Answers
Answer:
[tex]\dfrac{-8y}{y-3}[/tex]
Step-by-step explanation:
[tex]\sf \dfrac{49 - y^2}{6y^2 +42y}=\dfrac{7^2-y^3}{6y^2 +6*7y}\\\\[/tex]
[tex]\sf =\dfrac{(7+y)(7-y)}{6y(y + 7)}=\dfrac{(7+y)(7-y)}{6y(7+y)}\\\\\\=\dfrac{7-y}{6y}[/tex]
y² - 10y + 21
sum = -10
Product = 21
Factors = (-7) , (-3) {(-7)*(-3) = 21 & (-7)+ (-3) = -10}
y² - 10y + 21 = y² - 7y - 3y + 21
= y(y - 7) - 3(y - 7)
= (y - 7) ( y - 3)
[tex]\sf \dfrac{49 -y^2}{6y^2 + 42y}*\dfrac{48y^3}{y^2 - 10y + 21}=\dfrac{7-y}{6y}*\dfrac{48y^3}{(y-7)(y-3)}\\\\\\[/tex]
[tex]\sf = \dfrac{(-1)(y-7)}{6y}*\dfrac{48y^3}{(y-7)(y-3)}\\\\\\=\dfrac{(-1)*8y^2}{y-3}\\\\\\=\dfrac{-8y^}{y-3}[/tex]
Related Questions
Given reflections R₁ and Rk where "h" is a line with equation
x = -3 and "k" is a line with equation x = 2, how can you determine
the distance of the translation resulting from the composition
Rk Rh
Answers
The distance of the translation resulting from the composition of the two reflections Rk and Rh is equal to |1 + 2x|
How to determine the distance of the translationTo determine the distance of the translation resulting from the composition of two reflections Rk and Rh, we can calculate the difference in x-coordinates of the pre-image and image points.
Reflection Rk reflects points over the line x = 2,
So the x-coordinate of a point and its reflection would have a difference of 2 - x, where x is the x-coordinate of the original point.
Reflection Rh reflects points over the line x = -3,
So the x-coordinate of a point and its reflection would have a difference of -3 - x
When we compose the two reflections
The x-coordinate of a point and its image will have a difference of (2 - x) - (-3 - x)
Evaluate
Distance = 5
Hence, the distance is 5 units
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You spin a ball of mass 0.18 kg that is attached to a string of length 0.98 m at ω = 5.2 rad/s in a circle. What is the ball’s angular momentum?
Answers
The angular momentum of the the ball is 4.16kgrad/sec
What is angular momentum?Angular momentum is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity. This means that the total angular momentum of a closed system remains constant. Angular momentum has both a direction and a magnitude, and both are conserved. It is measure d in kgrad/sec
angular momentum = mass × angular velocity
mass = 0.18kg
angular velocity = 5.2 rad/s
therefore angular momentum = 0.18× 5.2
= 4.16 kg rad/s
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What percent of the area under the tandard normal ditribution lie within two tandard deviation of the mean?
Answers
Approximately 95.45% of the area under the standard normal distribution lies within two standard deviations of the mean.
Area Under Standard Normal Distribution Within Two Standard Deviations of the MeanThe standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. This means that 68.27% of the area under the standard normal distribution lies within 1 standard deviation of the mean, and 95.45% of the area under the standard normal distribution lies within 2 standard deviations of the mean.
This is because the standard deviation is a measure of the spread of the data; the larger the standard deviation, the more spread out the data is.
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Can someone please help me on this?
A linear function is plotted on the coordinate plane with the following points: (0, 3) and (2, 7). What is the rate of change (slope) and the initial value (y-intercept) for the linear function?
Answers
The rate of change for the linear function is 2.
The initial value for the linear function is 3.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The points on the coordinate plane:
(0, 3) and (2, 7)
Now,
The equation of the line.
y = mx + c
Slope = m
m = (7 - 3) / (2 - 0)
m = 4/2
m = 2
Now,
(0, 3) = (x, y)
3 = 2 x 0 + c
3 = 0 + c
c = 3
The y-intercept is 3.
Thus,
The rate of change is 2.
The initial value is 3.
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What is the slope of the line through the points (4,10) and (2, 20)
Answers
Explanation: y2 - y1. 20 - 10
—————- = ——————
x2 - x1 2 - 4
= 10/-2 = -5
A sign on the roadway at the top of a mountain indicates that for the next 4 miles the grade is 9. 5° (see figure). Find the change in elevation for a car descending the 4-mile stretch. (Round your answer to two decimal places. )
Answers
The change in elevation of the car is 0.66mile.
Now, According to the question:
Trigonometric functions are immensely useful when real-life examples form a right triangle. In such cases, sine, cosine, or tangent functions are used based on the given information to determine the unknown value. For example, suppose we are looking at the top of a building and we know the height of the building and our distance from the base of the building, using the tangent function, we can easily calculate the angle made by the line of sight above the ground.
d = 4 miles is the distance covered by the car on the inclined road.
θ = 9.5° is the angle made by the road above the horizontal.
Let:
h be the change in elevation of the car.
Using the sine function, we write:
[tex]sin\theta= \frac{opposite side}{hypontenuse}[/tex]
[tex]sin\theta =\frac{h}{d}[/tex]
h = dsinθ
h = (4 mile)(Sin(9.5°))
h ≈ 0.66 mile
Therefore, the change in elevation of the car is 0.66mile.
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Solve for x. Express your answer in simplest radical form if necessary.
81 = x²
Answers
Answer:
Step-by-step explanation:√81 = √x²
9 = square root cancel square = x
9=
x=
a number increased by 7 given 20
Answers
Answer:
13
Step-by-step explanation:
5x+y=9
10x−7y=−18
in substitution
Answers
Substitution is a method for solving systems of equations that involves solving for one variable in one equation and then substituting that value into the other equation.
Here's how we can use substitution to solve the system of equations:
5x+y=9
10x−7y=−18
Solve one equation for one variable, for example:
y = 9 - 5x
Substitute this expression of y into the other equation:
10x - 7(9 - 5x) = -18
Solve the equation resulting from the substitution
10x - 63 + 35x = -18
45x = 45
x = 1
Substitute this value of x back into one of the original equations to find the value of y.
5(1) + y = 9
y = 4
So the solution is (x,y) = (1,4)
You can check this solution by substituting it back into both original equations.
A newspaper charges a flat
fee plus a charge per day to
place a classified ad.
Number
of Days
2
4
6
Total
Charges
($)
8
13
18
Answers
Answer: This problem can be represented by the equation y = mx + b, where y is the total charges, x is the number of days, m is the charge per day, and b is the flat fee.
To find the values of m and b, we can use the given data points to solve for the equation.
For x = 2, y = 8, so 8 = m * 2 + b
For x = 4, y = 13, so 13 = m * 4 + b
For x = 6, y = 18, so 18 = m * 6 + b
We can then use a system of equations to solve for m and b:
m * 2 + b = 8
m * 4 + b = 13
m * 6 + b = 18
Using substitution or elimination methods:
m = 2
b = 2
Therefore, the equation is: y = 2x + 2
This means that the flat fee is $2 and the charge per day is $2.
Step-by-step explanation:
Brick San Antonio playing a game of counter Rick ha ome counter Selma ha twice a many counter a Rick Tony ha ix counter Leton Selma in total they have 54 counter the number of count a Rick ha: the number of count a Tony ha = 1: P work out the value of paid
Answers
The number of counters Rick has is equal to 12 counters.
The number of counters Tony has is equal to 1:1.5.
The value of p is 1.5.
In order to solve this word problem, we would assign variables to the unknown numbers and then translate the word problem into algebraic equation as follows:
Let R represent the number of counters Rick has.
Let S represent the number of counters Selma has.
Let O represent the number of counters Tony has.
Let T represent total number of counters.
Translating the word problem into an algebraic equation, we have;
S = 2R .....equation 1.
O = 2R - 6 ......equation 2.
T = R + S + O ......equation 3.
Substituting equation 1 and equation 2 into equation 3, we have:
T = R + S + O
54 = R + 2R + 2R - 6
54 = 5R - 6
5R = 54 + 6
5R = 60
R = 60/5
R = 12 counters.
For Tony, the number of counters is given by:
O = 2R - 6
O = 2(12) - 6
O = 24 - 6
O = 18 counters.
In ratio form, we have:
O = 1:P
O = 1:(18/12)
O = 1:1.5
The number of counters Rick has is equal to 12 counters.
The number of counters Tony has is equal to 1:1.5.
The value of p is 1.5.
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A chemistry class has learned how to read a sensitive high-caliber balance scale (this is not a digital scale). Since most students are very good at reading the scale, the instructor decides it’s time to test their skills. The instructor asks each student to weigh the same 1. 6 ounce bag of Peanut M&Ms, and then records each student’s reading of the balance scale. Which histogram shows the distribution of the students’ balance-scale readings?
Answers
Histogram II shows the distribution of the students’ balance-scale readings, so the correct answer is option (b).
It is stated that most students are very good at reading the scale. Thus, most of the students will read the scale accurately around the actual weight (i.e., around 1.6 ounces), and very few will read far below or far above the accurate weight of 1.6 ounces.
As a large portion of the understudy score tremendous and ought to have rough equivalent aptitude; in this manner, the histogram ought to be around symmetrical.
Therefore, histogram II (symmetrical distribution) shows the perfect distribution of the students' balance-scale readings.
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The complete question is:
A chemistry class has learned how to read a sensitive high-caliber balance scale (this is not a digital scale). Since most students are very good at reading the scale, the instructor decides it’s time to test their skills. The instructor asks each student to weigh the same 1. 6 ounce bag of Peanut M&Ms, and then records each student’s reading of the balance scale. Which histogram shows the distribution of the students’ balance-scale readings?
(a) Histogram I
(b) Histogram II
(c) Histogram III
(d) Histogram IV
students who score within 22 points of the number 78 will pass a particular test. write this statement using absolute value notation and use the variable x for the score.
Answers
The statement using absolute value notation will be x - 78 ≤ 22.
The student will pass the test which scores 22 points for the number 78
Absolute values are any digit's value without taking the sign into an account. Therefore, all negative numbers will be regarded as positive for absolute value. The absolute value of -5, for instance, will be 5, whereas that of -7, will be 7.
In essence, the absolute value calculates the distance from zero. Putting an absolute value on something does not imply that they are the same number but that they are the same distance from 0.
Le the score of student be = x
Forming the absolute value notation -
This can be expressed as,
x - 78 ≤ 22.
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How many solutions does this system have? x + 4 y = 6. y = 2 x minus 3a. one b. two c. an infinite number d. no solution
Answers
According to the graph, the system of equations x + 4y = 6 and y = 2 x -3 has one solution that is (2,1)
In math the term called graph is defined as a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.
Here we know that the following equation are known:
=> x + 4y = 6
=> y = 2x - 3
And here we need to find the number of solution for the equations.
Here we have to plot the equation on the graph then we get the graph like the following.
While we looking into the graph, we have identified that the intersection point in the graph is (2,1) and there is no other intersecting point.
Therefore, option (a) is correct.
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can someone help me please?
Answers
Answer:
Step-by-step explanation:
a) A(11) > M(11)
45 > 40
Go to x axis where t=11 then go straight up to find the y values (temp.) on each line
b) Look for where the lines intersect. This is where t≈47, t≈60
c) M(t) < A(t) where t=2, t=11
Look for where the Minn. line (dashed orange) is BELOW the Aspen line (solid blue)
y-0.8x=0.5
5y-2.5-4x
Answers
Answer:
x = -1
Step-by-step explanation:
y-0.8x=0.5
5y-2.5-4x
Get y by itself.
y = 1.3
Put 1.3 into the second equation
5(1.3) - 2.5 - 4x
6.5-2.5 - 4x
4 - 4x = 0
Get x by itself
-4x = 4
x = -1
I hope this was able to help you :D
It costs $5 per hour to rent a snowboard from a certain ski rental company, plus a $50 deposit. Another ski rental company charges $10 per hour to rent a snowboard, plus a $25 deposit. For what number of hours is the cost to rent a snowboard the same at each company? What is the cost of renting a snowboard for this number of hours?
Answers
The number of hours for which the cost is the same would be 5 hours.
The cost of renting a snowboard for 5 number of hours would be same as that point i.e. $5
By costs, what do you mean?
Costs are really the monetary value of purchases made for use by a company or other accounting entity of supplies, service, labor, products, equipment, and other items.
The cost of renting a snowboard from the first company is $5 per hour + $50 deposit = $5x + $50.
The cost of renting a snowboard from the second company is $10 per hour + $25 deposit = $10x + $25. To find the number of hours for which the cost is the same, we set the two costs equal to each other and solve for x:
$5x + $50 = $10x + $25
$5x - $10x = $25 - $50
$5x = $25 - $50
$5x = -$25
x = -5
As we will not take cost in negative so it would be 5
So, we can say that the cost is same at any point of time.
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At the third step, Han subtracts 39 from 39. How do you know that these numbers represent hundredths?
Answers
Answer: Because 2 places to the right of the the decimal.
Step-by-step explanation:
5/10 the students in Sam's class are girls. Of the girls, of them wear glasses. What
fraction of the student's wear glasses?
Answers
As 5/10 are Girls in Class And 1/5 of the girls wear glasses So on overall girls wear glasses is 1/10 in the whole class.
The fraction 5/10 is equal to 1/2 of the total and 1/5 of the girls wear glasses so if you multiply 1/2 and 1/5 you get 1/10, To get a total fraction of girls who wear glasses overall will be by multiplying both the fraction. So,
1/5*1/2 = 1/10
Here the answer is produced by multiplying the numerator with the numerator and similarly denominator with the denominator to get the answer of total friction of girls wearing glasses in the whole class.
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An angle of 2. 5 radians is subtended by an arc of a circle with a radius of 10cm. What is the length, in cm, of the arc?
Answers
The length of the arc of the given circle with radius 10 cm and an angle of 2.5 radians subtended by an arc of a circle is equal to 25 cm.
Let 'y' represents the length of the arc of the given circle.
Radius 'r' of the given circle is equal to 10 cm
Angle 'α' subtended by an arc of a circle is equal to 2.5 radians.
length of the arc = Angle subtended by an arc × Radius of the circle
⇒ y = rα
⇒ y = 10 × 2.5
⇒ y = 25 cm
Therefore, the length of the arc of a circle for the given radius 10cm and subtended angle 2.5 radians is equal to 25 cm.
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A group of students were asked which club they planned to join.
Club Percent of Students
Garden Club 0.1
Robotics Club 0.2
Technology Club 0.5
Zoology Club 0.2
Compare the probabilities of a randomly selected student joining a club and interpret the likelihood. Choose the statement that is true.
The student will be more unlikely to join the Robotics Club than the Garden Club because P(Robotics) < P(Garden).
The student will be equally likely to join the Zoology Club or Robotics Club because P(Robotics) = P(Zoology).
The student will be more likely to join the Zoology Club than the Robotics Club because P(Zoology) > P(Robotics).
The student will be more likely to join the Garden Club than the Robotics Club because P(Garden) > P(Robotics).
Answers
The statement that is most likely to be true in the question that we have here is that : The student will be equally likely to join the Zoology Club or Robotics Club because P(Robotics) = P(Zoology). Option 2
What is meant by probability?Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, if we are unclear of how an event will turn out. Statistics is the study of occurrences subject to probability.
In the question the probability of robotics is 0.2 while the probability of zoology club is 0.2 as well.
They have equal probability
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Answer: Answer B
Step-by-step explanation:
help me pls , thanks :)
its about funtions and i rlly need help on this
Answers
The given relations are:
1) It is a function.
2) not a function.
3)it is a function.
4) not a function.
Are the relations functions or not?A function is a relation that maps inputs into outputs, such that each output needs to be mapped into a single input.
1) For example, the first relation each input (left row) is mapped into a single output, thus, it is a function.
2) Here theinput 9 is mapped into two different outputs, then it is not a function.
3) The notation used here is (input, output), so we can see that no input is repeated,so it is a functon.
4) The input 9 is mapped into 3 different outputs, then it is not a function.
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of the 900 students at columbia middle school, there are 324 7th graders. If one student is chosen at random to lead the pledge at a school assembly, what is the probability the person chosen will be a 7th grader? Use prime factorization to reduce the answer.
Answers
Answer:
Step-by-step explanation:
im am sorry but i dont understand so i cant answer this question see you later!
what is the product for (2x+1) and (5-x)
Answers
The product for (2x+1) and (5-x) is -2x²+9x+5.
What is Fraction?A fraction represents a part of a whole.
We have to find the product of (2x+1)(5-x)
We use distributive property to find the product.
2x(5-x)+1(5-x)
10x-2x²+5-x
-2x²+10x-x+5
Add the like terms
-2x²+9x+5
Hence, the product for (2x+1) and (5-x) is -2x²+9x+5.
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A company produces a range of 5 computers models which bring in high volume
Assuming that the factory works equally to produce models for 9 hours days 7 days per week, which monitor bring in the highest revenue
Answers
The model with the highest revenue is model D
How to determine the model with the highest revenueFrom the question, we have the following parameters that can be used in our computation:
Model A Model B Model C Model D Model E
Time to manufacture (mins) (t) 15 18 13 20 17
% Of monitors sold (s) 75% 73% 84% 95% 81%
Cost per monitor (c) $175 $188 $145 $198 $170
The factor works 9 hours for 7 days
So, the total duration per unit time is
D = 9 hours * 7/t
D = 63/t
Convert t to hours
D = 63 * 60/t
D = 3780/t
The total revenue is then calculated as
R = c * D * s
So, we have
Model A = 175 * 3780/15 * 75% = 33075
Model B = 188 * 3780/18 * 73% = 28820
Model C = 145 * 3780/13 * 84% = 35444
Model D = 198 * 3780/20 * 95% = 35551
Model E = 170 * 3780/17 * 81% = 30569
The highest value above is 35551
Hence, the model is model D
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Complete question
Model A Model B Model C Model D Model E
Time to manufacture 15 minutes 18 minutes 13 minutes 20 minutes 17 minutes
% Of monitors sold per total products 75% 73% 84% 95% 81%
Cost per monitor $175 $188 $145 $198 $170
A company manufactures computer monitors. Among the various models are top
products, which bring high revenue.
Assuming the manufacturing lines are running for 9 hours a day for 7 days a week,
which model brings in the highest revenue?
Please help with this problem!
Answers
The maximized value of the objective function is 3
How to maximize the objective functionFrom the question, we have the following parameters that can be used in our computation:
C = x + y
Subject to
y >= 0
x >= 0
4x + 2y <= 8
2x - y <= 0
When the graphs of these inequalities are plotted (see attachment), we have the following feasible regions
(x, y) = (0, 0) and (1, 2)
This means that
C = 0 + 0 = 0
C = 1 + 2 = 3
3 is greater than 0
Hence, the maximized value is 3
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A line has a slope of –1/3 and a y-intercept of 5/3. Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
Answer:
The answer in intercept form will be
[tex] - 1 \div 3 = 5 \div 3x + c \\ [/tex]
you were taking a multiple-choice test that has six questions. Each of the questions has five answer choices, with one correct answer per question. If you select one of these choices for each question and leave nothing blank, and how many ways can you answer the questions?
Answers
The number of ways to answer the questions is given as follows:
15,625.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the number of outcomes for each trial as presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For this problem, there are six questions, each with five possible options, hence the number of ways to answer the questions is calculated as follows:
5^6 = 15,625 ways.
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are the following statements true or false? false 1. if two row interchanges are made in sucession, then the determinant of the new matrix is equal to the determinant of the original matrix. false 2. if is zero, then two rows or two columns are the same, or a row or a column is zero. false 3. the determinant of is the product of the diagonal entries in . false 4. .
Answers
Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.
What is matrix ?
A matrix is a rectangular array of numbers or other mathematical objects, typically arranged in rows and columns. Matrices are often denoted using capital letters, such as A, B, and C. Each element of a matrix is identified by its row and column indices,
1) False, If two row interchanges are made in succession, the determinant of the new matrix is the negative of the determinant of the original matrix.
2) False, If the determinant of a matrix is zero, it does not necessarily mean that two rows or two columns are the same or a row or column is zero, it only means that the matrix is singular, i.e. non-invertible and it also can mean that the matrix is linearly dependent.
3) False, The determinant of a matrix is not always equal to the product of the diagonal entries, it is a scalar value calculated through a specific method called matrix expansion which is based on the entries of the matrix and it depends on the size of the matrix.
4) False, The determinant of a matrix is a scalar value, it cannot be equal to another matrix.
Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.
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what is the probability that two randomly generated strings of length 9 in the dna alphabet ({a, c, g, t}) are identical?
Answers
The probability that two randomly generated strings of length 9 in the DNA alphabet is 729.
We have to find the probability that two randomly generated strings of length 9 in the DNA alphabet (a, c, g, t) are identical.
Probabilities are based on occurrences, and events can result from one or more observations or experiment results.
The total number of alphabet in word DNA is 3.
So, the probability that two randomly generated strings of length 9 in the DNA alphabet = 9 × 9 × 9
The probability that two randomly generated strings of length 9 in the DNA alphabet = 729
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