Answers
Answer:
Step-by-step explanation:
Part A
Given equation of the circle is,
x² + y² - 4x + 2y = b
Standard equation of the circle is given by,
(x - h)² + (y - k)² = r²
Here, (h, k) is the center and r = radius of the circle
Now we will convert this equation into a standard equation of the circle,
x² - 4x + y² + 2y = b
x² - 2(2x) + 2² + y² + 2y + 1² = b + 2² + 1²
(x² - 2(2x) + 4) + (y² + 2y + 1) = b + 4 + 1
(x - 2)² + (y + 1)² = √(b + 5)²
Therefore, (2, -1) will be the center of the given circle.
y-coordinate of the circle = -1
Part B
Since, radius of the circle is 7 units,
Therefore, [tex]\sqrt{b+5}=7[/tex]
b + 5 = 49
b = 49 - 5
b = 44
Related Questions
A car motercycle leaves at noon from the same location, heading in the same direction. The average speed of the car is 30mph slower than twice the speed of the motorcycle.
Answers
Answer:
speed of motorcycle = 40 mph
speed of car = 50 mph
Step-by-step explanation:
Here is the complete question
A car and a motorcycle leave at noon from the same location, heading in the same direction. The average speed of the car is 30 mph slower than twice the speed of the motorcycle. In two hours, the car is 20 miles ahead of the motorcycle. Find the speed of both the car and the motorcycle, in miles per hour.
Speed = distance / time
This question would be solved using simultaneous equation
let m = average speed of the motorcycle
c = average speed of the car
c = 2m - 30 equation 1
20 =(c - m) x 2 equation 2
insert equation 1 into equation 2 and divide through by 2
10 = (2m - 30) - m
solve for m
m = 40 mph
substitute for m in equation 1
2(40) - 20 = 50 mph
3⋅2^x/5=150 Which of the following is the solution of the equation?
Answers
Answer:
x=7.965784
Step-by-step explanation:
Can get a little help
Answers
Good luckvsvsvsbsbsjsjhsbsbsbsb
What is the value of x in the equation −8 + x = −2? (1 point) Group of answer choices −10 −6 6 10
Answers
Answer:
6
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
If you add 8 on each side to get x by itself you'll get
x=6
What is the gradient of the graph shown?
Give your answer in its simplest form.
Answers
Answer:
1/3
Step-by-step explanation:
i used the points (0,-2) and (3,-1) to find the slope:
(-2--1) / (0-3) = -1/-3 or 1/3
Diego scored 9 points less than Andre in the basketball game. Noah scored twice as many points as Diego. If Noah scored 10 points, how many points did Andre score? Write and solve the equation.
Answers
Answer:
Andre scored 14 points
Step-by-step explanation:
D = A - 9
N = 2D = 10
2D = 10
D = 5
5 = A - 9
14 = A
Answer:
Diego scored 14 points
x = 14
Plz help i am giving 30 points and dont put random anwser for points
Answers
Answer:
6 students
Step-by-step explanation:
first you wanna convert the 2/3 into 4/6 cause that makes it easier then add the 1/6 to it making it 5/6 and finally 5/6 of 36 is 30 and 36-30=6
Answer:
6 students
Step-by-step explanation:
Blue shirts: 1/6*36 = 36/6= 6
white shirts: 2/3*36= 72/3= 24
Blue + white= 24+6= 30 Students
36-30= 6 students didn't wear blue or white
Find the area of this circle.
Use 3.14 to approximate
A = ar2
20 ft
Answers
Answer:
314
Step-by-step explanation:
Answer:
314
Step-by-step explanation:
R= half of d
d= 20
20/2= 10
r=10
Plug into formula:
3.14(10)^2
= 314
Help! This is due today and I'm stuck on the last problem.
Brainiest for best answer.
NO LINKS! If you put a link, I will report you.
Find the area of the shaded region rounded to the nearest tenth.
Answers
Answer:
Step-by-step explanation:
Square
519450.2
Holes
Semi-circle: 1/2*pi*r^2
diameter = 700/2 = 350 =radius
1/2*pi*350 = 175*pi
Triangle
1/2 b*h
1/2 200*400
100*400
40000
Take out the semi circle and triangle
560000-40000-175*pi
520000-175*pi = 519450.2
equation of the line through (5,-6) and a slope of -1
Answers
Answer:
y=x-11 or in point slope form y+6=1(x-5)
The dot plot shows the heights of the players on two basketball teams.
Which statement is best supported by these data?
Answers
What is the volume of a cylinder, in cubic centimeters, with a height of 16 centimeters
and a base diameter of 4 centimeters?
Answers
Answer:
Volume = 200.96 cm³
Step-by-step explanation:
r = 4/2 = 2
Volume = πr²h = (3.14)(2²)(16) = 200.96 cm³
Function f is composed of an exponential piece and a polynomial piece.
Which inequality represents the domain of the exponential piece?
A) x ≥ -1
B) x > 1
C) x > 3
D) x ≤ -2
Answers
Answer:
Step-by-step explanation:
The exponential piece is to the left, and starts at -2. So all its x values are less than or equal to -2
Answer:
it's D you are very welcome :)
There is a stack of 10 cards, each given a different number from 1 to 10. Suppose we select a card randomly from the stack, replace it, and then randomly
select another card. What is the probability that the first card is an even number and the second card is less than 3?
Write your answer as a fraction in simplest form.
Answers
Answer:
1/10.
Step-by-step explanation:
The probability of getting an even card out of 10 cards numbered 1 - 10 is 1/2. The even numbers available are 2, 4, 6, 8, and 10 while the odd ones available are 1, 3, 5, 7, and 9. So half the outcomes could come out even.
The probability the second card is less than two is 1/5 (2/10 simplified). Since there are 10 cards with numbers 1-10, only two cards will have numbers less than 3, 1 and 2.
To find the total probability, multiply the two. (1/2) * (1/5) = 1/10. There is a 1 out of 10 chance that the first card is even and the second card is less than 3.
Convert 2 3/5 cups to pints.
Answers
Answer:
Decimal Form: 1.3
Exact Form: 13/10
Mixed Number Form: 1 3/10
Step-by-step explanation:
1 pint = 2 cups
Convert the mixed fraction into an improper fraction. 2 3/5 = 13/5 cups
You divide 13/5 by 2, since there are 2 cups in one pint, and you are trying to get pints. 13/5 divided by 2:
Decimal Form: 1.3
Exact Form: 13/10
Mixed Number Form: 1 3/10
Evaluate the six trigonometric functions of the angle 0
is right
Answers
Answer:
1. Sine θ = 1/3
2. Cos θ = 2√2 / 3
3. Tan θ = √2 / 4
4. Cosec θ = 3
5. Sec θ = 3√2 / 4
6. Cot θ = 2√2
Step-by-step explanation:
We'll begin by determining the adjacent. This can be obtained as follow:
Hypothenus (Hypo) = 9
Opposite (Opp) = 3
Adjacent (Adj) =?
Hypo² = Adj² + Opp²
9² = Adj² + 3²
81 = Adj² + 9
81 – 9 = Adj²
72 = Adj²
Take the square root of both side
Adj = √72
Adj = 6√2
Finally, we shall determine six trigonometric functions of the angle θ. This Can be obtained as follow:
1. Determination of Sine θ
Hypothenus = 9
Opposite = 3
Sine θ =?
Sine θ = Opposite / Hypothenus
Sine θ = 3/9
Sine θ = 1/3
2. Determination of Cos θ
Adjacent = 6√2
Hypothenus = 9
Cos θ =?
Cos θ = Adjacent / Hypothenus
Cos θ = 6√2 / 9
Cos θ = 2√2 / 3
3. Determination of Tan θ
Opposite = 3
Adjacent = 6√2
Tan θ =?
Tan θ = Opposite / Adjacent
Tan θ = 3 / 6√2
Tan θ = 1 / 2√2
Rationalise
(1 / 2√2) × (2√2 /2√2)
= 2√2 / 4×2
Tan θ = √2 / 4
4. Determination of Cosec θ
Sine θ = 1/3
Cosec θ =?
Cosec θ = 1 / Sine θ
Cosec θ = 1 ÷ 1/3
Cosec θ = 1 × 3/1
Cosec θ = 3
5. Determination of sec θ
Cos θ = 2√2 / 3
Sec θ =?
Sec θ = 1 / Cos θ
Sec θ = 1 ÷ 2√2 / 3
Sec θ = 1 × 3 / 2√2
Sec θ = 3 / 2√2
Rationalise
= (3 / 2√2) × (2√2 / 2√2)
= 3 × 2√2 / 4×2
Sec θ = 3√2 / 4
6. Determination of Cot θ
Tan θ = √2 / 4
Cot θ =?
Cot θ = 1 / Tan θ
Cot θ = 1 ÷ √2 / 4
Cot θ = 1 × 4 / √2
Cot θ = 4 / √2
Rationalise
= (4 / √2) × (√2 / √2)
= 4√2 / 2
Cot θ = 2√2
Can someone help me find the diameter of the copper ball ty
Answers
Answer:
The answer is 346.185 if its diameter is 22.
CAN SOMEONE PLZ HELP ME?? PLZ DO YOU KNOW ABOUT Coordinate Planes??!!
Answers
Answer:
(1.5,1) is the coordinate for point D
Answer:
point D = (1.5,2)
Step-by-step explanation:
The first number in the parentheses is the X coordinate, in this case it's 1.5
The first second in the parentheses is the Y coordinate, in this case it's 2
An airplane's altitude in feet during its descent can be found using the equation y=-150x + 30,500. After new government regulations become law, the descent isnow modeled by the equation y=-150x + 30,000. Which statement describes this change?
The airplane starts its descent from an altitude 500 feet lower.
The airplane descends 500 feet per horizontal mile slower.
The airplane descends 500 feet per horizontal mile faster.
The airplane starts its descent from an altitude of 500 feet.
Answers
Answer:
The airplane would starts its descent from an altitude 500 feet lower.
Step-by-step explanation:
The x-axis is horizontal and the y-axis is vertical (altitude). It would be 500 feet lower because they took 500 away from the 30,000.
pls help thanks!! lol
Answers
HELP I HAVE FSA GIVE ME SOME TIPSSS
Answers
Answer:
Plan ahead for medical expenses.
Spend your money.
Save your receipts.
Use your FSA to pay expenses your health plan doesn't cover.
Use your FSA to reach health plan financial milestones.
Know what your FSA covers.
Know your FSA balance.
Step-by-step explanation:
Answer:
Okay so I just took the FSA and my biggest tip is to just relax and don't overthink. Another tip that is kinda weird is to chew gum/mint. They normally hand it out to you but stopped for coronavirus. It helps you focus and it helps calm you. Make sure you double check your answers and if you don't know a question go back over it and re read it. Also pay attention to other questions because sometimes a question from the same passage helps you with a previous one. You're going to do well and good luck!
Step-by-step explanation:
Find lim h 0 f(2+h)-f(2)/ h if(x)=x^ 2 .
Answers
Answer:
4
Step-by-step explanation:
PLZ HELP! QUESTIONS ARE BELOW! :D
Answers
Answer:
1) 243 in.²
Step-by-step explanation:
1)
A = 18 in. * 18 in. - 9 in. * 9 in. = 243 in.²
I need help please. Find 4 solutions of the equation (sin x)^2 = 1/4 for x between 0 and 360. Please show how you found it if not u will be reported.
Answers
Step-by-step explanation:
(sinx)²=1/4sinx=√1/4sinx =1/2sinx=sin30°x=30°hope it helps.
Answer:
x = 30, 150, 210, 330 degrees.
Step-by-step explanation:
(sin x)^2 = 1/4
sin x = +/- √1/4
sin x = +/- /2
In the first quadrant x = angle whose sine is 1/2 = 30 degrees.
There is also a solution in the other 3 quadrants.
In second quadrant where sine = 1/2 , x = 180-30 = 150 degrees,
In 3rd and 4th where sine x = -1/2 the angles are 210 and 330 degrees.
3-(1/3) to the 4th power
Answers
Answer:
if im reading it right its 8.3521
Step-by-step explanation:
please help! will give brainliest! review the graph of function f(x) for which values of c does lim f(x) not exist?
(graph and answer choices pictured)
Answers
Answer:
-2
Step-by-step explanation:
Answer quickly please
Answers
Answer:
d is the answer
Step-by-step explanation:
ILJ and JKI
if 5article cost ed 1750 how many more arrivals can be bought with 2800
Answers
Answer:
3 more arrivals
Step-by-step explanation:
A regular octagon with side length a cm can be made by cutting off
the four corners of a square board. How long should the sides of the
board be?
Answers
Answer:
one side = [tex]\frac{a\sqrt{2}}{2}[/tex]
Step-by-step explanation:
if you draw an octagon on a piece of paper, you can draw a square around it, you should be able to see a diagram of this attached, ignore the 6.
Let's say TP = a
since it's a regular octagon, TP = HT
and using the Pythagoras Theorem, we know a² + b² = c² and thus:
√(AT² + HA²) = HT
and since AT = HA which we will call x, the equation becomes:
√(2x²) = HT = a
rearrange the equation to solve for x and you get:
2x² = a²
x² = [tex]\frac{a^{2} }{2}[/tex]
x = [tex]\frac{a}{\sqrt{2}}[/tex]
which, if you rationalise the denominator, you get:
x = [tex]\frac{a\sqrt{2}}{2}[/tex]
Leah walks to soccer practice on Saturday. She leaves her home and walks 600 meters north. Leah then turns east and continues on to the soccer field. The soccer field is 1000 meters from her home. How far east did Leah walk?
Answers
Answer:
800m
Step-by-step explanation:
this would be solved using Pythagoras theorem
we are to find the base
The Pythagoras theorem : a² + b² = c²
where a = length
b = base
c = hypotenuse
600² + b² = 100²
b² = 10000 - 3600
b² = 6400
take the square root of both sides
b = 800m