Answer:
Step-by-step explanation:
The correct answer is D. m∠6 + m∠7 = 180°.
When a transversal cuts two parallel lines, corresponding angles are equal and alternate interior angles are supplementary. This means that the sum of alternate interior angles is equal to 180°. In this diagram, ∠6 and ∠7 are alternate interior angles, so it is necessarily true that m∠6 + m∠7 = 180°.
The other options are not necessarily true. Option A states that m∠1 = m∠7, but this is only true if the two lines being cut by the transversal are perpendicular. Option B states that m∠3 = m∠6, but this is only true if the two lines being cut by the transversal are parallel. Option C states that m∠5 + m∠8 = 90°, but this is only true if the two lines being cut by the transversal are perpendicular.
ASAPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
48ft²
Step-by-step explanation:
Visualize the trapezoid as consisting of a rectangle with two triangles on either side. To find its total area, find the area of each and add them up.
Note that the formula for the area of a square is (base*height) and the formula for the area of a triangle is (0.5*base*height). The bottom of the trapezoid is 15ft and the top is 9ft, which makes the combined bases of the two triangles 15-9=6ft, meaning each triangle's base is 3ft.
Area of left triangle = 0.5*3*4 = 6ft²
Area of square = 4*9 = 36ft²
Area of right triangle = 0.5*3*4 = 6ft²
Therefore the total area is: 6ft² + 36ft² + 6ft² = 48ft²
Answer:
48ft?
Visualize the trapezoid as consisting of
a rectangle with two triangles on either
side. To find its total area, find the area of
each and add them up.
Both y and z are functions of xx. The function y is defined by the equation
y=4 x-3
The function z is represented by the following table.
If x equals −4, which is greater, y or z
If x equals 2, which is greater, y or z?
Enter the values of x for which it is known that z is greater than y, separated by commas. If there are no such values, enter None.
The values of x for which z is greater than y are 7.
In mathematics, an equation is a statement that two mathematical expressions are equal. The expressions can contain variables, constants, mathematical operations, and functions. An equation can be used to represent a relationship between two or more variables, and it is often used to solve problems by finding the values of the variables that satisfy the equation.
Equations can be represented in different forms, such as algebraic equations, differential equations, integral equations, and partial differential equations. Algebraic equations are the most common type of equations, and they involve algebraic operations such as addition, subtraction, multiplication, and division.
Equations can be classified according to their degree, which is the highest power of the variable in the equation. Linear equations are those with a degree of one, and they can be represented by a straight line on a graph. Quadratic equations have a degree of two, and they can be represented by a parabolic curve. Higher degree equations are generally more complex, and they may not have a simple geometric representation.
For x = -4, y = 4(-4) - 3 = -19 and z = -18, so y is greater.
For x = 2, y = 4(2) - 3 = 5 and z = 6, so z is greater.
For values of x where z is greater than y, we need to compare the values of z and y for each x value in the table.
At x = 3, y = 4(3) - 3 = 9 and z = 9, so they are equal.
At x = 7, y = 4(7) - 3 = 25 and z = 27, so z is greater.
At x = 10, y = 4(10) - 3 = 37 and z = 35, so z is not greater than y.
Therefore, the values of x for which z is greater than y are 7.
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Mark and John work the same amount of hours babysitting and tutoring. Mark gets paid $6 per hour for babysitting and $15 an hour tutoring. He makes $150 in one week. John Makes $10 an hour babysitting and $8 an hour tutoring and gets paid a total of $114. How many hours were spent babysitting and tutoring?
The requried hours spent babysitting and tutoring are 5 and 8 hours respectively.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Let the hours spent babysitting and tutoring be x and y respectively,
According to the quesiton,
Mark gets paid $6 per hour for babysitting and $15 an hour for tutoring. He makes $150 in one week.
6x + 15y = 150 - - - -(1)
John Makes $10 an hour babysitting and $8 an hour tutoring and gets paid a total of $114.
10x + 8y = 114 - - - - -(2)
Solving above equations 1 and 2 by elimination method we get x = 5 and y = 8
Thus, the requried hours spent for babysitting and tutoring are 5 and 8 hours respectively.
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The measure of an interior angle of a regular polygon is 156°. Find the number of sides in the polygon.
Which is the solution of [tex]-\frac{6}{x} -\frac{x-2}{4} \ \textgreater \ \frac{3-x}{3}[/tex]?
Multiple choice question.
A)
x= −6, x= 12, or x ≠ 0
B)
−6 < x < 0 or x > 12
C)
x < −6 or x > 12
D)
−12 < x < 0 or x > 6
Answer:
C) x < −6 or x > 12----------------------
Given inequality:
- 6/x - (x - 2)/4 > (3 - x)/3Consider x ≠ 0 and multiply all terms by x, 4 and 3:
- 6*12 - 3x(x - 2) > 4x(3 - x)-72 - 3x² + 6x > 12x - 4x²4x² - 3x² + 6x - 12x - 72 > 0x² - 6x - 72 > 0 x² - 12x + 6x - 72 > 0x(x - 12) + 6(x - 12) > 0(x + 6)(x - 12) > 0The x-intercepts are:
x = - 6 and x = 12This quadratic function has a positive leading coefficient and two zeros, and hence is positive when:
x < - 6 and x > 12, the x = 0 is excluded from the given interval, therefore the above is the solution.The matching choice is C.
question 4 i need help with
Answer:
$3.25 per hotdog
Step-by-step explanation:
This question can be written as a system of equations:
x = price of hotdogs
y = price of drinks
First family:
4x + 4y = 18
Second family
5x + 3y = 20
Multiply each equation so that one of the variables can cancel out:
-3(4x + 4y = 18)
4(5x + 3y = 20)
First equation:
-12x - 12y = -54
Second equation
20x + 12y = 80
Add the equations together
-12x - 12y = -54
20x + 12y = 80
8x = 26
Divide
x = $3.25
Insert the x into one of the original equations to find y:
4(3.25) + 4y = 18
13 + 4y = 18
4y = 5
y = $1.25
Approximate the area between the x-axis and the graph of f(x) = x² + 4 over the interval [0, 2]
by calculating the sum of the areas of 4 rectangles with equal widths along the interval. The
rectangles should be placed on the x-axis and the heights should be the function values at the right
endpoint of each subinterval, as shown below.
Answer:
To approximate the area between the x-axis and the graph of f(x) = x^2 + 4 over the interval [0, 2], we can use the right rectangle method, where the heights of the rectangles are given by the value of the function at the right endpoint of each subinterval. If we divide the interval [0, 2] into 4 equal subintervals of width 0.5, the right endpoint of each subinterval would be 0.5, 1, 1.5, 2.
The height of the first rectangle would be f(0.5) = 0.5^2 + 4 = 4.25, the height of the second rectangle would be f(1) = 1^2 + 4 = 5, the height of the third rectangle would be f(1.5) = 1.5^2 + 4 = 6.25, and the height of the fourth rectangle would be f(2) = 2^2 + 4 = 8.
The sum of the areas of the rectangles is equal to (0.5) × (4.25 + 5 + 6.25 + 8) = (0.5) × 24 = 12.
So, the approximate area between the x-axis and the graph of f(x) = x^2 + 4 over the interval [0, 2] is 12.
Can somebody help I’ll mark brainliest!!! How many servings of granola are in the box?
Mrs. Smith gave her Algebra class the following linear equation as part of their warm-up.
Picture attached!!
A.Both Maryanne's and Herb's equations have a different solution than the original.
B.Only Herb's equation has the same solution as the original equation.
C.Only Maryanne's equation has the same solution as the original equation.
D.Both Maryanne's and Herb's equations have the same solution as the original.
Answer:
C.Only Maryanne's equation has the same solution as the original equation.
The solution is : 39 is the solution to Mr. Smith's equation.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
here, we have,
given that,
the equation is:
(16-2w)^2 + (3y÷3z)
Let w=5 y=9 and z=3
(16-2*5)^2 + (3*9÷3*3)
PEMDAS says parentheses first
Multiply and divide in the parentheses
(16-10)^2 + (27÷9)
Then add and subtract in the parentheses
(6)^2 + (3)
Now the exponent
=36 +3
=39
Hence, The solution is : 39 is the solution to Mr. Smith's equation.
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complete question:
What is the solution to Mr. Smith's equation?
Graph the polygon with the given vertices and its image after a dilation with scale factor k.
A(0, 5), B( 10,-5), C(5,-5); k= 120%
The new triangle with vertices A'(0, 6), B'(12, -6), and C'(6, -6) would be larger than the original triangle by a factor of 120%.
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
To graph a polygon with vertices A(0,5), B(10,-5), and C(5,-5), we can plot these points on a coordinate plane and connect them to form a triangle.
Then, to find the image of this triangle after a dilation with scale factor k = 120%, we need to multiply each coordinate of the vertices by k = 1.2.
For vertex A, the new coordinates would be (0 × 1.2, 5 × 1.2) = (0, 6).
For vertex B, the new coordinates would be (10 × 1.2, -5 × 1.2) = (12, -6).
For vertex C, the new coordinates would be (5 × 1.2, -5 × 1.2) = (6, -6).
So, the new triangle with vertices A'(0, 6), B'(12, -6), and C'(6, -6) would be larger than the original triangle by a factor of 120%.
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Kara earns 9.75 per hour plus 15.50 in tips each night. If she works for 5 2/5 hours four nights this week how much money will she earn
Answer: $272.60
Step-by-step explanation:
9.75x5.4= 52.65
52.65+15.50=68.15
68.15x4=272.6
1. Items a company has purchased and paid for, but has not used are called
A. advanced
B.purchased
C.prepaid
D. long-term liability
items.
Answer:
the ans is advanced
I hope you get your ans
PLEASE I NEED HELP ASAP
A circle has a circumference of 21.98 inches. What is the diameter of the circle? (Use
3.14 for )
Answer:
Step-by-step explanation:
The formula for the circumference of a circle is C = 2 * π * r, where r is the radius of the circle. We can find the radius of the circle by rearranging the formula to r = C / (2 * π).
Substituting the given values into the formula, we get:
r = 21.98 inches / (2 * 3.14) = 21.98 inches / 6.28 = 3.50 inches
The diameter of the circle is equal to twice the radius, so we can find the diameter by multiplying the radius by 2:
d = 2 * r = 2 * 3.50 inches = 7.00 inches.
To find the diameter of a circle with a given circumference, you can use the following steps:
Define the formula for the circumference of a circle: The circumference of a circle is given by the formula C = 2πr, where π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.
Substitute the given circumference into the formula: If the circumference of the circle is 21.98 inches, we can substitute that into the formula to get 21.98 = 2πr.
Solve for the radius: To solve for the radius, we can divide both sides of the equation by 2π: 21.98 / 2π = r. Using 3.14 for π, this gives us 21.98 / (2 * 3.14) = r, which can be simplified to r = 2.01 inches.
Calculate the diameter: The diameter of a circle is twice the radius, so the diameter can be calculated as 2 * r = 2 * 2.01 = 4.02 inches.
So, the diameter of the circle with a circumference of 21.98 inches is 4.02 inches.
Over the last 3 evenings, Laura received a total of 68 phone calls at the call center. The third evening, she received 2 times as many calls as the first evening. The first evening, she received 8 more calls than the second evening. How many phone calls did she receive each evening?
On first evening she receives 19 calls and on second evening she receives 11 calls while on 3rd evening she receives 38 calls.
What is equation?A mathematical equation is a fοrmula that joins two statements and uses the equal symbol (=) tο indicate equality. A mathematical statement that establishes the equality of twο mathematical expressions is knοwn as an equation in algebra. Fοr instance, in the equatiοn 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the twο sentences oοn either side of a letter is described by a mathematical formula. Often, there is οnly one variable, which alsο serves as the symbol, fοr instance, 2x – 4 = 2.
X, Y, and Z represents the 1st , 2nd, and 3rd evenings
X + Y + Z = 68
⇒ X = Y + 8
⇒ Z = 2(Y + 8)
⇒ Y + Y + 8 + 2(Y + 8) = 68
Y = 11 calls
And
X = (11)+ 8 = 19 calls
Z = 2((11) + 8) = 38 calls
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PLSSS HELP ME DUE TODAY!!!
Meg is heading back to her car after a hike to Misty Falls. The waterfall is at an elevation of 4,000 feet, and the trail descends an average of 500 feet for every 1 mile she hikes. You can use a function to approximate Meg's elevation after she hikes x miles.
Write an equation for the function. If it is linear, write it in the form h(x)=mx+b. If it is exponential, write it in the form h(x)=a(b)x.
Step-by-step explanation:
Since every single mile it descends the same amount (which is 500ft), that means it's linear, so we'll use that they gave us, the h(x) = mx+b
To find m, we use the following equation
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
to find b, we have to find out the starting point. luckily they gave it to us, which is 4,000ft. B = 4000
Now every 500 feet, we go down 1 mile
Which means at 1000 feet, we go down 2 miles
500 and 1000 can be our y1 and y2
1 and 2 can be our x1 and x2
[tex] \frac{1000 - 500}{2 - 1} = \frac{500}{1} = 500 = m[/tex]
Now that we have our m and b, we just put it together
[tex]h(x) = - 500x + 4000[/tex]
A negative was placed before the 500 because they are descending, not ascending.
Points B and D are on the perpendicular bisector of ^ABC. The measure of
The measure of angle ABC in the figure of triangle attached is
< ABC = 46 degreesWhat are perpendicular bisectors?In geometry, a perpendicular bisector is a line or line segment that divides another line segment into two equal parts and is perpendicular to it.
From the definition of perpendicular bisector, we have that
< A = < C
and using triangle ABD
< A + < ABD = 90
< A + 28 = 90
< A = 90 - 28
< A = 62
Using triangle ABC
< A + < ABC + < C = 180
62 + < ABC + 62 = 180
< ABC = 180 - 62 - 62
< ABC = 56
OR
< ABD = < DBC = 28 degrees
and < ABC = < ABD + < DBC adjacent angles
< ABC = < ABD + < DBC
< ABC = 28 + 28
< ABC = 56 degrees
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complete question
The perpendicular bisector of side AB of triangle ABC intersects the extension of side AC at D. Find the measure of angle ABC if measurement of angle CBD=16 degrees and measurement of angle ACB=118 degrees
3. Mrs. Doyle asks Lowell to create a verbal
representation for the equation y = x - 25. Did
Lowell complete the task correctly? Justify
your answer.
A $25 charge is added for
rush delivery
Lowell's verbal representation of the equation y = x - 25 is "y is equal to x minus 25".
This verbal representation accurately describes the equation. In the equation, y is the dependent variable and x is the independent variable. The equation says that y is equal to x minus 25, which means that for every value of x, there is a corresponding value of y that is x minus 25.
So, Lowell has completed the task correctly.
Alyssa is 1. 65 meters tall. At 11 a. M. , she measures the length of a tree's shadow to be 27. 75 meters. She stands 23. 5 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
The height of the tree to the nearest hundredth of a meter is 10.77m.
Detailed explanation:
An illustration of identical triangles is shown in the diagram. View the illustration I included with my response to see how triangles can be used to solve this issue.
Because they both share an internal angle, the triangles made by Alyssa and her shadow and the triangle created by the tree and its shadow are examples of comparable triangles.
The ratios of the comparable sides on both sides are proportionate according to the similar triangles theorem.
Therefore, in order to determine the height of the tree, we must make a percentage of the corresponding sides of both triangles. Let x equal the tree's height.
[tex]\frac{BE}{BC} =\frac{DE}{AC}[/tex]
BE = 4.25 meters
DE = 1.65 meters
BC = 27.75 meters
AC = x meters
[tex]\frac{4.25}{27.75} =\frac{1.65}{x}[/tex]
Cross multiply is now used to find x.
4.25x= 1.65(27.75)
x = 10.77
Therefore, the height of the tree is 10.77 meters.
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Complete question:
Alyssa is 1. 65 meters tall. At 11 a. M. , she measures the length of a tree's shadow to be 27. 75 meters. She stands 23. 5 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
Identify the graph of f(x) = 4√x.
Answer:
choice B
Step-by-step explanation:
plug in a few test values of x to prove it. The other choice would be a cube root function of x.
Although 240° is a special angle on the unit circle, Aiden wanted to determine its coordinates using the sum and difference formulas.
Part A: Determine cos 240° using the cosine sum identity. Be sure to include all necessary work. (5 points)
Part B: Determine sin 240° using the sine difference identity. Be sure to include all necessary work. (5 points)
A. The value of cos 240° = [tex]\frac{-1}{2}[/tex]
B. The value of sin 240° = [tex]-\frac{\sqrt{3} }{2}[/tex]
What are basic Trigonometric functions?
The angles of sine, cosine, and tangent are the primary classification of functions of trigonometry. And the three functions which are cotangent, secant, and cosecant can be derived from the primary functions. Basically, the other three functions are often used as compared to the primary trigonometric functions.
Part A:
we know that, cos (a +b)=cos a cos b - sin a sin b
cos 240° = cos (60° +180°)
=cos 60° cos 180° - sin 60° sin 180°
=[tex]\frac{1}{2} *(-1)-\frac{\sqrt{3} }{2} *0[/tex]
=[tex]\frac{-1}{2}[/tex]
Part B:
we know that, sin(a- b)=sin a cos b - cos a sin b
sin 240° = sin(270° - 30°)
=sin 270° cos 30° - cos 270° sin 30°
=[tex]-1 *\frac{\sqrt{3} }{2}-0*\frac{1}{2}[/tex]
=[tex]-\frac{\sqrt{3} }{2}[/tex]
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Need helpppp with this problem!! thanks!
Answer:
20
Step-by-step explanation:
[tex]\sqrt[3]{64xy^{3}}[/tex] = [tex]\sqrt[3]{64}[/tex] × [tex]\sqrt[3]{x}[/tex] × [tex]\sqrt[3]{y^{3}}[/tex]
a = coefficient
= [tex]\sqrt[3]{64}[/tex]
∴a = 4
[tex]x^{b}[/tex] = [tex]x^{-2}[/tex]×[tex]\sqrt[3]{x}[/tex]
= [tex]x^{-2}[/tex]×[tex]x^{\frac{1}{3}}[/tex]
= [tex]x^{-2+\frac{1}{3}}[/tex]
= [tex]x^{\frac{-6}{3} + \frac{1}{3}}[/tex]
= [tex]x^{\frac{-6+1}{3}}[/tex]
[tex]x^{b}[/tex] = [tex]x^{-\frac{5}{3}}[/tex]
∴b = [tex]-\frac{5}{3}[/tex]
[tex]y^{c}[/tex] = [tex]y^{-4}[/tex]×[tex]\sqrt[3]{y^{3}}[/tex]
= [tex]y^{-4}[/tex]× [tex](y^{3})^{\frac{1}{3}}[/tex]
= [tex]y^{-4}[/tex] × [tex]y[/tex]
= [tex]y^{-4 + 1}[/tex]
[tex]y^{c}[/tex] = [tex]y^{-3}[/tex]
∴c = [tex]-3[/tex]
∴Product of a, b and c = [tex](4)[/tex]×[tex](-\frac{5}{3})[/tex]×[tex](-3)[/tex]
= 20
Yang Bai is investing $10,000 and wants a portfolio that is 80% stocks and 20% bonds. She has decided to accomplish this using just 2 exchange-traded funds (ETFs): a stock ETF trading for $50 per share and a bond ETF trading for $100 for share. What should she do to meet her asset allocation goal?
For the algebraic expression: -7+t
Identify the variable
Identify the constant
Answer:
Answer is in the attached photo.
Step-by-step explanation:
SolutionThe solution is in the attached photo, do take note a variable is a alphabet can be assigned to any value, while a constant is a fixed number or value.
Answers:
variable = t
constant = -7
Step-by-step explanation:
So we know that a variable is a letter while a constant is a number
in here -7 is the constant (the number) and t is the variable (the letter)
Therefore, the variable is t and the constant is -7.
Find the x - and y -components of the vector v⃗ = (3.0 cm/s , −x -direction).
Express your answer in centimeters per second. Enter the x and y components of the vector separated by a comma.
The x-components and y-components of the vector [tex]\mathbf{\hat v}[/tex] are -3.0 cm/s and 0 cm/s, respectively.
What is axis?In mathematics, an axis is a reference line used to locate points in space. It is often used to define a coordinate system, which is a system for representing points and geometric shapes in space using numbers or coordinates.
To find the x- and y-components of the vector [tex]\mathbf{\hat v}[/tex] = (3.0 cm/s, −x-direction), we need to determine the direction of the vector. The notation "-x-direction" means that the vector points in the opposite direction of the positive x-axis. Therefore, the angle between the vector and the negative x-axis is 180 degrees.
The magnitude (or length) of the vector is given by the first component, which is 3.0 cm/s.
The x-component of the vector can be found by multiplying the magnitude by the cosine of the angle:
x-component = magnitude x cos(angle) = 3.0 cm/s x cos(180°) = -3.0 cm/s
The negative sign indicates that the x-component is in the opposite direction of the positive x-axis.
The y-component of the vector can be found by multiplying the magnitude by the sine of the angle:
y-component = magnitude x sin(angle) = 3.0 cm/s x sin(180°) = 0 cm/s
Therefore, the x-components and y-components of the vector [tex]\mathbf{\hat v}[/tex] are -3.0 cm/s and 0 cm/s, respectively.
Expressed as an ordered pair, the components are (-3.0 cm/s, 0 cm/s).
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Which descriptions from the list below accurately describe the relationship
between AXYZ and AUVW? Check all that apply.
857-10
LSM
X62
16
37
← PREVIOUS
20
53M
12 W
A. Same size
B. Same shape
C. Similar
D. Congruent
SUBMIT
The same shape and similar are relationship between ΔXYZ and ΔUVW options (A) and (D) are correct.
What is the similarity law for triangles?
It is defined as the law to prove that two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the complementary angles are congruent.
We have given two triangles with dimensions.
Take the ratio of the corresponding sides:
12/24 = 5/10 = 13/26 = 1/2
The ratios of the corresponding sides are same which means the triangle are similar and having same shape.
Hence, the same shape and similar are relationship between ΔXYZ and ΔUVW option (A) and (D) are correct.
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The complete question is in the attached image.
I will give brainliest and ratings if you get this correct
A. The indifference curve of a consumer is negatively sloped to the right because it represents the consumer's preference for one good over another. As the consumer's income increases, their willingness to substitute one good for the other increases.
B. The indifference curve is convex to the origin because it shows the diminishing marginal rate of substitution of the two goods. As the consumer reaches the optimal combination of goods, the marginal rate of substitution between the two goods decreases.
C. Using the Lagrange method, the optimum combination of goods can be determined as follows:
Let L(X,Y) be the Lagrangian of this problem:
L(X,Y) = √X² + Y² - λ(200 - 3X - 4Y)
Where λ is the Lagrange multiplier.
The optimal solution is obtained by setting the derivatives of L with respect to X and Y to 0 and solving the equations simultaneously.
∂L/∂X = 0 -> X = 11.85
∂L/∂Y = 0 -> Y = 8.57
Therefore, the optimum combination of goods is X = 11.85 and Y = 8.57.
D. The slope of the indifference curve is equal to the slope of the budget line. This can be shown by comparing their respective equations and noting that their slopes are the same. The equation for the indifference curve is Y/X = (-2/3) and the equation for the budget line is Y/X = (-3/4). Since these equations are the same, it follows that the slopes of the two lines are equal.
Find the volume V of the solid obtained by rotating the region bounded by the graphs of the given expressions about the specified line. y2 = x, x = 3y; about the y-axis V=
The volume, V of the solid obtained by rotating the region bounded by the graphs of the expressions, y² = x, x = 3y; about the y-axis is equals to the 162π/5 cubic units.
We have a region bounded by the graphs of two expressions. These expressios are y² = x, x = 3y. We have to calculate the volume of solid obtained by rotating the bounded region about the y-axis. First determine the intersection points of
y² = x, x = 3y.
=> x = 3y --(1)
=> y² = 3y
=> y² - 3y = 0
=> y( y - 3 ) = 0
=> y = 0 or y - 3 = 0
=> y = 0 , y = 3
from (1), x = 3y => x = 0, x = 9
Let the intersection points be O(0,0) and P(3,9). Now, the volume of rotating region or due to shaded region is
[tex]V = π\int_{0}^{3} (R² - r²) dy [/tex]
where R = 3y , r = y²
[tex]V = π\int_{0}^{3} [(3y)² - (y²)²]dy [/tex]
[tex]V = π \int_{0}^{3} (9y² - y⁴)dy [/tex]
[tex]V = π[ \frac{9y³}{3}- \frac{y⁵}{5} ]_{0}^{3} [/tex]
[tex]V = π[ \frac{9(3)³}{3}- \frac{{3}^{5} }{5} - 0- 0 ][/tex]
[tex]V = π(81 - \frac{243}{5} ) = \frac{162π}{5} [/tex]
Hence, the required volume is 162π/5 cubic units.
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An account that earned 23% annual interest compounded quarterly for 3 years and currently has a balance of $6258.
The initial balance of the account was approximately $3541.83.
What is interest is compounded?This can be illustrated by using basic math: if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. You will wind up with $110.25 at the conclusion of the second year.
We can utilise the compound interest formula to find a solution to this issue:
A = P(1 + r/n)ⁿⁿ
In this case, we have P = the initial balance of the account, r = 0.23 (23% expressed as a decimal), n = 4 (since interest is compounded quarterly), t = 3 years, and A = $6258. We can solve for P by rearranging the formula:
P = A / (1 + r/n)ⁿⁿ
Substituting the values we know, we get:
P = 6258 / (1 + 0.23/4)⁴ˣ³
Simplifying this expression gives:
P = 6258 / 1.76757
P ≈ $3541.83
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A park has two rectangular, fenced playgrounds. The first playground has a perimeter of 160 feet. The second playground is twice as long and twice as wide as the first playground. Which of these could be the perimeter of the second playground in feet? pls help now ty
a. 640
b. 320
c. 240
d. 168
Answer:
So, the answer is (b) 320 feet.
Step-by-step explanation:
Let's call the length and width of the first playground "x".
The perimeter of the first playground is 160 feet, so 2 times the length plus 2 times the width is equal to 160:
2x + 2x = 160
Simplifying:
4x = 160
Dividing both sides by 4:
x = 40
So the length and width of the first playground are both 40 feet.
The second playground is twice as long and twice as wide as the first playground, so the length and width of the second playground would be 2 * 40 = 80 feet.
The perimeter of the second playground would then be 2 * 80 + 2 * 80 = 320 feet.
So, the answer is (b) 320 feet.
Find the missing values.
Select two answers.
Answer:
a= 12, b=4, Choices B and F
Step-by-step explanation:
2/2=1
8/2=4
12/2=6
