From the inequalities 30x + 20y ≤ 200 and x + y ≥ 6, Roger can buy 3 pants and 3 shirts.
What is an equation?An equation is an expression that shows the relationship between numbers and variables.
Inequalities is used for the non equal comparison of these numbers and variables.
Let x represent the number of pants that Roger buys and y represent the number of shirts he buys.
He can buy pants for $30 and shirts for $20. Roger received $200 for his birthday, therefore:
30x + 20y ≤ 200 (1)
Also:
He wants at least 6 new items. hence:
x + y ≥ 6 (2)
From both equations, the solution to these equalities is (3, 3)
Roger can buy 3 pants and 3 shirts.
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Stanley feeds each of his dogs 1/6 of a can of food each day. He uses a total of 1/2 of a can of food each day. How many dogs does Stanley have?
Answer: 3 dogs
Step-by-step explanation:
Each dog eats 1/6 cans of food
Stanley uses a total of 1/2 cans of food
[tex]\frac{1}{2}[/tex] / [tex]\frac{1}{6}[/tex] = 1/2 * 6
= 3 dogs
out of the 33 costumes for the school play, 17 need to be altered to fit an actor. 15 costumes need to be shortened and 11 costumes need to be taken in. what is the probability that a randomly selected costume needs both shortened and taken in?
The probability that randomly selected costume needs both shortened and taken in is 9/33
There are a total of n(T) = 33 costumes. Of these n(A) = 17 require alteration. The two sorts of change are shortening and taking in. n(S) = 15 costumes require shortening, and n(I) = 11 costumers require being taken in.
We are to determine the probability that a randomly selected costume requires both shortening and taken in.
The following is the formula for the union of sets.
P(S ∪ I) = P(S) + P(I) - P(S ∩ I)
∴ S ∪ I = A
∴ P(A) = P(S) + P(I) - P(S ∩ I)
∴ [tex]\frac{n(A)}{n(T)} = \frac{n(S)}{n(T)} + \frac{n(I)}{n(T)} - P(S \cap I)[/tex]
∴ [tex]P(S \cap I) = \frac{n(S)}{n(T)} + \frac{n(I)}{n(T)} - \frac{n(A)}{n(T)}[/tex]
Substituting the values:
∴ [tex]P(S \cap I) = \frac{15}{33} + \frac{11}{33} - \frac{17}{33}[/tex]
∴ [tex]\frac{26}{33} - \frac{17}{33}[/tex]
∴ [tex]\frac{9}{33}[/tex]
Therefore the probability that randomly selected costume needs both shortened and taken in is 9/33
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graph shows the relationship between time and the number of soda bottles a machine can make. Use the points (4,220) and (7,385) to find the number of soda bottles the machine can make each minu
55 is the number of soda bottles the machine can make each minute.
What is proportionality?the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.
Given, the graph shows the relationship between time and the number of soda bottles a machine can make. Use points (4,220) and (7,385)
Since this graph is a straight line graph and also it goes through the origin that means time is directly proportional to the number of soda can manufactures
To prove this theory
the ratio between cans to the time taken by machine = 220/4 = 385/7
Since the ratio is the same for two points.
Thus,
Soda machine makes in 4 hours = 220 cans
Soda machine makes in 1 hours = 220/4 = 55 cans
Therefore, the number of soda bottles the machine can make each minute is 55.
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Please Help I Need Help With This Problem.
The equation can be written as 6 + (-6y) = -6y - 1 + (7).
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
The given is an equation with missing parts.
The left hand side of the equation does not contain a term with variable, but the right hand side contains it.
Adding that term in the left hand side, we get, 6 + (-6y) in the left hand side.
So the right hand side must be equal.
So the expression in the right hand side is -6y - 1 + (7).
Hence the expressions are 6 + (-6y) on the left hand side and -6y - 1 + (7) on the right hand side.
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Jordan spent 5 hours over the weekend studying for 3 tests. He spent an equal amount of time studying for each test.
How long did Jordan spend studying for each test?
134 hours
35 hour
15 hour
123 hours
As per the concept of fraction, the amount time spend for each test is 1.67 hours
In math the term called fraction is known as the number is expressed as a quotient in which the numerator is divided by the denominator.
Here we have know that Jordan spent 5 hours over the weekend studying for 3 tests.
In order to find the amount of time spend for each test, we have to divide the total number of subject by the time spend by him.
Here the value of total subjects = 5 and the amount of time spend by him is 3.
Then the amount of time time spend for each test is calculated as,
=> 5/3
=> 1.67 hours
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Select ALL factors of 27. (Be sure to select ALL correct factors for full credit).
Question 4 options:
3
1
2
16
54
27
9
81
Answer:1, 3, 9, 27
Step-by-step explanation:
Wilon’ car hold 15 gallon of gaoline in it tank. Wilon had 8.4 gallon of gaoline in the tank. He ued 3.9 gallon on a recent trip.
The percent of the gas in the tank remaining is equals to the 53.6..
The capacity of Wilon's car's gas tank
= 15 gallons
The amount of gas in Wilon's car's tank
= 8.4 gallon
The amount of gas in tank used on a recent trip = 3.9 gallons
The remaining amount of gas in tank
= amount of gas in Wilon's car's tank before trip - amount of gas in tank used on a recent trip.
= 8.4 gallons - 3.9 gallons
= 4.5 gallons
Percent is calculated as the value diving by total value and then multiply with hundred. Now, the percent of the gas in the tank remaining = (4.5/8.4)× 100
=( 45/84)100
= 4500/84
= 53.57 ~ 53.6 %
Hence, the percent of the gas in the tank remaining is 53.6 .
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Complete question:
Wilon’ car hold 15 gallon of gaoline in it tank. Wilon had 8.4 gallon of gaoline in the tank. He used 3.9 gallon on a recent trip. What is the percent of the gas in the tank remaining?
What is the equation of the line that passes through the point (−6,−7) and has a slope of 1/3?
[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{-7})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{3} \\\\\\ \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}{(-7)}=\stackrel{m}{ \cfrac{1}{3}}(x-\stackrel{x_1}{(-6)}) \implies y +7= \cfrac{1}{3} (x +6) \\\\\\ y+7=\cfrac{1}{3}x+2\implies {\Large \begin{array}{llll} y=\cfrac{1}{3}x-5 \end{array}}[/tex]
Answer:
I think it is y=1/3x -7
Step-by-step explanation:
if i run 5280 feet in 5.00 minutes, what is my speed in miles per hour (to the appropriate number of significant figures)?
When I run 5280 feet in 5.00 minutes my speed is 12 miles per hour
What is velocity?It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).
The formula and procedure we will use to solve this exercise is:
v = x /t
Where:
x = distancet = timev = velocityInformation about the problem:
x = 5280 feett = 5 minutesv (miles/hour) = ?Applying the velocity formula, we get:
v = x /t
v = 5280 feet / 5 minutes
v = 1056 feet/ minutes
By converting the unit from feet to miles and from hours to minutes, we have:
1056 feet/ minutes * (1 miles / 5280 feet) * (60 minutes / 1 hour) = 12 miles/hour
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Algebra 2 volume 2 question 60
The value of function fg(x) is -x^4-4x^3.
What is a function?
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).
There are several types of functions in math. Some important types are:
Injective function or One to one function: When there is mapping for a range for each domain between two sets.
Surjective functions or Onto function: When there is more than one element mapped from domain to range.
Polynomial function: The function which consists of polynomials.
Inverse Functions: The function which can invert another function.
Now,
given functions are f(x)=-x^3 and g(x)=x+4
so, fg(x)=f(x)*g(x)=-x^3(x+4)
Therefore, the value of
fg(x) = -x^4-4x^3
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The value of function fg(x) is -x^4-4x^3.
What is a function?
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).
There are several types of functions in math. Some important types are:
Injective function or One to one function: When there is mapping for a range for each domain between two sets.
Surjective functions or Onto function: When there is more than one element mapped from domain to range.
Polynomial function: The function which consists of polynomials.
Inverse Functions: The function which can invert another function.
Now,
given functions are f(x)=-x^3 and g(x)=x+4
so, fg(x)=f(x)*g(x)=-x^3(x+4)
Therefore, the value of
fg(x) = -x^4-4x^3
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Anita is an airline attendant. Last week, she worked on flights on 1 small jet and 2 large jets, which could seat a total of 253 passengers. The week before, she was assigned to flights on 5 small jets and 4 large jets, which could seat a total of 725 passengers. How many seats were on each type of flight?
Answer:
Small jet seat capacity: 73
Large jet seat capacity = 90
Step-by-step explanation:
Let x be the number of seats on the small jet
Let y be the number of seats on the large jet
From the word description for last week:
Last week, she worked on flights on 1 small jet and 2 large jets, which could seat a total of 253 passengers
we can formulate the equation
1x + 2y = 253 .............(1)
For the week before:
The week before, she was assigned to flights on 5 small jets and 4 large jets, which could seat a total of 725 passengers
5x + 4y = 725 ...............(2)
Equation (1) x 2 ==>
2x + 4y = 2(253)
2x + 4y = 506 ..............(3)
So our two equations are:
5x + 4y = 725 . .............(2)
2x + 4y = 506 ..............(3)
Equation (2) - Equation (3) will eliminate the y terms making it possible to solve for x
(5x + 4y) - (2x + 4y) = 725 - 506
5x + 4y - 2x - 4y = 219
5x -2x +4y - 4y = 219
3x = 219
x = 219/3
x = 73
Plugging this value back into equation (1): 1x + 2y = 253 we get
1(73) + 2y = 253
73 + 2y = 253
2y = 253 - 73
2y = 180
y = 180/2
y = 90
Answer
Small jet seat capacity: 73
Large jet seat capacity = 90
9 thousands 2 tens x10 =
Answer: 90200
Step-by-step explanation:
9020 x 10 = 90200.
Just add one more zero when multiplying by ten.
a graph of a linear equation passes through (-2,0) and (0,-6). Is 3x-y=-6 an equation for this graph? (Yes or no question)3. Explain your reason of how you know
well, let's find the equation of the line through those points then, and let's see
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-6}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-2)}}} \implies \cfrac{-6 }{0 +2} \implies \cfrac{ -6 }{ 2 } \implies - 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}{0}=\stackrel{m}{- 3}(x-\stackrel{x_1}{(-2)}) \implies y = - 3 ( x +2) \\\\\\ y=-3x-6\implies \boxed{3x+y=-6} ~~ \ne ~~ 3x-y = 6[/tex]
(WILL GIVE BRAINLIEST)
The following table shows the number of goals that the Texas Sharpshooters scored in each of their 8 hockey games this season.
(Table with 3, 4, 1, 4, 1, 1, 2, 1)
Based on this data, what is a reasonable estimate of the probability that the Texas Sharpshooters score exactly 1 goal next hockey game?
Choose the best answer.
Choose 1 answer:
(Choice A)
A
0. 13
(Choice B)
B
0. 24
(Choice C)
C
0. 50
(Choice D)
D
1. 0
The probability that the Texas Sharpshooters score exactly 1 goal next hockey game is 0.5
The following figure accurately depicts the table.
Experimental probability is the likelihood of a future event based on past happenings.
Experimental probability is equal to the ratio of good results to all possible results.
To calculate the likelihood that the Texas Sharpshooters will score precisely
Next hockey game: 1 goal
As displayed in the table:
a successful outcome is repeated four times.
So, positive results equal 4
8 total results
likelihood = 4/8 = 0.5
So, The probability that the Texas Sharpshooters score exactly 1 goal next hockey game is 0.5
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Answer:
0.50 (Choice C)
Step-by-step explanation:
Khan Academy told me.
the second hand of a clock is 8 centimeters long. find the linear speed of the tip of this second hand as it passes around the clock face.
The linear speed of the tip of this second hand as it passes around the clock face is 0.84 cm/ seconds
What is velocity?It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).
The formula and procedure we will use to solve this exercise is:
speed = x /tLength of a circle = 2*pi*rWhere:
x = distancet = timespeed = velocityr = radiusInformation about the problem:
pi = 3.14r = 8 cmt = 60 secondsv = ?As the distance in the problem will be the circumference of the circle that second-hand makes in one complete revolution, we have:
Length of a circle = 2*pi*r
Length of a circle = 2*3.14*8
Length of a circle = 50.24 cm
The time it takes to complete one full revolution by second hand is 60 seconds, so applying the velocity formula with this time, we get:
speed = x /t
speed = 50.24 cm/ 60 seconds
speed = 0.84 cm/ seconds
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1. Patrick Mahomes throws a 5kg football to Tyreek Hill at 25m/s to win Super
Bowl LV. What was the Kinetic Energy of the football as it was traveling down the
field? PE = mxgx h PE = wxh KE =. 5 xm xv^2 g = 9. 8 m/s *
1225 J is the Kinetic Energy of the football as it was traveling down the
field.
Calculate the Kinetic Energy (KE) of the football.
KE = 0.5 x 5 kg x (25 m/s)^2
Calculate the Kinetic Energy of the football in Joules (J).
KE = 0.5 x 5 kg x (25 m/s)^2 x 9.8 m/s^2
Calculate the Kinetic Energy of the football in Joules (J).
KE = 0.5 x 5 kg x (25 m/s)^2 x 9.8 m/s^2 = 1225 J
The energy an object has as a result of motion is known as kinetic energy in physics. It is described as the effort required to move a mass-determined body from rest to the indicated velocity.
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There are 5 girls, 6 boys and some adults in a room. Jenny selects at random one of these people
If there are 5 girls, 6 boys and some adults in a classroom and probability that a girl is chosen is 1/3 , then the probability of an adult being chosen is 4/15 .
The number of adults in unknown .
So let "n" denote the number of adults.
the number of girls in the room is = 5 girls ;
the number of boys in the group is = 6 boys ;
So , the total number of people to choose from will be = 5 + 6 + n ;
= 11 + n ;
The probability of picking the girl from this group will be = 5/(11+n) ;
the probability of girl being selected is = 1/3,
Equating both the probabilities ,
we get ; 5/(11+n) = 1/3
On Cross multiplying we have : 11 + n = 15
which means ⇒ n = 4 and number of adults is = 4 ;
So ,the total number of people is = 11 + 4 = 15.
So , The probability of picking adult is = 4/15.
The given question is incomplete , the complete question is
There are 5 girls, 6 boys and some adults in a classroom. The probability that a girl is chosen is 1/3. What is the probability of an adult being chosen ?
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Please help with the math and explain every step ty and *40 points* will mark brainless
Answer:
see below
Step-by-step explanation:
5000
60% = 3000 in stocks
year 1 gain 9% = 3000*1.09 =3270
year 2 loss 4% = 3270*(1-4%) =3139.2
40% = 2000 in savings
year 1 earn 4.9% = 2000*1.049 = 2098
year 2 earn 4.9% = 2098*1.049=2200.8
TOTAL in 2 years = 3139.2+2200.8 = 5340
so gain = 5340-5000 =340
if all only in savings:
5000*(1.049)² = 5502
the isosceles triangle has two sides of equal length that are longer then the length of the base the perimeter of the triangle is 15.7 centimeters the equation 2a+b=15.7 models this information if one of the longer sides is 6.3 centimeters which equation can be used to find the length of the base
The length of the base is 3.1 cm when you subtract 12.6 from btohs ides b is15.7.
The definition of an isosceles triangle?There are two equal sides and two equal angles in an isosceles triangle. The word is a combination of the Greek words iso (same) and skelos (leg). Equilateral triangles are those in which all of the sides are equal, while scalene triangles are those in which none of the sides are equal.
Equilateral triangles are those in which all of the sides are equal, while scalene triangles are those in which none of the sides are equal.
The equal sides of an isosimple triangle are longer than the base's length.
We know that identical sides are greater, thus 6.3 is one of the identical sides in the perimiter=15.7 equation, which is 2a+b=15,7.
2a denotes the two identical sides: 2(6.3) + b = 15.7
The answer is base=3.1 cm when you subtract 12.6 from btohs ides b=15.7.
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Solve this equation in the
given domain: 0
*give answer in radians*
3 sin (2x-4)=2
There should be 4 answers.
look at attached photo
The solution to the equation in the given interval is 2.365
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
3sin(2x - 4) = 2
Divide both sides of the equation by 3
So, we have the following representation
sin(2x - 4) = 2/3
Take the arcsin of both sides
This gives
2x - 4 = 0.73
Evaluate the like terms
2x = 4.73
Divide by 2
x = 2.365
Hence, the value of x is 2.365
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solve the equations 2x+y=9 and 2x+5y=37 by combining the equations
Answer:
4x+6y = 46
Step-by-step explanation:
you just add by column
2x+2x
y+5y
9+37
Which of the following is equivalent to
O A 1 + √5
2
OB. 1-√√5
2
O C. √5-1
2
OD √5-2
2
1 + √5
2
The equivalent expression is (a) 1 + √5
How to determine the equivalent expressionFrom the question, we have the following parameters that can be used in our computation:
√5 + 1
The additive property of equality states that
a + b = b + a
using the above as a guide, we have the following:
√5 + 1 = 1 + √5
This means that the equivalent of √5 + 1 is 1 + √5
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Complete question
Which of the following is equivalent to √5 + 1
O A 1 + √5
OB. 1-√√5
O C. √5-1
OD √5-2
if a point is on the perpendicular bisect or if a segment then what is it
Answer: It is equidistant from the segment's endpoints
Step-by-step explanation: This can also be called "a locus of point" and this is now the perpendicular bisector theorem.
What reflections map the figure onto itself
A line of symmetry is the reflections map the figure onto itself.
What reflection map the figure onto itself?A line of symmetry is, in other words, a line that splits a figure into two mirror representations. This line's reflection maps the figure onto itself. While some figures lack symmetry, others do feature one or more lines of symmetry. An example of a form having reflection symmetry is a rectangle.
The symmetry axes are shown and given the letters m and n. The figure will map to itself when reflected across either (or both) of the symmetry axes. It seems like you want to call those reflections...
Ra, where
a = m, and
Rb, where
b = n
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Select 2 expressions that can be used to find the value of x.
14sin(55)
14cos(35)
14sin(35)
14cos(55)
Answer:
14sin(55) and
14cos(35)
Step-by-step explanation:
Greetings!!
just remember trigonometric ratios which are
[tex]sin = \frac{opposite}{hypotenus} \\ cos = \frac{adjecent}{hypotenus} \: and \\ tan = \frac{opposite}{hypotenus} [/tex]
following that substitute given values to solve for x.
[tex]sin55 = \frac{x}{14} [/tex]
solve for x
[tex]x = 14 \sin(55) [/tex]
And
[tex] \cos(35) = \frac{x}{14} [/tex]
solve for x
[tex]x = \cos(35) [/tex]
Hope it helps!!!
A student is simplifying the expression below. Find the student's error and correct it. -3(x + 2) + 6x = -3x + 2 + 6x = 3x + 2
The error is that the student did not distribute the -3 to the x and 2 inside the parentheses.
The correct answer is 3x - 6
How to find the student's error and correct it?Simplification of an algebraic expression is defined as a way of writing an expression in the most efficient and compact form without affecting the value of the original expression.
The student's error is that the student did not distribute the -3 to the x and 2 inside the parentheses when simplifying the expression.
The correct simplification of the expression is:
-3(x + 2) + 6x = -3x - 6 + 6x = -3x + 6x - 6 = 3x - 6
Therefore, the student's answer is 3x + 2, but the correct answer is 3x - 6.
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The student made error when removing the bracket. The correct simplification of the expression is 3x - 6
How do I determine the error of the student?We can spot the error of the student by carefully observing the student's answer. This is illustrated below:
-3(x + 2) + 6x = -3x + 2 + 6x = 3x + 2
From the student's work, we can see that the student made an error when removing the bracket.
How do I correct the student?We can correct the student's error by carefully removing the bracket as shown below:
-3(x + 2) + 6x
Remove bracket by multiplying through by -3
-3x - 6 + 6x
Rearrange by bring the numbers with x variables together
-3x + 6x - 6
3x - 6
Thus, the correct answer to the simplification is 3x - 6
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Ingrid has 14. 4 meters of string to hang 5 pennants and a banner at her school. She needs 0. 65 meter of string for the banner and the same length string for each pennant. What length of string will be used to hang each pennant? Write and solve a two-step equation
The length of string will be used to hang each pennant is 3.9 meters.
The term length in math is defined as the measurement or extent of something from end to end and it is used to identifying the size of an object or distance from one point to the other.
Here we have given that Ingrid has 14. 4 meters of string to hang 5 pennants and a banner at her school.
And here we have also know that she needs 0. 65 meter of string for the banner and the same length string for each pennant.
the length of the string needed for 5 pennants is calculated as,
=> 0.65 x (5 + 1)
=> 3.9 meter.
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Which of the following tables shows a rate greater than 1 kilometer per hour? The answer to that is B and the question after that says Hailey chose C as the correct answer. How might she have gotten that answer.
It should be noted that the rate will be gotten by dividing the distance by the time taken.
How to explain rate?A rate in mathematics is a ratio that contrasts two distinct quantities with dissimilar units. Typically, a rate is defined as the ratio of two quantities expressed in different units. The first quantity is typically written as the numerator of a fraction, and the second quantity is written as the denominator
By reducing them to their simplest form, we can express the rate. By way of illustration, if a person walks 30 steps in 20 seconds, their walking speed is 30 steps/20 seconds, or 3 steps/2 seconds.
The information above was given as your information is incomplete. The table wasn't shown.
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The value of a house increased by 30% to $156,000.
What was the original price of the house?
The original price of the house is 156,000
How to calculate the original price of the house?
From the question,
The house was increased by 30% which leads to an increase to 156000
To get the original price of the house
Let the value of the house be x
We then multiply the original price of the house(x) by 30%
we have 0.30*x
0.30x = 156000
Divide both sides by 0.30
x = 520,000
Hence, 520000 is the original price of the house
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Complete the rule that describes the translation.
Answer:
(2,4)
Step-by-step explanation:
The point that's on the origin (0,0) goes to the right by 2 which is your x-axis and goes up 4 which is your y-axis.
Answer:
Translation: (2,4)
Step-by-step explanation:
The dot/point that's in the middle which is always (0,0) goes to the right by 2 (x-axis) meaning that the first coordinate would be 2. It then goes up 4 (y-axis) meaning that the second coordinate would be 4.