Answer:
12
Step-by-step explanation:
There are 6 common factors of 12 and 60, that are 1, 2, 3, 4, 6, and 12. Therefore, the greatest common factor of 12 and 60 is 12.
1) Differentiate following equations with respect to x.
a) x² + xy + y² = 0
b) 1/x + 1/y =e^y
The differential equations are dy/dx = -x/y and dy/dx = e^y * (-1/x² + 1/y²).
What is the differential equation?
A solution of a differential equation is an expression for the dependent variable in terms of the independent one(s) which satisfies the relation. The general solution includes all possible solutions and typically includes arbitrary constants (in the case of an ODE) or arbitrary functions (in the case of a PDE.)
a) To differentiate x² + xy + y² = 0 with respect to x, we can use the power rule and the chain rule.
The power rule states that the derivative of x^n is nx^(n-1)
The chain rule states that if y = f(u) and x = g(u) then dy/dx = dy/du * du/dx
x² + xy + y² = 0
dx/dx (x² + xy + y²) = dx/dx (0)
2x + y = 0
dy/dx = -x/y
b) To differentiate 1/x + 1/y = e^y with respect to x, we can use the chain rule and the reciprocal rule.
The chain rule states that if y = f(u) and x = g(u) then dy/dx = dy/du * du/dx
The reciprocal rule states that the derivative of 1/x is -1/x²
1/x + 1/y = e^y
dy/dx = dy/dx (e^y)
dx/dx (1/x + 1/y) = dx/dx (e^y)
-1/x² - 1/y² = e^y
dy/dx = e^y * (-1/x² + 1/y²)
Hence, the differential equations are dy/dx = -x/y and dy/dx = e^y * (-1/x² + 1/y²).
To learn more about differential equations visit,
https://brainly.com/question/1164377
#SPJ1
Which is the common difference for this arithmetic series? 8, 30, 52, 74, 96, 118 a. d = 8 b. d = 22 c. d = 32 d. d = 38
Answer:
d = 22
Step-by-step explanation:
you add 22 to a number in the sequence to get the next number
8 + 22 = 30
30 + 22 = 52 and so on...
State the domain and range for the following relation. Then determine whether the relation represents a function. {( -4,6), (-4,7), (6,5), (7,9)} The domain of the relation is __. (Use a comma to separate answers as needed.) The range of the relation is ___ (Use a comma to separate answers as needed.) Does the relation represent a function? Choose the correct answer below. A. The relation is a function because there are no ordered pairs with the same second element and different first elements. B. The relation is a function because there are no ordered pairs with the same first element and different second elements. C. The relation is not a function because there are ordered pairs with 5 as the second element and different first elements. D. The relation is not a function because there are ordered pairs with - 4 as the first element and different second elements.
Since the input value of domain -4 has two different output values (7 and 6), the relation is not a function.
By definition, a relation is a function if each input value has only one output value.
Given the relation:
(-4,6)
(-4,7)
(6,5)
(7,9)
The domain is the set of the x-coordinates of each ordered pair (You do not need to write 4 twice):
domain ={-4 ,6,5}
The range is the set of the y-coordinates of each ordered pair :
range= {6,7,5,9}
Since the input value 4 has two different output values (7 and 6), the relation is not a function.
learn more about of domain here
https://brainly.com/question/12910480
#SPJ4
15. For the graph below, which of the following is a possible function for g?
The graph demonstrates that the function g's line goes through the locations (0,2) and (2,8). The slope of the line is 3, implying that its equation is g(x) = 3x + 2.
What is a slope?The steepness or inclination of a line, route, or surface is measured by slope. It is the vertical distance divided by the horizontal distance between two locations on a line, route, or surface.
According to the graph, the function g is a line with a slope of 3 and a y-intercept of 2. This suggests that the line's equation is g(x) = 3x + 2. According to this equation, increasing the y-coordinate by one increases the x-coordinate by three. The line connects the points (0, 2) and (2, 8), which means that when x = 0, y = 2 and when x = 2, y = 8. This may be demonstrated by plugging the x-values into the equation, which will produce the matching y-values.
To know more about graph, visit
brainly.com/question/17267403
#SPJ1
A person borrowed $2100 from his home equity line of credit to pay off his car loan. He then borrowed another $1200 to have his kitchen repainted. Represent how much
he owed on his home equity line of credit as a real number.
What is the real number that represents the amount he owed on his home equity line of credit?
The real number that represents the amount he owed on his home equity line of credit would be = $3,300
What is a real number?A real number is defined as the type of number that can be used to represent a one directional measurement which can be rational or irrational.
The first amount of money borrowed by a person from his home equity line of credit = $2100
The second amount of money borrowed by a person from his home equity line of credit = $1200
Therefore, the total amount that was borrowed= 2100+1200 = $3,300.
Learn more about real numbers here:
https://brainly.com/question/28550938
#SPJ2
Given f(x) = 3x^3+kx-13, and x-1 is a factor of f(x), then what is the value of k?
Answer: k=10
Step-by-step explanation:
The graph shows the number of gallons of water in a large tank as it is being filled. Based on the trend line, predict how long it will take to fill the tank with gallons of water.
The required time it will take to fill the tank with gallons of water is 18 minutes.
What is a line?A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.
Here,
From the figure, the equation of the trend line is given as,
y = 20.83x
Where y = gallons of water and x is time in minutes
Now, put y = 375
375 = 20.83x
x = 18 min
Thus, the required time it will take to fill the tank with gallons of water is 18 minutes.
Learn more about lines here:
brainly.com/question/2696693
#SPJ1
Complete question,
Make Sense and Persevere The graph shows the number of gallons of water in a large tank as it is being filled. Based on the trend line, predict how long it will take to fill the tank with 375 gallons of water.
pls help me
Josh is the owner of CranBog, a Cranberry Bog in Massachusetts. Cranberry production at CranBod can be represented by the inequality y ≤ 150x - 3100
under normal climate conditions, where y
is the annual production of cranberries at CranBog, in thousands of pounds, and x
is the number of acres of land that produce cranberries.
The TRUE statements about the inequality y ≤ 150x - 3100 are:
A) For a solution to be viable, both x and y must be integers.E) The ordered pair (40, 2900) is a solution to the inequality and means that with 40 acres of land, CranBog can produce 2,900 (in thousands of) pounds of cranberries.What is inequality?Inequality is a mathematical statement showing that two or more mathematical expressions are unequal or not equivalent.
Inequalities are represented by the following types and inequality symbols:
Less than (<)Greater than (>)Not equal to (≠)Less than or equal to (≤)Greater than or equal to (≥).Check:
Ordered pairs (40, 2900)
y ≤ 150x - 3100
y ≤ 150(40) - 3100
y ≤ 6,000 - 3100
y ≤ 2900
Learn more about inequalities at https://brainly.com/question/24372553
#SPJ1
toss a coin three times, and let x be the number of heads. find the probability mass function of x.
The probability mass function of x is P(0)= 1/8, P(1)= 3/8, P(2)= 3/8, P(3)= 1/8.
Here number of trials = 3
In tossing a coin for once, the outcomes of the trial are either head or tail.
The trials are independent.
probability of getting head(success)=p=1/2
probability of getting tail(failure)=1-p=1-(1/2)=1/2
Number of success=X
Since there are two mutually exclusive outcomes of independent trials, the probability mass function of Binomial = (nx)px(1−p)n−x(nx)px(1 − p)n−x {in this case n=3}
The probability distribution of X is -
= X=0, P(X=0)=1/8
= X=1, P(X=1)=3/8
= X=2, P(X=2)=3/8
= X=3, P(X=3)=1/8
Learn more about probability mass function on -
https://brainly.com/question/30070005?referrer=searchResults
#SPJ4
my grade depends on this, help!!
Answer:
x ≥ - 3-----------------------
We observe on the graph:
The relation is not a function because it fails the vertical line test. You can see the graph intersects with the y-axis twice.The domain is restricted at x = -3 and unrestricted on the positive side.The domain is:
x ≥ - 3Find the equation of the ellipse with the following properties.
The ellipse with foci at (4, 0) and (-4, 0); y-intercepts (0, 3) and (0, -3)
Step-by-step explanation:
The equation of the ellipse
[tex]\displaystyle\\\boxed {\frac{x^2}{a^2} +\frac{y^2}{b^2} =1}[/tex]
[tex]F^2=a^2-b^2[/tex]
Given: F₁(-4,0) F₂(4,0) b₁(0,-3) b₂=(0,3)
[tex]\displaystyle\\a^2=F^2+b^2\\\\a^2=4^2+3^2\\\\a^2=16+9\\\\a^2=25\\\\a_{1,2}=б5\\\\So,\ a_1(-5,0)\ \ \ \ a_2(5,0)\\\\Thus,\ \frac{x^}{(б5)^2} +\frac{y^2}{(б3)^2} =1\\\\\frac{x^2}{25}+\frac{y^2}{9} =1\ \ \ \ -\ the\ equation \ of\ the\ ellipse[/tex]
Nancy and Martin are making kites. The kites are similar figures. The side lengths of Nancy's kite are 16 inches, 16 inches, 24 inches, and 24 inches. The side lengths of Martin's kite are (5x + 5) inches, (5x + 5) inches, 10x inches, and 10x inches. Assume that 10x > 5x + 5. Find the perimeter of Martin's kite.
Answer: 100 inches
Step-by-step explanation:
Corresponding sides of similar figures have proportional side lengths, so:
[tex]\frac{10x}{24}=\frac{5x+5}{16} \\\\\frac{2x}{24}=\frac{x+1}{16}\\\\\frac{x}{12}=\frac{x+1}{16}\\\\16x=12x+12\\\\4x=12\\\\x=3\\\\[/tex]
So, the perimeter is [tex]5x+5+5x+5+10x+10x=100[/tex].
Emily was offered a job after college earning a salary of $35,000. She will get a raise
of $2,000 after each year working for the company. Answer the questions below
regarding the relationship between salary and the number of years working at the
company.
, and the
The independent variable, x, represents the
dependent variable is the
depends on the
because the
A function relating these variables is C(x)
So C(4)
meaning 4
Answer:
The independent variable, x, represents the number of years working at the company. The dependent variable, C(x), represents the salary. The salary depends on the number of years working at the company because the salary increases by $2,000 for each year of work. A function relating these variables is C(x) = 35,000 + 2,000x, where x is the number of years working at the company and C(x) is the salary. So C(4) = 35,000 + 2,000(4) = $43,000 meaning that if Emily works for 4 years, her salary will be $43,000.
three friends went to an icecream store and tried a new flavor the store was testing. After
trying the flavor, they were asked to rate the icecream on 9-point rating scale ranging from
1-Hate it to 9-Love it. The friends ratings were: Destiny 9, Taylor 6, Jeremiah 5. What is the
mean of their ratings?
The mean of their ratings is 7.
How to calculate the mean of their ratings?
Mean (also called the average) is used to describe the central tendency of a set of numerical data. It is calculated by summing up all the values in the data set and dividing by the number of values.
Since We have the ratings:
Destiny 9, Taylor 6, Jeremiah 5
Mean = (9 + 6 + 5)/3 = 20/3 = 7
Note: we divide by 3 because there are 3 people
Learn more about mean on:
brainly.com/question/20118982
#SPJ1
The graph below represents the distance of a dog from a trainer after a command is given.
A graph titled Dog Obedience School. The horizontal axis shows Time (seconds), numbered 1 to 10, and the vertical axis shows Distance (yards) numbered 4 to 40. The line shows an increase, then decrease, then constant distance.
Which statement could describe the dog’s movement at 5 seconds once the command was given?
The dog stopped to lie down and obey the trainer’s command.
The dog was running towards the trainer.
The dog was running away from the trainer.
The dog was stopped but began running towards the trainer.
The correct statement regarding the dog’s movement at 5 seconds once the command was given is given as follows:
The dog was running towards the trainer.
How to obtain the correct statement regarding the graph?The input and output variables for the function graphed are given as follows:
Input: time.Output: distance.At a time of 5 seconds, the distance between the dog and the trainer is decreasing, meaning that the dog was moving towards the trainer, and thus the second option is the correct option.
Missing InformationThe graph is given by the image presented at the end of the answer.
More can be learned about functions at https://brainly.com/question/24808124
#SPJ1
Answer:
The dog was running towards the trainer.
The baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 0.25, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.
A. Equally likely and unlikely
B. Likely
C. Unlikely
D. This value is not possible to represent probability of a chance event.
The baker made a batch of chocolate chips, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 0.25, the likelihood of randomly selecting a chocolate chip is B. Likely.
What is probability?Generally, Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.
A probability of 0.5, for example, would indicate that an event has a 50% chance of occurring. Probability can be used to make predictions and inform decision-making in a wide range of fields, including statistics, finance, and engineering.
A probability of 0.25 represents a 25% chance of a randomly selected cookie from the batch being a chocolate chip cookie, which is considered "likely" to occur.
Read more about probability
https://brainly.com/question/30034780
#SPJ1
Please Hurry!
A box of apples sells for $17. At this rate, which expression represents the cost, in dollars, of 100 apples?
A) 5/17•20
B) 5/20•17
C) 100/17•20
D) 100/20•17
E) 17•5•20
Answer: D
Step-by-step explanation:
20 apples cost $17
100 apples = 100/20 * 17 = D
Which equation can be used to find the area in square feet of the piece of glass?
Answer:
Area = length x width (in feet)
Step-by-step explanation:
The area of a 2-dimensional shape can be found by multiplying its length by its width. The equation to find the area of a rectangle is:
Area = length x width
So if you know the length and width of a piece of glass in feet, you can use the above equation to find its area in square feet. For example, if the length of the glass is 10 feet and the width is 5 feet, the area would be:
Area = 10 feet x 5 feet = 50 square feet
So the equation to find the area of a piece of glass in square feet is:
Area = length x width (in feet)
It's worth noting that this equation applies to any 2-dimensional shape that has a length and a width, not just a rectangle.
Please Help ASAP - 100pts + Brainliest!
Answer:
g(x) = e^(x+2) -3
Step-by-step explanation:
You want the transformed function g(x) of the parent function f(x) = e^x given that g(x) has a horizontal asymptote of -3 and goes through the point (-2, -2).
TranslationThe parent function goes through the point (0, 1), which has apparently been translated to (-2, -2) by the transformation. That translation looks like ...
g(x) = f(x -h) +k . . . . . . . . f(x) translated h units right and k units up
ApplicationOur function has been translated from 0 to -2 in the horizontal direction, or left 2 units: h = -2.
It has been translated from 1 to -2 in the vertical direction, or down 3 units: k = -3.
Then the translated function is ...
g(x) = f(x +2) -3
g(x) = e^(x+2) -3
can you include the full picture?
URGENT PLEASE HELP!!!!!!
Answer:
یه گل یک گل بام میی مه فیلم بام حس بام حس فمس یکم باشگاه هی یک گل یه حس سیم هی فکریه خشک پیل هر یک حس صب زی صب هم گچ نی بلن هر بر قل هم بی دو حس قیین
Step-by-step explanation:
سبک حس بام نی شیک حس
یا کمی سیم حس او
نی یک حس بکشم یک حس بام نی که خیلی تنیام که اما الا دیه انجام نمییم ای موضوع که دعوا خیلی تخفیف خیلی خوعه ای موضوع که اما الا دیمش خوش
۳ خشک هی یک هی بام نی با که اما ۷غ هه بام نی بلن کف بام نی بکر
به نمییم هی بام میی لاک حس بام
بلن هی یک
حالم ای زبونه فراموش که
فخ بیم فک
Which operation results in a binomial
A. -
B. +
C. •
Answer:
answer is d
Step-by-step explanation:
because of binomials connect to the plus sign but which solves the equations of the multiplicationsDistributive property c3/c when c=3
Answer: The answer is 9
Step-by-step explanation: 3^3/3=9
describe your sketch. the solid has no negative x-values. the solid has both positive and negative y-values. the solid has no negative z-values. the solid has a straight side and a curved side in the x y-plane. the solid has ---select--- in the x z-plane. the solid has ---select--- in the y z-plane.
The solid has a straight side in the x y-plane and a curved side in the x y-plane. In the x z-plane, the solid has a curved side, and in the y z-plane, the solid has a straight side.
The solid has no negative x-values, meaning all x-values are positive. It has both positive and negative y-values, indicating that it is symmetrical around the x-axis. The solid has no negative z-values, meaning all z-values are positive. In the x y-plane, the solid has a straight side and a curved side. In the x z-plane, the solid has a curved side and in the y z-plane, the solid has a straight side.
The solid has a straight side in the x y-plane and a curved side in the x y-plane. In the x z-plane, the solid has a curved side, and in the y z-plane, the solid has a straight side.
Learn more about plane here
https://brainly.com/question/27190150
#SPJ4
The dashed triangle is the image of the solid triangle for a dilation centered at the origin. What is the scale factor?
Option(c) is the correct answer i.e. the scale factor of the given triangle is 4/9.
What is Scale factor?
The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor.
Let's take the measurement of one side of the original triangle and dashed triangle.
The side of Original triangle is 18 units and,
The side of dashed(new) triangle is 8 units
We know that,
Scale factor = dimension of new figure ÷ dimension of original figure
= 8 units / 18 units
= 4/9.
Learn more about Scale factor from the given link:
brainly.com/question/25722260
#SPJ1
a child's toy harp is in the shape of a trapezoid as shown. in square inches, what is the area of the harp?
The area of a trapezoid is given by the formula A = 1/2(b1 + b2)h. In this case, b1 = 4, b2 = 3, and h = 8.
The area of a trapezoid can be determined using the formula A = 1/2h(b1 + b2), where A is the area, h is the height, and b1 and b2 are the lengths of the top and bottom bases of the trapezoid, respectively. To determine the area of a child's toy harp in square inches, we need to know the length of the top and bottom bases and the height of the trapezoid.
Therefore, the area of the harp is 1/2(4 + 3)8 = 20 square inches. To find the area of the harp, we first need to know the measurements of the base lengths, b1 and b2, as well as the height, h. Once we have these measurements, we can plug them into the formula for the area of a trapezoid and solve for A. In this case, the area of the harp is 20 square inches.
Learn more about area of a trapezoid here:
https://brainly.com/question/21025771
#SPJ4
Answer:
20 square inches
Correct Answer 100%. Pls, give me brainliest. Thank You.
Please help!! I can’t figure this out
Answer:
$3213
Step-by-step explanation:
You want to know the total spent on rent and food if rent is 7/20 of your budget and food is 1/2 of your budget of $3780 per month.
AmountsThe amount spent on each item is the product of the fraction of the budget it is and the total amount being budgeted (your income).
rent = 7/20 × 3780 = 1323
food = 1/2 × 3780 = 1890
The total spent on these items is the sum of these amounts:
rent + food = 1323 +1890 = 3213
A total of $3213 is budgeted for rent and food.
__
Additional comment
Your calculator can figure this handily.
You can factor out the income amount and add the fractions first:
(7/20·3780) +(1/2·3780) = 3780(7/20 +1/2) = 3780(7/20 +10/20)
= 3780(17/20) = 3213
k2 is 11,194.21 feet higher than mt. kenya. enter and solve an equation to find the elevation of mt. kenya. use x to represent the elevation of mt. kenya.
The elevation of mountain mt.kenya is, x = 17,057.1 feet by substitution method from the elevation of mountain K2 given.
Given that,
K2 is 11,194.21 feet higher than mt.Kenya, write and solve an equation to find the elevation of mt.Kenya.
x = mt. Kenya ( since given that x represents the elevation of mt.kenya)
Let us consider/assume ,
y = K2 (say)
Therefore, the relation between x and y:
x = y - 11,194.21 ( or )
y = x + 11,194.21
( since given that K2 is 11,194.21 more than mt.Kenya )
The elevation of K2 Mountain = 28251.31 feet
= y
substitute the value of y in x = y - 11,194.21
x = 28251.31 - 11,194.21
∴ x = 17,057.1 feet.
Therefore the elevation of mt.kenya found to be, x = 17,057.1 feet by substitution method.
Learn more about substitution method here :
https://brainly.com/question/14619835
#SPJ4
The complete question is :
K2(Which is 28251.31) is 11,194.21 feet higher than Mt.Kenya Write and solve an equation to find the elevation of Mt.Kenya. use x to represent the elevation of mt. kenya.
what is the slope of the line through the points (-2,9) and (-4,6) ?
Answer:
The slope is [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
The slope formula would be: [tex]\frac{y2-y1}{x2-x1}[/tex]
So for (-2,9) and (-4,6), we can plug in the variables: (x1, y1) and (x2, y2)
Let's use the numbers in the equation provided above:
[tex]\frac{6-9}{-4-(-2)}[/tex]
= [tex]\frac{-3}{-2}[/tex]
= [tex]\frac{3}{2}[/tex]
Answer:
3/2
Step-by-step explanation:
[tex]\frac{y2-y1}{x2-x1} = \frac{6-9}{-4-(-2)} = \frac{-3}{-2} =\frac{3}{2}[/tex]
Highway Design A section of highway connecting two hillsides with grades of 6% and 4% is to be built between two points that are separated by a horizontal distance of 2000 feet (see figure). At the point where the two hillsides come together, there is a 50-foot difference in elevation.
(a) Design a section of highway connecting the hillsides modeled by the function {eq}f(x) = ax^3 + bx^2 + cx + d (-1000 \le x \le 1000) {/eq}. At the points A and B, the slope of the model must match the grade of the hillside.
(b) Use a graphing utility to graph the model.
(c) Use a graphing utility to graph the derivative of the model.
(d) Determine the grade at the steepest part of the transitional section of the highway.
You need to find the four constants, a, b, c, and d. At x = -1000, you have a value for f(x).
A)Outline it:
f(-1000) = -1000 = a (-1000)^3 b(-1000)^2 + c (-1000) + d
At x = 1000, you have a value for f(x).
B)Outline it:
f(+1000) = a (1000)^3 + b (1000)^2 + c (1000) + d
You know the slope's value, f'(x), and when x = -1000, f'(-1000) equals 3 a (-1000)2 + 2 b (-1000) + c.
At x = + 1000 f'(1000), you have a value for the slope: 3 a (1000)2 + 2 b (1000) + c
C) That is four linear equations with a, b, c, and d as the four unknowns.
When you simultaneously solve all four equations, you will get the function and its derivative, which you may graph.
D) The steepest part is where the derivative's absolute value is at its highest.
You can find that extreme by setting the derivative of the derivative equal to zero.
6 a x + 2 b = 0
solve for x and calculate the slope at that point.
Know more about graph
https://brainly.com/question/19040584
#SPJ4
Dr. Chandler wants to print copies of
his thesis in hardcover book format. He
could use Washington Printing, paying a
setup fee of $41 and $6 for every book
printed. Or, he could go through Fairfax
University, paying an up-front fee of
$32 and $9 per book. For how many
books will the costs be the same? How
much is that?
Answer:
For 3 books, costs are the same
$59
Step-by-step explanation:
x = number of books
$41 + ($6/book)(x) = $32 + ($9/book)(x)
41 - 32 = 9x - 6x
9 = 3x
x = 9/3 = 3
41 + 6(3) = 32 + 9(3) = $59
