Georgetown passed an ordinance that requires a 5-cent water-bottle tax to be charged for every bottle of
water purchased. If a customer at a store in Georgetown paid 65 cents in water-bottle tax, how many bottles
of water did the customer purchase?
A 325
B 60
C 13
D 5

Answer:

x=10

Step-by-step explanation:

By the Trapezoid Midsegment Theorem, the midsegment of a Trapezoid is 1/2(the sum of the 2 bases.

4x-20=1/2(23+17)

4x-20=1/2(40)

4x-20=20

4x=40

x=10

Answer:

4186.15

Step-by-step explanation:

Answer:

418,615 or 4,186.15

Step-by-step explanation:i cant tell if it is a desimal or a full number if desimal 4,186.15 if not desimal 418,615

a) Cost of debt, I = 4.25%(annual)

b) After tax cost of debt = 3.315%

c) After tax cost of debt of 3.135% is more relevant.

Given:

FV = 100

Semiannual bond issued 3 years ago

Maturity = 27

Price, PV = 104

coupon rate = 4.5%

Tax rate = 22%

a) Semiannual bond issued 3 years ago

Maturity, n = 27 years × 2 = 54

Coupon C = 4.5%/2×100 = 2.25

Now,

Pretax cost of debt,

Cost of debt, I = [C+(FV-PV)/n] / (FV+PV)/2

= [2.25 +(100 - 104)/54] / [ 100+1040/2

= 2.12%

= 2.12×2

Cost of debt, I = 4.25%(annual)

b) After tax cost of debt = cost of debt × (1-T)

= 4.25% × (1-22%)

After tax cost of debt = 3.315%

c) After tax cost of debt is more relevant.

Hence we get the required answer.

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Given parameters:

 The coordinates are:

                 P1 (8, -4) and P2 (-3, 9)

Unknown:

The midpoint of the endpoints = ?

Solution:

     x₁  =  8

     y₁  = -4

     x₂  = -3

     y₂  = 9

  midpoints;     x\(_{m}\) , y\(_{m}\)  = \(\frac{x_{1} + x_{2} }{2} ,\) \(\frac{y_{1} + y_{2} }{2}\)

                                       = \(\frac{8 +(-3)}{2}\) , \(\frac{-4 + 9}{2}\)

                                       = \(\frac{5}{2}\) , \(\frac{5}{2}\)

   The coordinate of the x-axis is \(\frac{5}{2}\)

The slope, m, of the line that passes through (2, 7) and (-4, 19) is -2.

According to the question,

We have the following information:

A line is passing through two points (2,7) and (-4,19).

We know that the slope of the line is denoted by m and the following formula is used to find the slope of the line passing through two points:

m = (y2-y1)/(x2-x1)

(More to know: we can also easily find the equation of the line using the slope given and the points from which the line is passing.)

In this case, we have x1 = 2, y1 = 7, x2 = -4 and y2 = 19.

m = (19-7)/(-4-2)

m = 12/(-6)

m = -2

Hence, the slope, m, of the line that passes through (2, 7) and (-4, 19) is -2.

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Answer:

Step-by-step explanation:

(3x + 1)/x = 1/(x -3)                Cross multiply

(3x + 1)(x - 3) = x                   Remove the brackets. Use FOIL

f:3x*x = 3x^2

o:3x*(-3) = -9x

i:1*x = x

L : 1 * - 3 = -3

FOIL: 3x^2 -9x +x - 3

FOIL: 3x^2 - 8x - 3

3x^2 - 8x - 3 = x                  Subtract x from both sides

3x^2 - 8x -x - 3 = 0             Combine

3x^2 - 9x - 3 = 0                 Factor

It's rather ugly. I had to use the quadratic equation

a = 3

b = - 9

c = - 3

x1 = 3.3

x2 = - 0.3

Step-by-step explanation:

a vertex is a corner and the corner that both the quadrilateral and Pentagon share is a point at (-3, -5)

Answer:

Let ac=ab=5

With this, bc= 5√2

Step-by-step explanation:

So to find ad, Let ad be x

5√2=(2)(x)

(5√2/2)= x

This proves that bc=2ad

Answer: The anwser is Triangle 2

The given triangle is congruent to the second triangle because they same construction methods and the have same size and same shape.

Congruent triangles are those that are exactly the same size and shape. Congruent is represented by the symbol ≅ When the three sides and three angles of one triangle match the dimensions of the three sides and three angles of another triangle, they are said to be congruent.

We have given a congruent triangle in the picture.

After close observation, the second triangle has the same size and the same shape, and the same construction method by arc method.

Other triangles have different construction methods.

Thus, the given triangle is congruent to the second triangle because they same construction methods and the have same size and same shape.

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Answer:

x = 118.6°

Step-by-step explanation:

Law Of Cosines

In trigonometry, the law of cosines (also known as the cosine formula, cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles.

If a, b and c are three sides of a triangle and θ is the included angle of the sides a and b then the cosine rule states:

\(c^2 = a^2 + b^2 - 2ab\cos \theta\)

In this diagram we are asked to find angle x

The sides that include angle x are AB and BC

The third side is AC

We have

\(AB = 23\\BC = 20\\AC = 37\\\)

\(m\angle ABC = x^\circ\)

Therefore by the law of cosines,

AC² = AB² + BC² - 2(AB)(AC) cos(x)

⇒   37² = 23² + 20² - 2(23)(20) cos(x)

⇒   1369 = 529 + 400 - 920 cos(x)

Move -920cos(x) from right to left side(sign changes)
920cos(x) + 1369 = 929

Move 1369 to right side (sign changes)
920cos(x)  =  - 1369 + 929
                  = -440

Divide both sides by 920:

\(cos(x) = - \dfrac{440}{920} \\\\x = cos^{-1} \left(- \dfrac{440}{920}\right)\)

Using a calculator this works out to
x = 118.6° rounded to the nearest tenth

Answer:

80 Cubic Units

Step-by-step explanation:

5 x 4 = 20

20 x 4 = 80

Hope it helps :)

80 unites because 5 x 4 = 20 and 20 x 4 = 80

a) The equation represents an ellipse.

b) The equation represents a circle.

c) The equation represents a parabola.

In this problem we have general equations of the form A · x² + B · y² + C · x + D · y + E = 0, which have to be modified into standard form to infer its graphical form. This procedure can be done by algebra properties:

16 · x² + 4 · y² + 96 · x - 8 · y + 84 = 0

[(4 · x)² + 2 · 12 · (4 · x)] + [(2 · y)² - 2 · 2 · (2 · y)] = - 84

[(4 · x)² + 2 · 12 · (4 · x) + 144] + [(2 · y)² - 2 · 2 · (2 · y) + 4] = 64

(4 · x + 12)² + (2 · y + 2)² = 64

4² · (x + 3)² + 2² · (y + 2)² = 64

(x + 3)² / 4 + (y + 2)² / 16 = 1 : Ellipse

x² + y² + 8 · x - 6 · y - 15 = 0

(x² + 8 · x) + (y² - 6 · y) = 15

(x² + 2 · 4 · x + 16) + (y² - 2 · 3 · y + 9) = 40

(x + 4)² + (y - 3)² = 40 : Circle

x² + 6 · x + 4 · y + 5 = 0

x² + 6 · x + 5 = - 4 · y

y = - (1 / 4) · x² - (3 / 2) · x - (5 / 4) : Parabola

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The value of the functions operation (g-f)(2) is 0.

To find the result of (g-f)(2), we first need to subtract the function f(x) from g(x), and then evaluate the resulting function at x=2.

Step 1: Subtraction of two function :-  f(x) from g(x) to obtain (g-f)(x):
(g-f)(x) = g(x) - f(x)

          = (x^2 + 2x - 8) - (3x -6)

Step 2: Simplify the expression:
(g-f)(x) = x^2 + 2x - 8 - 3x +6

          = x^2 -x- 2

Step 3: Evaluate (g-f)(x) at x=2:
(g-f)(2) = (2^2) - 2-2

          = 4 - 4

          = 0

The result of (g-f)(2) is 0.

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Answer:

15: significant 16: research problem

x = 2

Hi there !

5x + 3 = 7x - 1

3 + 1 = 7x - 5x

4 = 2x

2x = 4

x = 4 : 2

x = 2

Good luck !

A connected graph can be disconnected by removing vertices if and only if it is not a complete graph.

A connected graph is one where there exists a path between any pair of vertices. Removing any vertex from a complete graph will result in a disconnected graph since there will be at least one pair of vertices that are no longer connected. Therefore, a complete graph cannot be disconnected by removing vertices.

On the other hand, if a graph is not a complete graph, it means that there exist at least two vertices that are not connected by an edge. By removing these vertices, we effectively disconnect the graph since there is no longer a path between them.

Thus, it is possible to remove vertices to disconnect a graph that is not a complete graph.

A complete graph cannot be disconnected by removing vertices, while a non-complete graph can be disconnected by removing appropriate vertices.

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To prove that triangle ABC is congruent to triangle EDC using ASA, the statement that is needed is "Angle BAC is congruent to angle EDC. Triangle ABC is congruent to triangle EDC using the ASA (angle-side-angle) theorem if the following conditions are met: Two pairs of corresponding angles are congruent in both triangles.

A pair of corresponding sides is congruent in both triangles. Therefore, to prove that triangle ABC is congruent to triangle EDC using ASA, the statement that is needed is "Angle BAC is congruent to angle EDC." To prove that triangle ABC is congruent to triangle EDC using the ASA (Angle-Side-Angle) theorem, we need to show that angle BAC in triangle ABC is congruent to angle EDC in triangle EDC, and also that the sides AB and AC in triangle ABC are congruent to sides ED and DC in triangle EDC. In other words, the two triangles are congruent if we can establish that one angle and the two sides adjacent to it in one triangle are equal to one angle and the two adjacent sides of the other triangle. In this case, we can use the ASA theorem, which states that if two angles and a side not between them in one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. Therefore, angle BAC is congruent to angle EDC is the statement we need to prove triangle ABC is congruent to triangle EDC using ASA.

So, the statement needed to prove triangle ABC is congruent to triangle EDC using ASA is that "Angle BAC is congruent to angle EDC."

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Answer: The answer is 279

Step-by-step explanation:

12 x 24=288

288-9=279

12(24)-9=279

The calculated surface area of the figure is 152 square feet

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

The triangular prism

The surface  area is calculated as

SA = hp + 2B

Where

h = height

p = perimeter of base

B = base area

From the figure, we have

B = 1/2 * 6 * 4 = 12

p = 5 + 5 + 6 = 16

h = 8

So, we have

SA = 8 * 16 + 2 * 12

Evaluate

SA = 152

Hence, the surface area is 152 square feet

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This expression represents the total amount of water leaked between time t = a and t = b.

On a routine inspection of the water system of Minneapolis, Alfonso discovers a pipe leaking at the rate of L(t) = 0.5t + 2 liters/hour, t hours after the leak begins.

The given information provides us with a leak rate function L(t) that describes the number of liters of water leaked per hour, depending on the time t in hours since the leak began. The function L(t) is defined as 0.5t + 2 liters/hour.

To understand the leak over a specific duration, we can integrate the leak rate function. The integral of L(t) with respect to t will give us the total amount of water leaked during that duration.

Let's say we want to determine the total amount of water leaked between time t = a and t = b, where a and b represent the start and end times, respectively. The integral of L(t) over this interval will be:

∫[a to b] (0.5t + 2) dt

To find the integral, we can apply the rules of integration:

∫[a to b] (0.5t + 2) dt = [0.25t^2 + 2t] from a to b

Evaluating the integral from a to b gives us:

[0.25b^2 + 2b] - [0.25a^2 + 2a]

This expression represents the total amount of water leaked between time t = a and t = b.

Therefore, using the leak rate function L(t) = 0.5t + 2 liters/hour, we can calculate the total amount of water leaked over a specific duration by evaluating the integral of the function within that time interval.

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Answer: 3x-3

Step-by-step explanation:

1. The Taylor series for f(x) = cos(x) centered at c = π/4 is:

f(x) = cos(π/4) - sin(π/4)(x - π/4) + (1/2)cos(π/4)(x - π/4)^2 - (1/6)sin(π/4)(x - π/4)^3 + ...

2. The Taylor series for f(x) = ln(x) centered at c = 1 is:

f(x) = ln(1) + (x - 1) - (x - 1)^2/2 + (x - 1)^3/3 - ...

3. The Maclaurin series for f(x) = ln(1 + x^9) is:

f(x) = x^9 - (1/2)x^18 + (1/3)x^27 - ...

1. The Taylor series expansion for cos(x) centered at c is derived by using the derivatives of the function evaluated at c. The general form of the series includes terms with alternating signs and higher powers of (x - c).

2. Similarly, the Taylor series expansion for ln(x) centered at c is obtained by finding the derivatives of the function and evaluating them at c. The resulting series includes powers of (x - c) with coefficients derived from the derivatives.

3. For the Maclaurin series, we center the Taylor series at c = 0. In the case of f(x) = ln(1 + x^9), we use the power series expansion of ln(1 + x) and substitute x^9 in place of x. The resulting series includes terms with positive powers of x^9 and coefficients determined by the power series for ln(1 + x).

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Answer:

no false it has infinite

Answer:

  x ≈ 50.1  or  49.0 — depending on how you solve the triangle

Step-by-step explanation:

In the given figure, ∆IJK is marked with angles that make it similar to ∆LMN. Side lengths are given as j = 77, k = 60, m = x, n = 39, and you are asked to find the length of x.

Angle J can be found from the other angles in ∆IJK.

  J = 180° -I -K

  J = 180° -63° -48° = 69°

You will observe that angles J and K have measures 69° and 48°, respectively, and that these are congruent to corresponding angles M and N. Since corresponding angles are congruent, the triangles are similar by the AA similarity postulate.

Using the given side lengths, we can write a proportion for corresponding sides, assuming similar triangles:

  m/n = j/k

  x/39 = 77/60 . . . . . . use the given values

  x = 39·77/60 = 50.05 ≈ 50.1

The length of side x is about 50.1 units.

If we ignore triangle IJK and solve triangle LMN using the law of sines, we have ...

  m/n = sin(M)/sin(N) . . . . . sides are in proportion to sin(opposite ∠)

  x/39 = sin(69°)/sin(48°)

  x = 39·sin(69°)/sin(48°) ≈ 49.0

Solving the triangle gives x = 49.0.

__

Additional comment

Triangle IJK is "overspecified." The figure of triangle IJK given cannot be drawn to scale because the angles and side lengths are inconsistent. This puts us in the awkward position of having to guess the procedure you're intended to use to answer the question.

The first solution above is based on relations between similar triangles. The proportion of corresponding sides doesn't consider that those side lengths are inconsistent with the angles shown.

The second solution above is based only on the information given in ∆LMN. It uses the combination of given sides and angles, without reference to ∆IJK. We prefer this solution, but we suspect your grader is looking for the other solution.

The simplified form of the expression

Some common rules of exponents are

\(a^b \times a^c = a^{b + c}\).

\(\frac{a^b}{a^c} = a^{b - c}\).

We can only add and subtract exponents only when we have the same base.

Given, An expression in exponent form is 4⁷68x⁸y⁵.

= 4⁷(4×17)x⁸y⁵.

= 4⁷2²17x⁸y⁵.

= 2¹⁴2²17x⁸y⁵.

= 2¹⁶x⁸17y⁵.

= 17(4x)⁸y⁵.

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Answer:

\(-2x^2 + 8x - 8\)

Step-by-step explanation:

To make \(-4 - x^2 + 4x - 4 - x^2 + 4x\) into standard form, we want to combine like terms to get a simplified expression.

In standard form, the highest exponent term always comes first, which here is the \(x^2\) term.

\(-x^2 - x^2 = -2x^2\)

Next comes the b term (bx).

\(4x + 4x = 8x\)

Then comes the constant (c).

\(-4 - 4 = -8\)

So in total we have \(-2x^2 + 8x - 8\).

Hope this helped!

Answer:

Hello! Mizuki here to help. The correct option you choose should be the second one(hoping you meet it)

Just hoping and not trying to achieve the goal won't help. The others are important step(s) to achieve a goal.

Step-by-step explanation:

Answer:

Same as the other guy

Step-by-step explanation:

Answer:

its (0,-1) ...................................

Answer:

what are the ordered pairs? then graph them and do the y axis number over the x axis number

Step-by-step explanation: