Write the absolute vale of |3-5|​

The value of x is 116°

Given that a circle, with two congruent chords, FG and DE we need to find the central angle x,

Here we will use the properties of circle,

Since, the chords are equal, so, the measure of the arc intercepted by them will be equal,

arc DE = arc FG = 116°

Also, we know that the central angle is equal to the measure of the arc intercepted by it,

Therefore, x = m arc DE

x = 116°

Hence, the value of x is 116°

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The Cobb-Douglas utility function satisfies the properties of local non-satiation, decreasing marginal utility for both goods, quasi-concavity, and homotheticity.

The Cobb-Douglas utility function u(x1, x2) = xi^(α) * x2^(β), where α and β are both greater than zero, satisfies the following properties:

(a) Local non-satiation:

This property states that at each point of the consumption set, there is always another bundle that is arbitrarily close and strictly preferred. Thus, the function has local non-satiation.

(b) Decreasing marginal utility for both goods 1 and 2: The marginal utility of a good measures the utility obtained by consuming one more unit of it. The marginal utility of x1 can be obtained as:

MU1 = α * xi^(α−1) * x2^(β)

The marginal utility of x2 can be obtained as:

MU2 = β * xi^(α) * x2^(β−1)

Therefore, both marginal utilities are decreasing in x1 and x2, satisfying this property.

(c) Quasi-concavity:

The Cobb-Douglas function is quasi-concave. This means that the upper contour set of any level set of the function is convex. This can be proved by taking the second partial derivative of the function and checking whether it is negative or not.

(d) Homotheticity:

The Cobb-Douglas function is homothetic. This means that its shape is independent of the total level of utility. The proof can be achieved by checking whether the function is homogeneous of degree one or not. This is true, since multiplying the inputs by any positive scalar λ leads to a proportional increase in the output.

In conclusion, the Cobb-Douglas utility function satisfies all four properties - local non-satiation, decreasing marginal utility for both goods 1 and 2, quasi-concavity, and homotheticity.

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Using linear function to solve this problem, for every 1 gallon of gas, Francisco travelled 27.9 miles

A linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with f(x), this function can be written as f(x) = 3x - 2. A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. where m is slope of the line and b is the y - intercept

We can use the data given in writing out our equation

390.6 = 14x

If 14 gallons = 390.6 miles

 1 gallon = x miles

x = 390.6 / 14

x = 27.9 miles

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The working to the problems shows the factorization method of solving quadratic equations.

A polynomial equation of degree 2 is a quadratic equation because it includes terms with variables raised to the power of 2.

We have that;

\(x^2 + 10x + 16 = 0\\x^2 + 8x + 2x + 16 = 0\)

x(x + 8) + 2 (x + 8) = 0

(x +2) (x + 8) = 0

x = -2 and -8

2)

\(x^2 - 6x + 5 = 0\\x^2 -5x - x + 5 = 0\)

x(x - 5) -1 (x - 5) = 0

(x - 5) (x - 1) = 0

x = 1 or 5

3)

\(x^2 - 2x - 8 = 0\\x^2 -4x + 2x - 8 = 0\)

x(x - 4) + 2(x - 4) = 0

(x + 2) (x - 4) = 0

x = -2 or 4

4)

\(2x^2 - 8x - 10 = 0\\x^2 - 4x - 5 = 0\\x^2 +x - 5x - 5 = 0\)

x(x + 1) -5(x + 1) = 0

(x + 1) (x - 5) =0

x = -1 or + 5

5)

\(4x^2 - 36 = 0\\x^2 - 9 = 0\)

x = ±3

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Answer:

B

Step-by-step explanation:

Answer:

31.4 m

Step-by-step explanation:

Tan of the 63 degree angle = opposite leg / adjacent leg

   opposite leg is the height  adjacent leg is 16 m

tan63 = height / 16

16 tan 63° = height =  31.4 m

Answer:

10 = 0.0048(x-50)^2+6

Step-by-step explanation:

Correct on EDGE

Answer:

B on E2020

Step-by-step explanation:

The next one is 21 ft. and 79 ft.

The table that represents the graph described is Table A - A 2-column table with 6 rows. Column 1 is labeled x - 0, 1, 2, 3, 4, 5. Column 2 is labeled y = 2x - 3 with -3, -1, 1, 3, 5, 7.

In order to solve this, look for the table that has x and y values that tally with the points on the graph.

The points on the graph are:

(0, -3), (1, -1), (2, 1), (3, 3), (4, 5), and (5, 7).

When you look at the first table, you see that the first x value corresponds with the y value of the first point on the graph. The second point on the graph of (1, -1) is also the same as the first table's x and y values.

In conclusion, option A is correct.

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Answer:

Its A

Step-by-step explanation:

Answer:

The ordered pair is (1, 2) ⇒ A

Step-by-step explanation:

In the function f(x) = y

That means any ordered pair (x, y) satisfy the function f(x) = y, lies on the graph of the function

∵ f(x) = 2x

→ That means y = 2x

∵ x = 1

→ Substitute the value of x in the function above

∴ f(1) = 2(1)

∴ f(1) = 2

→ That means at x = 1, y = 2

∴ The ordered pair is (1, 2)

Answer:

Step-by-step explanation:

A rectangular pyramid has five sides. It consists of a rectangular base and four triangular faces that meet at a common vertex or apex.

≧◉◡◉≦

Answer:

he  spent $75.80

Step-by-step explanation:

hope this helps:D

To isolate f in an equation, we make f the subject of the equation

From the question, we have the following parameters that can be used in our computation:

The statement that represents isolating the variable

Take for instance, the equation is

bc + fc = k

To isolate f we make f the subject

So, we have

f = (k - bc)/c

Hence, isolating f means solving for f

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W and is orthogonal to all vectors in W except itself, we have shown that any vector in Rn can be written as a linear combination of the n non-zero orthogonal vectors that span W, and hence W=Rn.

To show that W=Rn, we need to show that any vector in Rn can be written as a linear combination of the n non-zero orthogonal vectors that span W.

Let v be any vector in Rn. Since the n non-zero orthogonal vectors span W, we can write v as a linear combination of them:

v = c1v1 + c2v2 + ... + cnvn

where c1, c2, ..., cn are scalars, and v1, v2, ..., vn are the n non-zero orthogonal vectors that span W.

To show that v is in W, we need to show that v is orthogonal to all vectors in W except itself. Since the n non-zero orthogonal vectors are linearly independent, any linear combination of them that is orthogonal to v must be the zero vector.

Therefore, if w is any vector in W that is not equal to v, we have:

=  = c1 + c2 + ... + cn = 0

since v is orthogonal to all the non-zero orthogonal vectors. This means that v is orthogonal to all vectors in W except itself.

Therefore, since v is in W and is orthogonal to all vectors in W except itself, we have shown that any vector in Rn can be written as a linear combination of the n non-zero orthogonal vectors that span W, and hence W=Rn.

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Answer:

v/5*3

Step-by-step explanation:

The volume of 5 balls is V cm. Express the volume of 3 balls in terms of V

v/5*3

Step-by-step explanation:

5 balls volumes = V cm

1 ball volume = V/5 cm

:. 3 balls volumes = 3×V/5 = 3V/5 cm

the volume of 3balls is 3V/5 cm.

hope this helps you.

Answer:

Rise is vertical, run is horizontal

Step-by-step explanation:

Answer:

y= -4x                                                                                                                                                                                      

Step-by-step explanation:

hope this helps and lmk if you need anything!

Answer:

22

Step-by-step explanation:

Given that T is the midpoint of line PQ, PT and TQ are both equal segments of line PQ.

PT is given as 5x + 2,

TQ = 7x - 6

Therefore:

\( 5x + 2 = 7x - 6 \)

Solve for x

\( 5x + 2 - 7x = 7x - 6 - 7x \)

\( -2x + 2 = -6 \)

\( -2x + 2 - 2 = -6 - 2 \)

\( -2x = -8 \)

\( \frac{-2x}{-2} = \frac{-8}{-2} \)

\( x = 4 \)

PT = \( 5x + 2 \)

Input the value of x

\( PT = 5(4) + 2 = 20 + 2 = 22 \)

To find the nth term of the sequence, we add 4 to the (n-1)th term.

(a) To give a recursive definition of the sequence {an} where an = 4n - 2, we can define it as follows:

a1 = 2

an = an-1 + 4 for n > 1

This means that to find the nth term of the sequence, we add 4 to the (n-1)th term.

(b) To give a recursive definition of the sequence {an} where an = 1 (-1)^n, we can define it as follows:

a1 = 1

an = -an-1 for n > 1

This means that to find the nth term of the sequence, we multiply the (n-1)th term by -1.

(c) To give a recursive definition of the sequence {an} where an = n(n+1), we can define it as follows:

a1 = 2

an = an-1 + 2n + 1 for n > 1

This means that to find the nth term of the sequence, we add 2n+1 to the (n-1)th term.

(d) To give a recursive definition of the sequence {an} where an = n^2, we can define it as follows:

a1 = 1

an = an-1 + 2n - 1 for n > 1

This means that to find the nth term of the sequence, we add 2n-1 to the (n-1)th term.

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Answer:

B= 32q

Step-by-step explanation:

A bushel is equal to 32 quarts, while a peck is equal to 8 quarts, or a quarter of a bushel.

(-6, 14) and (2, -18)

The slope of the line that passes through the point.

y2 - y1 / x2 - x1

-18 - 14 / 2 + 6

= -32 / 8

= -4

Option D. -4

Total number of seats that remain unsold are 168.

What is statistics?

The branch of mathematics dealing with data collection, organization, analysis, interpretation and presentation.

Let's start by defining some variables to represent the unknowns in the problem:

From the problem, we know that:

We also know that the total revenue collected is $34,650:

27x + 45y = 34650

Now we can substitute y = 0.5x from the second equation into the third equation and simplify:

27x + 45(0.5x) = 34650

27x + 22.5x = 34650

49.5x = 34650

x = 700

So there were 700 $30-seats and 350 $50-seats.

The number of sold $30-seats is 0.9(30x) = 567, and the number of sold $50-seats is 0.9(50y) = 315.

Therefore, the total number of seats sold is 882, and the number of unsold seats is:

1050 - 882 = 168

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Answer:

x = 8

Step-by-step explanation:

Here, we want to find the value of x

According to the theorem;

45 = 1/2(147 - (7x-5))

90 = 147 -7x + 5

90 = -7x + 147

7x = 147-90

7x = 57

x = 57/7

x = 8.142 which is approximately 8

Answer:

The answer is "The discriminant is positive"

Step-by-step explanation:

When the discriminant is positive there is two real solutions.

When the discriminant is equal to 0, there is one real solution.

When the discriminant is negative, there is no real number solutions.

Answer:

Tank B holds more

Tank A:

35*95 = 3,325 *30= 99,750

Tank B: 65*35= 2,275 *45= 102,375

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Given data:

The given equation of the line is 3x+6y=-18.

The x-intercept is the point where the graph cuts the x-axis.

Substitute 0 for y in the given equation.

3x+6(0)=-18

3x=-18

x=-6

The y-intercept is the point where the graph cuts the y-axis, substitute 0 for x in the equation.

3(0)+6y=-18

6y=-18

y=-3

Thus, the x intercept is -6, and y intercept is -3.

Now draw a line which is passes through (-6,0) and (0,-3).