We can rewrite the circle equation as:
(x - 2)^2 + (y +4)^2 = 3^2
Then the correct option is the first one, the radius is 3 units and the center is (2, -4)
How to find the center and radius of the circle?
The equation for a circle of radius R and center (a, b) is written as:
(x - a)^2 + (y - b)^2 = R^2
Here the equation is:
x^2 + y^2 - 4x + 8y + 11 = 0
We need to complete squares, we can rewrite:
(x^2 - 4x) + (y^2 + 8y) + 11 = 0
(x^2 - 2*2x) + (y^2 + 2*4y) +11 = 0
Now we can add and subtract 2^2 and 4^2 in each parenthesis, so we get:
(x^2 - 2*2x + 2^2) - 2^2 + (y^2 + 2*4y + 4^2) - 4^2 + 11 = 0
(x - 2)^2 + (y + 4)^2 - 4 - 16 + 11 = 0
(x - 2)^2 + (y + 4)^2 = 9 = 3^2
(x - 2)^2 + (y +4)^2 = 3^2
So, the radius of the circle is 3 units, and the center of the circle is the point (2, -4)
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What are rational roots Class 10?
The rational root theorem, as its name suggests, is used to find the rational solutions of a polynomial equation (or zeros or roots of a polynomial function). The solutions derived at the end of any polynomial equation are known as roots or zeros of polynomials. A polynomial doesn't need to have rational zeros.
Rational root theorem, also called rational root test, in algebra, theorem that for a polynomial equation in one variable with integer coefficients to have a solution (root) that is a rational number, the leading coefficient (the coefficient of the highest power) must be divisible by the denominator of the fraction and the constant term (the one without a variable) must be divisible by the numerator.
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Your new warehouse robot will make things a lot easier; however you still need your staff to do the delicate part. Hence they need to learn each other. First time your warehouse employee tried replenishing a single order with the robot, it took 275 seconds. Calculate how much it will take after 17 repetitions with a learning rate of
80%?
Number of repetitions: ???
The time it will take after 17 repetitions with the learning curve having a rate of 80% is of:
6.19 seconds.
What is the Learning Curve Formula?The learning curve formula is an exponential function defined as follows:
[tex]y = ab^x[/tex]
In which the parameters are listed as follows:
a is the time it takes to make the first object.b is the rate.Then y gives the time it takes to make the xth object.
In the context of this problem, the values of the parameters are given as follows:
a = 275, as it is the time that it takes the employee on the first time.b = 0.8, as it is stated in the problem that the learning rate is of 80%.Then the time needed for the 17th repetition is of:
y = 275 x (0.8)^17 = 6.19 seconds.
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How do you solve a proof question?
To solve a proof question, firstly you have to identify the question and visualize it and then try to connect the given conditions.
Mathematical proofs can be difficult, but can be conquered with the proper background knowledge of both mathematics and the format of a proof.
To solve a proof question you have to remember following steps:
Identify the question = You must first determine exactly what it is you are trying to prove. Identify the question. You must first determine exactly what it is you are trying to prove. Draw diagrams = When trying to understand the inner working of a math problem, sometimes the easiest way is to draw a diagram of what is happening. Use the information given in the problem to sketch a drawing of the proof. Label the knowns and unknowns.Study proofs of related theorems = Proofs are difficult to learn to write, but one excellent way to learn proofs is to study related theorems and how those were proveTo know more about proof here
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The monthly rents (in dollars) paid by 10 people are given below. (Note that these are already ordered from least to greatest.) 735, 935, 960, 995, 1005, 1050, 1065, 1075, 1100, 1120 Suppose that one of the people moves. His rent changes from $735 to $535. Answer the following.
The mean will decrease when the rent decrease.
The median will stay the same.
What is a mean?It's important to note that a mean simply means the average of a set of numbers that are given. The mean is the average of the given numbers and is calculated by dividing the total number of numbers by the sum of the given numbers. A data set's mean (average) is calculated by adding all of the numbers in the set and then dividing by the number of values in the set.
Mean = (sum of all observations divided by the total number of observations)
In this case, the rents are 735, 935, 960, 995, 1005, 1050, 1065, 1075, 1100, 1120 and one of the people moves, and his rent changes from $735 to $535.
In this case, changing 735 to 535 will make the average lower.
On the other hand, the median isn't affected as it's still 1057.50.
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Which of the following graphs represents the equation:
y=3/2 x+1
Answer:
It looks like it could be the first one
Step-by-step explanation:
How to solve problems like this:
KEY FORMULA: y=mx+b
The b respresents the Y-INTERSCEPT (The number that the line crosses on the y-axis. In this case, it is 1. In the first graph, the line is crossing the 1 on the y-side.)
Mx = Slope. In this case, it is 3/2.
How to graph this: First, plot (0, 1), because 1 is the y-interscept. Then, since the slope is a POSITIVE, after the 1, you go right two, then up three. Then you draw your line.
What double facts can help you solve 8 7?
The double facts of 8 + 7 = 15 is (7 + 7) + 1 and ( 8 + 8) -1.
Double facts:
A doubles fact is a number sentence that repeats the same addend, such as 3 + 3 = 6 or 8 + 8 = 16.
Here we have to find the double facts of the equation:
Equation:
8 + 7 = 15
When a number is added to itself the result is twice that number
Example:
2 + 2 = 2× 2 = 4
3 + 3 = 2× 3 = 6
5 + 5 = 2× 5 = 10
Similarly, we have to solve for 8 + 7 = 15
So 8 + 7 = 7 + 7 + 1
= ( 7 + 7) +1
In the same manner, we can also do that:
8 + 7 = 8 + 8 -1
= (8 + 8) -1
Therefore the double facts of the equation are ( 7+7)+1 and (8+8)-1.
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help!! i’ve been stuck on this problem!
Answer:
x less than or equal to -2
Step-by-step explanation:
I believe that's the answer
Answer:
x < -2
Step-by-step explanation:
You want the domain of a function graphed as a curve with an open circle at x=-2, which is the right end of the curve.
DomainThe domain is the horizontal extent of the graph. It is the set of values for which the relation is defined.
ApplicationThe open circle at (x, y) = (-2, 0) means that point is not part of the graph. All x-values to the left of that point have corresponding y-values, so the extent of the graph can be said to be ...
x < -2
The domain of the relation is x < -2.
What is the double of 8 in math?
Using doubles plus one fact the sum of 8 + 8 + 1is equal to 17 it is done by simply adding 1 to the given number.
Doubles plus one fact is used to add numbers which are next to each other.
Doubles plus one fact is simply done by doubling the number and adding one to it.
The sum of 8 + 8 can be determined by using doubles plus one fact as:
Simply add 1 in 8 + 8 + 1 to get the result required.
8 + 8 + 1 = 17
Therefore by using doubles plus one fact the sum of 8 + 8 + 1 is equal to 17.
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A line is parallel to the line y = -x + 5 and passes through the point (4. - 1). Which of the following is an equation of the
line?
Answer:
y = -x + 3; could also be y + 1 = -(x - 4) or y = -(x - 4) - 1 or x + y = 3
Step-by-step explanation:
No options given, so I hope this helps.
1. Identify any of the equations that have the same slope as your given equation (-1). If there's only one, stop here.
2. Find the y-intercept by replacing (x,y)=(4,-1) in the equation y = -x + b and solve for b: -1 = -(4) + b ==> 3 = b
3. Replace b in the equation y = -x + b with 3.
Find the domain of the function.
f(x)= 3 x−2
Answer:
All real numbers
Step-by-step explanation:
In, a city had a population of 310,000 people. Each year since 2007, the population has grown by 4.8%.
Let t be the number of years since. Let y be the city's population.
Write an exponential function showing the relationship between t and y.
The exponential function showing the relationship between t and y is y = 310000(1.048)⁺
How to determine the exponential function?From the question, we have the following parameters that can be used in our computation:
Initial population = 310000
Rate of growth = 4.8%
These parameters can be represeted as
a = 310000 and r = 4.8%
An exponential function is represented as
y = a(1 + r)⁺
Substitute the known values in the above equation, so, we have the following representation
y = 310000 (1 + 4.8%)⁺
Evaluate
y = 310000(1.048)⁺
Hence, the function is y = 310000(1.048)⁺
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The Science Club has 30 members and needs to elect officers. They will need a President, Vice President, Secretary, Treasurer, and Historian. How many ways can a 5-member committee be formed?
150
3,735
142,506
17,100,720
The ways to select the candidates from the total is (c) 142,506
How to determine the ways of selection?From the question, we have
Total number of members, n = 30
Numbers to selection, r = 5
The number of ways of selection could be drawn is calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 30 and r = 5
Substitute the known values in the above equation
Total = ³⁰C₅
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have
Total = 30!/25!5!
Evaluate
Total = 142,506
Hence, the number of ways is 142,506
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Answer: The answer is 17,100,720 different ways, or D.
Step-by-step explanation: I took the FLVS test. This situation is a permutation because order DOES matter. If got 142,506, you used the combination formula which is incorrect for this situation.
Solve for w.
2w²-2w+32 = (w-5)²
[tex]2w^2-2w+32=(w-5)(w-5)[/tex]
[tex]2w^2-2w+32=w^2-10w+25[/tex]
Subtract [tex]w^2[/tex] from each side:
[tex]w^2-2w+32=-10w+25[/tex]
Add [tex]10w[/tex] to each side:
[tex]w^2+8w+32=25[/tex]
Subtract 25 from each side:
[tex]w^2+8w+7=0[/tex]
Factor:
[tex](w+1)(w+7)[/tex] =0
Both solutions work, so w=-1 and w=-7what is the rate of change/slope
Answer:
1/2
Step-by-step explanation:
Slope is rise over run. If we look at the points (0,0) and (2,1) and plug it into the slope formula...
m = y2 - y1 / x2 - x1
m = 1-0 / 2-0
m = 1/2
we see that the slope is 1/2.
Answer:
1/2
Step-by-step explanation:
The ROC=1/2 because of the rise over run.
Sorry about the bad handwriting. It's hard to write with a mouse.
PLEASE MARK BRAINLIESTAssume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.
P(X=15), n=17, p=0.6
0.01023 is the probability of obtaining a success
How to find the probability of obtaining a success?
Since we are dealing with a binomial probability distribution. We are going to use the binomial distribution formula for determining the probability of x successes:
P(X = r) = nCr . p^r . q^n-r
Given: number of trial (n) = 17, probability of success (p) = 0.6, X=15
probability of failure (q) = 1 - 0.6 = 0.4
P(X = 15) = 17C15 × 0.6¹⁵ × 0.4¹⁷⁻¹⁵
P(X = 15) = 17C15 × 0.6¹⁵ × 0.4²
P(X = 15) = 136 × 0.6¹⁵ × 0.16
P(X = 15) = 0.01023
Therefore, the probability of obtaining a success is 0.01023
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−8×(−10+(−7))
Evaluate the following expression.
Answer:
136
Step-by-step explanation:
solve the inside of the parentheses and you get -17, then multiply by -8
Are the triangles congruent Why or why not triangle congruence ASA and AAS?
ΔABC and ΔRQM are congruent triangles. They are congruent by either ASA or AAS.
Two triangles are said to be congruent if their all corresponding sides are equal and all corresponding angles are equal in measure.
For the given question,
We know that the sum of all angles of a triangle is 180°.
For ΔABC,
∠A + ∠B + ∠C = 180°
42° + 53° + ∠C = 180°
95° + ∠C = 180
∠C = 85°
For ΔABC and ΔRQM,
∠A = ∠R
∠C = ∠Q
AB = RM
So, by the AAS postulate, ΔABC and ΔRQM are congruent triangles.
For ΔRQM,
∠R + ∠Q + ∠M = 180°
42° + 85° + ∠M = 180°
∠M = 53°
For ΔABC and ΔRQM,
∠A = ∠R
∠B = ∠M
AB = RM
So, by the ASA postulate, ΔABC and ΔRQM are congruent triangles.
Therefore, ΔABC and ΔRQM are congruent triangles. They are congruent by either ASA or AAS.
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The complete question is -
Are the triangles congruent Why or why not triangle congruence ASA and AAS?
Please help! Need this by tonight thanks! Question 7 Click on picture
Answer:
Oh god, I don't really know much about this, but I am going to assume that the 25 represents the mn so maybe you have to put 25mn + 6600 on the first box?
Step-by-step explanation:
I just looked up how to do this. I think the form has to be a C=mn+b format. For the third box, I think you need to solve 54100=25mn+6600. On the second box I think you just need to solve C(3600)=25(3600)+6600. idrk
Please help asap!!!!!!
2. Claire is painting some windows that are all the same size. She used gallon of paint to paint 2 windows. How many gallons of paint are needed to paint 1 window?
Answer:3
Step-by-step explanation:
since 7 is a number and b is to u should just put 3 windows cause u need to add them all up i think, not sure but just do that, why not,
the diagram shows squares 1 2 and 3
(Area of 1) + (Area of 2) = (Area of 3) this statement about the squares must be true.
What is Right angle traingle?
A right-angled triangle is a particular kind of triangle in which one of the angles is 90 degrees. The combined angles of the other two are 90 degrees. The triangle's base and perpendicular sides both include the right angle. The longest of the three sides, known as the hypotenuse, is the third side.
we know that;
By applying the Pythagorean Theorem;
[tex]c^2 = a^2 + b^2[/tex] .............................(1)
Area of the square says A1;
A1 = a^2 unit^2 ...............................(2)
Area of the square says A2;
A2 = b^2 unit^2 .................................(3)
Area of the square says A1;
A3 = c^2 unit^2 ..................................(4)
Replace the A1, A2, and A3 values in the equation 1 ;
A3 = A1 + A2
therefore;
(Area of 1) + (Area of 2) = (Area of 3).
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Does 15 20 25 form a right triangle?
Any triple would still represent the sides of a right triangle if we multiplied it by a constant. Therefore, the sides of a right triangle would be represented by 6, 8, 10, 15, 20, and 25, among countless other numbers.
What is right triangle?
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and other angles of the right triangle.
Input the Pythagorean Theorem with the given numbers:
c^2 = a^2 + b^2
25^2 = 15^2 + 20^2
625 = 225 + 400
625 = 625
Yes, the numbers 15, 20 and 25 form a right triangle and the Pythagorean triple.
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5x-1=3x+5 an equation
Answer:
[tex]x = 3[/tex]
Step-by-step explanation:
[tex]5x-1=3x+5[/tex]
Get the x's on one side.
Add 1:
[tex]5x-1=3x+5\\\box \ \ +1) \ \ (\ \ \ \ +1)[/tex]
[tex]5x=3x+6[/tex]
Subtract 3x from both sides.
[tex]\ \ \ 5x=\ \: 3x+6\\\underline{-3x} \ \ \ \ \underline{-3x}\\[/tex]
[tex]2x = 6[/tex]
Finally, divide both sides by 2.
[tex]2x / 2 = 6/2[/tex]
[tex]x = 3[/tex]
Please help will mark Brainly
Answer: Horizontal Translation
Step-by-step explanation:
Newton and Descartes
each buy identical pastillas. Newton
cuts his into twelfths and eats 8 slices.
Descartes cuts his into sixths, eats
some, and has 2 slices left. Did Newton
and Descartes eat the same amount?
Explain.
Newton and Descartes eat the same amount based on the fraction calculated.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
From the information, Newton and Descartes
each buy identical pastillas. Newton cuts his into twelfths and eats 8 slices. This will be 1/12 each. Since there are 4 parts left, this will be:
= 1/12 × 4
= 4/12
= 1/3
Descartes cuts his into sixths, eats some, and has 2 slices left. This will be:
= 2 × 1/6
= 1/3
Therefore, Newton and Descartes eat the same amount.
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if the probability of selecting the number is 3/10, the what could the question be?
The question can be:
"From the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
What is the probability of randomly selecting a multiple of 3?"
The answer is that the probability is 3/2, as expected.
What could the question be?We want to find a question about probability, such that the answer is 3/10.
So we will have a set of 10 numbers, and 3 of them make a given event true, the probability of selecting one of these 3 numbers out of the whole set is:
P = 3/10
So, for example:
From the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
What is the probability of randomly selecting a multiple of 3?
There are 3 multiples of 3 on that set of 10 numbers, then the probability is P = 3/10.
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a rectange has the area of 60 in2. what can its dimentions be? copy and fill in the chart. length 1,2,10,30,120,3,_,5,_ width 60,_,_,_,_,_,5,_,100
PLS HELP FAST
The length and width of the rectangle can be 30 and 2 inches, 1 inches and 60 inches and 12 inches and 5 inches.
How to find the area of a rectangle?A rectangle is a quadrilateral with opposite sides equal to each other. Opposite sides of a rectangle is equal to each other.
A rectangle has the area of 60 in².
The dimension of the rectangle can be as follows:
area of a rectangle = lw
where
l = lengthw = widthTherefore,
60 = 30 × 2
60 = 1 × 60
60 = 12 × 5
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maya has $75 this is 30% of what she needs explain how you can work out how much she needs
Answer: $250. Step-by-step explanation: let the amount she need is $x. now. given that. 30℅ of x = $75. so. 30/100 × X = $75.
6 to the power of 2 - (8 - 4) to the power of 2 + 7 = ?
This is confusing
The simplification of the expression 6 to the power of 2 - (8 - 4) to the power of 2 + 7 = ? gives -262108
How to simplify an expression?
Simplification is a way of determining an answer for a complex calculation that may involve numbers on division, multiplication, square roots, cube roots, plus and minus, etc.
Given: the expression, 6 to the power of 2 - (8 - 4) to the power of 2 + 7 = ?
This can be written as 6² - (8 - 4)²⁺⁷. Thus:
6² - (8 - 4)²⁺⁷ = 6² - 4⁹
= (6×6) - (4×4×4×4×4×4×4×4×4)
= 36 - 262144
= -262108
Therefore, the expression 6² - (8 - 4)²⁺⁷ simplifies to -262108
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Combine like terms Y - (-3y)