The relation 'x' and 'y' vary inversely, when x = 4, y = 5/2.
What are ratio and proportion?In its most basic form, a ratio is a comparison between two comparable quantities.
There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.
If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.
Given, The variables x and y vary inversely.
Let, y ∝ 1/x.
y = k/x.
2 = k/5.
k = 10.
Now, x = 4.
y = k/x.
y = 10/4.
y = 5/2.
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What is the standard form of the equation of the parabola with focus: (0, 7) and the vertex at the origin?.
The standard form of the equation of the parabola with focus (0, 7) and the vertex at the origin is y = 1/28 x² + 7
A parabola is a symmetrical U-shaped curve that is defined by the set of all points that are equidistant to a fixed point, called the focus, and a straight line called the directrix. In a parabolic equation, the focus and the vertex are important points that determine the shape and position of the parabola.
In the case of the parabola with focus (0, 7) and the vertex at the origin (0,0), we can use the standard form of the equation of a parabola to write its equation. The standard form of a parabola is given by:
y = a(x - h)² + k
Where (h,k) is the vertex of the parabola and a is the coefficient that determines the direction and width of the parabola. To write the equation of this parabola, we need to find the value of a.
Since the focus is (0, 7) and the vertex is (0,0), we can use the formula:
a = 1/(4f)
Where f is the distance from the vertex to the focus. In this case, f = 7. Therefore, a = 1/(4 * 7) = 1/28.
Finally, we can substitute these values into the standard form to get the equation of the parabola:
y = 1/28 x² + 7
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How to solve this first order linear differential equation?
To find first-order linear differential equations solution, we have to derive the general form or representation of the solution.
With the help of the steps shown below, we can learn how to solve the first-order differential equation.
1. Reorder the terms in the given equation so that they have the form [tex]$\frac{dy}{dx}+Py=Q[/tex] where P and Q are constants or functions of the independent variable x only.
2. Integrate P (obtained in step 1) with respect to x and then put this integral as a power of e to determine the integrating factor.
[tex]$e^{\int P d x}[/tex] = IF
3. The linear first-order differential equation's two sides should be multiplied by the IF.
4. The L.H.S of the equation is always a derivative of [tex]$y \times M(x)$[/tex] i.e. L.H.S [tex]$= \frac{d(y \times I . F)}{dx}[/tex]
[tex]$d(y \times I . F) d x=Q \times I . F$[/tex]
5. In order to arrive at the solution, we simply integrate both sides with respect to x in the last step.
Therefore [tex]y \times I . F=\int Q \times I . F d x+C$,[/tex]
where C is some arbitrary constant
Similarly, we can also solve the other form of linear first-order differential equation [tex]$\frac{dy}{dx}+Py=Q[/tex] using the same steps.
P and Q are y's functions in this manner. We determine the solution, which will be, by using the integrating factor (I.F), which is
[tex]$(x) \times(I . F)=\int Q \times I . F d y+c$[/tex]
Now, to get a better insight into the linear differential equation, let us try solving some questions. where C is some arbitrary constant.
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Limosine Company P charges a rental fee plus an additional charge per hour. The equation y = 50 + 30x shows the total cost, y of renting the limosine, and the x represents the hours. The cost to rent a limosine from Company R is shown below in the table. Which statement is true?
A
Company R charges less money for 1 hour of service compared to Company P.
B
Company P has a lower rate of change than Company R.
C
Company P charges $25 more for its rental fee compared to Company R.
D
Company R charges a higher rental fee, but a cheaper rate of change to rent a limosine.
The correct statement is -
company {R} charges less money for 1 hour of service compared to company {P}.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Given is that Limousine Company {P} charges a rental fee plus an additional charge per hour. The equation {y} = 50 + 30x shows the total cost. The cost to rent a limousine from Company {R} is shown below in the table as -
Time : 1 2 3 4 5
Cost : $100 $125 $150 $175 $200
We can write the unit charge for company {P} as -
{r₁} = $30
We can write the unit charge for company {R} can be calculated as -
{r₂} = (125 - 100)/(2 - 1)
{r₂} = $25
We can conclude -
company {R} charges less money for 1 hour of service compared to company {P}.
Therefore, the correct statement is -
company {R} charges less money for 1 hour of service compared to company {P}.
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Explain why you cannot factor the trinomialx² - 12x + 6
There are no factors of 6 that add up to -12
There are no factors of -12 that add up to 6.
It can be factored
The quadratic equation x² - 12x + 6 = 0 is factorized and the solution to the equations are x = 6 ± √30
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
x² - 12x + 6 = 0 be equation (1)
Now , to calculate the solution of x ,
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
Substituting the values in the equation , we get
x = 12 ± √ ( 144 ) - ( 24 ) / 2
x = 12 ± 2√30 / 2
x = 6 ± √30
Hence , the solutions to the equation are x = 6 + √30 or x = 6 - √30
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please help me find x
Answer:
x = 4.5
Step-by-step explanation:
Using Pythagoras theorem,
Hyp² = Opp² + Adj²
From the question,
Hyp = 9
Adj = Opp
Since Adj = Opp
Let,
Adj = Opp = a
and,
Hyp = b
Therefore,
b² = a² + a²
9² = 2a²
Cancelling equal exponents,
2a = 9
a= 4.5
given 9x+7. evaluate the expression if x=3
Answer:
34
Step-by-step explanation:
Insert 3 in for x in the equation.
9(3) + 7
9*3 = 27
27 + 7 = 34
Answer: 34
Step-by-step explanation:
if x =3 the equation will become 9(3)+7
We multiply to get 27+7
Add to get 34
Find the age of the mammal hide to the nearest year.
Enter the correct answer.
The age of the mammal hide is 3567 years
How do you use radioactivity to find age?Radioactivity can be used to determine the age of rocks, minerals, and fossils through a method called radiometric dating. This method is based on the principle that certain isotopes of elements decay at a known rate over time, producing new isotopes. By measuring the relative amounts of the original parent isotope and the newly formed daughter isotope, scientists can determine how much time has passed since the rock, mineral, or fossil was formed.
0.70 = 1 * e^-0.0001t
Take the logarithm of both sides:
log0.70 = loge^-0.0001t
-0.1549 = -0.0001t * 0.43429
t = -0.1549 / (-0.0001 * 0.43429)
t = 3566.74
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If an employee earns $550 in 26 hours of work, what is the unit rate at which this employee is paid? Round to the nearest cent.
Answer:
21.15 550 divided by 26 = 21.15.
Step-by-step explanation:
I did the work on my paper. =)
How can I find a variable for 20 and 25
Answer: x/20=25
Step-by-step explanation:
You'll have to take the variable and divide it by 20 to equal 25.
How you do that is by subtracting 20 from 25, then you should get x=5, which would be your answer to the problem itself.
What is the length of the missing side?
A. 36
B. 37.43
C. 38
D. 39
Answer: I would say B.
Step-by-step explanation: why not pick B…..
Hope this help^^
what is106 inches in feet?
Converting inches to feet using the given value, we get, 106 inches is equal to 8.83 feet.
To convert inches to feet, we divide the number of inches by 12, since there are 12 inches in a foot.
So, 106 inches divided by 12 gives us:
106 ÷ 12 = 8.83 feet
Therefore, 106 inches is equivalent to 8.83 feet.
It's important to note that in the United States, Liberia, and Myanmar, feet and inches are commonly used units of length for measuring things like height and distance. While other countries may use the metric system, it's always important to make sure you're using the correct units of measurement for the context in which you're working.
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The scale of a map is 2 in = 7 feet. If the map distance is 11 inches what is the actual distance.
Answer:
the answer is 38.5 feet
Step-by-step explanation:
divide 7 by two the multiply by 11
Please help me out I'm having trouble
The correct statement regarding the similarity of the circles is given as follows:
A. Circle 1 is always similar to circle 2.
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
Two circles are similar when one circle is a dilation of the other circle, and in this problem, we have that:
Circle 1 is a dilation of Circle 2 with a scale factor of 2.Circle 2 is a dilation of Circle 1 with a scale factor of 1/2.Hence the two circles are always similar and option a is correct.
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ASAP PLEASE, WHOEVER ANSWERS ALL 7 CORRECTLY AND QUICKLY WILL GET THANKS, 5 STARS, AND BRANLIEST!!!
Question 1(Multiple Choice Worth 2 points)
(Linear Functions LC)
Which of the following graphs represents a linear function?
coordinate plane with a graph drawn that passes through the points 2 comma negative 2 and 2 comma negative 1 and 2 comma 0
coordinate plane with a graph drawn that passes through the points negative 1 comma 0 and 0 comma negative 2 and 1 comma negative 4
coordinate plane with a graph that passes through the points negative 2 comma 0 and 0 comma negative 4 and 2 comma 0
coordinate plane with a graph that passes through the points negative 3 comma 0 and 0 comma negative 3 and 3 comma 0 and 0 comma 3
Question 2(Multiple Choice Worth 2 points)
(Linear Functions MC)
Which statement best explains whether the data in the following table represents a linear or nonlinear function?
x y
−4 4
−1 2.5
0 2
4 0
The table represents a nonlinear function because the graph shows a rate of change that is decreasing.
The table represents a linear function because the graph shows a rate of change that is increasing.
The table represents a nonlinear function because the graph does not show a constant rate of change.
The table represents a linear function because the graph shows a constant rate of change.
Question 3(Multiple Choice Worth 2 points)
(Linear Functions MC)
Which of the following tables represents a linear function?
x −2 −1 0 1 2
y 5 2 1 2 5
x −2 −1 0 1 2
y 5 3 1 −1 −3
x 3 3 0 3 3
y −2 −1 0 1 2
x 0 1 2 3 4
y 0 −1 2 −3 4
Question 4(Multiple Choice Worth 2 points)
(Linear Functions MC)
Which statement best explains whether the following graph represents a linear or nonlinear function?
coordinate plane with a graph that passes through the points negative 4 comma 0 and negative 2 comma negative 1 and 0 comma negative 2
The graph represents a linear function because there is a constant rate of change.
The graph represents a linear function because the rate of change is not constant.
The graph represents a nonlinear function because there is a constant rate of change.
The graph represents a nonlinear function because the rate of change is not constant.
Question 5(Multiple Choice Worth 2 points)
(Linear Functions LC)
Which of the following equations represents a linear function?
2x − 4 = 6
x = −2
y equals one half times x squared
y equals two thirds times x plus 4
Question 6(Multiple Choice Worth 2 points)
(Linear Functions MC)
Which statement best explains whether the equation y = 3x2 represents a linear or nonlinear function?
The equation represents a linear function because it has an independent and a dependent variable, each with an exponent of 1.
The equation represents a linear function because its graph contains the points (−1, 3), (0, 0), and (1, 3), which are on a straight line.
The equation represents a nonlinear function because it has an independent and a dependent variable, each with an exponent of 1.
The equation represents a nonlinear function because its graph contains the points (−1, 3), (0, 0), and (1, 3), which are not on a straight line.
Question 7(Multiple Choice Worth 2 points)
(Linear Functions MC)
Which statement best explains whether the following table represents a linear or nonlinear function?
x −2 −1 0 1 2
y −4 −2 0 2 4
The table represents a nonlinear function because there is not a constant rate of change in the input values.
The table represents a nonlinear function because there is not a constant rate of change in the output values.
The table represents a linear function because there is a constant rate of change in the input and output values.
The table represents a linear function because there is not a constant rate of change in the input and output values.
Answer:
Step-by-step explanation:
1) = b im doing the test.
2)=The correct option is C) A coordinate plane is shown with a line crossing through the y axis at negative 3 and the x axis at 2.
3) its a
4)b
pls help asap I need to get this done by tmw
Marisol keeps the account open for 12 years if Marisol deposits $5,000 in a savings account earning 5.75% simple interest per year.
What is simple interest?It is defined as the interest based on the principal amount, it does not include the compounded amount. The interest calculates on the initial amount or borrowed amount.
Given that, Marisol deposits $5,000 in a savings account earning 5.75% simple interest per year.
Simple interest: SI = PRT
P = $5000
r = 5.75% = 0.0575
I = $8,450 - $5000 = $3450
3400 = 5000(0.0575[tex])^t[/tex]
t = 12 years
Thus, Marisol keeps the account open for 12 years if Marisol deposits $5,000 in a savings account earning 5.75% simple interest per year.
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If y varies directly as x, and y is 12 when x is 1. 2, what is the constant of variation for this relation? 1.
The constant of variation for this relation is 10.
If y varies directly as x, we can write it as y = kx, where k is the constant of variation. This constant represents the relationship between x and y, and it determines how much y changes for a given change in x.
To find the constant of variation, we need to know the value of y and x. In this case, we are told that y is 12 when x is 1.2. Using this information, we can solve for k by dividing both sides of the equation by x:
y = kx
12 = k * 1.2
12 / 1.2 = k
k = 10
So the constant of variation is 10. This means that for every change of 1 in x, y will change by 10. In other words, if x increases by 1, y will increase by 10, and if x decreases by 1, y will decrease by 10.
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How can I find the variable for this?
Answer:
i think Pythagorean theorem
Step-by-step explanation:
c^2=a^2+b^2
Please help quick!!!!
Answer:
19 and 12
Step-by-step explanation:
The rule is y = 2x - 1
If x = 10, y = 19 because 20 - 1 = 19
If y = 23, x = 12 because 24 / 2 = 12
Please help!!!!!!!!!!!!!!!!
The polynomial 6x³ - 8x⁴ + 5x + 12x² - 9 in standard form is -8x⁴ + 6x³ + 12x² + 5x - 9.
How to write polynomial in standard form?A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number.
The standard form of a polynomial is expressed by writing the highest degree of terms first then the next degree and so on.
Hence, let's write the polynomial in standard form as follows:
6x³ - 8x⁴ + 5x + 12x² - 9
Hence, in standard form,
6x³ - 8x⁴ + 5x + 12x² - 9 = -8x⁴ + 6x³ + 12x² + 5x - 9
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The circle x2 + y2 – 18x + 8y + 48 = 0 is translated one unit right and two units down. Which is the radius and center of the translated circle?
The radius and center of the translated circle are,
Radius = 7 units
Center = (10, - 2)
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
The equation of circle is,
x² + y² - 18x + 8y + 48 = 0
Now, We can simplify the equation as;
x² + y² - 18x + 8y + 48 = 0
x² - 18x + 81 - 81 + y² + 8y + 16 - 16 + 48 = 0
(x - 9)² + (y + 4)² = 49
(x - 9)² + (y + 4)² = 7²
Hence, The radius of circle = 7
And, Center = (9, - 4)
Let the center of circle after translated one unit right and two units down is, (h', k')
Hence, We get;
h' = 9 + 1 = 10
k' = - 4 + 2 = - 2
Thus, The equation of the translated circle is,
(x - 10)² + (y - (- 2))² = 7
Hence, the radius and center of the translated circle are,
Radius = 7 units
Center = (10, - 2)
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Please help with the question in the image
The measure of arc FB is 68 degrees.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
In the given circle BE is a semicircle
The measure of arc FC is 104 degrees.
We need to find the measure of arc FB
From the figure the measure of arc BC is 36 degrees
FC=FB+BC
104=36+FB
Substitute 36 from both sides
104-36=FB
68 degrees =FB
Hence, the measure of arc FB is 68 degrees.
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2.19g+59
Evaluate the expression when g = 3
A- 3.96
B- 7.16
C- 8.34
D- 8.93
Answer:
6.57+59=65.57 (I saw that 65.57 is not on there but that is the answer)
Step-by-step explanation:
Given:
[tex]2.19g+59[/tex] when [tex]g=3[/tex].
Substitute 3 into g.
[tex]2.19(3)+59[/tex]
Solve:
[tex]6.57+59=65.57[/tex]
HELP ASAP, WILL GIVE BRAINLIEST TO FIRST ANSWER
A marine biologist was interested in seeing the relationship between a manatee's weight and height. She gathered data and wanted to construct a graph to display the data in order to observe this relationship.
Is a scatter plot or a line graph more appropriate to construct for the data, given the context of the problem? Explain.
A scatter plot, because it would show the association or relationship between two variables
A scatter plot, because it would show how a variable changes over time between each data point given
A line graph, because it would show the association or relationship between two variables
A line graph, because it would show how a variable changes over time between each data point given
Answer:
A - scatter plot; it would show the relationship
Step-by-step explanation:
You want to determine if a scatter plot or line graph is a more appropriate way to represent the relationship between a manatee's weight and height.
VariablesThe variables of concern in the data are weight and height. Time is not involved. (Eliminates choices B and D.)
Functional relationshipIt seems likely there may not be a functional relationship between weight and height. That is, manatees of the same weight may have different height, and vice versa. This suggests a line graph would not be a useful way to represent the relationship
Scatter plotA scatter plot in this case would be used to relate weight on one axis to height on the other axis. Any relationship between them would show up as grouped data points, or data points that generally fall on a line or curve.
Since the "marine biologist [is] interested in seeing the relationship between a manatee's weight and height", ...
A scatter plot [is more appropriate] because it would show the association or relationship between the two variables.
__
Additional comment
As is often the case, the wording of the answer that matches the wording of the problem statement tells you which answer is appropriate.
Answer:A scatter plot, because it would show the association or relationship between two variables
Step-by-step explanation:
Use a model to divide 1/3 divided 4
Answer:
first
1/3 ÷ 4
we can use the kfc mode =
k= keep the first fraction the same
f= flip the division to multication
c=change the second fraction to it's inverse
the answer will be
1/3 ÷ 4
=1/3÷4/1
=1/3×4/1
= 4/3
Answer:
Step-by-step explanation:
3/4
Is 6z-2z+4 and 4+2z-6z simply
6z-2z+4 4+2z-6z
4z+4 4-4z
No
In science class, Mr. Brodell's students were directed to weigh a 400- gram mass on the balance scale. Erika weighed the object and reported 420 grams . What is the percent error of the weight of Erika's object
The percent error of the weight of Erika's object is given as follows:
5%.
How to obtain the percent error?The percent error is obtained applying the proportions in the context of the problem.
A proportion is applied as the percent error is calculated as the division of the error by the actual amount, divided by 100%.
The parameters for this problem are given as follows:
Error: 420 - 400 = 20 grams.Actual amount: 400 grams.Hence the percent error is given as follows:
20/400 x 100% = 5%.
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8 77/80 as a decimal
Answer: 8.875
Step-by-step explanation:
8 77/88
(77 ÷ 88) + 8
0.875 + 8
8.875
[tex]19.32 - 23.5[/tex]
Answer:
The answer to 19.32-23.5 is -4.18
Marco's charges an additional fee for toppings, but all toppings cost the same. Kevin got pepperoni, banana peppers, and black olives on his pizza for a cost of $15.74. Brian ordered mushrooms and eggplant on his pizza and paid $14.49. Using this information, write an equation for the cost of a pizza, C, as a function of the toppings, t, ordered.
Answer: Let's use x to represent the cost of each topping. Then, the cost of a pizza with t toppings can be expressed as:
C = x * t + 15
We know that Kevin's pizza with 3 toppings cost $15.74, so we can write an equation using this information:
15.74 = 3x + 15
Solving for x, we get:
x = (15.74 - 15) / 3 = 0.74
So, each topping costs $0.74. Now we can use the information about Brian's pizza to check our answer:
14.49 = 2x + 15
Substituting x = 0.74, we get:
14.49 = 2 * 0.74 + 15
Which simplifies to:
14.49 = 1.48 + 15
This confirms that x = 0.74 is the correct cost for each topping. Therefore, the equation for the cost of a pizza as a function of the toppings ordered is:
C = 0.74t + 15
Step-by-step explanation:
Find the Area of the figure below, composed of a rectangle and a semicircle.
The radius of the circle is shown. Round to the nearest tenths place.
13
6
Answer:
Hi dear !!
area of semicircle = πr²/2
=> 3.14× 6x6 /2
3.14× 6× 3
=> 56.52 cm².
area of rectangle= l x b = 13 x 12 = 169
total area = 169 +56.52 = 225.5 cm²