π/3, 2π/3, 4π/3, 5π/3.
When cos^2x - 1 = 0
cos x = +/- 1
x = 0, π.
x
The solution is : x = 0, π/3, 2π/3, π, 4π/3, 5π/3
What is simplification?Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
here, we have,
given that,
4cos^4(x) – 5cos^2(x) + 1 = 0 from [0, 2π)
so, we get,
4cos^4(x) – 5cos^2(x) + 1 = 0
(4cos^2(x) - 1)(cos^2(x) - 1) = 0
When 4cos^2(x) - 1 = 0
cos^2(x) = 1/4
cos x = +/-1/2
so x = π/3, 2π/3, 4π/3, 5π/3.
When cos^2x - 1 = 0
cos x = +/- 1
x = 0, π.
Hence, The solution is : x = 0, π/3, 2π/3, π, 4π/3, 5π/3.
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HELP PLEASE HURRY
THANKS
Answer:
Step-by-step explanation:
Given TVW,MZV = 90°, TV = 14, and VW= 9,
which of the following choices is used to find mZW?
here's the answer to your question
How much water should be added to 90ml of 45 percent acid solution to dilute it to 25 percent acid solution
Answer:
72 ml
Step-by-step explanation:
Let
x = amount of water that should be added
45% acid solution = 45/100 = 0.45
25% acid solution = 25/100 = 0.25
The equation is
90(0.45) = 0.25(x + 90)
40.5 = 0.25x + 22.5
40.5 - 22.5 = 0.25x
18 = 0.25x
Divide both sides by 0.25
x = 18/0.25
= 72
x = 72 ml
What is the rate of change of the amount earned with respect to hours worked for this function?
A) 1/13 hours per dollar
B) 2/5 hours per dollar
C) 3 dollars per hour
D) 13 dollars per hour
The rate of change of the amount earned with respect to hours worked for this function is D. 13 dollars per hour.
What is rate of change?The rate of change for the point defined on the graph can be deduced by calculating the ratio of the difference between the two coordinate points given, similar to calculating the gradient or slope :
Point a = (5, 65) = (x₂, y₂)
Point b = (2, 26) = (x₁, y₁)
Calculating the gradient or slope :
Rate of change = (y₂ - y₁) / (x₂ - x₁)
Rate of change = (65 - 26) / (5 - 2)
Rate of change = 39 / 3
Rate= 13 dollars per hour
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Complete question
The graph shows the amount of money Miguel earns after working x hours. What is the rate of change of the amount earned with respect to hours worked for this function? hours per dollar hours per dollar 3 dollars per hour 13 dollars per hour
The length of a rectangle is three times the width. The area of the rectangle is 108 sq. inches what’s the triangles width?
Answer:ÑÑÑÑÑÑÑÑÑññÑÑÑÑññññññÑÑÑÑÑÑÑÑÑñÑÑÑÑññ
Step-by-step explanation:
what is 8/9 divided 2/3
Answer:
4/3
Step-by-step explanation:
8/9 ÷ 2/3
Copy dot flip
8/9 * 3/2
Rewriting
8/2 * 3/9
4 * 1/3
4/3
Edwin hiked to a famous point with a beautiful view. It took 2 hours and 55 minutes to hike to the viewpoint and 25 minutes to hike back. Edwin spent 25 minutes enjoying the view at the top. He finished the hike at 11:45 A.M. What time did Edwin start the hike to the viewpoint?
Answer:
= 8:00 A.M.
Step-by-step explanation:
▪You first find the total time taken which will be :
2 hrs 55 min + 25 min
= 3 hrs 20 min + 25 min
= 3 hrs 45min
▪ Beginning time = Arrival time - Time taken
= 11:45 - 3:45
= 8:00 am
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The probability that Dan buys a sandwich is 0.2.
The probability that Dan gets the bus is 0.9.
Assuming the events are independent, what is the probability that Dan buys a sandwich
and gets the bus?
Answer:
0.18
Step-by-step explanation:
Find the probability that both independent events occur by multiplying the individual probabilities by each other:
0.2(0.9)
= 0.18
So, the probability is 0.18
What is the value of X?
Answer:
x=2
Step-by-step explanation:
A line that intersects a circle in two points is called a secant line, and this is the case for both line DE and AE.
For two secant lines that intersect outside of the circle, such as the ones here, we can say that
CE * DE = BE * AE
Therefore, we need to then define these lines.
CE is x+4, BE is x+1, AE = (BE + AB) = 11+x+1 = 12+x, and DE = (CE + DC) = 1+x+4 = 5+x
We then have
(x+4) * (5+x) = (x+1) * (12+x)
expand
5x + x² + 20 + 4x = 12x+x²+12+x
x²+9x + 20 = x²+13x+12
Next, we want to congregate all values to one side so we can solve for x. This can be done by subtracting both sides by (x²+13x+12) to get
-4x + 8 = 0
subtract 8 from both sides to isolate the x and its coefficient
-4x = -8
divide both sides by -4 to isolate the x
x = 2
The range of cells in column D and rows 1 to 10 is represented as:
1:10 D1:D10 D:D
Answer:
how?
Step-by-step explanation:
I didnt get question
As displayed on a production possibilities curve, what will an increase in technology allow a society to do? a. Produce more, as long as the resources are also available. c. It will not affect society’s production. b. Produce less, because more resources are spent on developing technology. d. The society will spend more on the same level of production. Please select the best answer from the choices provided A
Answer:
a. Produce more, as long as the resources are also available
Step-by-step explanation:
from brainly itself
scouteo
Ace
The correct answer is A) produce more, as long as the resources are also available.
As displayed on a production possibilities curve, an increase in technology will allow a society to produce more, as long as the resources are also available.
A production possibilities graph is a valid representation of the available ways an economy is able to use the resources. In this case, an increase in technology will allow a society to produce more, as long as the resources are also available means that as long there are enough resources in the market, technology in a country helps with the production of more things to be consumed or traded.
Help pleas like please ASAP
Answer:
(x+9)(x+5)
Step-by-step explanation:
find 2 numbers that add to 14 and multiply to 45
Please help me with this, i need help
Answer:
woa
i n
Step-by-step explanation:
