The distance between any coordinate (x,y) and the origin is given by the equation presented as follows:
D = square root of (x² + y²).
The angle between these coordinates and the positive x-axis is given as follows:
Angle = arctan(y/x).
How to obtain the distance and the angle?The distance between two points on a coordinate line is equivalent to the hypotenuse of a right triangle.
The sides of the triangle are represented by the differences of the x-coordinates and the y-coordinates of each point.
For the origin, the coordinates are (0,0), hence the distance of any point from the origin is given by the equation presented as follows:
D = square root of (x² + y²).
For the angle, we have that:
The opposite side to the angle is the difference between the y-coordinates.The adjacent side to the angle is the difference between the x-coordinates.Hence the tangent is applied, as follows:
tan(Angle) = y/x
Angle = arctan(y/x).
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A sight-seeing boat travels at an average speed of 21 miles per hour in the calm water of a large lake. The same boat is also used for sight-seeing in a nearby river. In the river, the boat travels 2.6 miles downstream (with the current) in the same amount of time it takes to travel 2 miles upstream (against the current). Find the current of the river.
Answer:
Step-by-step explanation:
Let's call the speed of the boat in the river x miles per hour. The boat travels 2 miles downstream in the same amount of time it takes to travel 2 miles upstream, so the speed of the boat relative to the water is the same in both directions. We can set up the following equation to represent this relationship:
21 - x = x + current speed
Solving for x, we find that the speed of the boat in the river is (21 - x)/2 = 10.5 miles per hour.
We can then use this value to find the current speed of the river. The boat travels 2.6 miles downstream in the same amount of time it takes to travel 2 miles upstream, so the speed of the boat relative to the ground is the same in both directions. We can set up the following equation to represent this relationship:
10.5 + current speed = 10.5 - current speed
Solving for the current speed, we find that it is (10.5 - 10.5)/2 = 0.
Therefore, the current speed of the river is 0 miles per hour.
What are some fractions rules that I need to know about?
Answer:
1. The denominator of a fraction represents the number of equal parts the whole is divided into.
2. The numerator of a fraction represents the number of parts being considered.
3. A fraction is in simplest form when the numerator and denominator have no common factors other than 1.
4. The denominator of a fraction must be greater than zero.
5. The numerator of a fraction must be greater than or equal to zero.
6. When two fractions have the same denominator, the fraction with the larger numerator is greater.
7. When two fractions have the same numerator, the fraction with the smaller denominator is greater.
8. To add and subtract fractions, the denominators must be the same.
9. To multiply fractions, multiply the numerators and denominators separately.
10. To divide fractions, invert the second fraction (flip the numerator and denominator) and then multiply.
Step-by-step explanation:
Answer:
For fractions to be added or subtracted, their denominators must match (the bottom value). It just requires adding or subtracting the numerators if the denominators are already equal (the top value). A common denominator must be determined if the denominators are dissimilar.
Step-by-step explanation:
Find the missing number so that the equation has no solutions
–2x + 11 = x + 21 + __x
a
5
b
-2
c
-3
d
2
Answer:
-3
Step-by-step explanation:
Combining like terms, [tex]x-3x=-2x[/tex]. Since this means the variable terms on both sides combine to have the same coefficient, this means there are no solutions (since the constant terms differ).
Answer:
C.) -3
Step-by-step explanation:
We're looking for an equation with NO SOLUTION.
A.) 5
-2x + 11 = x + 21 + 5x
x = -1.25.
A.) is INCORRECT
B.) -2
-2x + 11 = x + 21 + (-2)x
x = -10
B.) is INCORRECT
C.) -3
-2x + 11 = x + 21 + (-3)x
No solution
C.) is CORRECT
D.) 2
-2x + 11 = x + 21 + 2x
x = (-2)
D.) is INCORRECT
Compute GCD(1240, 6660)
The greatest common factor between the given two numbers will be 20.
What is the greatest common factor?The greatest common factor is the largest positive number which can be divided into given numbers evenly.
Given that the two numbers are 1240 and 6660. First, factorize each number and find the common multiple of both numbers.
1240 = 2 x 2 x 2 x 5 x 31
6660 = 2 x 2 x 3 x 3 x 5 x 37
The common numbers are,
2 x 2 x 5
4 x 5
20
Therefore, the greatest common factor between the given two numbers will be 20.
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A deck of cards contains 52 cards, of which 4 are aces. You are offered the following wager: Draw one card at random from the deck. You win $10 if the card drawn is an ace. Otherwise, you lose $1.
If you make this wager vary many times, what will be the mean amount you win?
The mean amount won based on the expectation formula of probability will be - 2/13.
What is probability?The probability of an event occurring is defined by probability.
Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.
Probability of winning = 4/52 = 1/13
Probability of lossing = 1 - 1/13 = 12/13
The mean amount or expectation is given as,
E(X) = 10 × (1/13) + - 1(12/13)
E(X) = 10/13 - 12/13
E(X) = - 2/13
Hence "The mean amount won based on the expectation formula of probability will be - 2/13".
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For each of the lines (A, B, C, and D) in the graph above, determine its relationship to the line y=3/4x and its equation.
Line A :
Line B:
Line C:
Line D:
Relationship to the line y=3/4x and its equation is line B.
What is an equation ?
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
y = mx+c
y = 3/4x [which shows that the line B as the points]
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In how many different ways can we distribute 5 different books among 10 children if any child can get any number of books?
Using the formula of combination and the provided condition that any child can get any number of books, The answer is 637.
What is combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. We use permutation to determine how many possible ways we have to arrange items from a collection system.
What is the formula of combination?The required formula is:
[tex]C(n,r) = \frac{n!}{r!(n-r)!}[/tex]
where, n= total number of objects in the set.
r= number of choosing objects from the set.
from the given data, total number of books = n= 5
number of children we need to distribute, r= 10
total possible ways of distribution= C(10,1)+C(10,2)+C(10,3)+C(10,4)+C(10,5)
=10+45+120+210+252
=637
hence, we have total 637 possible ways to distribute.
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amanda wants to put some of her books on 4 shelves with 6 books on each shelf can amanda arrange her books this way explain
The number of ways the 6 books can be arranged on the 4 shelves by Amanda is 360 ways
How to determine the ways of the books can be arranged?From the question, we have the following parameters that can be used in our computation:
Total number of books, n = 6
Total number of shelves, r = 4
The number of ways the books could be arranged on the shelves is calculated using the following permutation formula
Total = ⁿPᵣ
Where
n = 6 and r = 4
Substitute the known values in the above equation, so, we have the following representation
Total = ⁶P₄
Apply the permutation formula
ⁿPᵣ = n!/(n - r)!
So, we have the following representation
Total = 6!/2!
Evaluate the quotient
Total = 360
Hence, the number of ways is 360
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What is the common difference for the arithmetic sequence?
4.7, 6, 7.3, 8.6, 9.9, …
Answer:
1.3 is the common difference.
Step-by-step explanation:
Find sin2x,cos2x, and tan2x if sin x=12/13 and x terminates in quadrant IV.
sin2x=
cos2x=
tan2x=
Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).
Given:
sin x= 12/ 13
So, B = √13² - 12² = √169 - 144 = √25 = 5
cos x= 5/ 13
So, sin 2x= 2 sin x cos x =2 (12/13)(5/13) = 120/169
and, cos 2x= 1- 2 sin²x
= 1- 2( 144 / 169)
= -119/ 169
and, tan 2x = sin 2x/ cos 2x = 120/ 169 / (- 119/ 169)= 120/ 119
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Two trains leave the station at the same time, one heading west and the other east. The westbound train travels at 85 miles per hour. The eastbound train travels at 95 miles per hour. How long will it take for the two trains to be 396 miles apart?
Do not do any rounding.
The time it takes the trains 2.2 hours to be 396 miles apart.
What is time?Time is the duration of an event.
How to find how long will it take for the two trains to be 396 miles apart?Since two trains leave the station at the same time, one heading west and the other east. The westbound train travels at 85 miles per hour. The eastbound train travels at 95 miles per hour.
Let
d = distance travelled by first train = vt where v = speed of train = 85mph and t = timeAlso,
D = distance travelled by secnd train = Vt where V = speed of second train = 95 mph and t = timeSince both trains move in opposite directions and leave at the same time, their distance apart after time t is D' = d + D
= vt + Vt
= 85t + 95t
= 180t
Since D' = 396 miles, we have that
396 = 180t
t = 396 m/180 mph
t = 2.2 hours
So, it takes the trains 2.2 hours to be 396 miles apart.
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Hakeem leans a 26-foot ladder against a wall so that it forms an angle of 72^{\circ} ∘ with the ground. What’s the horizontal distance between the base of the ladder and the wall? Round your answer to the nearest hundredth of a foot if necessary.
Answer:
To solve this problem, we can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side of a right triangle. Since the angle formed by the ladder and the ground is 72 degrees, we can consider the horizontal distance between the base of the ladder and the wall to be the adjacent side of the right triangle, and the height of the ladder to be the opposite side.
We can set up the following equation to represent this relationship:
tan(72^{\circ}) = opposite/adjacent
Substituting the values given in the problem, we get:
tan(72^{\circ}) = 26 feet / adjacent
To find the value of the adjacent side, we can solve for "adjacent" in the equation above. We can do this by dividing both sides of the equation by 26 feet and then taking the inverse tangent (tan^(-1)) of both sides:
adjacent = 26 feet / tan(72^{\circ})
Using a calculator or a table of tangent values, we can find that the value of tan(72^{\circ}) is approximately 3.73. Substituting this value into the equation above, we get:
adjacent = 26 feet / 3.73
Solving this equation, we find that the horizontal distance between the base of the ladder and the wall is approximately 6.99 feet. Rounding this value to the nearest hundredth of a foot, we get an answer of approximately 6.99 feet.
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Answer: 8.03
Step-by-step explanation:
Find slope between 2 points (4,9) and (1,6)
Answer:
Step-by-step explanation:
-x²-22x - 121 = 0 quadratic
Answer: 11
Step-by-step explanation:
we know that : ax² + bx + c = 0
then,
a = −1
b = −22
c = −121
putting the values in the following equation:
x=−b±√b²−4ac ⁄ 2a
=−(−22)±√(−22)²−4⌈(−1)(−121)⌉ ⁄ 2(−1)
=22±√484−484 ⁄ −2
=22±√0 ⁄ −2
=22 ⁄ −2
=11 ⁄ −1
=11
Hence the answer for this equation will be 11.
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The rectangle is 82m long and 52m wide. Find the area of the training field. Use the value 3.14 for π, and do not round your answer. BE SURE TO INCLUDE THE UNIT IN YOUR ANSWER
The area of the rectangle training field is 4264 m².
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
We know the area of a rectangle is (length×width).
So, The area of the rectangle 82m long and 52m wide is,
= (82×52) m².
= 4264 m².
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For 3 and 4, find the slope of the line that passes through the given points.
3. (0, 10) and (24, 6)
4. (0, 6) and (20, 14).
5. The graph shows the number of centimeters a particular plant grows over time.
a. What is the slope of the line?
b. Apply Math Models What does the slope mean?
Answer: 4. -1/6, 5. 2/5
Step-by-step explanation:
1. The formula for slope is rise/run. To find the slope, you subtract the y coordinates (it doesnt matter the order, and you divide it by the difference of the x coordinates.
2. The y coordinates for 3 are 10 and 6, and the x coordinates are 0 and 24.
10-6/0-24 is 4/-24 which is -1/6.
3. you do the same thing for #4. The y coordinates are 6 and 14, and the x coordinates are 0 and 20. 14-6/20-0=slope. 8/20 is the slope, and that is equal to 2/5.
4. the slope for 3 is -1/6 and the slope for 4 is 2/5.
3. In the diagram at the right JK bisects ∠LJM ,. What is the m∠LJM ?
(1) 35
(2) 52
(3) 26
(4) 86
4. What is the area of the triangle shown on the graph below?
(1) 10
(2) 11
(3) 14
(4) 25
Answer:
3= 26
4= 11 because it is area of triangle
help please and thanks you
SHE IS A GIRL. HER NAME IS CHRIS. CHRIS IS A GIRLS NAME. IS THIS SYLLOGISM OR DETATCHMENT
It is Syllogism. It is an example of a type of reasoning where a conclusion is reached from two given or assumed propositions, each of which shares a term with the conclusion.
A syllogism is what?The Greek term "syllogismos," which means "conclusion, inference," is the source of the English word "syllogism." A logical argument employing assertions and deductive reasoning is known as a syllogism. The most important contribution to the topic of syllogisms is attributed to Aristotle. A major premise, a minor premise, and a conclusion make up a syllogism. One phrase from each of the premises and the conclusion are shared.
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question content area top left part 1 the functions f and g are defined by the following tables. use the tables to evaluate the given composite function. f^-1
After solving, the value of f^(-1)(g(7)) is 6.
In the given question, we have to find the f^(-1)(g(7)).
The given table of functions f and g is:
x f(x) y g(x)
-3 1 -2 -5
0 4 1 -4
1 5 5 2
6 -6 7 -6
To find the value of f^(-1)(g(7)) we put the value of g(7) from the table. As we can see in the table that at the value of g(x) at point 7 is -6.
Then we find the value of from the table of f(x).
f^(-1)(g(7)) = f^(-1)(-6)
The value of f^(-1)(-6) from the table f(x) is
f^(-1)(g(7)) = 6
Hence, the value of f^(-1)(g(7)) is 6.
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. The length of a rectangle is represented by 4x and the width by 2x + 1 Determine the perimeter of the rectangle as a simplified expression in standard form. (hint: perimeter=2w+21)
The perimeter of the rectangle can be expressed as 12x+2
What is perimeter of a rectangle?The perimeter of a rectangle is the total distance covered by its boundaries or the sides. Since there are four sides of a rectangle, thus, the perimeter of the rectangle will be the sum of all four sides.
The perimeter of a rectangle is given as 2(l+w)
where l is the length and w is the width.
If the length is represented by 4x and width by 2x+1, therefore the perimeter of the rectangle = 2(4x+2x+1)
= 2( 6x+1)
= 12x+2
the perimeter can also be found by adding all the four sides, this means that
perimeter = 4x+4x+2x+1+2x+1=8x+4x+2= 12x+2
therefore the perimeter of the rectangle is 12x+2.
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Elizabeth is going to drive from her house to city a without stopping. Elizabeth’s house is 120 miles from Cytie and she plans to drive at a speed of 30 mph. Make a table of values and then write an equation for D in terms of t representing Elizabeth distance from city A t hours after leaving her house
A table of values that models this situation is as follows;
Distance (miles) Time (hour)
120 0
150 1
180 2
210 3
240 4
An equation for D in terms of t representing Elizabeth's distance from city A, t hours after leaving her house is d = 30t + 120.
How to write a function for the distance and time?Mathematically, a constant of proportionality (time) for Elizabeth's journey (distance) with respect to time can be represented with the following mathematical expression:
d = kt
Where:
d represents the distance.t represents the time.k represents the constant of proportionality (speed).Therefore, the required function that relates the distance (d) and speed (s) at t hours is given by;
d = 30t + 120
Next, we would develop a table of value;
At time (t) = 1 hour, we have;
Distance, d = 30(1) + 120
Distance, d = 150 miles.
At time (t) = 2 hours, we have;
Distance, d = 30(2) + 120
Distance, d = 180 miles.
At time (t) = 3 hours, we have;
Distance, d = 30(3) + 120
Distance, d = 210 miles.
At time (t) = 4 hours, we have;
Distance, d = 30(4) + 120
Distance, d = 240 miles.
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Determine the quadratic function f whose graph is given.
The vertex is (3,-3) and the other given point is (2, -1).
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=3\\ y=-3 \end{cases}\implies y=a(x-3)^2 - 3\hspace{5em}\textit{we also know that} \begin{cases} x=2\\ y=-1 \end{cases} \\\\\\ -1=a(2-3)^2 -3\implies 2=a(-1)^2\implies 2=a~\hfill \boxed{y=2(x-3)^2 -3}[/tex]
Use the formula A=P\left(1+r/n)^nt to solve the compound interest problem.
Find how long it takes a 1700$ investment to earn 500$ interest if it is invested at 2% interest compounded quarterly.
500$ interest will be earned in approximately years. (Round to the nearest tenth.)
The total years taken to double the money according to Compounding will be 13.75 years.
What is compound interest?
Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.
Main body:
Given :
rate = 2%
amount = $1700
Total amount = $2200
Compounded monthly,
so formula becomes,
Total amount = amount (1+r/400)^4t
T = A([tex](1+r/400)^{4t[/tex]
2200 = 1700(1 +2/400)^4t
22/17 = (1 +1/200)^4t
22/17 = (1.005)^4t
1.29 = (1.005)^4t
taking log on both sides
0.11/0.002 = 4t
t = 13.75 years.
Hence the time taken to double the money is 13.75 years.
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For a total of 28seconds, a seagull flew east at 11meterspersecond. A sailor watched the seagull fly for one-quarter of that time. How far did the seagull fly while the sailor was watching?
Write your answer as a whole number.
meters
To find out how far the seagull flew while the sailor was watching, you can use the following steps:
Calculate the total distance the seagull flew in 28 seconds. You can do this by multiplying the seagull's speed (11 meters per second) by the time it flew (28 seconds):
Distance = Speed * Time
= 11 meters/second * 28 seconds
= 308 meters
Calculate the time the sailor watched the seagull fly. You can do this by dividing the total time the seagull flew (28 seconds) by 4:
Time = 28 seconds / 4
= 7 seconds
Calculate the distance the seagull flew while the sailor was watching. You can do this by multiplying the seagull's speed (11 meters per second) by the time the sailor watched the seagull fly (7 seconds):
Distance = Speed * Time
= 11 meters/second * 7 seconds
= 77 meters
Therefore, the seagull flew 77 meters while the sailor was watching.
What are conditional problems?
Conditional problems are problems that involve determining the likelihood or probability of an event occurring under certain conditions. They often involve the use of probability and statistics to evaluate the likelihood of different outcomes or to make predictions about future events.
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Find the equation of a line parallel to y = − x + 7 y=−x+7that passes through the point ( 4 , 5 )
The line parallel to line y= -x + 7 is y= -x + 9.
What is slope intercept form?
The intercept formula y = mx + b is used when you know the slope of the line you are examining, and the specified point is also the y-intercept (0, b). In this formula, b represents the y-value of the y-intercept.
Solution: We will use slope intercept formula y= mx + b
Given that the parallel line passes through (4,5), which means x=4 and y=5
Also, m = -1
Putting value of x and y in slope intercept form to find b, we get
y=mx + b
⇒ 5= (-1x4) + b
⇒ 5= -4 +b
⇒5 + 4= b
⇒b=9
Now putting value of b and m in slope intercept form, we get the parallel line
y= -x + 9
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olivia wants to have a 90 average in algebra, where tests count for 55%, quizzes count for 30% and homework counts for 15%.If she has a 92 test average and 100% HW average, what must her quiz average be? Let x = the average of the
Olivia's quiz average must be 24.4 to achieve a 90 average in algebra.
How to calculate for the quiz averageTo get the average for the quiz, we first evaluate for the sum of the test average and the homework average, and the subtract the result from 90 average in algebra.
the test average = (92/100) × 55
test average = 50.6
100% homework average implies Olivia got a homework average of 15
Let x be the quiz average, so that
x = 90 - (50.6 + 15)
x = 90 - 65.6
x = 24.4
Therefore, the quiz average of 24.4 is what Olivia needs to achieve a 99 average in algebra.
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Please help me the question image is attached to the question
Answer:
10-x
Step-by-step explanation:
Find an expression which represents the difference when (-x-3y)(−x−3y) is subtracted from (8x-9y)(8x−9y) in simplest terms.
The resulting expression after the expressions are subtracted is 9x - 6y
How to determine the resulting equation after the subtraction?From the question, we have the following parameters that can be used in our computation:
(-x-3y)(−x−3y) is subtracted from (8x-9y)(8x−9y)
Rewrite these expressions properly
So, we have the following representations
(−x−3y) is subtracted from (8x-9y)
When the first equation is subtracted from the second, we have the following representation
8x - 9y - (-x - 3y)
Open the brackets
So, we have
8x - 9y + x + 3y
Evaluate the like terms
9x - 6y
Hence. the solution is 9x - 6y
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Graph the function and select the y-intercept y = 2 times 3 Superscript x
y-intercept of given function is y = 1
How to graph the function?
The collection of ordered pairings with the (x,y). (x,y) sign is known as the graph of a function in mathematics, where f(x)=y. x and f(x) are Cartesian coordinates of points in two-dimensional space, and in the typical scenario where they are real numbers, they constitute a subset of this plane.
Given function , f(x) = 2· [tex]3^{x}[/tex]
Graph of the function is given below:
As the given graph is intersecting the y-axis at y=1 So, y-intercept of given function is y = 1
Therefore, y-intercept is y = 1
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