Fill in the blanks below in order to justify whether or not the mapping shown represents a function.
The mapping diagram above a function since
in where there
Answers
Answer:
This is a function
Step-by-step explanation:
For every input there is only one output.
Related Questions
The perimeter of the triangle BAG is 43. AG= 16, AB=x+4, and BG= 2x+2. What is the value of x?
Answers
Answer:
x=7
isosceles triangle
Step-by-step explanation:
To find the perimeter we just add all the sides so we do that for this too
(X+4)+(2x+2)+(16)
And we set it equal to 43 since that is perimeter
(X+4)+(2x+2)+(16)=43
Combine like terms
3x+22=43
-22. -22
3x=21
/3. /3
x=7
And if we fill in the x we find BG and AG are equal so this is an Isosceles triangle
Hopes this helps
Answer:
x = 7
Isosceles triangle
Step-by-step explanation:
The perimeter of a two-dimensional shape is the distance all the way around the outside.
Given values of triangle BAG:
Perimeter = 43AG = 16AB = x + 4BG = 2x + 2Therefore:
⇒ AG + AB + BG = perimeter
⇒ 16 + x + 4 + 2x + 2 = 43
⇒ x + 2x + 16 + 4 + 2 = 43
⇒ 3x + 22 = 43
⇒ 3x + 22 - 22 = 43 - 22
⇒ 3x = 21
⇒ 3x ÷ 3 = 21 ÷ 3
⇒ x = 7
Substitute the found value of x into the expressions for AB and BG to find their lengths:
⇒ AB = x + 4
⇒ AB = 7 + 4
⇒ AB = 11
⇒ BG = 2x + 2
⇒ BG = 2(7) + 2
⇒ BG = 14 + 2
⇒ BG = 16
As sides BG and AG are both 16 units in length, the triangle is an isosceles triangle (as it has two sides of equal length).
given s : t : u = 4 : 9 : 3 and t - u = 30. find the value of s
Answers
The value of s from the proportion s : t : u = 4 : 9 : 3 is s = 20
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
Given data ,
Let the proportion be in the form s : t : u
where the value of the proportion is
s : t : u = 4 : 9 : 3
And , t - u = 30
Now , assume the value of s = 4x
where x is the unknown we have to calculate
So , the value of t = 9x
And , the value of u = 3x
From the equation , t - u = 30
Substitute the value of t and u in the equation , we get
9x - 3x = 30
6x = 30
Divide by 6 on both sides of the equation , we get
x = 5
Therefore , the value of x is 5
Now , substituting the value of x in the above equation , we get
s = 4x
s = 4 x 5
s = 20
Therefore , the value of s from the proportion is 20
Hence , The value of s from the proportion s : t : u = 4 : 9 : 3 is s = 20
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Question 1 of 5
A canoe travels 5 miles per hour downstream and 1 mile per hour upstream.
Let x represent the canoe's speed with no water current (in still water) and y
represent the speed of the water current, in miles per hour. Then the situation
can be represented by this system of equations:
Choose the two correct options.
x + y = 5
x - y = 1
h
A. The speed of the water current is 3 miles per hour.
B. The speed of the canoe in still water is 3 miles per hour.
C. The speed of the canoe in still water is 2 miles per hour.
D. The speed of the water current is 2 miles per hour.
Answers
The speed of the canoe in still water is 3 miles per hour and the speed of the water current is 2 miles per hour. The correct options are B and D.
What is the system of equation?One or many equation having same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Given that the system of equations;
x + y = 5
x - y = 1
Solving the above equations by elimination we get
x = 3 and y = 2
Where, x represents the canoe's speed with no water current (in still water) and y represents the speed of the water current, in miles per hour.
Therefore, the speed of the canoe in still water is 3 miles per hour and
the speed of the water current is 2 miles per hour.
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Find two consecutive integers between which the solution to each equation is located. x^2=3
Answers
Step-by-step explanation:
Using squares of integers numbers, it is found that the solution of the equation is located between the integers x = 1 and x = 2.
The equation given is:
x^2=3
The solution of the equation given is:
X=√3
The squares of the integers numbers until the square root of 3 are:
1^2=1
2^2=4
Since , the square root of 3, which is the solution to the equation, is located between the integers x = 1 and x = 2.
In the 1960 Olympics, Wilma Rudolph of the United States won the women's 100 meter run in 11.0 seconds. In 1988, Florence Griffith-Joyner, also of
the United States, won with a time of 10.49 seconds, which is still the fastest women's time to this date. Find the percent of decrease in the winning
time. Round to the nearest tenth
% decrease
Answers
Hello,
I hope you and your family are doing well!
To find the percent of decrease in the winning time, you can use the following formula:
percent decrease = (old value - new value) / old value * 100%
Plugging in the values from the problem, we get:
percent decrease = (11.0 seconds - 10.49 seconds) / 11.0 seconds * 100% = 0.51 seconds / 11.0 seconds * 100% = 4.636363636363636%
Rounding to the nearest tenth, the percent of the decrease in the winning time is:
4.6%
This means that the winning time decreased by 4.6% between the 1960 Olympics and the 1988 Olympics.
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Find the measure of each numbered angle.
m∠1=_____ and m∠2=_____
Answers
Answer:
m∠1 = m∠2 = 17°
Step-by-step explanation:
You want to know the measures of the base angles of an isosceles triangle with an a.pex angle of 146°.
Angle sum theoremThe sum of angles in a triangle is 180°. We can use x to represent the measures of each of the two congruent base angles of the isosceles triangle:
x + 146° +x = 180°
2x = 34° . . . . . . subtract 146°
x = 17° . . . . . . . divide by 2
The measures of the angles are ...
m∠1 = m∠2 = 17°
What is the correct answer to this problem? g(x)=x2+6 find g(-3)=
Answers
Answer:
15
Step-by-step explanation:
How many pages are necessary to make 1,050 copies of a manuscript that is 423 pages long? (Print on one side only.)
Answers
Answer:
Step-by-step explanation:
Scenario: A researcher is interested in estimating the proportion of the population on a
particular construct characteristic within the researcher's area of scholarly interest [Fill
in with something that would be appropriate for your area of research interest]. A
measurement instrument has been created that can be used to categorize respondents as
either demonstrating the characteristic, or not. The researcher has obtained a population
frame to draw a sample from. The frame contains 3400 records.
Question: How large of a random sample is needed to estimate the population
proportion to within plus or minus 2% and be 95% sure the estimate is correct? Do
NOT take nonresponse into account. Remember, this is a sample size estimate, which
means you should round UP for your final answer.
Answers
To estimate the population proportion to within plus or minus 2% with 95% confidence, a sample size of at least 804 is needed.
How do we get the sample size for estimating a population proportion?This can be calculated using the formula for determining sample size for estimating a population proportion:
n = (Z^2 * p * (1-p)) / (E^2)
Where n is the sample size, Z is the z-score corresponding to the desired level of confidence (1.96 for 95% confidence), p is the estimated proportion of the population with the characteristic of interest (assumed to be 0.5 for this calculation), and E is the maximum margin of error desired (2% in this case). Plugging these values into the formula, we get:
n = (1.96^2 * 0.5 * (1-0.5)) / (0.02^2) = 803.84
Since this is a sample size estimate, we should round up to the next whole number, resulting in a sample size of 804.
Therefore, the correct answer is as given above
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Scott's Heating and Air
Conditioning
charges $80.00 for a service call and $30.00
for each hour of work. Create a graph to
show the relationship between the number
of hours worked and total cost of the repair
bill.
Answers
Cost function is fixed cost added with number of hours times the variable cost.
What is cost ?
The two primary categories of costs that organizations face are fixed and variable costs. While variable costs fluctuate with output, fixed costs do not.
Sometimes, fixed costs are referred to as overhead costs. They are incurred regardless of whether a company produces 100 or 1,000 widgets.
Given that charge for a service call is $80.00 and $30.00 for each hour of work. So fixed cost is 80 and variable cost is 30.
Cost function is fixed cost added with number of hours times the variable cost.
Thus we have the cost function here,
where x is the hours of work.
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8. A parabola has its focus at (1,2) and its directrix is y = -2. The equation of this parabola could be
1) y = 8(x + 1)²
2)y=1/8(x + 1)²
3)y =8(x-1)²
4)y=1/8(x-1)²
Answers
The equation of a parabola is y=1/8 (x-1)². Therefore, option 4 is the correct answer.
What is the parabola?A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.
Given that, parabola has its focus at (1,2) and its directrix is y= -2.
From graph, vertex is (h, k)=(1, 0) and p=2
Substitute (h, k)=(1,0) and p=2 in (x-h)²=4p(y-k), we get
(x-1)²=4(2)(y-0)
⇒ (x-1)²=8y
⇒ y=1/8 (x-1)²
The equation of a parabola is y=1/8 (x-1)². Therefore, option 4 is the correct answer.
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x^2+y^2+4x+6y-12=0 identify the radius and the center
Answers
Answer:
Center = (-2, -3)
Radius = 5
Step-by-step explanation:
Suppose f(x)=x^(2) and g(x)=(3x)^(2). Which statement best compares the graph of g(x) with the graph of f(x) ?
A. The graph of g(x) is horizontally compressed by a factor of 3 .
B. The graph of g(x) is shifted 3 units to the right.
C. The graph of g(x) is vertically stretched by a factor of 3 .
D. The graph of g(x) is horizontally stretched by a factor of 3 .
Answers
What is the solution of the inequality −3x−3>12 ?
Answers
Answer:
[tex]x < -5[/tex]
Step-by-step explanation:
-3x-3>12
Divide by -3, since you are dividing by a negative, flip the equality sign:
x+1<-4
Subtract 1 from both sides:
x<-5
Hello,
I hope you and your family are doing well!
To solve the inequality −3x−3>12, you can start by moving everything to one side of the inequality by adding 3 to both sides. This gives you −3x>15.
Next, you can divide both sides of the inequality by -3 to get x<-5.
Finally, you can simplify the inequality to its final form by flipping the direction of the inequality symbol, since you divided it by a negative number. This gives you the final solution: x>-5.
So, the solution to the inequality −3x−3>12 is x>-5. This means that any value of x that is greater than -5 will satisfy the inequality.
The answer is: x > -5
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Use Pythagoras' theorem to work out the height of the equilateral
triangle below.
Give your answer in centimetres (cm) to 1 d.p.
N
10 cm
allowed
M
10 cm
10 cm
Answers
The hypotenuse (longest side) of each right triangle is 10 cm, and its base is 5 cm (since there are two right triangles, we have to divide the base length of the equilateral triangle by 2, so 10/2=5).
Let’s call the hypotenuse of each right triangle ‘a’, the base ‘b’ and the height ‘c’
Pythagorean theorem = a^2 + b^2 = c^2
We need to find the height ‘c’ so:
a = 10 cm
b = 5 cm
c = ?
10^2 + 5^2 = c^2
100 + 25 = c^2
125 = c^2
c = square root of 125
c = 11.18 cm
So the height of the total equilateral triangle is 11.18 cm.
Here’s a picture to help you understand:
2. Zac has earned $ 200 and earns $ 20 every week walking his neighbor's dog. Jon is $ 100 in debt and earns $ 25 every week cleaning his neighbor's pool. In how many weeks ( w ) will both Zac and Jon earnings be the same?
A student claims the solution to the equation 200+20 w=-100+25 w is w=50 He shows his steps.
Given : 2 0 0+2 0 w=- 1 0 0}+2 5 w
Step 1: 300+20 w=25 w
Step 2: 300=5 w
Step 3: 60=w
Select the two correct justifications for the given steps.
Step 1: Addition Property of Equality
Step 2: Subtraction Property of Equality
Step 3: Division Property of Equality
Answers
1. In 60 weeks, both Zac and Jon will earn the same amount, equating to their different earnings.
2. The student's claim that the solution to the equation 200 + 20w = -100 + 25w is w = 50 is false as the solution shows that w = 60.
3. The two correct justifications for the given steps used in solving w are:
Step 1: Combining like termsStep 3: Division Property of Equality.How the equations are determined?The fixed earnings of Zac = $200
Zac's earnings per week = $20
The total earnings of Zac in w weeks = 200 + 20w
Jon's fixed debt so far = $100
Jon's earnings per week = $25
The total earnings of Jon in w weeks = -100 + 25w
To determine the weeks when the total earnings of Zac and Jon will be equal, we can equate the two expressions above as follows and solve for w:
200 + 20w = -100 + 25w
20w - 25w = -300
-5w = - 300
w = -300/-5
w = 60
Thus, we can conclude that in 60 weeks, the earnings of Zac and Jon will become equal.
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In the right-angled triangle ABC, cos C = 4/5 and BC = 16 cm, find the following:
i) AC
ii) AB
Answers
The value of (i) AC is the right angled triangle is 20 cm, For (ii) AB is 12 cm.
What is a right angled triangle?A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle.
(i) To calculate the value of /AC/, we use the formula below.
/AC/ = BC/cosC..................... Equation 1From the question,
Given:
BC = 16 cmcosC = 4/5Substitute these values into equation 1
AC = 16/(4/5)AC = 20 cm(ii) To calculate AB, use Pythagoras formula:
a² = b²+c².................. Equation 2From the diagram,
a = AC = 20 cmb = AB = ?c = BC = 16 cmSubstitute these values into equation 2 and solve for AB
20² = b²+16²b² = 20²-16²b² = 400-256b² = 144b = √144b = 12 cmAB = 12 cmLearn more about right angle triangle here: https://brainly.com/question/25016594
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Given a function value of an acute angle, find the other five trigonometric function values
Answers
The other five trigonometric function values are cos(∅) = 11/61, tan(∅) = 60/11, sec(∅) = 61/11, csc(∅) = 61/60 and cot(∅) = 11/60
How to determine the other five trigonometric function valuesFrom the question, we have the following parameters that can be used in our computation:
sin(∅) = 60/61
The cosine of the angle can be calculated using
sin²(∅) + cos²(∅) = 1
Substitute the known values in the above equation, so, we have the following representation
(60/61)² + cos²(∅) = 1
This gives
cos²(∅) = 1 - (60/61)²
Evaluate the like terms
cos²(∅) = 121/3721
Take the square root of both sides
cos(∅) = 11/61
The tangent of the angle can be calculated using
tan(∅) = sin(∅)/cos(∅)
Substitute the known values in the above equation, so, we have the following representation
tan(∅) = (60/61)/(11/61)
Evaluate
tan(∅) = 60/11
The other ratios of the angle are calculated as follows
sec(∅) = 1/cos(∅) = 61/11
csc(∅) = 1/sin(∅) = 61/60
cot(∅) = 1/tan(∅) = 11/60
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Marvin and Alicia are putting new carpet in there living room. The carpet cost $4.15 per square foot and $97 to have it stalled. Their total bill is $1, 789.50 how many square feet 9s their living room
Answers
There are 407.83 square feet living room.
What is linear expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Given that;
The carpet cost $4.15 per square foot and $97 to have it stalled.
And, Their total bill is $1, 789.50.
Now,
Let number of square feet living room = x
So, We can formulate;
⇒ 4.15x + 97 = 1,789.50
Solve for x as;
⇒ 4.15x = 1,789.50 - 97
⇒ 4.15x = 1,692.5
⇒ x = 1,692.5 / 4.15
⇒ x = 407.83 square feet
Thus, There are 407.83 square feet living room.
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Part 1: Two custodians are painting the hallway in the school, starting
at opposite ends at 10:00 a.m. By noon, if Jon has painted 1/5 of the
hallway and Dan has painted 25% of the hallway, who has painted the
most?
25
Part 2: What percentage of the job needs to be completed after lunch
Answers
Answer: Part 1: Dan, Part 2: 55%
Step-by-step explanation:
1. By noon, Jon has painted 1/5 (or 20%) of the hallway and Dan has painted 25% of the hallway. Therefore, Dan has painted more of the hallway than Jon.
2. In total, the two have painted 45% (20% + 25% = 45%) of the hallway by lunchtime. Therefore, 55% (100% - 45% = 55%) needs to be painted after lunch.
I need help!
The value of __ divided by 32 is greater than 1
Does anyone know?
Answers
[tex]x\div 32 > 1\implies \cfrac{x}{32} > 1\implies 32\left( \cfrac{x}{32} \right) > 32(1)\implies x > 32[/tex]
and that can be any value, so long is greater than that, 33 will do, but so does 1,000,000, and so on.
Answer: and that can be any value, so long is greater than that, 33 will do, but so does 1,000,000, and so on.
Step-by-step explanation:and that can be any value, so long is greater than that, 33 will do, but so does 1,000,000, and so on.
and that can be any value, so long is greater than that, 33 will do, but so does 1,000,000, and so on.
The solution to a system of equation is (1, 5).
Choose two equations that might make up the system.
(Select all that apply.)
y+ -3x-6
Y= 2x+3
Y= -7x+1
Y=x+4
Y=-2x-9
Answers
Answer:
y = 2x + 3 and y = x + 4
Step-by-step explanation:
the first equation:
y = -3x - 6
(5) =-3(1) - 6
5 = 3-6
5≠-3
second equation:
y = 2x + 3
(5) = 2(1) + 3
5 = 2 + 3
5 = 5
third equation:
y = -7x + 1
(5) = -7(1) + 1
5 = -7 + 1
5 ≠ -6
fourth equation:
y = x + 4
(5) = 1 + 4
5 = 5
last equation:
y = -2x - 9
(5) = -2(1) - 9
5 = -2 - 9
5 ≠ -11
The slope of a curve at each point (x,y) is given by 4x - 1. Which one of the following is an equation fo curve if it passes through the point (-2,3)? A) y = 4x^2 - x - 15 B) y = 2x^2 - x C)y=2r^2-r+7 D) y= 2x^2-1-7
Answers
The following is an equation fo curve if it passes through the point (-2,3) is y=2 x^2-x-7.
What is Slope?
A graph is a set of vertices—points—and edges—the lines connecting those vertices in discrete mathematics. Graphs come in a variety of forms, including connected and disconnected graphs, bipartite graphs, weighted graphs, directed and undirected graphs, and simple graphs.
Slope of the carne at (x, y) is 4 x-1
Let the curve is: y=2 x^2-x-7
[tex]$$\begin{gathered}\text { Slope: } \frac{d y}{d x}=\frac{d}{d x}\left[2 x^2-x-7\right] \\\frac{d y}{d x}=4 x-1\end{gathered}$$[/tex]
And passes Iowa's the point (-2,3).
[tex]$$\begin{aligned}& y=2 x^2-x-7 \\& 3=2(-2)^2-(-2)-7 \\& 3=8+2-7 \\& 3=10-7 \\& 3=3\end{aligned}$$[/tex]
Satisfied.
y=2 x^2-x-7
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4. The number of minutes a person uses each month often varies. Suppose that a Verizon customer uses the total number of minutes shown below.
Which plan would cost the consumer the least amount money over the year?
Answers
The annual cost for the 450 Plan is $645.03.
What is cost price?
The cost price represents the particular worth that represents unit worth purchased.
Main Body;
This consumer used less than 450 minutes a month every month except June and December. In June, they used 178 extra minutes and in December they used 189 extra minutes. In total, they used 367
extra minutes throughout the year. The basic fee for the 450 Plan is $39.99 per month so their annual cost is
annual cost = monthly fee* months + cost per minutes* extra minutes
=39.99 *12 +0.45* 367
=479.88+ 165.15
=645.03
Annual Cost Monthly fee months cost per minute extra minutes
The annual cost for the 450 Plan is $645.03.
The 900 Plan costs $59.99 per month for all 12 months for a total cost of $719.88. Even though the consumer had to pay extra during June and December, the 450 Plan was still less expensive than the 900 Plan.
Hence , The annual cost for the 450 Plan is $645.03.
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If 7 is added to twice a number and
this sum is multiplied by 2, the result is
the same as if the number is multiplied by
13 and 9 is added to the product. What is
the number?
Answers
Answer: x= -5
Step-by-step explanation:
2(7+2x) = 3x+9
14+4x=3x+9
isolate x
x=-5
hi!!! i’d appreciate it sm if someone could do 25 and 26 i’m thing to turn my work in tomorrow and these are the last ones i need, i’ll mark u brainliest when it pops up :) thank you
Answers
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.
[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-1)}}} \implies \cfrac{-4}{2 +1} \implies \cfrac{ -4 }{ 3 } \implies - \cfrac{ 4 }{ 3 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{- \cfrac{ 4 }{ 3 }}(x-\stackrel{x_1}{(-1)}) \implies y -3 = - \cfrac{ 4 }{ 3 } ( x +1) \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y-3)=3\left( - \cfrac{ 4 }{ 3 } ( x +1) \right)}\implies 3y-9=-4(x+1)\implies 3y-9=-4x-4 \\\\\\ 3y=-4x+5\implies \text{\LARGE 4}x+3y=5[/tex]
Sort 3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5 using quicksort with median-of-three partitioning and a cutoff of 3. The three elements are not pre-sorted when choosing pivot and pivot moved to end in each step. Show all steps.
Answers
Using quicksort with median-of-three partitioning and a cutoff of 3. we will get 1, 1, 3, 2, 3, 4, 5, 5, 5, 6, 9.
The Original input is 3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5.
We get on the basis of the median after sorting the first, middle, and final elements 3, 1, 4, 1, 5, 5, 2, 6, 5, 3, 9.
As a result, we select pivot = 5. It also provides after the pivot is removed or hidden 3, 1, 4, 1, 5, 3, 2, 6, 5, 5, 9.
It is necessary to swap the two fives. However, in the subsequent swap, p and q cross. turn is traded back with the p:
3, 1, 4, 1, 5, 3, 2, 5, 5, 6, 9
It is now time to quickly sort the first eight elements of the array in a recursive fashion:3, 1, 4, 1, 5, 3, 2, 5,
and after sorting the three relevant elements, we get 1, 1, 4, 3, 5, 3, 2, 5.
As a result, we select the pivot value of 3, and after hiding this pivot once more, we get:
1, 1, 4, 2, 5, 3, 3, 5
A switch takes place between 4 and 3: 1, 1, 3, 2, 5, 4, 3, 5
Now, because the next swap crosses the pointer, the pivot needed to be swapped: 1, 1, 3, 2, 3, 4, 5,
and the following is the result: 1, 1, 3, 2, 3, 4, 5, 5, 5, 6, 9
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Alfred is looking for a new part-time job as a butler. He responds to an ad position that pays $110,200 a year.
What would his weekly salary be to the nearest cent if he gets the job?
Answers
Alfred gets pay as $2119.23 per week for a new part-time job as a butler.
What is the division?The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
Given that, Alfred responds to an ad position that pays $110,200 a year.
We know that, there are 52 weeks in a year
Salary for one week =110,200/52
= $2119.23
Therefore, the weekly pay for Alfred is $2119.23.
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What are the equations of the asymptotes of the hyperbola?
(x+1)^2/25−(y−3)^2/16=1
Answers
The horizontal and vertical asymptotes of the hyperbola equation (x + 1)² / 25 - (y - 3)² / 16 = 1 are y = 4x / 5 + 19 / 5 and y = -4x / 5 + 11/5 respectively
Equation of AsymptotesAn asymptote of the curve y = f(x) or in the implicit form: f(x,y) = 0 is a straight line such that the distance between the curve and the straight line lends to zero when the points on the curve approach infinity. This can be said to be a line that a curve approaches but never touches.
Basically, we have three types of asymptotes which are horizontal asymptotes, vertical asymptotes and oblique asymptotes.
In the hyperbola equation given
(x + 1)² / 25 - (y - 3)² / 16 = 1
The equation of asymptotes are;
Horizontal asymptotes : y = 4x / 5 + 19 / 5
Vertical asymptotes : y = -4x / 5 + 11/5
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What is the equation in slope-intercept form of the line that passes through the point (3,4) and is parallel to the line represented by y=3x−2?
y=3x+7y
y=3x−5y
y=−3x+5y
y=−3x−7
Answers
The equation of the line in slope intercept form that passes through the point (3,4) and is parallel to the line represented by y=3x−2 is y = 3x - 5.
How to find equation of a line?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the line that passes through the point (3,4) and is parallel to the line represented by y = 3x − 2.
Parallel line have the same slope. Therefore, the slope of the line is 3.
Let's find the y-intercept using (3, 4).
y = 3x + b
4 = 3(3) + b
4 - 9 = b
b = -5
Therefore, the equation is y = 3x - 5
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