Center = (5,7)
Radius = 5
======================================================
Explanation:
The circle must be tangent to the y axis, and it has a radius of 5, so that means the center (h,k) must either be on the line x = 5 or x = -5, since those vertical lines are exactly five units away from the y axis.
But we're also told that (10,7) must be on the circle. That rules out x = -5 because the distance from (10,7) to (-5,k) is going to be larger than 5. I recommend drawing out a right triangle to see why this is the case.
So the center (h,k) must be on the line x = 5.
The center is the point (h,k) = (5,k)
Plug that h value along with (x,y) = (10,7) and r = 5 into the equation below
Solve for k.
(x-h)^2 + (y-k)^2 = r^2
(x-5)^2 + (y-k)^2 = 5^2 .... plug in h = 5 and r = 5
(10-5)^2 + (7-k)^2 = 25 ... plug in x = 10 and y = 7
25 + (7-k)^2 = 25
(7-k)^2 = 25-25
(7-k)^2 = 0
7-k = sqrt(0)
7-k = 0
-k = 0-7
-k = -7
k = 7
The center is (h,k) = (5,7)
We have (x-h)^2 + (y-k)^2 = r^2 updating to (x-5)^2 + (y-7)^2 = 25
The equation of the circle is (x-5)^2 + (y-7)^2 is25 . The center of the circle is Center is (5,7) .Radius of the circle is 5
What is equation of the circle?Circle's basic equation is represented by:
(x-h)2 + (y-k)2 = r2
where the radius is r and the circle's center's coordinates are (h,k).
Let's first consider what a circle is before determining its equation. A circle is a collection of all points in a plane that are uniformly distanced from a fixed point. The fixed point is referred to as the circle's center. The radius of a circle is the separation between the center and any point along its circumference. In this article, we'll explain what a circle's equation looks like in standard form and show you how to calculate a circle's equation when its center is both the origin and another point.
The center (h,k) of the circle, which must be tangent to the y axis and have a radius of 5, must either be on the line x = 5 or x = -5 since both vertical lines are both located exactly five units from the y axis.
The need that (10,7) be on the circle is also stated, though. That eliminates the possibility of x = -5 because the distance from (10,7) to (-5,k) will be more than 5. To understand why this is the case, I advise you to sketch a right triangle.
Therefore, the line x = 5 must contain the center (h,k).
The point (h,k) = is the center (5,k)
Given ,
In the equation below, enter that h value along with (x,y) = (10,7) and r = 5.
Calculate k using the formula.
(x-h)^2 + (y-k)^2 = r^2
(x-5)^2 + (y-k)^2 = 5^2 add a h = 5 and r = 5 plug.
(10-5)^2 + (7-k)^2 = 25 Input x = 10 and y = 7
25 + (7-k)^2 = 25
(7-k)^2 = 25-25
(7-k)^2 = 0
7-k = sqrt (0)
7-k = 0
-k = 0-7
-k = -7
k = 7
(h,k) = is the center (5,7)
Updated to (x-5) + (y-7) = 25, we have (x-h) + (y-k) = r2.
Therefore The equation of the circle is (x-5)^2 + (y-7)^2 is25
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What is the vertex of the graph of the function f(x) = x2 + 6x + 9?
0 A. (-3,0)
B. (0, -3)
C. (0, 3)
O D. (3, 0)
The vertex of the given quadratic function is (-3, 0).
What is vertex form of a quadratic equation?The vertex form of a quadratic equation or function is [tex]f(x)=a(x-h)^{2} +k[/tex].
Where,
(h, k ) is the vertex
And, a is constant.
According to the given question
We have a quadratic function
[tex]f(x) = x^{2} + 6x + 9[/tex]
The above function can be written as
[tex]f(x) = x^{2} +2(3x) +9[/tex]
⇒[tex]f(x) = x^{2} + 2(3x) + (3^{2}) -(3)^{2} + 9[/tex]
⇒[tex]f(x) = (x+3)^{2} -9+9[/tex]
⇒[tex]f(x) = (x+3)^{2} + 0[/tex]
Comparing the above equation with the standard vertex form of quadratic function we get
h = -3 and k = 0
Hence, the vertex of the given quadratic function is (-3, 0).
Thus, option A is correct.
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Which compound inequality is represented by the graph?
GU
-5 -4 -3 -2 -1 0 1 2
3
4 5
-35x<1
-3
O xs-3 or x > 1
O x<-3 or 21
The compound inequality represented by the graph is -3 ≤ x < 1
From the graph, we have the following highlights
The line number starts from -3 and ends at 1The dot at 3 is closed, while the dot at 1 is openedThe above means that:
-3 is included in the inequality values, while 1 is not.
Hence, the compound inequality represented by the graph is -3 ≤ x < 1
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Use the formula an = aj(r)a- to write a formula for the geometric sequence below.
3, 6, 12, 24, 48, ...
Answer:
[tex]a_{n}[/tex] = 3[tex](2)^{n-1}[/tex]
Step-by-step explanation:
There is a common ratio r between consecutive terms in the sequence, that is
6 ÷ 3 = 12 ÷ 6 = 24 ÷ 12 = 48 ÷ 24 = 2
This indicates the sequence is geometric with n th term
[tex]a_{n}[/tex] = a₁[tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = 3 and r = 2 , thus
[tex]a_{n}[/tex] = 3[tex](2)^{n-1}[/tex]
eleven times onennumber is 9 more than 8 times another number. the first number minus four is half the second number. find the numbers
Answer:
I'm pretty sure its 11 and 14
Step-by-step explanation:
Sorry if i'm wrong or can't help more.
PLEASE HELPPP ASAP 50 POINTS !!!!!!!!!!!!!!!!!!! PIC BELOW
The ratio of boys to girls at a school is 12 to 13. If 300 students attend the school, how many are boys?
144
277
156
25
Answer: 144
Answer:
144
Step-by-step explanation:
300 divided by 13
For each expression, x = 9 and y = 3.
2x · 4y - 10
a. 12
b. 10
c. 20
d. 6
Answer
the answer is C. 20 :)
Step-by-step explanation:
hope it helps!
Why do candidates want to win states
like Texas, Florida, and New York?
What is 1 3/8 minus 5/8
Answer:
-4 (-2/8)
Step-by-step explanation:
1-5=(-4)
3-5=(-2)
hope this helps :3
Answer:
3/4
Step-by-step explanation:
Given f(x) = 3x^2 - 6x + 2 find f(3)
HELP PLEASE ‼️‼️‼️
Answer: 47
Step-by-step explanation:
You simplify it giving you 47
Answer:
f(3)=11
Step-by-step explanation:
3(3)^2=27
-6(3)=-18
27-18+2=11
1. Armando started a new job as a mechanical engineer for a coal plant with an
annual salary of Php 200 000.00 in 2010. If she receives a Php 24 000.00 raise
each year, how much will her annual salary be in 2020?
Answer:
224,000
Step-by-step explanation:
annually she earns 200,000and a raise of 24,000 each year hence the sum of the two will get you an asnwer
D 145
which expression is equivalent to 5(4x + 3) - 2?
А
187 + 15
B
187 + 3
C 7x + 8
D 2r + 8
Answer:
C
Step-by-step explanation:
No option is equal to the expresion, but.C is similar.
Points A, B, and C are collinear. Point B is between A and C. Solve for x
AB= 3x, BC= 2x - 2 , and AC= 18. Find x.
Answer:
x=4
Step-by-step explanation:
You set the equation up like this
3x+2x-2=18
5x-2=18
5x=20
x=4
Table function rule of y=4x+1
Answer:
y=5
Step-by-step explanation:
y equals 5 because x is 1 when you get it alone
All of the following statements are true, except . . .
The product of a and c is negative.
The product of b and c is positive.
The product of b and 0 is 0.
The product of a and b is positive.
Answer:
The product of b and c is positive.
Step-by-step explanation:
b is negative as its less than 0
c is > 0 and is thus positive
multiply these would be negative result
Answer:
The product of b and c is positive.
Step-by-step explanation:
had this question
Please help! Will give brailiest!
What is –96 ÷ +3? im a little confused when it comes to math
Caroline walks 912 inches per second. As unit rate
Answer:
specify please
Step-by-step explanation:
Answer:
I have been trying to get this answer for the longest
Step-by-step explanation:
what is the answer for this question?
Answer:
18
Step-by-step explanation:
Hope this helps
Identify the set of numbers that best describes the situation. Explain your choice.
The weight of a person in pounds.
129.3lb
please help will give brainiest
Answer:
Step-by-step explanation:
it's a rational number because it can't be a whole number with the decimal point and it can't be an integer because it's not a negative or positive number it also can't be an irrational number because an irrational number isn't a terminating or repeating decimal its a rational number because it's a terminating number
A student calculated the density of copper to be
8.37 g/cm3. The accepted value for the density of
copper is 8.92 g/cm3. What is the percent error in the
density?
Answer:
0.55/8.92×100
55/8.92
=6.17%
A farmer stores bags of seed in 4 rows. There are 4 bags
in each row. How many bags of seed are there in all?
Answer:
16 bags in all
Step-by-step explanation:
4x4=16
Answer:16
Step-by-step explanation:
4*4 or 16/4 = 16
Nine students were absent on the first day of a painting class and 12 students on the second day of the class. If p is the percent increase in the number of students who were absent, which proportion can be used to calculate p?
Answer:
ITS A
Step-by-step explanation:
Took DA TEST
Answer:
a
Step-by-step explanation:
hard questions (for me anyway) pls help
Answer: 1. 80 2. 1/3 3. -300 4. 120 pages Equation: 0.7p = 84, p=120
round 314,759 to the number of the underlined digit
Answer:
Um I think that it might be 315,000 if that's what they mean
a unit rate is a rate in which the unit in the denominater is?
Answer: a unit rate is a rate with 1
Step-by-step explanation:
PLEASE HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Is the following formula recursive or explicit? *
Uo = 13
Un = Un-1 - 3
Answer plz
Answer:
Recursive.
Step by step explanation:
N is the number of the term in the sequence, so Un-1 is the term previous to Un and since you’re subtracting 3 from the previous term, that means it’s recursive
Lee combines 7.63 ounces of strawberries with 5.26 ounces of blueberries to make a fruit bowls. He pours the fruit equally into 2 bowls, and has 1.37 ounces of fruit left over. How many ounces of fruit are in each bowl?
Answer:
7.63 ounces of strawberries + 5.26 ounces of blueberries
7.63 + 5.26= 12.89 - 1.37 left over = 11.52 to be split between 2 bowls equally
11.52/2 = 5.76 per bowl
5.76 ounces of fruit in each bowl.
What is mathematical expression?
A mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given,
strawberries = 7.63 ounces
blueberries = 5.26 ounces
Put the fruits into two equal bowls in equal amounts
let the amount be x
remaining amount = 1.37 ounces
According to the statements, we can state that,
2x + 1.37 = 7.63 + 5.26
2x = 11.52
x = 5.76
Therefore, the two bowl contains 5.76 ounces of fruit each.
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Raquel can type 63 words every minute. Rick can type 73 words every minute. How many more words can Rick type than Raquel in 135 minutes?
Group of answer choices
Answer:
1350 words
Step-by-step explanation:
8505 is the amount of words raguel can type in 135 minutes. 9855 is the amount Rick can type in 135 min. 9855-8505=1350 which is the answer