The puck travelled a distance of 53.8 meters when the puck is 120 centimeters before the opponent's goal and puck travelled a distance of 56.2 meters when the puck is 120 centimeters after the opponent's goal.
Given that the distance to the opponent's goal from the player's current position is 55 meters. And after the shot, the puck is 120 centimeters from his opponent's goal.
We need to find out how many meters the puck travelled.
Also given there are 100 centimeters in 1 meter.
So, 55 meters = 55 × 100 centimeters
⇒ 55 metets = 5500 centimeters
Now, we are given that the puck is 120 centimeters from the opponent’s goal. It is not clear whether the puck landed before or after the goal post. So, considering both cases.
Case 1: the puck is 120 centimeters beyond the opponent's goal.
So, the distance travelled by the puck is
5500 centimeters + 120 centimeters = 5620 centimeters
Divide 5620 by 100 to convert centimeters to meters.
The puck travelled a distance of 5620 cm or 56.2 meters.
Case 2: the puck is 120 centimeters before the opponent's goal.
So, the distance travelled by the puck is
5500 centimeters - 120 centimeters = 5380 centimeters
Divide 5380 by 100 to convert centimeters to meters.
The puck travelled a distance of 5,380 cm or 53.8 meters.
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The right triangle on the right is a scaled copy of the right triangle on the left. Identify the scale factor. Express your answer as a whole number or fraction in simplest form.
Answer:
scale factor = 3
Step-by-step explanation:
the scale factor is the ratio of corresponding sides, copy to original , so
scale factor = [tex]\frac{12}{4}[/tex] = [tex]\frac{9}{3}[/tex] = 3
how would you express b⃗ b→b vec using unit vectors? express your answers in terms of the unit vectors x^x^x unit and y^y^y unit . use the button under the menu in the answer box to create unit vectors. b⃗ b→b vec
The given vector can be expressed as B = B (cos θ x ^ + sin θ y ^)
The strength of the field and its angle with respect to a particular coordinate axis must be known in order to express the magnetic field B using unit vectors. Trigonometry can be applied after this information is known.
Let's utilize trigonometry if the angle we have is with respect to the x-positive axis's side.
cos θ = Bₓ / B
sin θ = B / B
Bx = By cos θ
B_{y} = B sin θ
so the resulting vector is
B = Bₓ i ^ + B_{y} j ^
unit vectors
x ^ = i ^
y ^ = j ^
B = B (cos θ x ^ + sin θ y ^)
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what is the equation in point-slope form of the line passing through (0, 5) and (−2, 11)? (1 point) y − 5
According to the question, the line is through the points [tex](0,5)[/tex] and [tex](-2,11)[/tex]
To calculate the slope using standard formula that is :
[tex]m = \frac{(y(2)-y(1))}{(x(2)-x(1))} = \frac{(11-5)}{(-2-0)} =\frac{6}{-2} = -3[/tex]
Now the slope equation will be: [tex]m(x(2)-x(1)) = (y(2)-y(1))[/tex]
[tex]y-5 =(-3)(x-0) = y = -3(x)+5[/tex]
The slope-intercept form is:[tex]y = -3x+5[/tex]
What is the equation of the line?
To represent the set of points in an algebraic form is known as the equation of line. The set of points represent lines in the coordinate system. The parameters can be calculated and those parameters are slope and y-intercept.
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if a researcher wishes to conclude something about a population from a sample, it is best that the sample be
If a researcher wishes to conclude something about a population from a sample, it is best that the sample be taken randomly.
What is a random sample?Sampling is the process by which a representative number is taken from a population for the purpose of study. The sample must be taken in such a way that it reflects the properties of the whole.
Thus, if a researcher wishes to conclude something about a population from a sample, it is best that the sample be taken randomly.
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56% of the students at a college are from in-state. if 2,380 students are from in-state, how many students attend the college?
Answer:
Step-by-step explanation:
Answer is 4250 students attend the college
4250 x .56 = 2,380
prove the sum of two rational numbers is rational where a, b, c, and d are integers and b and d cannot be zero. stepsreasons 1. a over b plus c over dgiven 2.multiply to get a common denominator 3. ad plus cb all over bdsimplify fill in the missing step in the proof. (1 point)
The missing step in the rational number proof is; Reason 2; Multiply to get a common denominator
How to prove Rational Numbers?
Let a/b and c/d be two rational numbers, where b and d are not zero and a, b, c and d are integers.
Step 1; a/b + c/d
Reason 1; Given
Step 2; a/b + c/d = ad/bd + cb/bd
Reason 2; Multiply to get a common denominator
Step 3; a/b + c/d = ad/bd + cb/bd = (ad + cb)/bd
Reason 3; Simplify
Since b and d cannot be zero, then bd cannot be zero. Also, since a, b, c, and d are integers, then bd, ad, bc and ad + bc are integers too. Thus, the fraction(ad + cb)/bd is a rational number.
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-9 = -7+w what is W???????!!!!!!!!!!!!!
need help asap please help
Answer:
the answer is -2, substitution took place tht is why w turned to -w
Step-by-step explanation:
-W=9 - 7
-W= 2.
W=-2
f(x)=2x³+6 and g(x)= -5x+4
Find f(-4) and g(5)
[tex]f( - 4) = - 122[/tex]
And
[tex]g(5) = - 21[/tex]
Step-by-step explanation:
Greetings !
For the first expression
[tex]f(x) = 2x {}^{3} + 6[/tex]
plug in -4 at the variable x and solve the expression.
[tex]f( - 4) = 2( - 4) {}^{3} + 6[/tex]
Follow the PEMDAS order of operations
calculate the exponents
[tex]( - 4) {}^{3} = - 64[/tex]
Apply exponent rule
[tex]( - a) {}^{n} = - a {}^{n} . \: if \: n \: is \: odd[/tex]
Thus,
[tex]( - 4) {}^{3} = - 4 {}^{3} = - 64[/tex]
Multiply and divide (left to right )
[tex]2( - 64) = - 128[/tex]
[tex] = - 128 + 6 \\ = - 122[/tex]
Fairly follow the same. process for the second function
Hope it helps !!
HELP ASAPPPPPPPPPPPPPPPPPPPPPPPPPPP
Pearce needs to choose a variable to represent the number of wallabies in an exhibit. Which variable would be the best choice? Explain.
The variable that would be the best choice when Pearce needs to choose a variable to represent the number of wallabies in an exhibit will be D. let w= the number of wallabies on the exhibit.
What is a variable?It should be noted that a variable simply means a symbol that's used to represent a situation in mathematics.
In this case, the variable that would be the best choice when Pearce needs to choose a variable to represent the number of wallabies in an exhibit so be let w= the number of wallabies on the exhibit.
This is because of the first alphabet used which is w.
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How many unit segments are there from 3 to 7?
The unit segments from 3 to 7 are infinite.
The number from 3 to 7 is given.
We have to find out the no. of segments between the two numbers.
What is algebra ?
Algebra is the branch that deals with various symbols and the arithmetic operations such as addition , division , etc.
As per the question ;
Consider any number x such that 3 < x < 6
Then ;
The segment from x to x+1 is a unit segment and, by definition, it will lie within the interval to 7.
As, there are infinitely many possible choices for x, then there are infinitely many unit segments.
i.e.,
from 3 to 4
from 3.1 to 4.1
from 3.01 to 4.01
from 3.00002 to 4.00001
and you can keep adding decimal digits forever.
Thus , there are infinite unit segments from 3 to 7.
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The second-order decomposition of hi has a rate constant of 2.80 x 10-3 m-1s-1. how much hi remains after 78.3 s if the initial concentration of hi is 3.56 m?
In the Second order decomposition, 2.0008 m are needed after 78.3 s, the concentration of the remaining HI is 3.56 m.
Second-Order Reaction:
A second-order reaction system with a single reactant species will have a squared dependence of the reaction rate on this reactant's molarity value. Therefore, the rate will show an exponential decrease over time as the reactant is consumed.
The integrated rate law for a second-order reaction is
1/[A]t = 1/[A]0 + kt
where
[A]t = the concentration of A at time t
[A]0 = the concentration of A at time 0 (i.e., at the beginning of the reaction)
k = the rate constant for the reaction
Given,
The second-order decomposition of hi has a rate constant of 2.80 x 10⁻³ m⁻¹s⁻¹.
Time = 78.3 s
Initial Concentration = 3.56 m
Here we need to find the second order decomposition.
Apply the values on the formula,
Then we get,
=> 1/[A]t = 1/(3.56 m) + 2.80 × 10⁻³ m⁻¹s⁻¹ x 78.3 s
=> 1/[A]t = 0.28 m⁻¹ + 0.2192 m⁻¹
=> 1/[A]t = 0.4992 m⁻¹
=> 1/[A]t = 1/0.4992 m
=> 1/[A]t = 2.0008 m
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4. find the equation, in parametric scalar form, for the line that passes through the points (5,2,7) and (8,–6,1) then determine whether the point (17,–30,31) is on the line.
The parametric equation of the line that passes through the points (5,2,7) and (8,–6,1) is [tex]\vec r= < 5,2,7 > +\lambda < 3,-8,-6 >[/tex]
Also, the point (17,–30,31) does not lie on the line.
for given question,
We need to find the parametric equation of the line that passes through the points (5,2,7) and (8,–6,1)
Let [tex]\vec r_0= < 5,2,7 >[/tex]
and
[tex]\vec v= < 8-5,-6-2,1-7 > \\\\\vec v= < 3,-8,-6 >[/tex]
where vector v is the direction vector.
So, the equation of the line would be,
[tex]\vec r=\vec r_0+\lambda \vec v\\\\\vec r= < 5,2,7 > +\lambda < 3,-8,-6 >[/tex]
Now we need to determine whether the point (17, -30, 31) is on the line.
Let [tex]< 17,-30,31 > = < 5,2,7 > +\lambda < 3,-8,-6 >[/tex]
For first component,
⇒ 17 = 5 + 3λ
⇒ 3λ = 12
⇒ λ = 4
For the second component,
⇒ -30 = 2 - 8λ
⇒ -8λ = -32
⇒ λ = 4
For third component,
⇒ 31 = 7 - 6λ
⇒ -6λ = 24
⇒ λ = -4
since the values of the λ are not consistent, the point (17,–30,31) does not lie on the line.
Therefore, the parametric equation of the line that passes through the points (5,2,7) and (8,–6,1) is [tex]\vec r= < 5,2,7 > +\lambda < 3,-8,-6 >[/tex]
Also, the point (17,–30,31) does not lie on the line.
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coffiecient of y in 2y² +2y
Answer: let's see... the coefficient of a number is Placed in front of a variable like 2y. so it's 2y
Step-by-step explanation: your welcome
what is 6(2-7v)+2(v+4)=20
Answer:
v= 0
6(2-0)+2(4)=20 is the simplified version of the equation.
What does 60 - r represent? What are the units associated with 6(60-r)?
Answer:
360 - 6r
Step-by-step explanation:
just simplify the expression
An orca is swimming at the surface of the water and dives below the surface 25.5 feet. Then the orca swims up 1214feet. What is the location of the orca relative to the surface of the water?
The location of the orca relative to the surface of the water is 13.36 below the surface
How to determine the location of the orca relative to the surface of the water?The given parameters are
Initial = 0 feet i.e surface of the water
Dives below = 25.5 feet.
Swims up = 12.14 feet.
The location of the orca relative to the surface of the water is calculated as
Location = Initial - Dives below + Swims up
This gives
Location = 0 - 25.5 + 12.14
Evaluate
Location = -13.36
Hence, the location of the orca relative to the surface of the water is 13.36 below the surface
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Estimate: 48 divided by 7
After estimating 48 ÷ 7, we get the result as 7.
We are given an expression
48 ÷ 7
We need to estimate the result.
First, we will divide 48 by 7
So, we get that:
48 ÷ 7 = 6.857
Now we will estimate it.
We will round of the result.
as 6 > 5, we will get it as:
48 ÷ 7 ≈ 7
Therefore, after estimating 48 ÷ 7, we get the result as 7.
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What is NOT a component of a design recipe?
O Example Tests
O Expressions
O Definition Function
O Contract
Answer:
Contract
Step-by-step explanation:
when $555 {10}$ is expressed in this base, it has 4 digits, in the form abab, where a and b are two different digits. what base is it?
In some base [tex]B[/tex], we have
[tex]abab_B \equiv 555_{10}[/tex]
so that
[tex]aB^3 + bB^2 + aB + b = 555[/tex]
Factorize the left side.
[tex]aB (B^2 + 1) + b (B^2 + 1) = 555[/tex]
[tex](aB + b) (B^2 + 1) = 555[/tex]
Now, [tex]B[/tex] is a positive integer greater than 1, and [tex]a,b[/tex] are positive integers taken from [tex]\{0,1,2,\ldots,B-1\}[/tex]. So consider the prime factorization of 555 on the right side.
[tex](aB + b) (B^2 + 1) = 3\times5\times37[/tex]
which we can write as
[tex](aB + b) (B^2 + 1) = 15\times(6^2 + 1) = (2\times6 + 3) \times (6^2+1)[/tex]
and so the base is 6, and the number in question is 2323₆.
A rental car company charges $62.12 per day to rent a car and $0.05 for every
every mile
driven. Faith wants to rent a car, knowing that:
She plans to drive 500 miles.
She has at most $440 to spend.
●
Which inequality can be used to determine d, the maximum number of days Faith
can afford to rent for while staying within her budget?
x ≤ 7 days is the maximum number of days Faith can afford to rent while staying within her budget.
What is multiplication?When you take a single number and multiply it by several, you are multiplying. There are a number distinct indications of amplification that people utilize. The "x" sign represents the most typical, however, other symbols like the "*" sign are also occasionally used.
Information that is given
Renting a car from a rental car agency costs $62.12 per day plus $0.05 for every mile traveled.
Considering that she will be traveling 500 miles,
She can only spend up to $440.
Assume that the number of days will be x
cost per day will be 62.16 × x
Miles per day will be 0.05 × 500
The inequality used will be
62.16x + 0.05 × 500 ≤ 500
62.16x ≤ 500 - 25
62.16x ≤ 475
x ≤ 475 ÷ 62.16
x ≤ 7.64 days
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Suppose you buy 3 shirts and 2 pairs of slacks on sale at a clothing store for 72. The next day, a friend buys 2 shirts and 4 pairs of slacks for 96. If the shirts you each bought were all the same price and the slacks were also all the same price, then what was the cost of each shirt and each pair of slacks?
Taking into account the definition of a system of linear equations, the cost of each shirt is 12 and the cost of each pair of slacks is 18.
System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values of the unknowns must be found and they must give the solution proposed in both equations.
This caseIn this case, a system of linear equations must be proposed taking into account that:
"S" is the cost of each shirt."PS" the cost of each pair of slacksYou buy 3 shirts and 2 pairs of slacks on sale at a clothing store for 72. The next day, a friend buys 2 shirts and 4 pairs of slacks for 96.
So, the system of equations to be solved is
[tex]\left \{ {{3S + 2PS=72} \atop {2S + 4PS=96}} \right.[/tex]
To solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
Isolating the variable S from the first equation, you obtain:
3S= 72 - 2PS
S= (72 - 2PS)÷3
S= 72÷3 - 2PS÷3
S=24- 2/3PS
Replacing this expression in the second equation:
2(24 - 2/3PS) + 4PS= 96
Solving:
2×24 - 2×2/3PS+ 4PS= 96
48 - 4/3PS + 4PS= 96
48 + 8/3PS= 96
8/3PS= 96 - 48
8/3PS= 48
PS= 48÷ 8/3
PS= 18
Replacing this value in the expression S=24- 2/3PS, you obtain:
S= 24 -2/3×18
S= 24 - 12
S= 12
Finally, the cost of each shirt is 12 and the cost of each pair of slacks is 18.
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Point B (3,1) is translated 2 units to the right and 1 unit up. What is the coordinates of B'?
If Point B [tex](3,1)[/tex] has translated 2 units to the right and 1 unit up, new coordinates of point B' are [tex](5,2)[/tex]
As per the question statement, Point B [tex](3,1)[/tex] is there on a cartesian plane. Point B is translated 2 units to the right and 1 unit up.
Before solving this question, we need to know about cartesian plane system in which, there are four quadrants which are made using positive and negative axes known as positive X and negative X (same for Y axis).
Now point B[tex](3,1)[/tex] lies in the first quadrant and value "3" describes the location of point on X axis and value "1" describes the location of point on Y axis.
If point B [tex](3,1)[/tex] is translated 2 units to the right and 1 unit up, the locations of X and Y axes will change to value "5" on X axis and value "2" on Y axis.
Hence the coordinates of point B' are [tex](5,2)[/tex]
Cartesian Plane: The x-axis and y-axis intersect to form the two-dimensional coordinate plane known as the cartesian plane in mathematics. The origin is the point at which the x- and y-axes cross perpendicularly.To learn more about cartesian plane and coordinate geometry, click on the link given below:
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How many weeks does it take her to have $250 in her bank account? Mark this point on the graph.
Answer:
Could you show how the graph looks like?
Step-by-step explanation:
roslyn has twenty boxes. thirteen of the boxes contain pencils, nine of the boxes contain pens, and three of the boxes contain neither pens nor pencils. how many boxes contain both pens and pencils?
The number of boxes containing both pens and pencils is 2.
What is set?
A set is defined as a well-defined collection of distinct objects. It is denoted by the capital letters of the English alphabet. Its value remains the same for every individual.
Calculation for the number of boxes containing both pens and pencils
Total number of boxes is given by the union of two sets A and B; i.e. A∪B= 20
Boxes having pencils is given by the set A = 13
Boxes having pens is given by the set B = 9
Boxes having neither pens nor pencils, A'∩B' = 3
Boxes containing both pens and pencils are given by the intersection of the sets, A∩B
A∩B = A + B - A∪B
= 13 + 9 - 20
= 2
Hence, the number of boxes containing both pens and pencils is 2.
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need help with homework
Answer:
third one for me same thing.
For three angles A, B, and C, the measure of Bis twice the measure of A, the measure of C is three times the measure of A, and the sum of the angle measures is 180. What is the measure of each angle?
Answer: A=30 degrees, B=60 degrees, C=90 degrees
Step-by-step explanation:
B=2A
C=3A
A+B+C=180
A+2A+3A=180
6A=180
A=30 degrees
B=2A
B=2(30)
B=60 degrees
C=3(30)
C=90 degrees
Answer:
Angle A = 30°
Angle B = 60°
Angle C = 90°
Step-by-step explanation:
Let x represent the measure of A. Using this information, we can figure out the measure of B and C in terms of x.
Since B is twice the measure of A, then it would be 2x. Similarly, C is three times the measure of A, thus it would b 3x.
We also know that the sum of the angles is 180 degrees. We can use this information to set up an equation.
Setting up an EquationWe know that:
Angle A + Angle B + Angle C = 180
Substituting the values we gave for A, B, and C, we find:
x + 2x + 3x = 180
Now, we solve the equation for x.
Solving the EquationStart by combining like terms:
6x = 180
Now, divide both sides by 6:
x = 30
Since we know the value of x, we can find the values of the angles.
Finding the Values of Each AngleA = x = 30°
B = 2x = 60°
C = 3x = 90°
Asha hikes into a canyon. she takes a break at the rest stations every 23 mile she descends. if she started at sea level and has hiked down to the fourth rest station, what is sasha’s elevation now, in miles?
Sash's elevation is -8/3 miles with respect to the sea level, by basic algebra.
What is basic algebra?Numbers, variables, constants, expressions, equations, linear equations, and quadratic equations are all part of the basics of algebra. Additionally, the algebraic expressions contain the fundamental arithmetic operations of addition, subtraction, multiplication, and division.Now,
Given:
Break is taken after every 2/3rd of the mile descended.Starts at sea level.Has hiked to the fourth rest station.To find: Sasha's elevation in miles?
Finding:
We know that the sea level is zero (0). Thus, as Sasha will descend, the values will keep becoming more and more negative.As she is taking a break after every 2/3rd of a mile descended, after four rest stations, we get that, by basic algebra:=> She will be down by 4 (2/3) = 8/3
But as stated above, since she is going lower than the sea level, her elevation level will turn out to be negative.Hence, Sasha's elevation now is -8/3 miles.To learn more about basic algebra, refer to the link:https://brainly.com/question/723406
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Which relation is a function?
Answer: I hope this helps you.
Step-by-step explanation:
rita traveled 1,250 miles in the first 3 days of her trip. at this rate, how long will it take her to travel 1,875 miles? how much would it cost
The number of days took by Rita to travel the distance of 1,875 miles is 4.5 days.
What is termed as unitary method?We will learn how to calculate the value of such a unit from value of a multiple and thus the value of a multiple from value of a unit using the unitary method.
In general, we first calculate the value of one article from value of a multiple, and then calculate the value of the preferred number of articles from value of one. Typically, this method involves both multiplication and division operations.If we know the cost of one object, we can calculate the cost of many objects besides multiplying the cost of one object by the number of objects.Now, as per the given question;
The total day taken by Rita to cover 1,250 miles is 3.
Thus, 1250 miles ----> 3 days
Let number of days taken by Rita to cover 1875 miles is 'x'.
So, 1875 miles ----> x
Then, the total distance will be
1875×(3) = 1250x
x = (1875×3)/1250
x = 4.5 days
Therefore, the total time taken by Rita to finish the distance of 1,875 miles is 4.5 days.
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