Equation of circle G: [tex]\bold{(x-3)^{2} + (y-4)^{2} = 49}[/tex]
Equation of circle with center-radius form:"An equation of a circle with center (p, q) and radius r is:[tex](x-p)^{2}+ (y-q)^{2}=r^{2}[/tex] "
Midpoint Formula:"The coordinates of the midpoint M of two points (a, b) and (x, y) :
[tex]M(\frac{a+x}{2} ,\frac{b+y}{2} )[/tex] "
Distance formula:"The distance between two coordinate points (a, b), (m, n):
[tex]d=\sqrt{(n-b)^{2} +(m-a)^{2} }[/tex] "
What is diameter of circle?"A diameter of a circle is the straight line that from one side of a circle to other side and passes through the center."
For given question,
The line segment connecting the two points B(-4,4) and D (10,4) is a diameter of the circle.
This means, the midpoint of the diameter BD would be the center of a circle G.
Let M represents the center of the circle.
First we find the coordinates of the center of the circle.
Using midpoint formula,
⇒ M = [tex](\frac{-4+10}{2} ,\frac{4+4}{2} )[/tex]
⇒ M = (6/2 , 8/2)
⇒ M = [tex](3,4)[/tex]
Now, we find the distance between points B(-4,4) and D (10,4) to determine the diameter of a circle G.
Using distance formula,
⇒ [tex]d=\sqrt{(4-4)^{2} +(10-(-4))^{2} }[/tex]
⇒ [tex]d=\sqrt{0+(14)^{2} }[/tex]
⇒ [tex]d=14[/tex] units
So, the radius of the circle r would be,
r = d/2
⇒ r = 14 / 2
⇒ r = 7 units
Now, we find the equation of circle with center M(3, 4) and radius r = 7 units.
Using center - radius form equation of circle would be,
[tex](x-3)^{2} + (y-4)^{2} = 7^{2}[/tex]
⇒ [tex]\bold{(x-3)^{2} + (y-4)^{2} = 49}[/tex]
Therefore, option (A) is the correct answer.
Learn more about equation of circle here:
https://brainly.com/question/10618691
#SPJ2
Simplify the following expression
Simplifying expressions
8th grade math
Algebra 1
Can someone explain why
(-5k^2m)(2km)^4(3km^4)^2
——————————————
k^2m^3
Simplifies to -720k^6m^10
But 3m/m^4 simplifies to 3/m^2
Even though their both fractions how come only one stays a fraction? What’s the difference so I can figure out in the future?
Answer:
1. [tex]\frac{(-5k^{2}m)(2km)^{4} (3km^{4}) ^{2}}{k^{2}m^{3}}[/tex] = -720[tex]k^{6}m^{10}[/tex]
2. [tex]\frac{3m}{m^{4} }[/tex] = [tex]\frac{3}{m^{3} }[/tex] (or 3[tex]m^{-3}[/tex])
Step-by-step explanation:
1. The given expression is:
[tex]\frac{(-5k^{2}m)(2km)^{4} (3km^{4}) ^{2}}{k^{2}m^{3}}[/tex]
With respect to the principle of exponential, we have;
[tex]\frac{(-5k^{2}m)(2^{4}k^{4} m^{4})(3^{2}k^{2}m^{8})}{k^{2} m^{3} }[/tex] = [tex]\frac{(-5k^{2}m)(16k^{4} m^{4})(9k^{2}m^{8} }{k^{2}m^{3} }[/tex]
Applying the law of indices,
= [tex]\frac{(-5*16*9)(k^{2+4+2})(m^{1+4+8}) }{k^{2} m^{3} }[/tex]
= [tex]\frac{-720k^{8} m^{13} }{k^{2}m^{3} }[/tex]
= -720[tex]k^{8}m^{13}[/tex] x [tex]k^{-2} m^{-3}[/tex]
= -720[tex]k^{8-2} m^{13-3}[/tex]
= -720[tex]k^{6}m^{10}[/tex]
2. [tex]\frac{3m}{m^{4} }[/tex]
divide the numerator and denominator with common factor m,
= [tex]\frac{3}{m^{3} }[/tex]
This can not be simplified further since there are no more common factors, so that;
[tex]\frac{3m}{m^{4} }[/tex] = [tex]\frac{3}{m^{3} }[/tex] (or 3[tex]m^{-3}[/tex])
Help plz and thanks you for helping me
Answer:
12.5
Step-by-step explanation:
x= 5 when y = 12
y = 30 = 12 x 2.5 (do the same to the other number)
5 x 2.5 = 12.5
Ace C.a.r.l.o.s.
What does y stand for in math
Answer:
The vertical value in a pair of coordinates. How far up or down the point is. The Y Coordinate is always written second in an ordered pair of coordinates (x,y) such as (12,5). In this example, the value "5" is the Y Coordinate. Also called "Ordinate"
Step-by-step explanation:
Answer:
In math a letter is always a variable. If you are solving an equation and the letter y is there you have to solve for y. So in math y stands for a variable.
Step-by-step explanation:
Please can someone help me.
Answer:
4
Step-by-step explanation:
Answer:
y = 4[tex](2)^{x}[/tex]
Step-by-step explanation:
An exponential function in standard form is
y = a[tex]b^{x}[/tex]
Substitute points from the graph into the equation to find a and b
Using (0, 4 ), then
4 = a[tex]b^{0}[/tex] [ [tex]b^{0}[/tex] = 1 ], so
a = 4
y = 4[tex]b^{x}[/tex]
Using (1, 8 ), then
8 = 4[tex]b^{1}[/tex] = 4b ( divide both sides by 4 )
b = 2
y = 4 [tex](2)^{x}[/tex] ← exponential equation
Are these fractions equivalent or nonequivalent?
4x/7y 8x/14y
Answer:
[tex] \frac{8x}{14y} = \frac{ \frac{8x}{2} }{ \frac{14y}{2} } = \frac{4x}{7y} \\ [/tex]
Hence, they are equivalent.
Write an equation of the line with a slope of 2/3 and y-intercept of −8.
Answer:
F(x)=2/3x-8
Step-by-step explanation:
HELP PLEASEEEE it’s due in 10 minutes
Answer:
24.187
Step-by-step explanation:
help anyone? its pretty easy im just lazy
what do i write i need help so i can do this
Answer:
Step-by-step explanation:
First what you want to is subtract 7 from both sides, then you want to divide -2/3 from both sides.
To isolate the variable you need to remove the terms from the side with the variable to remove the terms you need to do the same thing on both sides.
-2/3n + 7 = 15
First step is to subtract 7 from both sides to get:
-2/3n = 8
Now divide both sides by -2/3 to get:
N = 8 / -2/3
Then to solve for n simplify to get:
N = -12
I GIVE BRAINLIEST AND 20 POINTS. please someone solve me these. Explain how and it would be better wth a pic. thank u.
Answer:
A = 12
B = 0
r = 2
Step-by-step explanation:
A) √121 + 3/5 + 2/5 = 11 + 1 = 12
B) √100 - 3 -7 = 10 - 3 - 7 = 0
r) 1/2 - 1/2 + √4 = 2
Use the space below to explain how you know if the statement is correct or incorrect:
Andy has been saving his pocket money. He began the month with $44 and ended with $110.
He said the end of the month amount was 250% of his original amount.
Answer:
Yes, it is correct.
Step-by-step explanation:
Word Version: Andy is correct, forty-five dollars multiplied by two-hundred-fifty percent is equal to one-hundred-ten dollars.
Number version: Andy is correct, $44 x 250% = $110
✧brainliest appreciated✧
Which two points are on the graph of y=x+3?
Answer:
(0, 3) and (-3, 0) are just two out of an infinite number of other points
Step-by-step explanation:
I found these 2 points by plugging in 0 for x and y would equal 3
Then I plugged in 0 for y and x would equal -3
150% of 50 is what number?
Answer:
75
Step-by-step explanation:
Solve for x: -4x - 12 < 12
Seems like you are an imposter ;). This is Middle School math.
Anyways...
Answer:
x>6
Step-by-step explanation:
-4x-12<12
Add 12 on both sides.
-4x<24
Divide both sides by -4 to isolate x. Remember that if you are dividing by a negative, flip the sign!
x>6
Hope this helps!
Multiply 2 [4 1 0 -2 ]
Answer:
[ 8 20 -4 ]
Step-by-step explanation:
2[4 10 -2 ]
=[8 20 -4]
$100 into a savings account that earns 6% annual intrest compounded monthly for 5 years
Answer:
$141.94
Step-by-step explanation:
Basically multiply 100 by .06, add the answer too 100. Which gets 106.
Multiply 106 by .06 and add the answer to 106, do that 5 times(which counts as the five years) and vuala, you got your answer.
And since it said an annual
interest, then the monthly compounding doesn't matter.
Jill measures some scrap boards in her garage to
see if she has enough to make a border around her
garden. She needs 10 meters total. The boards
measure 2.75 meters, 3.2 meters, 1.65 meters, and 2.6
meters. Does Jill have enough?
Answer: Yes, Jill has enough scrap boards to create a border around her garden.
Step-by-step explanation:
2.75 + 3.2 + 1.65 + 2.6 = 10.2 m
Answer:
Yes
Step-by-step explanation:
If you add all of them together, they make 10.2, which is enough
2/5 of a number is 40. What is 1/10 of the number
Please help me
Answer:
10
Step-by-step explanation:
Answer:
1/10 of the number is 10.
Step-by-step explanation:
We know that 40 is 2/5 of this unknown number, so 4/5 would be 80. Then, to fill up the other 1/5, we must split 40 into half.
1/2 of the number 40 is equal to the number 20.
80 + 20 = 100, so 5/5 would be equal to 100.
Now, we have to find one tenth of the number 100.
1/10 of the number 100 is the number 10. (1/10 of 100 = 10)
The answer to the question is 10.
What’s 7^4 simplified
24 POINTS HELP QUICK AA
Answer:
2401
Step-by-step explanation:
because 7*7*7*7=2401
Answer:
2,401
Step-by-step explanation:
The question states what is 7^4 simplified, meaning what is 7 to the 4th power!!
=2,401
Lucy invested $19,000 in an account paying an interest rate of 3% compounded annually. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 8 years?
Answer:
23560
Step-by-step explanation:
3% of 19k is 570
570*8=4560
4560+19000=23560
What is 58.65 divided by 6.9
Answer:
8.5
Step-by-step explanation:
58.65/6.9= 8.5
Answer:
Step-by-step explanation:
Find the distance between the ordered pairs. A (-1, 7) , B (5, 7)
Answer:
[tex]\displaystyle d = 6[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Algebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Point A(-1, 7)
Point B(5, 7)
Step 2: Find distance d
Simply plug in the 2 coordinates into the distance formula to find distance d
Substitute in points [DF]: [tex]\displaystyle d = \sqrt{(5--1)^2+(7-7)^2}[/tex](Parenthesis) Simplify: [tex]\displaystyle d = \sqrt{(5+1)^2+(7-7)^2}[/tex](Parenthesis) Add/Subtract: [tex]\displaystyle d = \sqrt{(6)^2+(0)^2}[/tex][√Radical] Exponent: [tex]\displaystyle d = \sqrt{(6)^2}[/tex][√Radical] Evaluate: [tex]\displaystyle d = 6[/tex]Which equation has a solution of 34 for y?
4y=6
y−1=−14
214+y=4
8y=9
Answer:
I believe there is an error because none of them are the answers
Step-by-step explanation:
4y=6
y=6/4
y-1=-14
y=-13
214+y=4
y=-210
8y=9
y=9/8
Which list shows the integers in order from lest to greatest ? -8 , -5 , 0 , 2 , 6 0 , 2 , -5 , 6 , -8 -5 , -8 , 0 , 2 , 6 0 , -8 , -5 , 2 , 6
Answer:
a.-8,-5,0,2,6
Step-by-step explanation:
We have to find the list which shows the integers in order from least to greatest.
We know that when we left side of zero on a number line then the values decrease and we go right side of zero then the value increases.
a.-8,-5,0,2,6
-8<-5<0<2<6
Hence, it is true.
b.0,2,-5,6,-8
-8 least and 6 is greatest
Therefore, it is false.
c.-5,-8,0,2,6
It is false.
d.0,-8,-5,2,6
It is false.
Option a is true,
At a resort, the housekeeper and the concierge may have different levels of education and perform different tasks in their lines of work, but they both still work in the Lodging pathway of the Hospitality and Tourism cluster. Question 1 options: True False
Answer:
the answer is true
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
The test said it is right
i need to find the slope from two points i don’t know how to do this!show work please
Answer:
2
Step-by-step explanation:
Ok, so they gave you these two points, since I can't actually graph it, then we can just make a table...
x y
4 6
6 10
From 6 to 10, you add 4 (this is for the y section)
From 4 to 6 you add 2 (this is for the x section)
Now you need to divide the y by the x....
y/x = 4/2 = 2
And 2 will be the answer for your slope, given these 2 points.
Hope this helped!
HELP PLZZZZZZZZZZ I WILL GIVE BRAINLIEST
Solve the following system of equation susing the combination method: 3x - 4y = -4 X + 3y = - 10
Answer:
x=3
Step-by-step explanation:
Write the equation of the line, in slope-intercept form, that has a slope of -8/5and contains the point
Answer:
y = -8/5x + 23/5
Step-by-step explanation:
Complete question
Write the equation of the line, in slope-intercept form, that has a slope of -8/5and contains the point (6, –5)
The equation of a line in pint slope form is expressed as;
y - y0 = m(x-x0)
Given
m = -8/5
(x0, y0) = (6, -5)
Substitute into the formula
y - (-5) = -8/5(x-6)
y+5 = -8/5(x-6)
Multiply through by 5
5(y+5) = -8(x-6)
5y + 25 = -8x + 48
5y = -8x +48 - 25
5y = -8x + 23
y = -8/5x + 23/5
Hence the equation in slope intercept form is y = -8/5x + 23/5
HELP PLEASE WILL GIVE I 100 POINTS And mark brainly
Answer:
-9/3 or -3
Step-by-step explanation:
[tex]Slope= \frac{y_{2} -y_{1} }{x_{2}- x_{1} }[/tex]
Lets start with the y's, substitute:
-6-3=-9
Then the x's, substitute:
5-2=3
Substitute back into the fraction:
-9/3 or
-3
Answer:
m = -3
Step-by-step explanation:
y2-y1
--------
x2-x1
-6-3/5-2
-9/3
-3
Therefore, your answer for slope would be m = -3
