Answer:
center (0, 3) and radius 2√2
Step-by-step explanation:
Equation of a circle
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where:
(a, b) is the centerr is the radiusGiven equation:
[tex]x^2+y^2-6y+1=0[/tex]
Subtract 1 from both sides:
[tex]\implies x^2+y^2-6y=-1[/tex]
To create a trinomial with variable y, add the square of half the coefficient of the y term to both sides:
[tex]\implies x^2+y^2-6y+\left(\dfrac{-6}{2}\right)^2=-1+\left(\dfrac{-6}{2}\right)^2[/tex]
[tex]\implies x^2+y^2-6y+9=8[/tex]
Factor the trinomial with variable y:
[tex]\implies x^2+(y^2-6y+9)=8[/tex]
[tex]\implies x^2+(y-3)^2=8[/tex]
Factor [tex]x^2[/tex] to match the general form for the equation of a circle:
[tex]\implies (x-0)^2+(y-3)^2=8[/tex]
Compare with the general form of the equation for a circle:
[tex]\implies a=0[/tex]
[tex]\implies b=3[/tex]
[tex]\implies r^2=8 \implies r=2\sqrt{2}{[/tex]
Therefore, the center is (0, 3) and the radius is 2√2
How much acetic acid is in a 5 - liter container of acetic acid and water that is marked 80% acetic acid ? How much is water ?
Two dice are rolled. What is the probability that the sum of the numbers rolled is either 10 or 11? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answer:
P(Event) = N(Favorable Outcomes) / N (Total Outcomes)
P(sum of 10 or 11) = 5/36
Step-by-step explanation:
Probability states how likely an event is about to happen. The probability of an event can exist only between 0 and 1 where 0 indicates that event is not going to happen i.e. Impossibility and 1 indicates that it is going to happen for sure i.e. Certainty.
The higher or lessen the probability of an event, the more likely it is that the event will occur or not respectively. For example – An unbiased coin is tossed once. So the total number of outcomes can be 2 only i.e. either “heads” or “tails”. The probability of both outcomes is equal i.e. 50% or 1/2.
So,
P(Event) = N(Favorable Outcomes) / N (Total Outcomes)
Sample Space:
All the possible outcomes of an event are called Sample spaces.
Examples-
• If two dice are rolled together then total outcomes will be 36 and
Sample space will be
[ (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) ]
Probability of rolling a sum of 10 or 11 with two dice:
When two dice are rolled together then total outcomes are 36 and
Sample space is
[ (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) ]
So, pairs with sum 10 or 11 are (4, 6) (5, 5) (6, 4) (5,6) (6,5) i.e. total 5 pairs
Total outcomes = 36
Favorable outcomes = 5
Probability of getting the sum of 10 or 11 = Favorable outcomes / Total outcomes
= 5 / 36
So, P(sum of 10 or 11) = 5/36
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what is the name of the shape graphed by the function theta=-4pie/3
Step-by-step explanation:
On a polar plane, the shape will be a line that goes through the pi/2- pi quadrant , and 3pi/2- 2pi quadrant
On a Cartesian or rectangular plane, the shape will be a line as well passing through 2nd and 4th quadrant
Ryan also found that he could model the height of his plant with the equation h = 0.5d + 4, where d is the number of days and h is the height in centimeters. part b question 2
The domain is {0, 1, 2, 3, 4, 5, 6} and range is {4, 4.5, 5, 5.5, 6, 6.5, 7}.
What is Domain and Range?The domain of a function is the set of values that we are allowed to plug into our function.
The range of a function is the set of values that the function assumes.
The complete question is
Ryan also found that he could model the height of his plan with the equation H = 0.5D + 4 where D is the number of days and H is the height in centimeters. Determine the domain and the range for this relationship.
Given:
h = 0.5d + 4
The Domain of the function is: {0, 1, 2, 3, 4, 5, 6}
and the Range is: {4, 4.5, 5, 5.5, 6, 6.5, 7}
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twice a number increased by 8 is 20. find the number
Answer:
Answer is 6
Step-by-step explanation:
Let the number be ×
Twice a number is 2×
Twice a number increase by 8 is 2×+8
hence the equivalent will be
2×+8=20
2×=12
×6
Answer:
6
Step-by-step explanation:
Let n be the unknown number.
"Twice a number" means to multiply the number by 2:
⇒ 2n
"Increase by 8" means to add 8:
⇒ 2n + 8
"Is 20" means equals 20:
⇒ 2n + 8 = 20
Therefore, the equation is: 2n + 8 = 20
To solve, subtract 8 from both sides:
⇒ 2n + 8 - 8 = 20 - 8
⇒ 2n = 12
Divide both sides by 2:
⇒ 2n ÷ 2 = 12 ÷ 2
⇒ n = 6
Therefore, the unknown number is 6.
find the measure of angle S and angle TRS pls help
Answer:
60°
Step-by-step explanation:
since angle on straight line is 180° you take the sum of the exterior angle of R and its interior angle then divide both sides by the coefficient of y to find y then things get easier from there
Answer:
Step-by-step explanation:
Plan
7y and 5y are made on the same straight line. Therefore they are supplementary and add to 180 degrees. <s has to be found by finding 3x and 5y first. Find <s by solving 3y + 5y + x = 180 degrees.
Solution
7y + 5y = 180 degrees Combine the left
12y = 180 degrees Divide by 12
12y/12 = 180/12
y = 15
3y + 5y + x = 180 Combine the left side
8y + x = 180 Substitute 15 for y
8*15 + x = 180 Combine
120 + x = 180 Subtract 120 from both sides
120 -120 +x =180 - 120 Combine
x = 60
Answer
s = 60 degrees
<TRS = 5y = 75
an airplane that is flying at an altitude of 30 000 ft is beginning to descend at a rate of 1000 feet per minute. a helicopter is beginning its trip, starting at an altitude of zero feet. the helicopter ascends more slowly than the airplane, going up at a rate of 500 feet per minute. after how many minutes will the airplane and the helicopter be at the same altitude
Using linear functions, it is found that the airplane and the helicopter will be at the same altitude after 20 minutes.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The functions that gives the height of the airplane and the helicopter, after t minutes, is given by:
A(t) = 30000 - 1000t.H(t) = 500t.They will be equal when:
A(t) = H(t).
Hence:
30000 - 1000t = 500t
1500t = 30000
t = 30000/1500
t = 20 minutes.
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A person buys a used car with a down payment of $1,200 and makes monthly payments of $275 for 3 years.What is the total amount of the person pays for the car?PLEASE EXPLAIN
A.$2,025
B.$9,900
C.11,100
D.13,500
Answer:
2025 $
Step-by-step explanation:
275 multiply 3 +1200
Answer:
A.$2,025
Step-by-step explanation:
$275 x 3 years + $1,200
= $2,025
The graph of the cube root parent function y = RootIndex 3 StartRoot x EndRoot is translated to form f(x) shown on the graph.
On a coordinate plane, a cube root function goes through (negative 7, 0), has an inflection point at (negative 6, 1), and goes through (2, 3).
Which equation represents f(x)?
f(x) = RootIndex 3 StartRoot x + 6 EndRoot + 1
f(x) = RootIndex 3 StartRoot x minus 6 EndRoot + 1
f(x) = RootIndex 3 StartRoot x + 6 EndRoot minus 1
f(x) = RootIndex 3 StartRoot x minus 6 EndRoot minus 1
Step-by-step explanation:
The graph of the cube root parent function y = RootIndex 3 StartRoot x EndRoot is translated to form f(x) shown on the graph.
On a coordinate plane, a cube root function goes through (negative 7, 0), has an inflection point at (negative 6, 1), and goes through (2, 3).
Which equation represents f(x)?
f(x) = RootIndex 3 StartRoot x + 6 EndRoot + 1
f(x) = RootIndex 3 StartRoot x minus 6 EndRoot + 1
f(x) = RootIndex 3 StartRoot x + 6 EndRoot minus 1
f(x) = RootIndex 3 StartRoot x minus 6 EndRoot minus 1
Answer:
Step-by-step explanation:
The translation of the parent function is:
g(x) = ∛(x + 6) + 1
How do translations work?
There are two types of translations, these are:
Horizontal translation:
For a function f(x), a horizontal translation of N units is written as:
g(x) = f(x + N)
If N is positive, the translation is to the left.
If N is negative, the translation is to the right.
Vertical translation:
For a function f(x), a vertical translation of N units is written as:
g(x) = f(x) + N
If N is positive the translation is upwards.
If N is negative the translation is downwards.
Here we start with the parent function:
f(x) = ∛x
And we apply two translations such that:
g(x) = ∛(x + a) + b
Such that:
g(-7) = 0
g(2) = 3
Then we have the system of equations:
∛(-7 + a) + b = 0
∛(2 + a) + b = 3
From the options, the only ones that make the first option true are:
g(x) = ∛(x + 6) + 1
Such that when evaluated in x = -7 we get:
g(-7) = ∛(-7 + 6) + 1 = ∛(-1) + 1 = 0
When evaluated in x = 2 it gives:
∛(2 + 6) + 1 = ∛(8) + 1 = 2+ 1 = 3
So the only option that meets these conditions is:
g(x) = ∛(x + 6) + 1
Which is a translation to the left of 6 units and up 1 unit.
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Question 7 of 10
Classify the following triangle. Check all that apply.
Answer:
A,C,E
(if you find a better answer choose that.)
Step-by-step explanation:
This one has two acute angles and one obtuse.
This one is a scalene.
So, tick A,C,E
g(x)=f(x)-3 which statement best describes the graph of g(x) with the graph of f(x)
Answer: The graph of g(x) is the graph of f(x) shifted 3 units down.
3. How many more paintings,
sculptures, and photographs would
the artist need to sell to make
another $500?
answer
Step-by-step explanation:
there are only one
painting, sculpture and photograph.
he roots of the quadratic function describing the relationship between the number of products produced and overall profit margins are x= 0 and 150. the vertex is (75, 10000).
The question was incomplete. Below you will find the missing parts of the question.
The company actually loses money on their first few products as it costs them more to make them, but once they hit ? they break even again. The worst case scenerio is that they produce ? items, as they will have a profit of ? dollars. The first root tells us that the profit will be 0 when ? products are sold.
Answer: The company actually loses money on their first few products as it costs them more to make them, but once they hit 150 they break even again. The worst case scenerio is that they produce 75 items, as they will have a profit of 10000 dollars. The first root tells us that the profit will be 0 when 0 products are sold.
Because the roots are x = 0 and 150, the vertex is (75, 10000).
So, the function is y = [tex]-\frac{10000}{5625}(x-75)^{2} +10000[/tex]
When, y = 0,
[tex]0=-\frac{10000}{5625} (x-75)^{2} +10000[/tex]
⇒ [tex]\frac{10000}{5625} (x-75)^{2}=10000[/tex]
⇒ [tex](x-75)^{2} = 10000(\frac{5625}{10000})[/tex]
⇒ [tex](x-75)^{2} = 5625[/tex]
⇒ [tex]x-75=75[/tex]
⇒ x = 150
When y=0, then x =150, their income was in balance.
When x = 75, then y=10000, they will have a profit of 10000 dollars.
The first root tells us that the profit will be 0 when 0 products are sold.
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solve for x -
[tex]\bold{x {}^{2} + 5x + 6 = 0}\\\\[/tex]
ty! ~
The solution of the given quadratic equation is x=-2 or x=-3.
The given quadratic equation is x²+5x+6=0.
What are different methods to solve a quadratic equation?The different methods of solving quadratic equations are factoring, completing the square or using the quadratic formula.
By using the splitting middle term method we can solve x²+5x+6=0.
That is, x²+2x+3x+6=0
⇒x(x+2)+3(x+2)=0
⇒(x+2)(x+3)=0
⇒(x+2)=0, (x+3)=0
⇒x=-2 or x=-3.
Therefore, the solution of the given quadratic equation is x=-2 or x=-3.
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Which of the following is a list that follows this pattern with its numbers: prime, prime, prime, composite, prime, prime 1, 5, 7, 9, 11, 13 1, 2, 5, 7, 9, 15 2, 4, 6, 8, 10, 12 11, 9, 3, 2, 5, 4, 8
The correct answer is option A which is the pattern {prime, prime, prime, composite, prime, prime} is followed by 1, 5, 7, 9, 11, 13.
What are prime and composite numbers?Prime numbers:-
The prime number is defined as the number which is divided by 1 and itself.
Composite numbers:-
The number is defined as the composite number when the number is divided by 1 itself and any other numbers also.
From the given options we need to choose the pattern of the series { prime, prime, prime, composite, prime, prime } so we can see that in option A correct pattern is followed.
Pattern { 1, 5, 7, 9, 11, 13 }
1 → prime
5 → prime
7 → prime
9 → composite
11 → prime
13 → prime
Therefore the correct answer is option A which is the pattern {prime, prime, prime, composite, prime, prime} is followed by 1, 5, 7, 9, 11, 13.
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Some children research their classmates' favourite colour. They show the results in a pie chart. 40 children were asked about their favourite colour. How many children chose each colour? red = green = blue =
Step-by-step explanation:
Can you attach the questions please? Thanks
Please answer this question!! <3 <4 <5 <6 <9
The correct answer is option C which is the angle LMO is 50°
What is trigonometry?The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle termed trigonometry.
Given that:-
∠O = 70°
∠L = 60°
∠LMO =?
As we know that the sum of the three angles are 180 degree applying this relation:-
∠LOM + ∠OLM + ∠LMO = 180
70 + 60 + ∠LMO = 180
∠LMO = 180 - 70 - 60 = 50
Therefore the correct answer is option C which is the angle LMO is 50°
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Sasha's bank account earns 4% simple interest. How much must she deposit in the account today if she wants it to be worth $1,000 in 5 years?
If Sasha wants her account to be worth $1,000 in 5 years, then she must deposit $833.34.
What is simple interest?Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,
SI = PRT
where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.
Sasha's bank account earns 4% simple interest. Therefore, if she wants it to be worth $1,000 in 5 years then the principal amount must be,
Account balance = PRT + P
$1,000 = P[(0.04×5)+1]
$1,000 = 1.2 P
P = $833.34
Hence, if Sasha wants her account to be worth $1,000 in 5 years, then she must deposit $833.34.
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P, Q and R are points in the same
horizontal plane. The bearing of
Q from P is 150° and the bearing
of R from Q is 060°.
If |PQ| = 5m and QR = 3m,
Find the bearing of R from P.
correct to the nearest degree./
Answer: 119°
Step-by-step explanation:
From the positive y-axis, all angles are measured clockwise
PR = PQ + QR = 5[150°] + 3[60°]
X = 5*sin150 + 3*sin60 = 5.1
Y = 5*Cos150 + 3*Cos60 = -2.83
TanA = X/Y
A = -61° = 61° East of South = 119° Clockwise
Therefore, the bearing of R from P is 119°
b) 1/16 + 3/64 + 9/256 + 27/1024 ....
The sum of the geometric series will be 1/4. And the sum of the series will be the negative 0.13.
The complete question is attached below.
What is the sum of the geometric series?Let a be the first term and r be the common ratio. Then the sum of the geometric series will be
S = a / (1 – r) if r < 1
S = a / (r – 1) if r > 1
The series is given below.
1/16 + 3/64 + 9/256 + 27/1024 ....
Then we have
a = 1/16
r = (3/64) / (1/16) = 3/4
Then the sum of the series will be
S = (1/16) / [1 – (3/4)]
S = (1/16) / (1/4)
S = 1/4
Let [tex]\rm S = (-0.13)^m[/tex], where m = 1
Then the value of S will be
S = (-0.13)¹
S = -0.13
Hence, the sum of the series will be the negative 0.13.
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juan tiene 400 y rosa 350. ambos se compran
what is the missing pattern 7, 11, 2, 18, -7
The missing pattern behind the sequence 7, 11, 2, 18, -7 is described by the formula [tex]n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}[/tex], equivalent to the recurrence formula [tex]a_{n+1} = a_{n} + (-1)^{i+1}\cdot (i + 1)^{2}[/tex].
What is the missing element in a sequence?
A sequence is a set of elements which observes at least a defined rule. In this question we see a sequence which follows this rule:
[tex]n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}[/tex] (1)
Now we prove that given expression contains the pattern:
n = 0
7
n = 1
7 + (- 1)² · 2² = 7 + 4 = 11
n = 2
7 + (- 1)² · 2² + (- 1)³ · 3² = 11 - 9 = 2
n = 3
7 + (- 1)² · 2² + (- 1)³ · 3² + (- 1)⁴ · 4² = 2 + 16 = 18
n = 4
7 + (- 1)² · 2² + (- 1)³ · 3² + (- 1)⁴ · 4² + (- 1)⁵ · 5² = 18 - 25 = - 7
The missing pattern behind the sequence 7, 11, 2, 18, -7 is described by the formula [tex]n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}[/tex], equivalent to the recurrence formula [tex]a_{n+1} = a_{n} + (-1)^{i+1}\cdot (i + 1)^{2}[/tex].
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my dad began paying me an allowance when i was in eighth grade. what is the indirect object?
Answer:
Step-by-step explanation:
The answer would be "me" as the indirect object
What is the length of leg s of the triangle below? 45 √32 45° A. √4 B. 1.5 C. 16
Answer:
s = 4 unitsStep-by-step explanation:
Given is isosceles right triangle, since its interior angles are 45°, 45° and 90°.
The missing length is therefore same as the length of the other leg:
s = 4Note: This is not included in the answer choices.
Answer:
4 units
Step-by-step explanation:
We can use the converse theorem of the isosceles triangle to find the missing leg.
Converse Isosceles triangle theorem: If two angles are congruent in a triangle, then sides opposite to those angles are also congruent.
Therefore,
As there are two 45° angles, the opposite sides to those are also congruent.
∴ s = 4
Work out (4 x 3)² ÷ 6
An expression is defined as a set of numbers, variables, and mathematical operations. The solution of (4 x 3)² ÷ 6 is 24.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The solution of the expression (4 x 3)² ÷ 6 is,
(4 x 3)² ÷ 6
= (12)² ÷ 6
= 144 ÷ 6
= 24
Hence, the solution of (4 x 3)² ÷ 6 is 24.
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Solve the system of equation for y using Cramer's rule. Hint: The determinant of the coefficient matrix is -23.
Answer:
-4 option (c)
Step-by-step explanation:
Cramer rule : In this method, the values of the variables in the system are to be calculated using the determinants of matrices
if , D :determinant of the coefficient matrix
[tex]{D}_{x}:[/tex]determinant of the matrix with coefficients except x
then,
[tex]x=\frac{{D}_{x}}{D}[/tex]
similarly,
[tex]y=\frac{{D}_{y}}{D}[/tex]
[tex]z=\frac{{D}_{z}}{D}[/tex]
given,
D = -23
[tex]D_{y}[/tex] = [tex]det\left[\begin{array}{ccc}5&7&-1\\2&6&-2\\3&-7&2\end{array}\right][/tex]
[tex]D_{y}[/tex] = 92
therefore, y = 92/(-23)
y = -4 answer
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A piecewise function is represented by the graph below.
On a coordinate plane, a piecewise function has 2 lines. The first line is made up of 2 lines. One line goes from (negative 5, 3) to (negative 1, negative 1) and then goes up to a closed circle at (1, 1). The second line has an open circle at (1, 2) and then continues up through (3, 4).
What is the domain for the piece of the function represented by f(x) = x + 1?
x < –1
–1 ≤ x ≤ 1
1 ≤ x < 2
x > 1
Because we have an open circle at (1, 2), and then the line continues up, we conclude that the domain is:
D: x > 1.
What is the domain for the piece of the function represented by f(x) = x + 1?
Here we know that:
"The second line has an open circle at (1, 2)"
This means that the value x = 1 is not on the domain of the second line, and we know that the line "then continues up through (3, 4)"
(notice that these are two points on the line y = x + 1).
So we conclude that x = 1 is the lower bound of the domain of that line (and we can't tell that there is an upper bound).
Then we can just write the domain as:
D: x > 1.
So the last option is the correct one.
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Another day, another math problem 3
If f(x)=x²+2 and g(x)=x²+5 then the domain of the (fog) (x) is (-∞,∞).
Given the f(x)=x²+2 and g(x)=x²+5
We have to find the domain of the (fog) (x)
The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.
then,(fog) (x)= (x²+5)²+ 2
=x⁴+25+10x²+2
= x⁴+27+10x²
Now on any real value of x the value of (fog) (x) exists therefore (fog) (x) can take all the values of the real number.
So domain (fog) (x)= (-∞,∞).
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Will mark brainliest if you can help!
Answer:
ln(20) = 2.9957
Here given:
ln(4) = 1.3863
ln(5) = 1.6094
Evaluating with that:
[tex]\rm \Rightarrow ln\left(20\right)=ln\left(5\right)+ln\left(4\right)\\[/tex]
[tex]\rm \Rightarrow ln\left(20\right)=1.3863 \ + \ 1.6094[/tex]
[tex]\rm \Rightarrow ln\left(20\right)=2.9957[/tex]
a telephone company charges $0.98 for the first minute, $0.82 for each additional minute, and a$1.56 service charge if the cost is 11.56 how long did the person talk
Answer:
12 minutes
Step-by-step explanation:
added in the picture