if the circle passing through the point (-1,0) touches the y- axis at (0,2) then what's the equation of the circle?
Answers
Answer:
(x +2.5)² +(y -2)² = 6.25
Step-by-step explanation:
A radius of a circle is perpendicular to the tangent line at the point of tangency. This means the center of the circle lies on the horizontal line through the point (0, 2), which is on the vertical tangent x=0 (the y-axis).
The center of a circle lies on the perpendicular bisector of any chord, so the perpendicular bisector of the given two points will pass through the circle center.
__
equation of the chord bisectorThe slope of the chord between the given points is found using the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (2 -0)/(0 -(-1)) = 2 ⇒ perpendicular has slope -1/2
The midpoint of the chord is ...
M = (A +B)/2 = ((0, 2) +(-1, 0))/2 = (-1, 2)/2 = (-1/2, 1)
The point-slope form of the perpendicular through the midpoint of the chord is ...
y -1 = -1/2(x -(-1/2))
__
center of the circleFor y = 2, the x-value is ...
2 -1 = -1/2(x +1/2)
-2 = x +1/2 . . . . . . multiply by -2
-2.5 = x . . . . . . . subtract 1/2
The circle center is (-2.5, 2), and the radius is 2.5 (distance from center to y-axis).
__
equation of the circleThe equation can be written as ...
(x -h)² +(y -k)² = r² . . . . . . circle with center (h, k) and radius r
(x -(-2.5))² +(y -2)² = 2.5²
(x +2.5)² +(y -2)² = 6.25
Related Questions
Is y = 1/x linear or non linear
Answers
Answer: This answer is non-linear.
Step-by-step explanation:
The problem [tex]y=\frac{1}{x}[/tex] has Vertical Asymptotes,
Horizontal Asymptotes,
and No Oblique Asymptotes making, [tex]y=0[/tex] and [tex]x=0[/tex].
A linear function is a form of [tex]y=mx+b[/tex].
This answer would be non-linear
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what are the zeros of this function? f(x) = 3x^2 + 2x - 8
Answers
Answer:
4/3, -2
Step-by-step explanation:
how many ways can 3 city council members from a list of 20 candidates be selected
Answers
These questions kinda hard help
Answers
Answer:
Step-by-step explanation:
Remark
All of the given listed figures have the property of 4 sides and 4 angles. There is also some relationship between the angles or pairs of angles. Only the square follows the same path. The others cannot be chosen because the sides differ and the angle properties are quite different.
Answer: Square
PLEASE HELP WILL MARK BRSINLIEST!!!!!
Answers
Answer:
a) Yes
b) Not a right triangle
Step-by-step explanation:
Part (a)The sum of the lengths of any 2 sides of a triangle is greater than the length of the 3rd side.
7 + 8 = 15 > 9
7 + 9 = 16 > 8
8 + 9 = 17 > 7
Therefore, a triangle with side lengths 7, 8 and 9 can be made.
Part (b)To determine if the triangle is a right triangle, use Pythagoras' Theorem:
a² + b² = c² (where a and b are the legs, and c is the hypotenuse)
The hypotenuse is the longest side, therefore:
a = 7b = 8c = 9Substituting these values into the formula:
⇒ a² + b² = c²
⇒ 7² + 8² ≠ 9²
⇒ 113 ≠ 81
As 7² + 8² ≠ 9² then the triangle is not a right triangle.
The product of two consecutive positive even numbers is 960. What are the numbers?
Answers
Consecutive positive even numbers
I found it by finding the square root and using that (30.98) as my midline to try numbers near it.
A chemistry teacher needs to mix a 20% salt solution with an 80% salt solution to make 20 qt of a 40% salt solution. How many quarts of each solution should the teacher mix to get the desired result?
Answers
Answer:
6 2/3 qt 80%13 1/3 qt 20%Step-by-step explanation:
It is often convenient to solve a mixture problem by letting a variable represent the quantity of the higher-concentration contributor to the mix.
__
We can let x represent the number of quarts of 80% solution needed. Then (20-x) is the number of quarts of 20% solution needed. The amount of salt in the final mix is ...
0.80x +0.20(20-x) = 0.40(20)
0.60x = 0.20(20) . . . . . . . . subtract 0.20(20) and simplify
x = 20/3 = 6 2/3 . . . . . . . . . divide by 0.60; quarts of 80% solution
(20 -x) = 13 1/3 . . . . . . . . . . amount of 20% solution needed
The teacher should mix 6 2/3 quarts of 80% solution with 13 1/3 quarts of 20% solution.
Can someone please help me with this? Thank you so much! <33
Answers
Answer:
Q63. B
Step-by-step explanation:
5 cars = 2 houses
1 house = 10 pools = 2.5 cars
1 car = 10÷2.5 = 4
Giving brainliest and 50 points
Answers
Answer:
mean: 26
minimum: 0
first q (lower): 5
median: 27
third q (upper): 44
max: 45
(all your answers for Aaron are correct as well:)
hope this helps:)
I need help on these 2 questions how did I get it wrong? and for question 3 I'm not supposed to have the = sign so what am I supposed to replace it with?
Answers
Answer:
3.
m + 7 ≥ 20
Subtract 7 on both sides,
m ≥ 20 - 7
m ≥ 13
The answer is m ≥ 13.
( you need to include both > and =, that is ≥ )
4.
2.1x = 23.1
Divide 2.1 on both sides,
x = 23.1 / 2.1
x = 11
Answer:
For problem #3, we are given [tex]m+7\geq 20[/tex] so we would just subtract 7 from both sides to get rid of the 7 on the left and that would end up subtracting 7 from 20 also leaving us with [tex]m\geq 13[/tex].
For problem #4, we are given [tex]2.1x=23.1[/tex] so we would just divide both sides by 2.1 which would get rid of the 2.1 on the left and that would also make us divide 23.1 by 2.1 leaving us with [tex]x=11[/tex].
Hope this helps! Let me know if you have any questions
*
Drag each graph to show whether it is a function of x or not a function of x. If there is
not enough information to tell
Answers
By using the vertical line test, we conclude that graphs 4 and 5 don't represent functions.
Which of the shown graphs are not functions?
The criteria to know when a graph represents or not a function, is to draw a vertical line and see if the line intersects the graph in more than one point. (This is called the vertical line test).
If you do that with graphs 4 and 5, you will see that these two do not represent functions.
For the other graphs is immediate to know that:
graph 1: represents a linear function.graph 2: represents a constant linear function.graph 3: represents a quadratic function.graph 6: represents a piecewise function.If you want to learn more about functions:
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Suppose that a gated community consisting of 40 houses requires:
500 liters of water everyday for common utilities of the community, and
a certain amount of water everyday per house.
Assuming that the water tanker supplies no more than 4500 liters of water per day to this community, what is the maximum amount of water that can be used by each house on a daily basis?
liters
Answers
Step-by-step explanation:
Given:
40 houses,
500 liters of waters everyday for common utilities
Unknown amount of water per house which we will call x.
4500 max liters for the gated community
Solve:
4500=40x+500
subtract 500 from both sides
4000=40x
divide by 40
100=x
Check:
40(100)+500=4500
4000+500=450
correct
Answer:
100 liters of water can be used by each house.
What is the surface area of this triangular prism?
Answers
Answer:
384 cm^2.
Step-by-step explanation:
This equals the area of 2 triangles + 3 rectangles.
= 2 * 1/2 * 6 * 8 + 14 * 6 + 14 * 8 + 14 * 10
= 48 + 84 + 112 + 140
= 384 cm^2.
Simplify the following expression using prim factorization 9+2*24
Answers
An expression is defined as a set of numbers, variables, and mathematical operations. The simplification of the given expression 9 + (2×24) is 57.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The prime factorization of the expression can be done as,
9 + (2×24)
= (3×3) + (2×2×2×2×3)
= 3 [3+(2×2×2×2)]
= 3 [3 + 16]
= 3 (19)
= 57
Hence, the simplification of the given expression 9 + (2×24) is 57.
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Hannah purchased a box of greeting cards with assorted designs. The box contains four cards of each design: daisies, sunflowers, lilies, birds, puppies, butterflies, dolphins, and landscapes. She selects one card at random from the box.
Calculate the following probabilities.
selecting a card with a sunflower or butterfly design
selecting a card with a lily, daisy, puppy, or bird design
selecting a card with a landscape design
selecting a card with a dolphin, sunflower, or landscape design
selecting a card with a bird or puppy design
Now, determine the events that have the highest and lowest probabilities and graph the values on the number line
Answers
The probability of selecting a card with a sunflower or butterfly design is 1/4, and the probability of selecting a card with a lily, daisy, puppy, or bird design is 1/2.
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
Total outcomes = 4×8 = 32 (because 4 cards of 8 design)
The probability of selecting a card with a sunflower or butterfly design:
= 4/32 + 4/32
= 8/32 = 1/4
The probability of selecting a card with a lily, daisy, puppy, or bird design:
= 4(4/32)
= 1/2
The probability of selecting a card with a landscape design:
= 4/32 = 1/8
The probability of selecting a card with a dolphin, sunflower, or landscape design:
= 3(4/32)
= 3/8
Similarly, we can calculate the rest of the probability.
Thus, the probability of selecting a card with a sunflower or butterfly design is 1/4, and the probability of selecting a card with a lily, daisy, puppy, or bird design is 1/2.
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√343k please simplify this
Answers
Answer:
the answer of√343k is 18k
__[???]___, is the capacity to do work.
A: Energy
B: Velocity
C: Heat
D: Momentum
Answers
Hope this helps!!
Is 8 yards equal to less than or greater than 24 feet?
Answers
Answer:
Equal
Step-by-step explanation:
3 feet is equal to 1 yard, so 8 times 3 is 24, so they are equal to.
how many numbers between 75 and 500 are divisible by 7?
Answers
The number of multiples of 7 between 75 and 500 = (497 - 77)/7 + 1 = 61
Find the x- and y-intercepts of the graph of the equation y = x2 – 2.
Answers
Answer:
See below ~
Step-by-step explanation:
X-intercept(s) : Take y = 0
0 = x² - 2x = ±√2X-intercepts are : (-√2, 0) and (√2, 0)Y-intercept : Take x = 0
y = (0)² - 2y = -2Y-intercept is : (0, -2)The area of the circle is square
inches and the circumference is
inches.
16л, 8л
8л, 16
O 161, 641
o 640, 165
Answers
Answer:
16л, 8л
Step-by-step explanation:
r=4
area=4*4л
=16л
circumference= 2л*4
=8л
A designer needs 4 1/3 yards of material for each dress he makes. How much material will he need to make 15 dresses?
Answers
Answer:
65 yards
Step-by-step explanation:
4 1/3 = 13/3
13/3 times 15 = 65
6x - 3 - 2x = 5. What is the value of x?
Answers
6x-2x = 5+3
=> 4x=8
=> x = 8/4
=>[tex]\fbox{x=2}[/tex]
Hope this helps you :)
Answer:
x=2
Step-by-step explanation:
6x - 3 - 2x = 5
Combine like terms
4x -3 = 5
Add 3 to each side
4x-3+3 = 5+3
4x = 8
Divide each side by 4
4x/4 = 8/4
x = 2
Which expression can be used to find the volume of the cone in this composite figure?
A cylinder and cone. Both have a radius of 4 centimeters. The cylinder has a height of 7 centimeters and the cone has a height of 8 centimeters.
V = one-third pi r squared h = one-third (4) squared (8)
V = one-third pi r squared h = one-third pi (8) squared (4)
V = one-third pi r squared h = one-third pi (4) squared (7)
V = one-third pi r squared h = one-third pi (8) squared (8)
Answers
The expression that represents the volume of the cone is one-third pi r squared h = one-third (4) squared (8).
What is the volume of the cone?A cylinder is a three-dimensional object. It is a prism with a circular base. A cone is a three-dimensional object made up of a circular base and a vertex.
volume of a cylinder = πr²h
= pi x r² x 7
volume of a cone = 1/3 πr²
= 1/3 pi x 4² x8
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Answer:
A is Correct
Step-by-step explanation:
a storage bin in the corner of joes room has the dimensions shown below.
what is the volume of the bin?
Answers
Answer:
26^3 ft is what i got.
5ft x 5ft x 2ft = 50ft
3ft x 4ft x 2ft = 24ft
50ft - 24ft = 26ft
Answer:
36 ft³
Step-by-step explanation:
Formula of a rectangular prism :
Volume = Length x Width x Height
Volume of the bin :
Volume of the smaller part + Volume of the larger part3 x 2 x 2 + 6 x 2 x 26 x 2 + 6 x 412 + 2436 ft³Amy read 25 minutes each day. She has read 14 minutes. How many more
minutes does she need to read?
FREE EASY POINTS, JUST GIVE THE RIGHT ANSWER PLSS!!
Answers
Answer:
11 minutes
Step-by-step explanation:
25 - 14 = 11
) Your 2 year investment of $5,300 earns 2.9% and is compounded annually. What will
your total return be?
Answers
The total amount of return will be 5611.8573. The principal amount is compounded annually.
What is compound interest?Compound interest is computed on a loan or deposit based on the starting principle and the preceding period's accrued interest.
The given data;
P(PRINCIPAL)=5300
r(rate)=2.9%
n=1
t(time)=2
The total amount of return is found as;
[tex]\rm A= 5300 (1+\frac{29}{100} )^2 \\\\ A=5611.8573[/tex]
Hence,the total amount of return will be 5611.8573.
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Choose the answer.
Use the net to determine the total surface area.
Answers
length = 12 + 12 = 24
area of the net (big triangle) = 1/2 x 24 x 20.8 = 249.6
answer : 249.6cm^2
Find the distance between each pair of points.
on graph paper.
K = (-21, -29) and L = (0, 0)
Answers
Answer:
~36 units apart
Step-by-step explanation:
(-21 - 0) = -21 (-29 - 0) = -29-21^2 = 441 -29^2 = 841441 + 841 =1282square root of 1282 is 35.8035.80 is ~36~36 units
What is the slope of a line that is parallel to the line shown?
-4/3
-4
-3/4
-2/3
Answers
Answer:
m = -4/3
Step-by-step explanation:
m = y2-y1/x2-x1
therefore at (-3,2) and (0-2)
m = -2-2/0 - (-3)
m = -4/3