The Image of the point W(7,3) after the translation is W'(5,6),hence the x-coordinate of the translated point is 5
Translation is used in co-ordinate geometry to find the co-ordinates of an image after moving the point from its original position.
A point on the cartesian plane is represented in the form of (x,y). Where x represents the position of the point along the x-axis and y represents the position of the p[point from the y-axis.The distance of the point from the origin is calculated by the distance formula based on Pythagorean theorem.When a points is translated to the left or downwards x and y coordinate values are decreased.When a points is translated to the right or upwards x and y coordinate values are increased.The given point is W(7,3). The point is translated 2 units to the left and 3 units upwards. Hence the new coordinates of the point is given by:
W(7,3)→W'(5,6)
Therefore the x-coordinate of the translated point is 5.
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Find the equation of the line that contains the point (4, -2) and is perpendicular to the line y =
○ y = -x
Oy=2x-10
O y = -2x+6
Oy=x-4
- 2x + 8.
Answer:
b
Step-by-step explanation:
Simplify each expression.
3¹/₃ . 9¹/₃
Express 3 and 9 as a product of their prime factors then in index form. 9=3x3=3^2. 3=3^1. Apply the power rule (a^m)^n = a^mn to simplify. Indices depict: a^m x a^n = a^m+n
9= 3^2
3= 3^1
(3^1)^1/3 x (3^2)^1/3 = 3^1/3 x (3^2)^1/3 = 3^1/3 x (3^1x3^1)^1/3
3^1/3x3^1/3x3^1/3= 3^(1/3+1/3+1/3) = 3^1
=3
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Rachael is on a hiking trip with her friends. After 3 hours of hiking and at 6 miles from their starting point, they decide to take a one-hour break to eat lunch and take pictures.
After 4 more hours, they reach their campsite 16 miles away from their starting point.
Which graph correctly models this situation?
A graph shows the hiking in the number of hours on the x-axis and distance in miles on the y-axis. The function starts from (0, 0), (3, 6), (4, 6), and (8, 10).
A graph shows the hiking in the number of hours on the x-axis and distance in miles on the y-axis. The function starts from (0, 0), (3, 6), (4, 6), and (8, 16).
A graph shows the hiking in the number of hours on the x-axis and distance in miles on the y-axis. The function starts from (0, 0), (2, 6), (4, 6), and (8, 16).
A graph shows the hiking in the number of hours on the x-axis and distance in miles on the y-axis. The function starts from (0, 0), (3, 12), (4, 12), and (8, 16).
The graph that correctly models the situation is option B which has it that A graph shows the hiking in the number of hours on the x-axis and distance in miles on the y-axis. The function starts from (0, 0), (3, 6), (4, 6), and (8, 16)
Given data
After 3 hours of hiking and at 6 miles from their starting point
one-hour break to eat lunch and take pictures
4 more hours, they reach their campsite 16 miles away from their starting point
How to model the journeyx representing number of hours and y representing the distance travelled in miles
The started from origin
( 0, 0 )
3 hours of hiking and at 6 miles from their starting point
( 0 + 3, 0 + 6 ) = ( 3, 6 )
one-hour break to eat lunch and take pictures, no distance covered
( 3 + 1. 6 + 0 ) = ( 4, 6 )
4 more hours, they reach their campsite 16 miles away from their starting point. ( 16 hours is the total distance covered )
( 4 + 4, 16 + 0 ) = ( 8, 16 }
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In 1992, the moose population in a park was measured to be 3590. By 1999, the population was measured again to be 4500. If the population continues to change linearly
A.) Find a formula for the moose population, P, in terms of t, the years since 1990.
P(t)= ____
B.) What does your model predict the moose population to be in 2006?
Answer:
A.) P(t) = 130t +3330
B.) P(16) = 5410
Step-by-step explanation:
Given the ordered pairs (t, P(t)) = (2, 3590) and (9, 4500), you want a linear model that describes the relation. You also want the value of P(16).
A.) Linear modelWe can write the formula for P(t) starting with the point-slope equation for P in terms of t. To do that, we need the slope:
m = (P2 -P1)/(t2 -t1)
m = (4500 -3590)/(9 -2) = 910/7 = 130
The point-slope equation will be ...
P -P1 = m(t -t1)
P -3590 = 130(t -2)
Solving for P, we find ...
P = 130t -260 +3590 . . . . . eliminate parentheses, add 3590
P(t) = 130t +3330
B.) PredictionThe value of P(16) will be ...
P(16) = 130(16) +3330 = 2080 +3330 = 5410
The moose population is predicted to be 5410 in 2006.
__
Additional comment
The value of t is years since 1990, so the relevant values are ...
1992: t = 1992 -1990 = 2
1999: t = 1999 -1990 = 9
2006: t = 2006 -1990 = 16
Values of moose population by linear model A.) P(t) = 130t +3330 B.) P(16) = 5410
What does the term "linear model" mean?
In a linear model, the terms are added rather than multiplied, divided, or provided as a non-algebraic function, as has been the case thus far in this section. A linear model is not just a straight line or its higher dimensional equivalent.Given the ordered pairs (t, P(t)) = (2, 3590) and (9, 4500), you want a linear model that describes the relation. You also want the value of P(16).
A.) Linear model
We can write the formula for P(t) starting with the point-slope equation for P in terms of t. To do that, we need the slope:
m = (P2 -P1)/(t2 -t1)
m = (4500 -3590)/(9 -2) = 910/7 = 130
The point-slope equation will be
P -P1 = m(t -t1)
P -3590 = 130(t -2)
Solving for P, we find
P = 130t -260 +3590 . . . . . eliminate parentheses, add 3590
P(t) = 130t +3330
B.) Prediction
The value of P(16) will be
P(16) = 130(16) +3330 = 2080 +3330 = 5410
The moose population is predicted to be 5410 in 2006.
(B) The value of t is years since 1990, so the relevant values are
1992: t = 1992 -1990 = 2
1999: t = 1999 -1990 = 9
2006: t = 2006 -1990 = 16
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Find the indicated angle measure.
The required measure of the alternate opposite angle is 25°
Given that,
The figure has been shown in which measure of the angle is to be dtermined.
The angle can be defined as the one line inclined over other line. the measure of an angle is measured in two units of degrees and in radiants.
Here,
2x - 1 = 5x - 40
5x - 2x = 40 - 1
3x = 39
x = 13
Now,
measures of the angle,
= 2x - 1 = 2 * 13 - 1
= 25°
and
5x - 40 = 5*13 - 40
= 65 - 40
= 25°
Thus, the required measure of the alternate opposite angle is 25°.
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During a science experiment,the temperature of a solution in beaker 1 was 5 degrees below zero. The temperature of a solution in Beaker 2 was the opposite of the temperature in beaker 1. What was the temperature in beaker 2?
A. - 5 degrees
B- 0 degrees
C- 5 degrees
D- 10 degrees
AB formed by A(2, -7) and B(2, 3);CD formed by C(-4, 0) and D(-4, -5)
The length of the line AB is 10
The length of the line CD is 5
What is a line segment?A line segment is bounded by two distinct points on a line.
We have,
AB formed by A(2, -7) and B(2, 3)
CD formed by C(-4, 0) and D(-4, -5)
The distance between two points (a, b) and (c, d) is given by:
= √(c - a)² + (d - b)²
The length between A and B:
= √(2 - 2)² + (3 +7)²
= √100
= 10
The length of C and D:
= √(-4 + 4)² + (-5 - 0)²
= √25
= 5
Thus,
The length of the line AB is 10
The length of the line CD is 5
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3 to the power of -6 as a fraction
Answer:
[tex]3^{-6} = \left(\frac{1}{3}\right)^{-6}[/tex]
Answer:
Step-by-step explanation:
Exponent Law a^-r = 1/a^r
(1/3^6)
Don't mind the work that I drew on the top.
Answer:
is the solve for x the question
Step-by-step explanation:
the magical coin that doubles every day.
will the value of the magical coin exceed to a million dollars within 28 days? explain or show your reasoning.
yes, if the value of the coin is 1 dollar, then it will exceed the million dollars within 28 days.
Will the value of the magical coin exceed to a million dollars within 28 days?
It will depend on the original value of the coin, value that we don't know, so I will assume that the value of the coin is $1.
If this coin doubles each day, then the day zero its value is $1.
After one day its value is 2*$1 = $2
After another day its value is 2*$2 = $4
And so on, this is modeled by the exponential equation:
y = $1*(2)^x
Where y is the total value and x is the number of days.
After 28 days (this means we use x = 28) the value will be:
y = $1*(2)^28 = $268,435,456
That is a lot more than one million dollars.
So yes, if the value of the coin is 1 dollar, then it will exceed the million dollars within 28 days.
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Each pair of values is from an inverse variation. Find the missing value. (2,5),(4, y)
The missing value of inverse variation is 2.5
What is Inverse variation ?The inverse variation property states that , whenever the product of values of two quantities is a constant value then there is opposite variation between these two corresponding values. Or we can also say that if the productive nature of two corresponding values is constant, then one quantity is inversely varies with second quantity.
Let say if x and y are two values and k is a constant value, then
According to inverse variation
k = xy or y = k/x
In the given question,
Take the order pair (2,5)
As it is an inverse variation, we can substitute it
y=k/x
5=k/2
K=10
Now find the inverse variation equation
y=k/x
Also, k=10
Solve this equation for the second pair (4,y)
As, y=k/x
y = 10/4 = 5/2 = 2.5
Therefore, missing value is 2.5
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0.25 (5 is recurring) decimal to fraction
Since the digit "5" is a recurring (repeating) in the given decimal, its fraction is equal to 23/90.
What is a fraction?A fraction can be defined as a numerical quantity which isn't expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.
The parts of a fraction.In Mathematics, a fraction comprises two (2) main parts and these include the following:
NumeratorDenominatorSince the digit "5" is a recurring (repeating) in the given decimal, its fraction can be written as follows:
0.25555556 = (25 - 2)/90
0.25555556 = 23/90
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A basketball team played 15 games and won 80% of them.if the teamhow many more games must it win to finish the season with a 90% winning percentage
Answer:
1.5 more games to win 90% which would mean a total of 13.5 games.
80% of 15 = 12
10% of 15 = 1.5
12+1.5=13.5
Help plssssssssssssssssssss
Answer: Distributive Property
Step-by-step explanation:
if you multiply x by y it is xy and if you multiply x by z its xz so that makes it equal to xy+xz
PLEASE HELP QUICK
The equation of a line is y = 3/5x + 7.
(a) What is the slope of a line parallel to it?
(b) What is the slope of a line perpendicular to it?
a. The slope of a line that is parallel to y = 3/5x + 7 is: 3/5.
b. The slope of a line that is perpendicular to y = 3/5x + 7 is: -5/3.
How to Determine the Slope of Parallel Lines?Given a line is represented by the equation, y = 3/5x + 7, the slope (m) of the line is 3/5.
Any line that is parallel to y = 3/5x + 7 will have a slope (m) = 3/5 [same slope value].
On the other hand, any line that is perpendicular to y = 3/5x + 7 will have a slope of -5/3 [negative reciprocal].
Therefore:
a. The slope of a line that is parallel to y = 3/5x + 7 would be: 3/5.
b. The slope of a line that is perpendicular to y = 3/5x + 7 would be the negative reciprocal of 3/5, which is: -5/3.
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The endpoints of CD are C (1, -6) and D (7, 5). Find the coordinates of the midpoint M by using the Midpoint Formula.
the mid point of the points C and D is M = ( 4 , - 1 / 2 ).
We are given the coordinates of the point:
C ( 1 , - 6 )
D ( 7 , 5 )
We need to find the mid point M for it.
Here, we have:
x₁ = 1
x₂ = 7
y₁ = - 6
y₂ = 5
We know that the formula for mid point is given by:
M = ( x₁ + x₂ / 2, y₁ + y₂ / 2 )
Substituting the values, we get that:
M = ( 1 + 7 / 2 , - 6 + 5 / 2 )
M = ( 8 / 2 , - 1 / 2 )
M = ( 4 , - 1 / 2 )
Therefore, we get that, the mid point of the points C and D is M = ( 4 , - 1 / 2 ).
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Processes
- &Practices 3
Draw a Conclusion Myron has $1,698 in his
savings account. Robert has $1,898 in his savings account.
Toby has $100 less than Robert in his savings account.
Who has the least amount of money
Myron has least amount of money which is $1,698
According to the question
Given that ,
amount of saving of Myron is $1,698
amount of saving of Robert is $1,898
Toby has $100 less than Robert
amount of saving of Toby is $100 less than Robert
Robert has $1,898
amount of saving of Toby = $1,898 - 100
= $ 1,798
Myron has least amount of money which is $1,698
Savings account is a basic account type that lets you deposit money safely with a bank. It ensures safety and access to your money whenever you need. You can withdraw your funds, either digitally or in person, at any point in time.
Having a savings account is a liquid investment, so you have the ease of using your funds any time for transactions. A savings account also earns decent returns;
A savings account is like a virtual locker that safeguards your money and pays a certain amount of interest. As opposed to a fixed deposit (FD), you can use the money in your savings account whenever you need. A savings account also has other uses.
With your savings bank account, you make transactions, receive payments, pay your credit bills, and make investments. You can also pay for utilities such as electricity bills, ration, mobile phone recharges, and shopping. A savings account safeguards your money from theft and misplacement and reduces the stress that comes with carrying too much cash.
how to calculate saving
If the daily amount is Rs 3 lakhs and the interest rate on the savings account is 4% per year, the computation will be Interest on a monthly basis = Daily Balance * (Number of days) *Interest / (Days in the year)3 lakhs * 30 * (4/100) / 365 = Rs 986 per month in interest Daily
balance: 3 lakh
Number of days: 30
Interest: 4%
Days in the year: 365
According to Bank, "Savings bank interest will be calculated on the daily balances maintained in your account. Savings Bank interest will be paid at quarterly intervals."
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Triangle PQR is formed by connecting the midpoints of the side of triangle MNO. The lengths of the sides of triangle PQR are shown. What is the length of MN? Figures not necessarily drawn to scale.
The length of segment [tex] \overline{MN} [/tex] found using properties of an equilateral triangle and segment addition postulate is 10
What is segment addition postulate?Segment addition postulate states that a line AC contains a point B if we have AB + BC = AC
The sides of ∆PQR are equal to 5, therefore, ∆PQR is an equilateral triangle
According to the mid segment theorem, we have;
RQ || MN
RQ = 0.5 × MN
RP || ON
RP = 0.5 × ON
PQ || MO
PQ = 0.5 × MO
Therefore, from alternate interior angles theorem, we have;
‹PRQ = ‹RPM
‹PQR = ‹QPN
‹QRP = ‹RQO
However, ‹PRQ = ‹PQR = ‹QPR = 60°, which gives;
∆MRP and ∆QPN are equilateral triangles of side length 5
From which we have;
MR = RP = MP = 5
PN = QN = PQ = 5
MN = MP + PN; Segment addition postulate
Therefore;
MN = 5 + 5 = 10
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A large corporation is hosting a conference. So far, 3,600 attendees from the United States
have registered, as well as 3 attendees from other countries. How many total attendees have
registered?
so so much to do with the way you are you going to be able to get the vaccine and I will be there in a few minutes to get the vaccine and I will 57
I need this answered please
Using substitution method, solve
3x-y=0
2x+y=5
Answer:
x=1 y=3
Step-by-step explanation:
Hello!
So, this says to use the substitution method. The substitution method is where you set one equation equal to one of the letters, and then put that whole equation in the other equation.
So->
3x-y=0
if we move the y to the other side we have:
3x=y
then we have our second equation:
2x+y=5
Now, we don't know what NUMBER y is yet, but we do know that it is equal to 3x. Thus, we can put it into the equation like this.
2x+(3x)=5
Then, we can add like terms and get:
5x=5
Dividing each term by five, we get
x=1
We could have also done this be solving for x in the equations and then substituting that in instead of y.
Now that we have x, we can easily put it into the equations and solve for y.
3x-y=0
3(1)-y=0
3=y
So now we know that x is equal to 1 and y is equal to 3.
The temperature is -2° C. If the temperature rises by 15° C, what is the new temperature?
Answer:13
Step-by-step explanation:
If log x=5 , what is the value of 1/x ?
If the equation is log x=5 then the value of 1/x is equal to 0.00001.
Given that the equation is log x=5.
We are required to find the value of 1/x.
Equation is basically the relationship between two or more variables that are represented in equal to form. It may be linear equation,quadratic equation and cubic equation and many more depending on the power of variables present in the equation. The given equation contains logarithm.
The equation is log x=5.
Take the base of the log and raise it to both the sides of the equation:
[tex]10^{log x}[/tex]=[tex]10^{5}[/tex]
x=100000 (log 100000=5)
1/x=1/100000
1/x=0.00001
Hence if the equation is log x=5 then the value of 1/x is 0.00001.
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WILL GIVE YOU EXTRA BRAINLIEST POINTS IF YOU ANSWER THANKS
Based on the formulas given for PR and QR, the length of PR is 19.8 units.
What is the length of PR?The shape that is given is an equilateral triangle. This allows us to know that all the sides of the shape are equal.
This means that PR and QR are the same:
PR = QR
Equate both formulas as:
2n + 9 = 7n - 18
You can then solve for the value of n:
7n - 2n = 18 + 9
5n = 27
n = 5.4
The length of PR can then be solved by using substitution:
= 2n + 9
= 2 (5.4) + 9
= 19.8 units
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Multiply. Write your answer as a fraction in lowest terms.
One half of a number is more than six less than the same number. Describe what numbers will work.
The numbers that will work are all numbers less than 12
How to describe what numbers will work?The statement is given as:
One half of a number is more than six less than the same number
Let the number be represented with x
So, the mathematical expression is
1/2x > x - 6
Subtract x from both sides
-1/2x > -6
Multiply both sides by -2
x < 12
Hence, the numbers that will work are all numbers less than 12
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Jim made $238 for 17 hours of work.
At the same rate, how many hours would he have to work to make 126 ?
The number of hours in which Jim will make $126 is equal to 9 hours.
What is the unit rate ?
An unit rate is a ratio that is used for comparing two different kinds of quantities which have different units.
It is given that Jim has made $238 after working for 17 hours.
If we try to find out the unit rate that how much he earn in 1 hour then it can be find out by dividing money earned by no. of hours he has worked.
So , the in 1 hour Jim will make money :
= 238 / 17
= $14
Now , we have to find out that how many hours he has to work to make 126. So , for this we need to divide it by 14 which is the unit rate.
The no. of hours in which Jim will make $126 will be :
= 126 / 14
= 9 hours
Therefore , the number of hours in which Jim will make $126 is equal to 9 hours.
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the length of a rectangle is 5 units longer than one third of the width w. Write an expression that represents the perimeter of the rectangle (use one variable and a fraction) Simplify the expression.
The expression that represents the perimeter of the rectangle is: 8/3w + 10 units
How to Determine the Perimeter of a Rectangle?Perimeter of rectangle = 2(length + width).
Let the width be represented as variable w
Width = w
Length of the rectangle = 1/3w + 5 units
Thus, substitute the values into the formula
Perimeter of the rectangle = 2(1/3w + 5 + w)
Simplify
Perimeter of the rectangle = 2(4/3w + 5)
Perimeter of the rectangle = 8/3w + 10 units
Therefore, the expression that represents the perimeter of the rectangle is: 8/3w + 10 units
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Write each expression in exponential form. ∛y⁸
The exponential form of the expression= [tex]y^{8/3}[/tex]
To expresses it in an exponential form we have expression:
[tex]\sqrt[3]{y^{8} }[/tex]
As we have to express as
[tex]a^{m}[/tex]/ [tex]a^{n}[/tex] = [tex]a^{m}[/tex][tex]a^{-n}[/tex]
= [tex]a^{m-n}[/tex]
From the question we have
[tex]\sqrt[3]{y^{8} }[/tex]
[tex](y^{8}) ^{1/3}[/tex]
[tex]y^{8/3}[/tex]
Therefore the exponential form of the expression is [tex]y^{8/3}[/tex]
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x-intercept = -4, y-intercept = 3 graphed is?
Answer:
The slope is 4/3
Step-by-step explanation:
An x-intercept is the value of
x when y = 0
, so an x-intercept of 3
can be written as a coordinate on the graph as
(3,0).
Likewise, an
y
-intercept is the value of
y
when
x
=
0
, so an
y
-intercept of
−
4
can be written as a coordinate on the graph as
(
0
,
−
4
)
Now we have two points,
(
3
,
0
)
and
(
0
,
−
4
)
.
To find the slope given two points, we use the formula
rise
run
, or
y
2
−
y
1
x
2
−
x
1
.
Plug in the given points into the formula:
−
4
−
0
0
−
3
=
−
4
−
3
=
4
3
Therefore, the slope is
4
3
.