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
To learn more about equation of the circle refer to:
https://brainly.com/question/24810873
#SPJ2
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. The lengths of two sides of the triangle are 13 feet and 23 feet. Find the possible lengths of the third side.
Answer:
Between the lengths of 10 and 36 (exclusive).
Step-by-step explanation:
Since the lengths of any two sides is always greater than the third, the shortest possible length of the third side must be greater than 23 when added to 13. 23-13 = 10, so the third side must be greater than 10.
However, the third side also cannot exceed the length of the sum of the other two sides. 23+13 = 36, therefore the length must be less than 36.
The possible lengths of the third side lie between 10 and 36 (exclusive).
If we use 'l' for length, this range can be represented as follows:
[tex]10 < l < 36[/tex]
Hope this helped!
what do temperature and elevation have in common
Answer: As you increase in elevation, there is less air above you thus the pressure decreases. As the pressure decreases, air molecules spread out further (i.e. air expands) and the temperature decreases. If the humidity is at 100 percent (because it's snowing), the temperature decreases more slowly with height.
Step-by-step explanation:
Trust me
Madyson goes to a restaurant with her best friend, Taylor. The two girls order a meal, Madyson's meal costs $23.75 and Taylor's meal is $15.00. They want to leave a tip of 15% how much money would it cost altogether without tax?
Answer:30.75
$23.75 +$15.00=30.75
5+3=6
21=3
Rewrite the expression without parentheses.
14m-(-5m-4)
If A ⊂ B, then A ∩ B = A ∪ B. a) sometimes b) always c) never
The Answer is Never- Hope this helps and have a great day!
Explanation:
We are given that set A⊂B .
This means that set A is properly contained in set B.
i.e. A≠B
This means that there are some elements in set B which are not in set A.
Now we have to show whether the following property A∩B=A∪B
always, sometimes or never hold.
As A is a proper set of B.
This means that: A∩B=A ( Since A is a smaller set)
Also, A∪B=B (Since B is a bigger set)
Hence, A∩B ≠ A∪B (Since A≠ B)
Credit to -virtuematane
Is x = 1 a solution of the equation 2 – 8x = –6?
Let's verify by substituting 1 to x.
2 - 8x = -6
2 - 8(1) = -6
2 - 8 = -6
-6 = -6
It is equal, therefore x = 1 is the solution.
Answer:
yes
Step-by-step explanation:
Substitute x = 1 into the left side of the equation and if equal to the right side then it is a solution.
2 - 8(1) = 2 - 8 = - 6 = right side
Thus x = 1 is a solution of the equation
How do you find the value of x with 98 & 50?
Answer:
Assuming this has something to do with the interior angles of a triangle?
98 + 50 + x = 180, add 98 and 50.
148 + x = 180, subtract 148 from both sides.
x = 32
Help how do I do it?
A
B
C
D
C
x = 50
Step-by-step explanation:If the two angles add up to 140 then that means 40° + 2x° equals 140
Set up an equation from that evaluation and solve
40 + 2x = 140
Subtract 40 from both sides
2x = 100
Divide both sides by two
x = 50
Hope this helps.
What is the solution for the equation 6x - 8 = 4x? x =
Answer:
x = 4
Step-by-step explanation:
6x - 8 = 4x
subtract 4x from both sides of the equation
6x - 4x -8 = 4x - 4x
2x - 8 = 0
add 8 to both sides of the equation
2x - 8 + 8 = 0 + 8
2x = 8
divide both sides of the equation by 2
2x/2 = 8/2
x = 4
Answer:
x = 4.
Step-by-step explanation:
6x - 8 = 4x
6x - 4x - 8 = 0
6x - 4x = 8
2x = 8
x = 4.
how did you get the product of sum and differences of terms?
Answer:
Step-by-step explanation:
The the terms be x and y
The sum of the terms = x+y
Difference of terms = x-y
Product of the sun and differences will be expressed as:
(x-y)(x+y) = x²-xy+xy-y²
(x-y)(x+y) = x²-y²
Hence the product of the terms is equivalent to the difference of two squares of the terms
HELP HELP HELP
A house painting company charges $350 plus $15 per hour. Another company charges $275 plus $20 per hour. Write an equation that represents when both companies will cost the same amount. How long will the job be when both companies charge the same amount? How much will they charge?
Question 1: Write an equation.
Question 2: How long will the job be when both companies will cost the same amount?
Question 3: How much will they charge?
Answer:
BelowI hope it helps ♥Step-by-step explanation:
1. Equation representing when both companies will cost the same amount :
[tex]350 + 15x = 275 + 20x[/tex]
2. Let x equal the number of hours a job takes , then the first house painting company will charge 350+15x , the second house painting will charge 275 +20x. If the two companies charge the same amount , we will have;
[tex]350 +15x = 275+20x\\\\350 - 275 = 20x - 15x\\\\75 = 5x\\\\\frac{75}{5} = \frac{5x}{5} \\\\15 = x\\\\x = 15\:hours[/tex]
3. For a job that takes 15 hours , the first company will cost ;
[tex]350 + 15(15) = 575[/tex]
For a job that takes 15 hours , the second company will cost ;
[tex]275+20x\\\\275+20(15)\\\\275 +300\\\\=575[/tex]
us
How many milliliters are in
12 teaspoons?
1 tsp = 5 mL
12 tsp = [?] mL
Enter
Vijay’s wages were increased from £115 per week to £130 per week.
What was the percentage increase to one decimal place?
NO SILLY ANSWERS OR REPORT!
Answer:
13%
Step-by-step explanation:
The percentage decrease is calculated by the formula below;
( new value - old value)old value * 100%
old value is 130
new value is 115
So the percentage increase will be;
(130-115)/115 * 100%
= 15/115 * 100% = 13.043%
To one decimal place, this is 13%
2.(03.01)
The range of the following relation R {(3,-2), (1, 2), (-1,-4), (-1, 2)} is (1 point)
O {-1, 1, 3}
O {-1,-1, 1, 3}
O {-4, -2, 2, 2)
O {-4, -2, 2}
I will mark as brainliest
Answer:
{-4,-2,2}
Step-by-step explanation:
Helppppp! I dot know the answer
Answer:
L
Step-by-step explanation:
the square root is 7.2111111. thats the closest
Answer:
C. l
Step-by-step explanation:
The square root of 52 is about 7.211.
Since there is a negative sign in front of the square root, then it means that the answer is about -7.211.
On the number line you have a little bit over -7.3, a little less than -7.3 and a little more than -7.2. The closest answer would be the point that is a little more than -7.2.
Please correct me if I am wrong. I hope this helps!
The number of girls in a class varies directly with the number of boys in the class. If a class contains seven boys and 21 girls, how many girls are in a class with 11 boys?
Answer:
17
Step-by-step explanation:
The first integer is
A. 1
B.0
C.-1
D.None of the above
Answer:
a
Step-by-step explanation:
Answer:
its B
Step-by-step explanation:
what is the quotient of 3/5 and 2/3
Answer:
The quotient of 3/5 and 2/3 is 9/10
Explanation:
3/5 divided by 2/3 is 9/10
Or a easier way to divide fractions is this way:
3/5 divided by 2/3 = ?
Flip the second fraction (from 2/3 to 3/2)
And then multiply:
3/5 x 3/2 = 9/10
(Simplify if needed but in this problem there is no need to simplify)
Please help me with these questions! Legit answers only please!
Answer:
Values of y are:
2 1 -1
2 -1 -4
Does this image have a vertical reflection, horizontal reflection, and rotation? I'll give brainiest!
Answer:
Reflection with respect to the x axis
Step-by-step explanation:
Reflection with respect to the x avis, or horizontal reflection.
easy questions pls help (question in picture)
Answer:
1. P= 80
60/.75=80
2. x= 5/3
-27/25x / -27/25= -9/5 / -27/25
-9/5 / -27/25 --- -9/5 x -25/27
3. -300
-2.7/-2.7 = 810/-2.7
4. 120
84x100/70
84/x = 70/100
1. p=80
=(60×4)÷3
=240÷3
=80
2.x=1.6667
={-9/5}×{-25/27}
=1.6667
3.t=-300
=(810÷-2.7)
=(810×10)÷(-2.7×10)
=(8100÷(-27)
=300
Help me please !!!!!!!!
Answer: Since x is 157 degrees the missing value,m, is 23 degrees because a line is 180 degrees, n is also 23 degrees so it would be the same
Step-by-step explanation:
If 1 gallon of orange juice cost 6.25. How much does it cost for 128 ounces of oj?
Answer:
$6.25
step-by-step explanation:
a gallon of oj coat 6.25
there are 128 ounces in a gallon
so 6.25 for 128 ounces is just a gallon
so 128=1 gallon. so its just $6.25
Rewrite each expression in its equivalent form.
8pq - 3pq
ASAP PLZ HELPPP
Answer:
i believe its 5pq
Step-by-step explanation:
if you do the math of it it should still be the same
Answer:
5pq
Step-by-step explanation:
Step 1: Write expression
8pq - 3pq
Step 2: Combine like terms.
Since both have a pq term in it, we can simply subtract.
8 - 3 = 5
5pq
Determine the y-intercept of the following parabola:
y = 3x2 - 12x - 5
Answer:
-5
Step-by-step explanation:
Find the y-intercept by plugging in x = 0:
y = 3x^2 - 12x - 5
y = 3(0^2) - 12(0) - 5
y = 0 - 0 - 5
y = -5
(0, -5)
Josue knows that his aunt earns more money. than his uncle. He asked how much his aunt earns each month and was told, "$600 less than twice what your uncle earsn." If his aunt earns $4,200 per month, how much money does his uncle earn each month?
Answer:
Uncle's earnings is $2400
Step-by-step explanation:
Represent his uncle's earnings with x
$600 less than twice what your uncle earns is represented as:
[tex]2x - 600[/tex]
Since, his aunt's earnings is $4200.
We have:
[tex]2x - 600 = 4200[/tex]
Add 600 to both sides
[tex]2x - 600 + 600= 4200 + 600[/tex]
[tex]2x = 4800[/tex]
Solve for x
[tex]x = 4800/2[/tex]
[tex]x = 2400[/tex]
Hence, His uncle's earnings is $2400
The probability that a randomly-selected person at a show has seen the band play live before is 50%. A "superfan" is defined as someone who has seen the band play live at least 5 times. The probability that a person at a show is a "superfan" is 30%. Two people are selected at random. What is the probability that both people have both seen the band perform live before, and are "superfans?"
Answer:
0.25 and 0.09
Step-by-step explanation:
The probability that a randomly-selected person at a show has seen the band play live before is 50%=0.50
The probability that a person at a show is a "superfan" is 30%=0.30
Two people are selected at random.
The probability that both people have both seen the band perform live before
= The probability that the first person has seen the band live before and the second person also has seen the band live before.
=0.50 x 0.50
=0.25
Similarly, the probability that both are "superfans"
=The probability that the first person is a superfan and the probability that the second person is a superfan.
=0.30 x 0.30
=0.09
Hence, the probability that both people have both seen the band perform live before, and are "superfans" are 0.25 and 0.09 respectively.
Decide whether or not each equation represents a proportional relationship. A.The remaining length (L) of 120-inch rope after x inches have been cut off: 120−x=L b.The total cost (t) after 8% sales tax is added to an item's price (p): 1.08p=t c.The number of marbles each sister gets (x) when m marbles are shared equally among four sisters: x=m4 d.The volume (V) of a rectangular prism whose height is 12 cm and base is a square with side lengths s cm: V=12s2 Problem 3
Answer and Step-by-step explanation: An equation represents proportional relationship when dividing the quantities of the equation results in a quotient that is always the same. For example, in general:
Equation: y = mx
[tex]\frac{y}{x}[/tex] = m
m is a constant value, which means is the same.
A. Equation: 120 - x = L
Equation from alternative A is NOT proportional since the division of the quantities doesn't result in a constant.
B. Equation: 1.08p = t
Dividing total cost per item's price, will always give the sales tax, which is constant. So, this equation IS proportional.
[tex]\frac{t}{p}=1.08[/tex]
C. Equation: [tex]x=\frac{m}{4}[/tex]
This equation is proportional because dividing marbles per how much each sister gets, always gives the number of sisters:
[tex]\frac{m}{x}=4[/tex]
D. Equation: [tex]V=12s^{2}[/tex]
This equation is NOT proportional because side length is squared, so it is not constant linearly.
Answer:
Step-by-step explanation:
A. Equation: 120 - x = L
Equation from alternative A is NOT proportional since the division of the quantities doesn't result in a constant.
B. Equation: 1.08p = t
Dividing total cost per item's price, will always give the sales tax, which is constant. So, this equation IS proportional.
C. Equation:
This equation is proportional because dividing marbles per how much each sister gets, always gives the number of sisters:
Solve the equation please!!!!!
write an expression for the area of the following quadrilateral with the fewest terms. all sides are congruent. ALSO PLEASE SHOW ME HOW YOU GOT IT