Daniel is given the following information to construct a triangle. Determine what type of triangle will be constructed.
40 40 80 degrees.
A. a unique triangle
B. more than one triangle
C. not a triangle
D. a right triangle

1. Marginal utilities:
To find the marginal utility of x (MUx), we take the partial derivative of the utility function with respect to x. In this case, MUx = (2/3)X^(-1/3)Y^(4/5).
To find the marginal utility of y (MUy), we take the partial derivative of the utility function with respect to y. In this case, MUy = (4/5)X^(2/3)Y^(-1/5).

2. Marginal rate of substitution (MRSxy):
The MRSxy represents the rate at which a consumer is willing to trade one good (x) for another good (y) while maintaining the same level of satisfaction. Mathematically, MRSxy is equal to the ratio of the marginal utilities: MRSxy = MUx/MUy.
Substituting the expressions for MUx and MUy derived earlier, we have MRSxy = [(2/3)X^(-1/3)Y^(4/5)] / [(4/5)X^(2/3)Y^(-1/5)].
Simplifying the expression, we get MRSxy = (5/6) * [(X/Y)^(1/3) * (Y/X)^(1/5)].
Thus, the expression for the marginal rate of substitution (MRSxy) is (5/6) * [(X/Y)^(1/3) * (Y/X)^(1/5)].

3. Indifference curves for perfect substitutes:
When two goods are perfect substitutes, it means that the consumer is equally satisfied with any combination of the two goods, as long as the ratio between them remains constant. In this case, the indifference curves would be straight lines with a constant slope.
For example, if the two goods are apples and oranges, and the consumer is equally satisfied with any combination of these two goods, the indifference curves would be straight lines with a constant slope of -1. This means that the consumer is willing to give up one apple for one orange and vice versa, without any change in satisfaction.

4. Indifference curves for complements:
When two goods are complements, it means that the consumer's satisfaction is maximized when the goods are consumed together in fixed proportions. In this case, the indifference curves would be L-shaped or right angles.
For example, if the two goods are coffee and sugar, and the consumer's satisfaction is maximized when the coffee and sugar are consumed together in a fixed proportion, the indifference curves would be L-shaped. This means that the consumer does not derive any satisfaction from consuming only coffee or only sugar, but rather from consuming them together in the right proportion.

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The function expressing the volume of water t minutes after the plug was pulled is V(t) = -2.4t^2 + 11.2t + 46,b)tub had 46 liters of water when the plug was pulled and will be empty at 2.16 minutes,c) the least amount of water predicted by the model is -52.6667 liters which is not reasonable as the volume of water can't be negative.

What is parabola ?

A parabola is a symmetric, U-shaped geometric shape.

a)V(1) = 38.4 = a(1)^2 + b(1) + c

V(2) = 21.6 = a(2)^2 + b(2) + c

V(3) = 9.6 = a(3)^2 + b(3) + c

Solving the system of equations, we get ,

a = -2.4 , b = 11.2 , c = 46 , V(t) = -2.4t^2 + 11.2t + 46.

b)We can find the initial volume of water in the tub by plugging in t = 0 into the function V(t) = -2.4t^2 + 11.2t + 46. This gives us V(0) = 46 liters, so the tub had 46 liters of water when the plug was pulled.

c)t = (-11.2 +/- sqrt(11.2^2 - 4*(-2.4)46))/(2(-2.4))

t = (11.2 +/- sqrt(124.48 + 552.8))/-4.8

t = (11.2 +/- sqrt(677.28))/-4.8 = (11.2 +/- 26.16)/-4.8 = -14.96 or 2.16

d)V(4.6667) = -2.4*(4.6667)^2 + 11.2*(4.6667) + 46 = -2.4*21.778 + 46.4 + 46 = -52.6667. So the least amount of water the model predict is -52.6667 liters. This number is not reasonable as the volume of water can't be negative.

e) The graph of the function V(t) = -2.4t^2 + 11.2t + 46 is a parabola that opens downward and has its vertex at (4.6667, -52.6667). Any portion of the graph for t < 0 or t > 2.

The function expressing the volume of water t minutes after the plug was pulled is V(t) = -2.4t^2 + 11.2t + 46,b)tub had 46 liters of water when the plug was pulled and will be empty at 2.16 minutes,c) the least amount of water predicted by the model is -52.6667 liters which is not reasonable as the volume of water can't be negative.

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The required probability is 0.132 .

What is normal approximation?

The sampling distribution of averages or proportions from a large number of independent trials approximately and the expectation of a sample proportion or average is the corresponding population value.

On solving using mean sampling method, we get

P(E) = 0.132

Hence, the required probability is 0.132 .

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All you need to do is that Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

21x+7=133

subtract 7 from both sides:

21x=126

divide 21 by both sides:

x=6

Answer:

slope is 3/5

Step-by-step explanation:

-10-2/-16-4

12/20

6/10

3/5

Answer:

n = -3

Step-by-step explanation:

11(n – 1) + 35 = 3n

Distribute

11n -11 +35 = 3n

Combine like terms

11n +24 = 3n

Subtract 11n from each side

11n+24 -11n = 3n -11n

24 = -8n

Divide by -8

24/-8 = -8n=-8

-3 =n

Thus we only take the positive root:x = 27/8 = 3.375Answer: 3.375 feet.

The problem states that a rectangular garden that measures 50 feet wide and 45 feet long is enclosed by a uniform width of x feet paved path. To solve the problem,

we can use the formula of the combined area of the garden and the paved path and equate it to 2646 square feet. The combined area is computed by adding the area of the garden and the area of the paved path.

Garden area:Length of garden = 45 ftWidth of garden = 50 ftArea of garden = Length x Width= 45 x 50= 2250 square feet

Paved path:

If the garden has a uniform width of x feet paved path, then the width of the paved path would be x + 2x + x= 4x. The width is multiplied by 2 because there are two widths surrounding the garden.

Length of paved path = length of garden + 2 (width of paved path)= 45 + 2 (4x)= 8x + 45Width of paved path = width of garden + 2 (width of paved path)= 50 + 2 (4x)= 8x + 50

The area of the paved path is computed by subtracting the area of the garden from the combined area.Area of paved path = Combined area - Garden area2646 square feet

= (8x + 45) (8x + 50) - 2250= 64x² + 760x + 675

We then solve for the value of x by factoring the quadratic equation.2646 square feet = 64x² + 760x + 6752646 - 2646

= 64x² + 760x + 675 - 264664x² + 760x - 1971

= 0(8x - 27) (8x + 73) = 0

The value of x cannot be negative,

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Answer:

i think 150 degrees

Step-by-step explanation:

the 30° angle and ∠1 are a linear pair, and are supplementary. therefore they add up to 180°
∠1 + 30° = 180°

angleD=(7b+1)angle E=(2b+1)and angle F=(b+8)

Answer:

<E = 35

Step-by-step explanation:

7b + 1 + 2b + 1 + b + 8 = 180

combine like terms

7 + 2 + 1 = 10

10b

1 + 1 + 8 = 10

10b + 10 = 180

substract 10 from 180

= 170

10b = 170

170 divided by 10

= 17

now plug in for b for angle E

2 (17) + 1

= 35

Answer:

(-10, -2)

Step-by-step explanation:

Multiply each of the coordinates x 2

Answer:

x = 25

Step-by-step explanation:

First we need to show that these two triangles are similar.  Add up the angles 68 and 38 degrees in the first triangle, and then subtract this sum from 180 degrees.  This results in 74 degrees, which matches 74 degrees in the second triangle.

Next we write and solve an equation of ratios:

 6        10

----- = -------

15         x

Cross multiplying returns 6x = 150, so that x = 25.

Note that 6/15 is the ratio of the shortest sides, and 10/x is the ratio of the longest sides.

I'm not quite sure what the question is, but I think that John's age would be the independent variable, and John's height would be the dependent variable.

Answer:

It is true because it is true.

Step-by-step explanation:

Why else would it be false?

By applying the formula for the monthly payment on an amortizing loan, we can calculate the monthly payment by substituting the given values. The monthly payment for the sailboat is approximately $216.67. To find the total interest paid, we subtract the total amount financed (loan amount minus down payment) from the total amount repaid (monthly payment multiplied by the total number of payments). The total interest paid for the sailboat is approximately $7,400.40.

To find the monthly payment and the total interest paid for the sailboat, we can use the formula for the monthly payment on an amortizing loan. The formula is:

PMT = (P * r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

PMT = Monthly payment

P = Loan amount (principal)

r = Monthly interest rate

n = Total number of payments

Given:

Loan amount (principal) = $22,866

Down payment = 20% of $22,866 = $4,573.20

Remaining loan amount = $22,866 - $4,573.20 = $18,292.80

Interest rate = 8.4% per year, compounded monthly

Loan term = 10 years = 10 * 12 = 120 months

First, we need to calculate the monthly interest rate:

Monthly interest rate = 8.4% / 12 = 0.7% = 0.007

Substituting the values into the formula, we can calculate the monthly payment:

PMT = ($18,292.80 * 0.007 * (1 + 0.007)^120) / ((1 + 0.007)^120 - 1)

PMT ≈ $216.67

Therefore, the monthly payment for the sailboat is approximately $216.67.

To calculate the total interest paid, we can subtract the total amount financed from the loan amount:

Total interest paid = (Monthly payment * Total number of payments) - Loan amount

Total interest paid = ($216.67 * 120) - $18,292.80

Total interest paid ≈ $7,400.40

Therefore, the total interest paid for the sailboat is approximately $7,400.40.

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Answer:

Domain: (-∞,∞) Range: {y|y = 35}

Step-by-step explanation:

Find the domain by finding where the function is defined. The range of values that correspond with the domain.

Answer:

d = 13

Step-by-step explanation:

First, the distance formula is needed:

\(d = \sqrt{(x_{2} - x_{1} )^{2} +(y_{2} - y_{1 })^{2} }\)

Next we assign the points

(2,-4) is point 1, (7,8) is point 2

\(d = \sqrt{(7 - 2 )^{2} +(8 - (-4))^{2} } \\d = \sqrt{5^{2} +12^{2} } \\d = \sqrt{25 + 144}\\ d = \sqrt{169} \\d = 13\)

Given two points (2,-4) and (7,8)

To find - The distance between given points.

We know the formula that is used to find the distance is given as

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

We let P = (2,-4)

and Q = (7,8)

\(x_1=2, y_1=-4\\x_2=7,y_2=8\)

on substituting we get

\(d=\sqrt{(7-2)^2+(8+4)^2}\\ d=\sqrt{(5)^2+(12)^2} \\d=\sqrt{25+144} \\d=\sqrt{169}\\ d=13\)

Hence we get the distance between (2,-4) and (7,8) is 13.

Final answer - The distance is 13.

Answer:

2\3 cups will be needed..good luck

The center of the circle with the equation ( x - 5 )² + ( y + 5 )² = 5 is (5,-5).

The standard form equation of a circle with center (h, k) and radius r is:

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the center of the circle, and r is the radius.

Given the equation of the circle:

( x - 5 )² + ( y + 5 )² = 5

Comparing the given equation with the standard form (x - h)² + (y - k)² = r², we see that the center of the circle is at the point (h, k), which corresponds to the values inside the parentheses. So we have:

h = 5

k - 5

This means that the center of the circle is at the point (5, -5).

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Answer:

Step-by-step explanation:

yyyyyyyyyyyyyyyyyyyyyyyyyyyy

Answer:

It would be 6$ each person

Answer:

I would say yes they are

Step-by-step explanation:

because you multiply the small one's numbers by 2 and get the big triangle

Answer:

they are similar! :)

Step-by-step explanation:

the best way to figure this out is just by looking to see if they have anything in common. in this case, the larger figure is just two times more on each side than the smaller figure.

Answer:

56°

Step-by-step explanation:

The interior angles of a triangle add up to 180.

You would first set up the following problem:

91 + 33 + x = 180

You would now subtract 91 from both sides.

33 + x = 89

You would now subtract 33 from both sides.

x = 56

The value of x is 56 degrees.

Angle of triangle D is 56 degrees.

"A triangle is a simple closed curved made of three segments. A triangle has three sides and three angles, and all three sides and angles are called six elements of the triangle."

We have

Angle sum property of a triangle = \(180^{0}\)

<B + <C + <D =  \(180^{0}\)

⇒ \(91^{0}+33^{0} +x^{0}=180^{0}\)

⇒ \(x^{0}=180^{0}-91^{0}-33^{0}\)

⇒ \(x^{0}=56^{0}\)

The value of x is 56 degrees.

Hence, angle of triangle D is 56 degrees.

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Answer:

2x + 3

Step-by-step explanation:

two sides measure (x-1) which gives 2(x-1) or 2x - 2

subtract 2x - 2 from 6x + 4 to get 4x + 6

4x + 6 represents twice the length so divide it in half to get:

2x + 3

Answer:

The perimeter of a rectangle is represented by the expression 6x + 4. If the width of the rectangle is represented by the expression x – 1, which expression represents the length?

Step-by-step explanation:

EDGE 2021

Answer

Step-by-step explanation:

Answer:

y= *greater than or equal to sign* 2500x+17500

The answer is: A

Step-by-step explanation:

Hope this help   :)

Answer:

It's C

Step-by-step explanation:

I put in A for my exam but it said it was incorrect and it said the answer was C :')

A. Bisects ∠BAC: Needed             B. Is perpendicular to BC: Not needed

C. Point O is the midpoint of BC: Not needed

D. Is an altitude: Not needed

To complete the proof using the ASA (Angle Side Angle) congruence theorem, we need to ensure that certain conditions are met. Let's analyze each statement in order to determine if it is needed or not needed for the proof:

A. "Bisects ∠BAC": This statement refers to drawing the line segment AO that bisects angle BAC. This step is necessary to divide angle BAC into two congruent angles, which is important for establishing the congruence of the triangles. Therefore, this statement is needed.

B. "Is perpendicular to BC": This statement suggests that line segment AO is perpendicular to side BC. However, the ASA congruence theorem does not require the presence of a perpendicular line. Therefore, this statement is not needed for the proof.

C. "Point O is the midpoint of BC": This statement indicates that point O divides side BC into two equal segments. While it is true that in an isosceles triangle, the line segment connecting the midpoint of the base to the vertex is an altitude, this information is not necessary for the ASA congruence theorem. Thus, this statement is not needed.

D. "Is an altitude": This statement suggests that line segment AO is an altitude of triangle ABC, which means it is perpendicular to the base BC. However, as mentioned earlier, the ASA congruence theorem does not require this condition. Therefore, this statement is not needed for the proof.

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Answer:

40,000

Step-by-step explanation:

can I have branliest

Answer: 40,000

Step-by-step explanation: Well it doubles every 440 minutes. Since it is asking for the size after 880 minutes, and the starting size is 20,000 just double 20,000 because 440 times 2 equals 880.

Answer: -2

Step-by-step explanation:

-Distribute : 5+5n=-5

-Set both sides : 5n=-10

-Divide : -10/5n = -2