The above statement describes the equation of a circle whose endpoints of a diameter are (-0,0) and (4,-6):
(x + 2)² + (y + 3)² = 3.6
How do we calculate the formula of a circle?The simple form equation of a circle is: (x – x1)² + (y – y1)²= r², where (x, y) are arbitrary coordinates upon that circumference of the circle, r seems to be the radius of the circle. and (x1, y1) are indeed the coordinates of the circle's center.
According to the given data:Given points are:
(-0,0) and (4,-6)
Find that diameter's length using the locations of the locations as well as the distance formula.
d = √((x₂ - x₁)² + (y₂ - y₁)²)
= √((4 - (-0))² + (-6 - 0)²)
= √((4 )² + (-6 )²)
= √(16 + 36)
= √(52)
= 7.2
Radius will be r/2
7.2/2
= 3.6
To obtain the coordinates of the center, use the interest in obtaining and the midpoint formula.
[tex]C=\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}[/tex]
C = (-0 + 4)/2 , (-6 + 0)/2
C = -2 , -3
To write this circle equation, use the radius and the center coordinates.
(x - h)² + (y - h)² = r²
(x - (-2))² + (y - (-3))² = 3.6
(x + 2)² + (y + 3)² = 3.6
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Find the dimensions of a rectangle if the perimeter is 318 inches and the
length is half the width plus nine inches.
The dimensions of the rectangle are 59 by 50 inches
How to fnd the dimensions of a rectangle?The given parameters are
Length (l) = 1/2 width (w) + 9
Perimeter (P) = 318
Perimeter is calculated as
P = 2 (l + w)
Substitute l = 1/2w + 9 in P = 2(l + w)
So, we have
2 * (1/2w + w + 9) = 318
Evaluate the like terms
2 * (1.5w + 9) = 318
Divide by 2
1.5w + 9 = 159
So, we have
1.5w = 150
Divide by 15
w = 100
Substitute w = 100 in l = 1/2w + 9
l = 1/2 * 100 + 9
Evaluate
l = 59
Hence. the dimensions of the rectangle are 59 by 50 inches
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Need help right now again
Answer:
I gotchu! The answer is 80.
Step-by-step explanation:
To find the mean, you need to add up all the scores and divide it by how many scores there are. In this case, there are 5 scores, so we can first add them all up.
70+75+80+85+90=400
Now, since there are 5 scores, you need to divide 400 by 5.
400/5=80
The mean would be 80.
Hope that helped!
Have a great day!
:D
Show your work given the rule of (x,y)—->(x-7.5,y+6.8)
Original coordinate (5,3)
The translation of the point, (5, 3) according to the rule, (x, y) → (x - 7.5, y + 6.8), gives the point, (-2.5, 9.8)
What is a translation transformation?A translation transformation is one in which the image of a pre–image is located at a position according to a rule. such that the difference between the image and the pre-image is a change in location.
Given parameters;
The coordinates of the given point = (5, 3)
The rule for the given transformation = (x, y) → (x - 7.5, y + 6.8)
The original coordinates of the point = (5, 3)
The coordinates of the image following the transformation is therefore;
[tex](5, 3) \: \underrightarrow{ T } \: (5 - 7.5,\: 3 + 6.8) [/tex]
Where;
[tex]T = T_{ (- 7.5,\: 6.8)}[/tex]
(5 - 7.5, 3 + 6.8) = (-2.5, 9.8)
Which gives;
[tex](5, 3) \: \underrightarrow{ T_{( - 7.5,\: 6.8)} } \: ( - 2.5,\: 9.8) [/tex]
The transformation of the point (5, 3) according to the rule (x, y) → (x - 7.5, y + 6.8), gives (-2.5, 9.8)
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The mass of a textbook is approximately 0.00165 metric ton. How is this number written in scientific notation?
Answer: 1.65 × 10⁻³
Step-by-step explanation: hope this helps!!!
please help me !! :)
i absolutely suck at this & have yo submit this assignment in 10 minutes
Answer: a=123
b=230
Step-by-step explanation:
3(-4x-2)=-6
X=???????
I need help with this :)
Answer:
-2 1/4Correct placement.Absolute values:
Absolute values are specific values in math interpreted by vertical bars and a plus/minus symbol to represent addition, subtraction, or if they are negative / positive. Mostly, if the absolute value is positive, you can write the vertical bars to represent its absolute value. No need for a plus symbol. However, negative numbers are often different.
Exempli gratia(e.g): |2|, |-2|, |+2|
which term best describes the number of solutions that will maximize the function below given the constraints listed? (assume that and .) 3x 2y a. one optimal solution c. unbounded b. alternate optimal solutions d. infeasible please select the best answer from the choices provided a b c d
The best term that describes the number of solutions that will maximize the function is one optimal solution (a).
Number of Solutions in linear equations:
There are 3 possible types of solutions to the set of linear equations. They are:
Unique Solution - linear equation represents that there exists only one point, which on substitution, L.H.S becomes equal to R.H.S. In the case of simultaneous linear equations in two variables, the solution should be an ordered pair (x, y).
No Solution - linear equations are parallel, then the system of linear equations has no solution.
Infinitely Many Solutions - graph for the system of linear equations with infinitely many solutions is a graph of straight lines that overlaps each other.
Given,
Here we need to find the number of solutions that will maximize the function below given the constraints listed.
the constraints are 3x and 2y.
We know that, linear equations in two variables, the solution should be an ordered pair (x, y).
So, here we have exactly only one solution that is a unique solution.
Then the option (a) one optimal solution is correct
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Point L is the midpoint of JK . JK intersects MK at K . If MK ≅ JL , prove that LK ≅ MK
You can see that JL = LK and MK ≅ JL, hence according to the transitive property, we can conclude that LK ≅ MK
Midpoint of coordinateA midpoint is a point that divides a line of a segment into two equal parts. It also means that the point bisects the given line.
If the point L is the midpoint of JK, then;
JL + LK = JK and;
JL = LK .........1
Similarly, K intersects MK at K, then;
MK ≅ JL..........2
From equation 1 and 2, you can see that JL = LK and MK ≅ JL, hence according to the transitive property, we can conclude that LK ≅ MK
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every student in a homeroom class takes a biology course or a spanish course or both. if 18 take biology, 13 take spanish and 5 take both, how many students are in the homeroom classroom?
=====================================================
Work Shown:
A = 18 take bio
B = 13 take Spanish
C = 5 take both
A+B-C = 18+13 - 5 = 26 students total
------------------------------
Another approach:
18 take bio and 5 take both, so 18-5 = 13 take bio only
13 take Spanish and 5 take both, so 13-5 = 8 take Spanish only
We then have 13+8+5 = 26 students
Both methods only work when each student is in either bio, Spanish, or both. We cannot have a student who is in neither class.
A quantity increases from 225 to 250. what is the percentage increase? round your answer to the nearest tenth of a percent.
The percentage increase for given quantity is 11.1%
In this question,
A quantity increases from 225 to 250.
So, the absolute change in the quantity would be,
|225 - 250| = 25
The relative increase of the quantity would be,
R = [tex]\frac{|225 - 250|}{225}[/tex]
R = 25 / 225
R = 0.111
We know that, the percentage increase of the quantity is the relative increase multiplied by 100.
So, the percentage increase of given quantity would be,
P = 0.111 × 100
P = 11.1%
Therefore, the percentage increase for given quantity is 11.1%
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The average of a list of 4 numbers is 88.0. A new list of 4 numbers has the same first three numbers as the original list, but the fourth number in the original list is 82, and the fourth number in the new list is 96. What is the average of this new list of numbers?
A. 90
B. 91.5
C. 92
D. 92.5
E. 93.5
Answer:
C. 92
Step-by-step explanation:
88 + 96 = 184
184/2 = 92
Hope this helps :)
A circular table top has a radius of 90 cm. A force of 810 N is applied to the whole table top. Calculate the pressure in N/m2 to 4sf.
The pressure of the circular table top has a radius of 90 cm. A force of 810 N is applied to the whole table top = 287.23 N/m².
The force defined as:A force seems to be an influence that could also cause an object's motion to change. A force can cause a mass item's velocity or acceleration to alter. The force can be expressed intuitively as a push or perhaps a pull. Because it has both magnitude and direction a force is a vector quantity.
What exactly do you mean by pressure?The force applied against the surface of an item per unit area across which that force is spread is referred to as pressure (symbol: p or P).
According to the given data:Force = 810N
Radius of the circular table = 90cm.
Pressures = force /area
Finding the area of circular table = πr²
= π x 90 x 10⁻² (1 cm = 10⁻²)
= 2.82 m²
substituting the value in the formula.
Pressures = force /area
= 810/2.82
= 287.23 N/m²
The pressure of the circular table top has a radius of 90 cm. A force of 810 N is applied to the whole table top = 287.23 N/m²
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Simplify 1 3/4 and 2 1/2
Answer: 1 3/4=7/4
2 1/2=5/2
Step-by-step explanation:
1 3/4=
1 + 3/4=
4/4 + 3/4=
(4+3)/4=7/4
2 1/2=
2+1/2=
4/2+1/2=5/2
A line passes through the point (-1,-2) and has a slope of
-5.
Write an equation in slope intercept form for this line.
Answer:
y = - 5x - 7
Step-by-step explanation:
A line has a function:
y = ax + b
Because the line has a slope of - 5
=> a = - 5
=> y = - 5x + b
Because the line goes through point (- 1; - 2)
=> - 2 = (- 5).(- 1) + b
=> 5 + b = - 2
=> b = - 7
=> The slope intercept from of the line:
y = - 5x - 7
PLEASE HELP ASAP!! will mark brainlest
Answer: read first :)
Step-by-step explanation:
the first equation, x= -4 + 3y/5
y= 20/3 + 5x/3
the second equation, x= 4 - 2y/3
y= 6 - 3x/2
What is 6•w•w•z•z in exponent
6w^2z^2
I hope this helps!
What is the formula for the sum of two whole numbers is 72. The difference is 48 what are the two numbers
Answer:
It works in both equations, so the two numbers are 60 and 12.
Step-by-step explanation:
Is it possible to draw a triangle with angles 150˚, 20˚ and 20˚ and explain answer
Answer: False; the sum of the angles is not equal to 180
Answer:
No
Step-by-step explanation:
The sum of angles in a trigngle has tp be 180.
150+20+20 is 190, there fore you cant
Need the answer as soon as possible.
Bianca spent 1/2 of an hour playing on her phone . that used up 1/3 of her battery how long would she have to play on her phone to use the entire battery
Bianca should play with her phone for 1.5 hours to use the entire battery.
What exactly are fractions?A fraction is a portion of a whole or, to put it another way, any number of equal parts.A fraction in everyday English refers to the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters.Bianca spent 1/2 of an hour playing on her phone which used up 1/3 of her phone's battery.
So, 1/3 × 3 = 3/3 = 1So, if she plays with her phone 3 times more she will use the entire battery of the phone.Then,
1/2 × 3 = 3/2 = 1.5 hoursTherefore, Bianca should play with her phone for 1.5 hours to use the entire battery.
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Nina has $40 in the bank. She writes a check for $63, deposits $80 and writes another check for $140. What is her balance?
Answer:
-$83
Step-by-step explanation:
Create an equation to model Nina's balance.
[tex]40-63+80-140=-83[/tex]
x^2+3 divided by x-2
Answer:
x2 + 3x − 2
Explination: trust pls
Explain how to graph the function using transformations seen in the function. f(x)=3(x+7)^3 - 9
Answer:
Step-by-step explanation:
f(x)=3(x+7)³-9
1. Let's graph the function у=3х³
2. Shift the graph of the function to the left by 7 units along the х-axis
3. Slide the graph of the function down 9 units along the y-axis
please I want a beautiful and nice sentences in12 words:bedrock,robust,isolation,eliminate,ritual, endure, diagnose, outlive, relieve,ailment, relentless and mortality.and thanks
Answer:
Step-by-step explanation:
Pls pls help whoever gets it right gets a crown
Answer its the first one
Step-by-step explanation:
an isosceles trapezoid has legs of length 30 cm each, two diagonals of length 40 cm each and the longer base is 50 cm. what is the trapezoid’s area?
768 cm'^2 is the trapezoid’s area.
What is isosceles trapezoid?
Isosceles trapezoids have equal length non-parallel sides, hence the name "isosceles" which means "equal legs". The "legs" are another name for these equal sides.
Let 50 cm = the bottom base
We can find the area of one of the triangles that comprise the area of the trapezoid.....its sides are 30, 40 and 50 cm
Let s be the semi-perimeter of one of the triangle = [ 50 + 40 + 30 ] / 2 = 60 cm
And the area of of this triangle = sqrt [ s ( s - a) (s - b) ( s -c) ] where a,b, c are the sides
So...we have sqrt [ 60 ( 60 - 30) (60 - 40) (60 - 50) ] = sqrt [ 60 * 30 * 20 * 10 ] =
sqrt [ 1800 * 200] = sqrt [ 3600 * 100] = 60 * 10 = 600 cm ^2
Now the base of this triangle = 50 and the height can be found as
follows :
Area = (1/2) 50 * height
600 = 25 * height
height = 24 cm and this is the height of the trapezoid
Now....the top base can be found as 50 - 2 sqrt [ 30^2 - 24^2 ] = 14 cm
So....the area of the trapezoid = (1/2) height ( sum of the bases) = (1/2) (24) ( 50 + 14) = 12 ( 64) = 768 cm'^2
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two and half of a number added to three quarters of the same number gives you 13.find the number.
Answer:
52/21
Step-by-step explanation:
Translate the word equation into an algebraic equation as follows:
Let the number be X
two-and-a-half of a number --> (2 1/2) X
2 1/2 = (2 x 2 + 1) = 5/2
So two-and-a-half of a number --> (9/2)X = 9X/2
three-quarters of the same number --> (3/4)X --> 3X/4
two and half of a number added to three quarters of the same number becomes 9X/2 + 3X/4
gives you 13 --> = 13
So we get the equation:
9X/2 + 3X/4 = 13
Multiply both sides by 4 to get rid of the denominators
4.(9X/2) + 4(3X/4) = 4 x 13 = 52
36X/2 + 12X/4 = 52
==> 18X + 3X = 52
==> 21X = 52
==> X = 52/21
BOOKWORK Code: L82
allowed
Using Pythagoras' theorem, calculate the length of the hypotenuse in this right-
angled triangle.
Give your answer in centimetres (cm) to 1 d.p.
8 cm
3.9 cm
Not drawn accurately
The length of the hypotenuse in this right-angled triangle = 6.98 cm².
What exactly is the Pythagorean Theorem?The Pythagorean theorem states that the total of the squares on the legs of a right triangle equals the square upon that hypotenuse (the side opposite the right angle)—or, in popular algebraic notation, a2 + b2 = c2.
What is the triangle's formula?The basic formula for calculating the area of a triangle is the half square product of its base as well as height, i.e., A = 1/2 b h. This formula applies to all triangles, whether they are scalene triangles, isosceles triangles, or equilateral triangles.
According to the information:Hypotenuse (c) = 8 cm
Base (b) = 3.9 cm
Length =
C² = (a² + b³)
a² = C² - b²
a = √((8)² - (3.9)²)
= 6.98 cm²
The length of the hypotenuse in this right-angled triangle = 6.98 cm².
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what is 9 4/9 dividedby 5/9
Answer:
17
Step-by-step explanation:
Answer:
17
Step-by-step explanation:
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