write the equation in standard form for the circle passing through (-3,0) centered at the origin.
Answers
Answer:
x^2 + y^2 = 9
Step-by-step explanation:
The equation of a circle is (x^2) -a)^2 + (x^2) - b)^2 = r^2, where a and b are the center of the circle. Because the center of the circle is (0,0), it'll just be x^2+y^2 for one half of the equation. If the circle passes through (-3,0), that would mean the radius of the circle is 3. r^2 is 3^2, which is 9, so the equation of the circle is x^2 + y^2=9. Hope this helps!
The equation of the circle is x² + y² = 9
What is a Circle?A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
The equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
Given data ,
Let the point be represented as A ( -3 , 0 )
Now , the center of the circle = O ( 0 , 0 )
And , standard form of a circle is
( x - h )² + ( y - k )² = r²
where In this case, we know that the circle passes through the point (-3, 0) and is centered at the origin (0, 0). Therefore, the radius of the circle is the distance from the origin to (-3, 0), which is:
r = √((-3 - 0)² + (0 - 0)²) = √(9)
r = 3 units
So the equation of the circle in standard form is:
(x - 0)² + (y - 0)² = 3²
On simplifying , we get
x² + y² = 9
Hence , the equation in standard form for the circle passing through (-3,0) centered at the origin is x² + y² = 9
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Related Questions
.
Which line is parallel to the line that passes through the points of (2,-5) and (-4,1)
Answers
Answer:
y= -x-5
Step-by-step explanation:
m=1-(-5)/-4-2
m=-1
-1= -x
y=-x-5
QUESTION 58
Calculate graduation rates using the following information: In 2012, 3,388 student entered the freshman class at
CMU. Of the 3,388 27.4% graduated in 4-years. The 5-year graduation rate (those that graduated in 5-years of
less) was 54.2%. The 6-year graduation rate was 60.9%.
How many students graduated in 4 years or less?
How many additional students (beyond the number of students who graduated in 4-years) graduated in their 5th
year?
How many additional students (beyond the number of students who graduated in 5-years) graduated in their 6th
year?
For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).
Answers
Diagonal of a square is 4 root 2. Find the length of a side of a square
Answers
Check the picture below.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=\stackrel{hypotenuse}{4\sqrt{2}}\\ a=\stackrel{adjacent}{s}\\ b=\stackrel{opposite}{s}\\ \end{cases}\implies (4\sqrt{2})^2~~ = ~~s^2~~ + ~~s^2 \\\\\\ 4^2\sqrt{2^2}~~ = ~~2s^2\implies 16(2)=2s^2\implies 32=2s^2\implies \cfrac{32}{2}=s^2 \\\\\\ 16=s^2\implies \sqrt{16}=s\implies \boxed{4=s}[/tex]
Frankie wants to build a path from one corner of his yard to the opposite corner. His yard measures 20 ft. x 32 ft. What will be the length of his path to the nearest tenth of a foot? 21.5 ft 25.0 ft 32.6 ft 37.7 ft
Answers
Answer:
37.7 ft
Step-by-step explanation:
This is Pythagorean Theorem aka A^2+B^2=C^2
20^2+32^2=C^2
400+1024=C^2
1424=C^2 (now square root both sides)
37.7359…
Closest answer is 37.7 ft
Answer: [tex]37.7ft[/tex]
Step-by-step explanation:
[tex]a=32, b=20[/tex]
[tex]look[/tex] [tex]for~ the ~hypotenuse~ c[/tex]
[tex]a^2+b^2=c^2[/tex]
[tex]\sqrt{32^2+20^2} =37.7ft[/tex]
If each student needs 1/3 of a stick of clay to do an art project,and there are 4 sticks of clay, how many students can do the art project?
Answers
Answer:
12 students
Step-by-step explanation:
Because the total is 4 sticks, and each student needs 1/3 of a stick, we would have to see how many 1/3 sticks fit into 4 sticks. Because 3 of the 1/3 sticks fit into 1 stick, then 4 sticks would be 4*3=12 of the 1/3 sticks, which means 12 students can do it.
We could also just do: 4/(1/3)= 4*(3/1)=12
This is fractional division. The second value of the division process, we switch the numerator and denominator's, and the expression turns to a multiplication expression, where we can just multiply.
A construction company needs to remove 10 tons of dirt from a construction site. They can remove 2/5 tons of dirt each hour. How long will take to remove the dirt?
Answers
Step-by-step explanation:
You can just divide 10 by 2/5 and you get 25 or try this
Set up proportions and cross multiply 2/5 / 1 = 10/x which you can read as : if 2/5 can be done in 1 hour then 10 tons can be done in x hours cross multiplying, you get 2x/5 = 10 and x = 25
The point B (3, -1) has been translated from A by the Vector (4∗3) . What are the coordinates of A?
Answers
If point B (3, -1) has been translated from A by the Vector (4, 3). Then the coordinates of A will be (12, -3)
What is a transformation of a point?A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.
Point B (3, -1) has been translated from A by the Vector (4, 3).
Then the coordinates of A will be
Point B (3, -1) x (4, 3)
Point B (3 x 4, -1 x 3)
Point B (12, -3)
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What is the surface area of the cylinder with height 3 km and radius 3 km? Round your answer to the nearest thousandth.
Answers
Answer:
A≈113.1km²
Step-by-step explanation:
At her Fourth of July party, Marcy serves her famous grilled chicken. Her secret is to use 6 fluid ounces of lemon-garlic marinade for every pound of chicken. Marcy plans to grill 4 pounds of chicken. How many cups of marinade should she use?
cups
Answers
3 number of cups will be needed to marinade 4 pounds of chicken for grill.
What is Ounce?Ounce is the small unit of weight which is generally equal to the one by 16th of the pounds.
Here we have the data from the question:-
Marcy will use 6 fluid ounces of lemon-garlic marinade for every pound of chicken.
Marcy plans to grill 4 pounds of chicken.
So total marination required will be:-
Total marination =6x4=24 ounces
Now we know that the conversion:-
1 fluid Ounce = 0.125 Cup
24 fluid ounce =0.125 Cup
Hence 3 number of cups will be needed to marinade 4 pounds of chicken for grill.
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Which compound inequality has a solution set of all real numbers?
Question 5 options:
a) x > -2 or x < 1
b) x < -1 and x > 2
c) x < -1 and x > 2
d) x < -3 or x > -2
Answers
Answer:
If the number on the other side of the inequality sign is negative
Step-by-step explanation:
I just know okay
A standard NBA basketball has a diameter of 24.1 cm. What is the volume of a standard NBA basketball?
a.7,329 cm3
b.270 cm3
c.58,633 cm3
d.1,629 cm3
Answers
The volume of a standard NBA basketball is 7,329 cm³.
What is the volume of a sphere?The volume of a sphere is given by the formula,
V = 4/3×π×r³
Given the diameter of the ball is 24.1 cm, therefore, the radius of the ball will be 12.05cm (half the diameter of the ball). Thus, the volume of the NBA basketball will be,
V = 4/3 × π × (12.05)³
V = 7,329.084 cm³ ≈ 7,329 cm³
Hence, the volume of a standard NBA basketball is 7,329 cm³.
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What is the perimeter of the rectangle in the coordinate plane?
14 units
28 units
36 units
45 units
Answers
Answer:
45 units^2
Step-by-step explanation:
W x H = area
9 x 5 = 45 units^2
Answer:
28 units
Step-by-step explanation:
Length (l) = 9 units
Breadth (b) = 5 units
Perimeter of the rectangle will be,
→ 2(l + b)
→ 2(9 + 5)
→ 2 × 14
→ 28 units
Hence, the perimeter is 28 units.
Ronald's bill at the end of his lunch was $20.00. Using a proportion, determine the amount of his bill that he must leave for a 19% tip.
Answers
Answer:
23.80$
Step-by-step explanation:
[tex]\frac{20}{x} =\frac{100percent}{19percent}[/tex]
X = (20 × 19) ÷ 100
X =380 ÷ 100
X = 3.8$
20.00+ 3.8=
23.80
What are the values of mode and median in the following set of numbers? 1,3,3,6,6,5,4,3,1,1,2 Mode: 1, 2, Median: 2 Mode: 1,3, Median: 3 Mode: 2,3, Median: 2 Mode: 1,3, Median: 2.5
Answers
[tex]1 \: 3 \: 3 \: 6 \: 6 \: 5 \: 4 \: 3 \: 1 \: 1 \: 2[/tex]
to find:the mode and median of the given numbers set.
solution:mode:the most frequently occurred number.
[tex]mode = 1 \: and \: 3[/tex]
median:first arrange all the numbers in either decending or ascending order, then find the number in the middle.
[tex]1 \: 1 \: 1 \: 2 \: 3 \: 3 \: 3 \: 4 \: 5 \: 6 \: 6[/tex]
[tex]median = 3[/tex]
hence, the median of the following data set is 3 and the mode is 1 and 3
Please answer QUICK!! for brainliest!!!
Answers
Answer:
1
Step-by-step explanation:
The 2 equations have different slopes, so they have 1 solution.
Orlando is mixing nuts and cereal squares to make a party mix. Nuts sell for $7 a pound and cereal squares sell for $4 a pound. If Orlando wants to make 30 pounds of party mix at a cost of $6.50 a pound, how many pounds of nuts and how many pounds of cereal squares should he use?
Answers
Answer:
5 lbs cereal squares.
25 Ibs nuts.
Step-by-step explanation:
Let x be the weight of nuts in pounds and y be the weight of cereal squares in pounds.
Total weight of the party mix is 30 pounds.
[tex]x+y=30[/tex] ..... (1)
It is given that,
Cost of nuts = $7 per pound
Cost of cereal = $4 per pound
The cost of mix = $6.50 per pound.
[tex]7x+4y=6.50*30[/tex]
[tex]7x+4y=195[/tex] ..... (2)
Substitute the value of x in equation (2) from equation (1).
[tex]7(30-y)+4y=195[/tex]
[tex]210-7y+4y=195[/tex]
[tex]-3y=195-210[/tex]
[tex]-3y=-15[/tex]
Divide both sides by -3.
[tex]y=5[/tex]
Substitute y=5 in equation (1).
[tex]x+5=30[/tex]
Subtract both sides by 5.
[tex]x=30-5[/tex]
[tex]x=25[/tex]
Therefore, he use 25 lbs of nuts and 5 lbs cereal squares for party mix.
Part A
If Wendell creates a scale drawing using the scale 1 inch to 10 feet, what will the dimensions of the deck in the scale drawing be?
Part B
In the scale drawing, what will the length of the east side of the backyard be?
Part C
In the scale drawing, what will the length of the south side of the backyard be?
Part D
In the scale drawing, what will the length of the west side of the backyard be?
Part E
In the scale drawing, what will the length of the north side of the backyard be?
Part F
Two corners of the backyard are right angles. The third corner forms an obtuse angle measuring 127º. The fourth corner forms an acute angle measuring 53º. When transferring these angle measurements from the real world to the scale drawing, will their measures increase, decrease, or stay the same?
Part G
In the scale drawing, what is the area of the lawn (that is, the area of the whole backyard, except for the deck)?
Answers
Answer:
234
Step-by-step explanation:
Use the Pythagorean Theorem to find the distance between (3, 0) and (7,-6). Round
to the nearest tenth.
Answers
Answer:
14.4
Step-by-step explanation:
6^2+12^2=x^2
64+144+x^2
208=x^2
square root of 208= 14.4
x=14.4
What is the sum of 9 7/8 plus 11 2/8?
Answers
Answer:
169/8
Step-by-step explanation:
9 7/8 = 79 / 8
11 2/8 = 90 / 8
90/8 + 79/8
The denominator (8) stays the same
90+79 = 169
169/8 or 21 1/8
A bag contains 2 gold marbles, 8 silver marbles, and 20 black marbles. The rules of the game are as follows: You randomly select one marble from the bag. If it is gold, you win $5, if it is silver, you win $2. If it costs $1 to play, what is your expected profit or loss if you play this game?
Answers
Answer:
expected loss of 4/30 ≈ 0.13 dollars
Step-by-step explanation:
profit = revenue - expenses
expected profit= expected revenue - expected expenses
how i solve this is by multiplying each revenue and expense by its probability and solving from there
revenue of gold = 5
revenue of silver = 2
revenue of black = 0
this exhausts all of our revenue options
total marbles = 2+8+20 = 30
# of gold marbles = 2
probability of gold = 2/30
# of silver marbles = 8
probability of silver = 8/30
# of black marbles = 20
probability of black = 20/30
expected revenue = sum of possible revenues multiplied by their probability
= 5 * 2/30 + 2 * 8/30 + 0 * 20/30 = 10/30 + 16/30 = 26/30
cost = 1 no matter what
expected profit = expected revenue - expected expenses
= 26/30 - 1
= -4/30
= an expected loss of 4/30
4/30 ≈ 0.13
Pls help me and show work! Thank you <3
Answers
Answer: 27
Step-by-step explanation:
By the same-side interior angles theorem, [tex]x+72+3x=180 \longrightarrow x=\boxed{27}[/tex]
solve equation 3x +4/5=8
Answers
Answer:
x=2.4
Step-by-step explanation:
3x +4/5=8
3x = 8 -4/5
3x =7.2
x = 7.2/3
x=2.4
Heeeeelp please
An arithmetic series has ay = 3 and d= - 3. Find S20-
Answers
The first term is 3 and the common difference is negative 3. Then the sum of the first 20 terms will be negative 510.
What is a series?A series is a sum of sequence terms. That is, it is a list of numbers with adding operations between them.
The first term (a₁) = 3 and the common difference (d) = -3. Then the sum of the first 20 terms will be
Sₓ = (x/2) [2a₁ + (x - 1)d]
Then we have
S₂₀ = (20/2) [2 × 3 + (20 - 1)-3]
S₂₀ = 10 [6 + (19)(-3)]
S₂₀ = 10 [6 - 57]
S₂₀ = 10 [51]
S₂₀ = -510
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£6846 is shared equally between 7 people. How much does each person get?
Answers
Answer: Each person gets £978
Step-by-step explanation: £6846 divided by 7 is £978
help asap please bbbbb
Answers
Answer:432 whats the other option 4300
Step-by-step explanation:
Which table contains only values that satisfy the following? y = x - 1
Answers
Write an exponential function in the form y=ab^x that goes through points (0,14) and (3,4802).
Answers
[tex]y = ab^x \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=0\\ y=14 \end{cases}\implies 14~~ = ~~ab^0\implies 14=a(1)\implies 14=a~\hfill \underline{y=14b^x} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=3\\ y=4802 \end{cases}\implies 4802~~ = ~~14b^3\implies \cfrac{4802}{14}=b^3 \\\\\\ 343=b^3\implies \sqrt[3]{343}=b\implies 7=b~\hfill \underline{y=14(7)^x}[/tex]
A shipping box in the shape of a rectangular prism has a volume of 15,000
cm3. The length of the box is 20 cm, and the width is 25 cm. What is the
height of the box?
A. 15 cm
B. 30 cm
C. 37.5 cm
D. 24 cm
Answers
Answer:
Option (B) 30cm.Step-by-Step explanation:
Given:
Volume of Rectangular Prism is 15,000cm³.
Length (l) ➠ 20 cm Width (w) ➠ 25 cmWe know that,
★ Volume of Rectangular Prism = whl ★
Let "h" be the height.
➛ 25 × h × 20 = 15,000
➛ h × 20 × 25 = 15,000
➛ h × 500 = 15,000
➛ h = 15,000 ÷ 500
➛ h = 30
Thus, height of the box is 30 cm.
Mr. Linares manages a construction company which is currently hiring. If today he interviewed 4 carpenters and 2 masons, what is the probability that the first applicant he saw was a carpenter?
Answers
Answer:
2/3
Explanation:
total people: 4 + 2 = 6 people
carpenters: 4 carpenters
probability = favourable outcomes/total possible outcomesprobability = 4/6 ≈ 2/3
Answer:
P (carpenter) = 2/3 or 0.67
Step-by-step explanation:
Probabilty of seeing a Carpenter first
Number of carpenters = 4Total number of applicants = 4 + 2 = 6P = No. of carpenters / Total applicants⇒ P (carpenter) = 4/6
⇒ P (carpenter) = 2/3 = 0.67
What is the slope of a line through (-3, 4) and
(5, 6)?
Answers
Answer:
slope= x2- x1/y2 -y1
= 5-(-3)/6-4
8/2= 4
