The standard equation of a circle is expressed as:
[tex]x^2+y^2+2gx+2fy+C=0[/tex]
Centre is (-g, -f)radius = √g²+f²-CGiven a circle whose equation is [tex]x^2 + y^2 - 2x - 8 = 0.[/tex]
Get the centre of the circle
2gx = -2x
2g = -2
g = -1
Similarly, 2fy = 0
f = 0
Centre = (-(-1), 0) = (1, 0)
This shows that the center of the circle lies on the x-axis
r = radius = √g²+f²-C
radius = √1²+0²-(-8)
radius =√9 = 3 units
The radius of the circle is 3 units.
For the circle x² + y² = 9, the radius is expressed as:
r² = 9
r = 3 units
Hence the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Learn more on circles here: https://brainly.com/question/23226948
Answer:
a, b and e
Step-by-step explanation:
i got it correct on edge
Jerry wants to buy his grandpa’s old car for $500.00. He works 10 hours a week at $7.50 an hour. How many weeks will he need to work before he earns enough money to buy the car?
Answer:
she needs to save up for 3 months
Step-by-step explanation:
Translate into an algebraic expression:40 increased by x%
Answer:
2/5x
Step-by-step explanation:
x% of 40= x/100×40
= 40/100x = 2/5x
HELP PLEASEEEEEEEEEE
Answer:
x = -1/4(y +3)2 - 2.
Step-by-step explanation:
Here are the steps:
Find if parabola is horizontal or vertical
Find vertex and substitute into equation of step 1
Use another point to find a in the equation.
--------------------------------------------------------------------------------
Parabola is obviously vertical.
that means we use x = a(y - k)2 + h
Our vertex is (-2,-3), and it's also (h, k)
so, our current equation is x = a(y - -3)2 - 2 and if we simplify it,
we get x = a(y +3)2 - 2.
It's not over yet, cuz we still need a.
so, we substitute in a point (x, y). We can use (-4, 1).
We plug in and get -4 = a(1 +3)2 - 2.
We solve like a one variable linear equation and get a = -1/4
Thus our equation is x = -1/4(y +3)2 - 2.
HELP ASAP!!!!!!
A given line has the equation 10x+2y=-2.
What is the equation, in slope-intercept form, of the line that is parallel to the givereline and passes through the
12)
5x+12
5*
1250x-0)
Answer:
y = -5x + 12
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Step 1: Write given line in slope-intercept form
2y = -2 - 10x
y = -1 - 5x
A parallel line has the same slope but different y-intercept. Therefore, our answer is the 1st Option.
Answer:
A. y = -5x + 12.
Step-by-step explanation:
10x + 2y = -2
2y = -10x - 2
y = -5x - 1
If there is a line parallel to the one listed above, the slope of the second line will be the same as the first.
That means that the line would have a slope of -5.
Since the question asks us to leave the answer in slope-intercept form, we will find an answer that has a slope of -5 in the form of y = mx + b.
Hope this helps!
What is the line of best fit? Why do we want the sum of the residuals to be as close to zero as possible?
Answer:
Step-by-step explanation:
What sis line of best fit?
The line of best fit may be explained as a straight line which is drawn to pass through a set of plotted data point which gives the best and most approximate relationship between the data points. A line of best fit is required to give the best approximate value between the set of plotted data points such that it allows making inference on new data points while also ensuring the least possible deviation from the original data points.
Why do we want the sum of the residuals to be as close to zero as possible?
The line of best fit will be the line which gives the least value of residual error. The residual error is reffered to as the difference between the line drawn and the individual data point plotted. These errors are squared and summed together, the line which produces the least residual error is Considered as the leading ne of best fit for the data.
We want the sum of our residual error to be as close to zero as possible, this is to reduce the deviation between our original or plotted data and the modeled data produced by our line of best fit.
Answer:
Step-by-step explanation:
We wan the residuals to be closest to zero because they will help use later in the equation.
What is the solution to this equation?
8 - 2x + 6x = 24
A. X= 4
B. x = 8
C. x= -4
D. x = -8
Answer:
A
Step-by-step explanation:
Given
8 - 2x + 6x = 24 , that is
8 + 4x = 24 ( subtract 8 from both sides )
4x = 16 ( divide both sides by 4 )
x = 4 → A
factorising can someone plz helpw itht the last one than you
Answer:
3x^2(3+x)
Step-by-step explanation:
Answer: 3x^2(3+1)
Because it is divisible by 3 and x^2
Work out the area of this circle.
Take it to be 3.142 and give your answer to 1 decimal place.
4 cm
→Answer:
[tex]50.3cm^2[/tex]
→Step-by-step explanation:
Well the formula for the area of a circle is [tex]\pi r^2[/tex].
→Given information
Pi is 3.142
radius is 4 cm
answer must be rounded to the nearest tenth
____________________________________________________________
So now we have to plug in the given information into the following formula [tex]\pi r^2[/tex].
(3.142)(4)^2
So now we have to solve this formula using PEMDAS.
So 4 squared is 16 and 16*3.142 is 50.272cm^2.
The question clearly states the given answer must be rounded into the nearest tenth so 50.272 is 50.3 cm^2.
__________________I do hope this helps!__________________________
help plzzzSolution set of 25x2 – 1 = 0 is ____________.
Answer:
x = 1/5 , and x = - 1/5
Step-by-step explanation:
25x² – 1 = 0
5²x² - 1² = 0
(5x - 1)(5x + 1) = 0
5x -1 = 0, 5x + 1 = 0
x = 1/5 , x = - 1/5
Question 26: write the equation that describes the line with slope=5 and y-intercept =8 in slope intercept form.example: y=mx+b
Answer:
y = 5x + 8
Step-by-step explanation:
Start with y = mx + b: general slope-intercept form, equation of a line:
Replace m with 5, y with 8 and x with 0 (since the y-intercept is (0, 8):
8 = 5(0) + b. Then b must be 8, and the desired equation is
y = 5x + 8
Lapid.
(ii) Find the remainder when f(x) is
divided by (x - 1)(x + 2).
14) The remainder when the expression
ax' + bx + 2x + c is divided by x-1
is twice of that when it is divided by
x + 1. Show that c = 3a - b + 6.
ii) When a polynomial f(x) is divided by (x-1) and (x+2) it leaves remainder 5 and 17 respectively. find the remainder when f(x) is divided by (x-1) (x+2)
14) The remainder when the expression ax³ + bx² + 2x + c is divided by x-1
is twice of that when it is divided by x + 1. Show that c = 3a - b + 6.
Answer:
ii) R(x) = -4x + 9
14) c = 3a - b + 6 ( Proved)
Step-by-step explanation:
14) The correct expression is [tex]ax^3 + bx^2 + 2x + c[/tex]
To get the remainder when the expression [tex]ax^3 + bx^2 + 2x + c[/tex] is divided by
x - 1, let x - 1 = 0; x = 1
Remainder:
[tex]R_1(x) = a(1)^3 + b(1)^2 + 2(1) + c\\R_1(x) = a + b + 2 + c[/tex]
When [tex]ax^3 + bx^2 + 2x + c[/tex] is divided by x + 1
Let x + 1 = 0; x = -1
Remainder:
[tex]R_2(x) = a(-1)^3 + b(-1)^2 + 2(-1) + c\\R_1(x) = -a + b - 2 + c[/tex]
According to the question, R₁(x) = 2R₂(x)
a + b + 2 + c = 2(-a + b - 2 + c)
a + 2a +b - 2b + 2 + 4 = 2c - c
c = 3a - b + 6 ( Proved)
ii)
The dividend is f(x)
(x - 1)(x + 2) is the divisor, i.e. D(x) = (x - 1)(x + 2)
Let the quotient = A(x)
Let the Remainder, R(x) = ax + b..............(1)
Therefore, f(x) = A(x)D(x) + R(x)
f(x) = A(x)(x - 1)(x + 2) + R(x)...................(2)
When f(x) is divided by x - 1, x = 1
Put x = 1 into equation (2) knowing that R(1) = 5
f(1) = R(1) = 5
R(1) = a(1) + b = 5
a + b = 5....................(3)
When f(x) is divided by x + 2, x = -2
Put x = -2 into equation (2) knowing that R(-2) = 17
f(-2) = R(-2) = 17
R(-2) = a(-2) + b = 17
-2a + b = 17..................(4)
Subtracting equation (1) from (2)
-3a = 12
a = -12/3
a = -4
Substitute the value of "a" into equation (4)
-2(-4) + b = 17
8 + b = 17
b = 9
Since R(x) = ax + b
R(x) = -4x + 9
Here are the ingredients needed to make 8 pancakes. 250 ml milk 1 egg 140g flour 5g butter Craig makes 20 pancakes. Work out how much flour he needs.
Answer: 56g flour
Step-by-step explanation: 140/20 = 7g
7 x 8 = 56g
solve the problem -5/3*(-1/8)
Answer:
0.20833333333 or 5/24
Step-by-step explanation:
Hope this helps UwU <33
Answer:
-5/24
Step-by-step explanation:
-5/3×(-1/8)
= -5/24
In the figure below, XZ =DF and _X = D.
JA
X
F
Which additional information would be enough to prove
that AXYZ ADEF?
1.XY =YZ
2.YZ = ED
3.YZ DE
4:XY = DE
Answer:
Option (4)
Step-by-step explanation:
Given : XZ ≅ DF and ∠X ≅ ∠D
To prove : ΔXYZ ≅ ΔDEF
Statements Reasons
1). XZ ≅ DF 1). Given
2). ∠X ≅ ∠ D 2). Given
3). XY ≅ DE 3). Required information
4). ΔXYZ ≅ ΔDEF 4). By SAS property of congruence
Therefore, Option (4) will be the answer.
V-100 = ? + ?i NEED HELP
Answer: V+100
Step-by-step explanation: If your trying to get 0 then there is your answer
Answer:
V-100 = 0 + 10i
so 0 and 10
Step-by-step explanation:
The correlation coefficient between two quantitative variables is approximately 0.02. What does the value of this correlation coefficient indicate about how well the model fits the data?
Answer:
The correlation coefficient "tell us" that the model in question does not fit the data well (the correlation coefficient is near zero), in whose case we need to find another that can do it.
Step-by-step explanation:
Roughly speaking, the correlation coefficient "tell us" if two variables could present the following behavior:
As one variable increases, the other variable increases too. In this case, the correlation coefficient is high and positively correlated. As the correlation coefficient is near 1, the correlation between two quantitative variables is almost perfect.As one variable decreases, the other variable decreases too. In this case, the correlation coefficient is also high, but negatively correlated. As the correlation coefficient is near -1, this correlation is almost perfect for this case.There could be no correlation at all. In this case, the correlation coefficient is near a zero value.As we can follow from the question, a correlation coefficient of 0.02 is near to zero. In this case, the correlation coefficient is "telling us" that the two variables do not follow the cases 1 and 2 above described. Instead, it follows the case 3.
Therefore, the model in question does not fit the data well, in whose case we need to find another that can do it. For example, if the model is linear, we need to test an exponential model.
It is important to remember that the correlation coefficient does not tell us anything about that one variable causes the other variable, only behaviors as described above.
I need help fasttt please
Answer:
x≥5
Step-by-step explanation:
The function f(x)=2*sqrt(x-5) is transformed from the parent function f(x)=sqrt(x) by:
vertically stretched by a factor of 2
right 5 units
a parent rational equation has a domain of [0,+∞)
this certain equation is moved 5 units to the right, so the domain is:
[0+5,+∞)⇒[5,+∞)
So the domain of f(x)=2*sqrt(x-5) is [5,+∞)
which as an inequality is x≥5
What's the difference?
Answer:
first one is the right one
Step-by-step explanation:
A equação quadrática é escrita na forma a.X² + b.X + c = 0. Na equação quadrática seguinte 9.X² - 2.X + 6 = 0 , a soma dos valores dos coeficientes (a + b + c) vale:
Answer:
a+b+c =13
Step-by-step explanation:
[tex]\left\begin{array}{ccccccc}aX^2&+&bX&+&c&=&0\\ \downarrow&&\downarrow&&\downarrow&&\downarrow\\9.X^2&-&2.X &+& 6 &=& 0\end{array}\right \implies \left\{\begin{array}{ccccccc}a=9\\b=-2\\c=6\end{array}\right[/tex]
[tex]\implies a+b+c = 9+(-2)+6\\=9-2+6\\=7+6\\=13\\\\\therefore a+b+c =13[/tex]
12: PLEASE HELP Evaluate the expression a*b where a=6 and b=15
Answer:
90
Step-by-step explanation:
You're equation is a * b, and that is equal to 6 * 15.
so, it is 90.
pls i want helpon this sum
Answer:
x+3
Step-by-step explanation:
notice how each time you add three
-1+3 = 22+3= 55+3= 8how did I khew that we add 3?
simply by substracting a term from the next one
so 8-5= 3
A polynomial of the 5th degree with a leading coefficient of 7 and a constant term of 6 choose 1 answer: . 7x^5+2x^2+6 .6x^7-x^4+5 .6x^5+x^4+7 .7x^6-6x^4+5
Answer:
7x^5+2x^2+6
Step-by-step explanation:
7x^5+2x^2+6
6x^7-x^4+5
6x^5+x^4+7
7x^6-6x^4+5
5th degree polynomial means the the term with highest degree has degree 5.
7x^5+2x^2+6
6x^7-x^4+5
6x^5+x^4+7
7x^6-6x^4+5
Leading coefficient is the coefficient of the term with highest degree.
Constant is the number with no variable.
7x^5+2x^2+6
Help!!!!! please!!!!!
Answer:
108cm[tex]^{3}[/tex] (B)
Step-by-step explanation:
Find the area of the triangle first.
6 * 4 = 24/2 = 12
Multiply by the width.
12 * 9 = 108
Hey there! :)
Answer:
B. V = 108 cm³.
Step-by-step explanation:
Find the volume of the triangular prism using the formula:
V = 1/2(bh) where b = l × w
Solve for the base:
b = 4 × 9
b = 36 cm²
Plug this into the formula for the volume:
V = 1/2(36 · 6)
V = 1/2(216)
V = 108 cm³. The correct answer is B.
What is the value of x in the equation 2x + 12x + 2(1+x) = 29?
Answer:
The value of x is as follows:
Exact form: x = 27/16
Decimal form: x = 1.6875
Mixed number form: x = 1 & 11/16
Answer:
x=27/16 or x= 1.6875
Step-by-step explanation:
2x + 12x + 2 + 2x =29
16x + 2 =29
16x =29 - 2
16x= 27
x = 27/16 or 1.6875
Which best describes the range of a function?
The range of a function may refer to either of two closely related concepts: The codomain of the function The image of the function
MARK BRAINLIEST PLEASE DEAR...THANKS I LOVE U
Suppose that g(x)=f(x)+5 2which statement best compares the graph of g(x) with the graph of f(x)
A.the graph of g(x) is the graph of f(x) shifted 5 unites up.
B.the graph of g(x) is the graph of f(x) shifted 5 units to the right.
C.The graph of g(x) is the graph of f(x) shifted 5 units down.
D.the graph of g(x) is the graph of f(x) shifted 5 units to the left.
Answer:
A
Step-by-step explanation:
Given f(x) then f(x) + c represents a vertical translation of f(x)
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Given
g(x) = f(x) + 5
Thus the graph of g(x) is the graph of f(x) shifted 5 units up → A
Using this distribution, find the probability
that a teenager has 4 or more pairs of shoes
in their closet.
Answer:
P = 0.3
Step-by-step explanation:
Here, we are to use the probability distribution in the table to calculate the probability that a children has 4 or more shoes in his or her closet
When we say 4 or more, what we mean by this is that the teenager has 4 shoes or 5 shoes
In probability expressions, when we use the term ‘or’ we are simply talking about adding the terms involved
So what we can do here is to add the probability that the teenager has 4 shoes to the probability that the teenager has five shoes
From the table that would be; 0.1 + 0.2 = 0.3
TEA TIME!!! During a catered lunch, an average of 4 cups of tea are poured per minute. The lunch will last 2 hours. How many gallons of tea should the caterer bring if there are 16 cups in one gallon?
Answer: 30 gallons
Step-by-step explanation:
First translate 2 hours into 120 minutes. Then multiply 120 * 4 = 480. Then divide 480/16 = 30
Which of the following ordered pairs is a solution of the given system of
linear equations?
(4x + 8y = 8
x + 3y = 13
Answer:
x=-14 and y = 9
Step-by-step explanation:
hello
4x + 8y = 8 <=> divide by 4 both parts
(1) x + 2y = 4
(2) x + 3y = 13
(2) - (1) gives
x + 3y -x - 2y = 13 - 4 = 9
<=> y = 9
we replace in (1) x + 2*9 = 4
<=> x = 4 - 18 = -14
so x = -14
hope this helps
please read the question and help me out