1. The circle C has centre (5,k), where k is a constant. The line y = 2x + 1 is tangent to C at point
A (3,7). Find the equation of C.
Answers
Answer:
[tex](x-5)^2+(y-6)^2=5[/tex]
Step-by-step explanation:
Equation of the Circle
A circle centered at (h,k) and radius r can be written with the equation:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
We are given the center (5,k), thus:
[tex](x-5)^2+(y-k)^2=r^2[/tex]
We know the point (3,7) belongs to the circle. This means the distance between the center and this point is the radius.
Given two points (x1,y1) and (x2,y2), the distance between them satisfies:
[tex]d^2=(x_2-x_1)^2+(y_2-y_1)^2[/tex]
Calculating the radius, we have:
[tex]r^2=(7-k)^2+(3-5)^2[/tex]
[tex]r^2=(7-k)^2+4\qquad\qquad [1][/tex]
Now we use the fact that the line y=2x+1 and the circle are tangent at (3,7). The radius and the line are perpendicular at that point. Two perpendicular lines with slopes m1 and m2 satisfy the condition:
[tex]m_1\cdot m_2=-1[/tex]
The line y=2x+1 has a slope of m1=2, thus the slope of the segment from (5,k) to (3,7) has a slope of -1/2:
The slope is calculated as:
[tex]\displaystyle \frac{7-k}{3-5}=-\frac{1}{2}[/tex]
Operating:
[tex]\displaystyle \frac{7-k}{-2}=-\frac{1}{2}[/tex]
Multiplying by -2
[tex]\displaystyle 7-k=1[/tex]
Solving:
k=6
From [1] the radius is:
[tex]r^2=(7-6)^2+4[/tex]
[tex]r^2=1+4[/tex]
[tex]r^2=5[/tex]
Finally, substituting into the equation of the circle:
[tex]\mathbf{(x-5)^2+(y-6)^2=5}[/tex]
The graph can be seen in the figure below.
Answer:
Step-by-step explanation:
Related Questions
what is the equation of a line that passes through (4,6) and is parallel to y=2x+2 ?
Answers
Answer:
y=2x-2
Step-by-step explanation:
my work is in the picture I attached. lmk if you'd like me to explain more
Answer:
y = 2x - 2
Step-by-step explanation:
let equation of the line be y = mx + c
since it is parallel to y = 2x + 2, gradient/slope of the two lines would be the same
therefore, m = 2
since it passes through (4, 6),
sub (4, 6):
6 = 2(4) + c
c = -2
therefore equation of the line is y = 2x - 2
Carter can bake 11 cookies with each scoop of flour. With 4 scoops of flour, how many cookies can Carter bake?
Answers
Answer:
44 cookies
Step-by-step explanation:
1 scoop = 11 cookies
11 cookies * 4 scoops = 44 cookies
A number times 7 is at least the number plus 6.6.
Write the inequality.
Answers
Answer:
7x ≥ x + 6
A number signifies x.
Replace "a number" with x and then write out the inequality.
Rick owns a rectangular lot that is 52.3 m long and 85.62 m wide. How many
meters of fencing material does he need?
Answers
Answer:
he needs about 137.92 I guess
Write an equation of the line shown. Then use the equation to find the value of x when y=150
Answers
Answer:
Step-by-step explanation:
x = 12
Step-by-step explanation:
The slope-intercept form formula, , can be used to write an equation for the line.
Where,
m = slope =
b = y-intercept, which is the point at which the line intercepts the y-axis. At this point, x = 0.
Let's find the slope (m) using the coordinates of the two points given, (0, 30), (3, 60).
Let,
y-intercept of the line, b = 30
Equation for the line would be:
Using the equation, find x when y = 150.
Simply substitute the value for y in the equation to find x.
Subtract 30 from both sides
Divide both sides by 10
x = 12
This should help.
Plz mark mine brainiest
Question #1 Find the unit rate if the graph below
A
150
135
120
105
90
75
Toys
60
45
30
15
3 6 9 12 15 18 21 24 27 30
Cartons
Answers
Answer:
The unit rate is 5 toy per carton on the graph
please help me this question
Answers
Step-by-step explanation:
Please mark me as the brainliest answer
Answer:
x^3 - 7x^2 + 72
Step-by-step explanation:
you just subtract both equations
Choose the correct answer below for the following problem:
(‒489) + (‒764) =
A.
‒1,253
B.
275
C.
1,253
D.
‒275
Answers
Step-by-step explanation Answer:
A -1253
-489-764 = -1253
Can someone help me with the questions in the picture?
Answers
Y = -2x + b
Plug in the point (2, -4)
-4 = -4 + b, b = 0
Equation: y = -2x
8. Perpendicular slope: -2
Y = -2x + b
Plug in the point (-3,5)
5 = 6 + b, b = -1
Equation: y = -2x - 1
9. Perpendicular slope: -3/2
Y = -3/2x + b
Plug in the point (-2, 4)
4 = 6 + b, b = -2
Equation: y = -3/2x - 2
10. Perpendicular slope: 1/2
y = 1/2x + b
Plug in the point (-4, 0)
0 = -2 + b, b= 2
Equation: y= 1/2x + 2
Those are what I got :)
Complete the steps to find the value of x.
2xº
1282
Answers
Explanation: We know this because 2x=128, so if you divide 128/2 you’ll find x which is 64!
Hope this helps :)
Write in simplest form: what is 2^-3 in simplest form
Answers
Answer: 1/8
[tex]2^{-3}=\frac{1}{2^{3} }=\frac{1}{8}[/tex]
Step-by-step explanation:
Answer:
1/8
Step-by-step explanation:
5x+4=2(x+2)
please help me i tried it and i got it wrong I got 2/5
Answers
Answer: x= 0
Step-by-step explanation:
5x + 4 = 2(x + 2) First distribute on the right side of the equation
5x + 4 = 2x + 4 Subtract 2x from both sides
-2x -2x
3x + 4 = 4 Subtract 4 from both sides
-4 -4
3x = 0 Divide both side by 3
x = 0
What is the x-intercept of the line described by the equation? 14x - 8y = 56
Answers
Answer:
The x intercept is (4,0) and the y intercept is (0,-7)
Step-by-step explanation:
Answer:
Step-by-step explanation:
The x-intercept of a line is when the y-coordinate is 0. To find that point on this line, we first want to rearrange the equation into the form
[tex]y = mx + b[/tex]
we are given
[tex]14x - 8y = 56\\so, \\14x - 56 = 8y\\\frac{14x}{8} - \frac{56}{8} = \frac{8y}{8} \\y = \frac{7}{4}(x) - 7[/tex]
now, we can set y to 0 and solve
[tex]\frac{7}{4}(x) = 7\\7x = 28\\x = 4[/tex]
The x-intercept is (4, 0)
how many solutions does -2 + x -3 = 2x + 5 -x have?
Answers
Answer:
No solutions
Step-by-step explanation:
Can Somebody Help With Geometry?
Answers
Answer:
SAS
Step-by-step explanation:
II side (given)
Angles between the congruent sides (vertically opposite angle)
III side (given)
Hence by, SAS the Triangles are congruent.
Which expression represents a quadratic expression in standard form? *
5x-4
-21-x^2
-15+2x-x^2
x^2-2x-63
Answers
A 3-gallon jug of orange juice costs $10.44. What is the cost of the orange juice per quart?
A.
$1.07
B.
$0.87
C.
$2.06
D.
$0.98
Answers
Answer:
B. $0.87
Step-by-step explanation:
Divide $10.44 by 12 (how many quarts are in 3 gallons) to get the answer.
Dee spends $0.25, $0.30, $0.10 and $0.04.
How much $ does she spend in all?
Answers
explanation: 0.25 + 0.30 + 0.10 + 0.04 = 0.69
By adding all the money she spend we get $0.69
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We are given that Dee spends $0.25, $0.30, $0.10 and $0.04.
We need to find the money she spend in all.
Therefore, we have to add all the expenditure
0.25 + 0.30 + 0.10 + 0.04 = 0.69
The total money she spend could be 0.69.
Learn more about the unitary method, please visit the link given below;
https://brainly.com/question/23423168
#SPJ2
x^2 − 15 = 1 please help
Answers
Answer:
x^2-15=1
x^2=16
4 x 4 = 16
THerefore...
x=4
Depending on how many choices there are -4 is also correct.
Any number squared is a positive.
x=4, x=-4
Step-by-step explanation:
Until the scale was changed in 1995, SAT scores were based on a scale set many years ago. For Math scores, the mean under the old scale in the 1990s was 470 and the standard deviation was 110. In 2013 the mean was 515 and the standard deviation was 116. Gina took the SAT in 1994 and scored 500 on the Math test. Her cousin Colleen took the SAT in 2013 and scored 530 on the Math test. Who did better relative to their peers, and how can you tell? Group of answer choices Colleen—she scored 30 points higher than Gina. Gina—the standard deviation was bigger in 2013. Gina—her standardized score is higher than Colleen’s. Colleen—her standardized score is higher than Gina’s.
Answers
Answer:
Gina—her standardized score is higher than Colleen’s.
Step-by-step explanation:
Until the scale was changed in 1995, SAT scores were based on a scale set many years ago.
We solve this question using z score formula also know as standardized score formula which is given as:
z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.
For Gina
Gina took the SAT in 1994 and scored 500 on the Math test.
For Math scores, the mean under the old scale in the 1990s was 470 and the standard deviation was 110.
x = 500
μ = 470
σ = 110
Hence, the z score is given as:
z = 500 - 470/110
z = 0.27273
Gina's z or standardized score is 0.27273
For Colleen
Her cousin Colleen took the SAT in 2013 and scored 530 on the Math test.
In 2013 the mean was 515 and the standard deviation was 116.
x = 530
μ = 515
σ = 116
Hence, the z score is given as:
z = 530 - 515/116
z = 0.12931
Colleen's z or standardized score is 0.12931
The person who did better relative to their peers is Gina and this is because her standardized score is higher than Colleen’s.
The equation F= 9/5 C+32 relates temperature measured in degrees Celsius, C , to degrees Fahrenheit, F. Determine whether there is a proportional relationship between C and F.
Answers
Answer:
The relationship between F and C is proportional
Step-by-step explanation:
The relationship between Celsius and Fahrenheit temperatures is a direct proportionality. Both scales have their ice and steam points as well as their fundamental intervals.
When the temperature in Celsius increases, the temperature in Fahrenheit increases and vice versa.
There are a total of 24 people at Camp Float-Away. If 4 of the people are counselors, what is the ratio of campers to counselors?
Answers
Answer:
5:1
Step-by-step explanation:
Since there are 4 counselors, the other 20 people are campers. You divide 20 by 4 (to determine how many campers equal 1 counselor) and you get 5. So 5:1
WILL MARK brainiest answer
Answers
Answer:
i Think it would be B
Step-by-step explanation:
What does ø mean ? Can someone explain it based off the problem in the photo ?
Answers
Answer:
It means something mathematical
Step-by-step explanation:
The slashed zero glyph is often used to distinguish the digit "zero" ("0") from the Latin script letter "O" anywhere that the distinction needs emphasis, particularly in encoding systems, scientific and engineering applications, computer programming (such as software development), and telecommunications.
Simplify the expression.
Can someone explain to me how to get the answer? Thanks!
Answers
Answer:
11x^2+2x+9
Step-by-step explanation:
2+(2+6)⋅x^2+2x+3x^2+7
2+(8)⋅x^2+2x+3x^2+7
2+8x^2+2x+3x^2+7
9+8x^2+2x+3x^2
9+8x^2+2x+3x^2
11x^2+2x+9
Stefanie swam four-fifths of a lap in the morning and seven-fifteenths of a lap in the evening. How much farther did Stefanie swim in the morning than in the evening?
Answers
4/5 - 7/15
12/15 - 7/15 = 5/15
5/15 = 1/3
Deon has $600 in his saving account
•He spends $15 per month on Netflix
•He spends $5 per month in Hulu
If he does not make any more purchases, select all of the months that he can continue to have the subscription before he goes into debt.
Answers
Answer:
30 months total
Step-by-step explanation:
15+5=20
600÷20=30
What addition statement does this show?
A. 10 + 3 = 13
B. 10 + (–3) = 7
C. –10 + 3 = –7
D. –10 + (–3) = –13
please answer as soon as you can!<3
Answers
Answer:
I think the answer is A sorry if I am wrong
Step-by-step explanation:
Answer:
The answer is b
Step-by-step explanation:
10 + (-3) = 7
A man walks around a circular park 4 times in 12 minutes. The radius of the park is 49m. Find the speed of the man in km/ h.
Answers
Wish I could have helped earlier but they already gave you the right answer
PLEASE HELP I DONT WANT TO FAIL