PLZZ HELP

When dividing fractions, the ________ term becomes the reciprocal.

Neither
Second
Both
First

tan(41π/36) can be written in terms of the tangent of a positive acute angle as (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

To express tan(41π/36) in terms of the tangent of a positive acute angle, we need to find an angle within the range of 0 to π/2 that has the same tangent value.

First, let's simplify 41π/36 to its equivalent angle within one full revolution (2π):

41π/36 = 40π/36 + π/36 = (10/9)π + (1/36)π

Now, we can rewrite the angle as:

tan(41π/36) = tan((10/9)π + (1/36)π)

Next, we'll use the tangent addition formula, which states that:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

In this case, A = (10/9)π and B = (1/36)π.

tan(41π/36) = tan((10/9)π + (1/36)π) = (tan((10/9)π) + tan((1/36)π)) / (1 - tan((10/9)π)tan((1/36)π))

Now, we need to find the tangent values of (10/9)π and (1/36)π. Since tangent has a periodicity of π, we can subtract or add multiples of π to get equivalent angles within the range of 0 to π/2.

For (10/9)π, we can subtract π to get an equivalent angle within the range:

(10/9)π - π = (1/9)π

Similarly, for (1/36)π, we can add π to get an equivalent angle:

(1/36)π + π = (37/36)π

Now, we can rewrite the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Since we are looking for an angle within the range of 0 to π/2, we can further simplify the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Therefore, tan(41π/36) can be written in terms of the tangent of a positive acute angle as the expression given above.

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Answer:

42

Step-by-step explanation:

6*(-3) = (-18)

24-(-18) = 42

Answer:42

Step-by-step explanation:

the potential at the center of the equilateral triangle is 3kq√3 / a.To find , we can use the formula for the electric potential due to a point charge:

V = kq / r

where k is the Coulomb constant, q is the charge, and r is the distance between the point charge and the center of the triangle.

Assuming the charges are all positive, the potential at the center due to each charge will be the same, so we can find the total potential by multiplying the potential due to one charge by three.

The distance from the center of the equilateral triangle to each charge is a/√3, since the height of the equilateral triangle is √3/2 times the side length.

Therefore, the potential at the center is:

V = 3(kq / (a/√3))

Simplifying:

V = 3kq√3 / a

Hence, the potential at the center of the equilateral triangle is 3kq√3 / a.

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Answer:

d) RTS

Step-by-step explanation:

1) match up the points visually, by angle

M=R

O=T

N=S

2) select the correct answer :)

The statement of congruence is: ΔMONX ≅ ΔASTR. The correct option is C.

Congruence is a term used in geometry to describe the relationship between two geometric figures that have the same shape and size.

Two figures are said to be congruent if they have exactly the same dimensions and shape, and can be transformed into each other by a combination of rotations, reflections, and translations.

In a congruence statement, the order of the vertices matters. The triangles are congruent because they have the same size and shape, and their corresponding sides and angles are equal.

The vertices of ΔMONX correspond to the vertices of ΔASTR in the following way:

M corresponds to A

O corresponds to S

N corresponds to T

X corresponds to R

Therefore, the correct statement of congruence is ΔMONX ≅ ΔASTR, which can also be written as ΔASTR ≅ ΔMONX. The answer is C. ASTR.

The graph shows the  inequality x² ≤ 16

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4.

Inequalities are often used to describe conditions or constraints in real-world problems.

You will notice that the values represented in the graph ranges from -4 to 4. Thus, solving x² ≤ 16 will produce these values. That is:

x² ≤ 16

x ≤ ±√16

x ≤ ±4

x ≤ -4 or x ≤ 4

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Answer:

The region of acceptance gets bigger and the null hypothesis is mostly accepted as it lies in the acceptance region.

Step-by-step explanation:

As the level of significance is decreased the area for the favorable outcomes is increased. The value of ∝= 0.1 has a narrower area of favorable outcomes then the values of ∝= 0.05 or 0.01 because the value 0.1 ( 1%) is closer to the middle value or at the extreme values of the distribution as the case may be for 2 tailed or 1 tailed test.

Significance level        Two tailed Test          One tailed test

0.1                                   ± 1.645                               ±1.28

0.05                                 ±1.96                                ± 1.645

0.01                                ± 2.58                                 ±  2.33

So if the middle point is taken as zero we see that the spread of the area of the favorable values increases as the value of ∝ significance level decreases.

The region of acceptance gets bigger and the null hypothesis is mostly accepted as it lies in the acceptance region.

If the diameter of the reserve tank is 30.51 cm, the shortest height the reserve tank should be is 0 cm.

How to find?

The shortest height of the reserve tank can be determined using the formula for the volume of a cylinder.

The formula for the volume of a cylinder is \(V = π * r^2 * h\),

Where V is the volume, π is a constant approximately equal to 3.14159, r is the radius, and h is the height.

To find the shortest height, we need to find the maximum volume of the tank. Since the diameter is given as 30.51 cm, we can calculate the radius by dividing the diameter by 2.

radius = diameter / 2

= 30.51 cm / 2

= 15.255 cm

Substituting the values into the volume formula, we get:

\(V = π * (15.255 cm)^2 * h\)

To find the maximum volume, we need to maximize the height. Since we want the shortest height, we want to minimize the volume. Therefore, we set the volume equal to zero:

\(0 = π * (15.255 cm)^2 * h\)

Solving for h:

\(h = 0 / [π * (15.255 cm)^2]\)

h = 0 cm

Therefore, the shortest height the reserve tank should be is 0 cm.

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The shortest height for the reserve tank is approximately 0.0184 cm (rounded to four decimal places).

To determine the shortest height of the reserve tank, we need to use the formula for the volume of a cylinder, which is V = \(\pi r^2h\), where V represents the volume, π is a constant approximately equal to 3.14159, r is the radius, and h is the height of the cylinder.
Given that the diameter of the reserve tank is 30.51 cm, we can calculate the radius by dividing the diameter by 2. Thus, the radius (r) is 30.51 cm / 2 = 15.255 cm.

To find the shortest height, we need to consider that the volume of the reserve tank should be non-zero. Therefore, we'll assume the minimum value for the height is 0.0001 cm.
Now, we can substitute the values into the formula and solve for the volume:
V = \(\pi r^2h\)
V = 3.14159 * (15.255 cm)^2 * 0.0001 cm
V ≈ 0.018411 \(cm^3\) (rounded to six decimal places)

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Permutations for each word can be calculated by considering the number of unique letters in it and taking factorial of it.

a) Inverary: There are 8 letters in the name "Inverary" (I, N, V, E, R, A, R, Y), so there are 8! (8 factorial) permutations of all the letters in the name. This equals 40320 permutations.

b) Beamsville: There are 9 letters in the name "Beamsville" (B, E, A, M, S, V, I, L, E), so there are 9! (9 factorial) permutations of all the letters in the name. This equals 362880 permutations.

c) Mattawa: There are 7 letters in the name "Mattawa" (M, A, T, T, A, W, A), so there are 7! (7 factorial) permutations of all the letters in the name. This equals 5040 permutations.

d) Penetanguishene: There are 14 letters in the name "Penetanguishene" (P, E, N, E, T, A, N, G, U, I, S, H, E, N), so there are 14! (14 factorial) permutations of all the letters in the name. This equals 87178291200 permutations.

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The tangential component of the acceleration vector represents the change in speed or direction along the path. The normal component of the acceleration vector represents the change in direction perpendicular to the path.

To find the tangential and normal components of the acceleration vector, we need the velocity vector and the curvature of the path. The tangential component of acceleration (at) represents the change in speed or direction along the path. It is given by the derivative of the velocity vector with respect to time. The normal component of acceleration (an) represents the change in direction perpendicular to the path. It is given by the curvature of the path multiplied by the square of the speed.

In mathematical terms:

at = dV/dt

an = (V^2) / R

where:

V is the velocity vector

t is time

R is the radius of curvature of the path.

The tangential component of the acceleration vector represents the change in speed or direction along the path. The normal component of the acceleration vector represents the change in direction perpendicular to the path.

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The sequence of operations is multiply the first equation by –3 and add the result to the second equation to eliminate y and solve for x. The correct option is - b)

From the question, we are to determine the sequence of operations that would produce the correct x- or y-value of the solution to the given system of equations

The given systems of equations are

2x+y=9

x+3y=-13

That is

-3 × (2x+y=9)

-6x-3y=-27

-6x-3y=-27

+(x+3y=-13)

-----------------

-5x = -40  

Thus, we can solve for x

These sequence of operations will enable us to eliminate y and solve for x

Hence, the sequence of operations that would produce the correct x- or y-value of the solution to the system of equations is multiply the first equation by –3 and add the result to the second equation to eliminate y and solve for x. The correct option is - b)multiply the first equation by –3 and add the result to the second equation to eliminate y and solve for x

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Answer: b<15

Step-by-step explanation: Divide each term by

20 and simplify inequality form: b<15

We are asked to determine the graph of a line that has a slope -1 and passes through the point (3,3). To do that we need to have into account that since the slope is negative the line must be going downwards. Also, it must go through the point (3, 3), therefore, it must be similar to:

The only graph that has these properties is graph A.

Answer:

Step-by-step explanation:

If Ellen mixed \(\frac{1}{4}\)kg of flour with \(\frac{2}{9} kg\) of sugar together, the reasonable estimate for the amount of flour and sugar combined can be gotten by taking the sum  of both masses of ingredients as shown;

Mass of flour = \(\frac{1}{4}kg\\\)

MAss of sugar = \(\frac{2}{9} kg\)

Combined masses = \(\frac{1}{4}+\frac{2}{9}\)

\(= \frac{9+8}{36} \\= \frac{17}{36}kg\)

The amount of flour and sugar combined is 17/36 kg

The equation that can be used to solve the cost of the shirt before tax is 83.85 = x + ( 7.25% × x) where the cost of the shirt before tax is approximately $78.18

Total cost of shirt and tax = Cost of shirt before tax + (Percentage of tax × Cost of shirt before tax)

83.85 = x + ( 7.25% × x)

83.85 = x + (0.0725 × x)

83.85 = x + 0.0725x

83.85 = 1.0725x

x = 83.85 / 1.0725

x = 78.18181818181818

Approximately,

x = $78.18

Therefore, the the cost of the shirt before tax is approximately $78.18

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Answer

The equation of the required line in slope-intercept form is

y = (-2x/3) + (7/3)

Comparing this with y = mx + c,

Slope = m = (-2/3)

Intercept = c = (7/3)

Explanation

The slope and y-intercept form of the equation of a straight line is given as

y = mx + c

where

y = y-coordinate of a point on the line.

m = slope of the line.

x = x-coordinate of the point on the line whose y-coordinate is y.

c = y-intercept of the line.

So, to solve this, we have to solve for the slope and then write the eqution in the slope-point form which we can then simplify to the slope-intercept form

The general form of the equation in point-slope form is

y - y₁ = m (x - x₁)

where

y = y-coordinate of a point on the line.

y₁ = This refers to the y-coordinate of a given point on the line

m = slope of the line.

x = x-coordinate of the point on the line whose y-coordinate is y.

x₁ = x-coordinate of the given point on the line

The point is given as (x₁, y₁) = (-4, 5)

Then, we can calculate the slope from the information given

Two lines with slopes (m₁ and m₂) that are perpendicular to each other are related through

m₁ × m₂ = -1

From the line given,

y = (3/2)x - 2

We can tell that m₁ = (3/2), so, we can solve for m₂

(3/2) (m₂) = -1

m₂ = (2/3) (-1) = (-2/3)

We can then write the equation of the given line in slope-intercept form

y - y₁ = m (x - x₁)

y - 5 = (-2/3) (x - (-4))

y - 5 = (-2/3) (x + 4)

y - 5 = (-2x/3) - (8/3)

y = (-2x/3) - (8/3) + 5

y = (-2x/3) + (7/3)

Hope this Helps!!!

The system of equations -3x + y = 4 and -9x + 5y = -1 has the solution (-3.5 , -6.5).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations. This is what is called as the solution.

Given two equations in x and y,

-3x + y = 4     (equation 1)

-9x + 5y = -1     (equation 2)

Rewrite equation 1 as an equation of y and substitute to equation 2.

(equation 1) -3x + y = 4     ⇒     y = 3x + 4

-9x + 5y = -1     (equation 2)

-9x + 5(3x + 4) = -1

-9x + 15x + 20 = -1

6x = -21

x = -3.5

Substitute the value of x in equation of y and solve for y.

y = 3x + 4

y = 3(-3.5) + 4

y = -6.5

Hence, the solution to the following system of equations is (-3.5 , -6.5).

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Answer:

(-3.5 , -6.5)

Step-by-step explanation:

Answer:

One real root (multiplicity 2).

Step-by-step explanation:

-3=x^2+4x+1

x^2 + 4x + 4 = 0

Discriminant = 4^2 - 4*1*4 = 0

There is one real root (multiplicity 2).

The equation has 1 real solution.

The quadratic function is given as:

\(-3=x^2+4x+1\)

Add 3 to both sides of the equation

\(3-3=x^2+4x+1 + 3\)

This gives

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

Rewrite the equation as:

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

A quadratic equation is represented as:

\(ax^2+bx+c = 0\)

By comparison, we have:

\(a =1\)

\(b =4\)

\(c = 4\)

The discriminant (d) is calculated as:

\(d =b^2 - 4ac\)

So, we have:

\(d =4^2 - 4 \times 1 \times 4\)

\(d =16 - 16\)

Evaluate like terms

\(d = 0\)

Given that the discriminant value is 0, it means that the equation has 1 real solution.

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b) the current number of shares is 1440, and the market value of your investment is $17,280.

To calculate the current number of shares and the market value of your investment, we need to take into account the stock splits and stock dividends.

Given:

Initial investment: $1,000

Initial number of shares: 200

Current price per share: $12

a. Calculate the current number of shares:

First, let's consider the stock splits and stock dividends:

1. 2-for-1 stock split:

This means that for each existing share, you now have two shares. So the number of shares is doubled.

New number of shares = Initial number of shares * 2 = 200 * 2 = 400 shares.

2. 20% stock dividend:

A 20% stock dividend means you receive an additional 20% of your current number of shares. To calculate the number of shares received:

Shares received = Current number of shares * (20% / 100%)

Shares received = 400 * (20 / 100) = 80 shares.

Total number of shares after the dividend = Current number of shares + Shares received = 400 + 80 = 480 shares.

3. 3-for-1 stock split:

This means that for each existing share, you now have three shares. So the number of shares is tripled.

New number of shares = Total number of shares after the dividend * 3 = 480 * 3 = 1440 shares.

The current number of shares you have is 1440.

b. Calculate the market value of your investment:

Market value = Current number of shares * Current price per share

Market value = 1440 * $12 = $17,280

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Answer:

When the absolute value of the scale factor is lower than 1, it decreases the size of the shape.

When the absolute value of the scale factor is greater than 1, the shape will increase in size.

How to Remember it:

Think if the number is a fraction, the shape will be a fraction of the size.

Answer:

10 percant off how much would i have

We Prοved that tanθ + cοtθ = secθcscθ using trigοnοmetry identified.

Trigοnοmetry is a branch οf mathematics that deals with the study οf angles, triangles, and their relatiοnships with each οther. It invοlves the study οf the prοperties and functiοns οf triangles, as well as the relatiοnships between angles and sides οf triangles.

Tο sοlve the equatiοn Tanθ + cοtθ = secθcscθ, we can start by expressing each term in terms οf sine and cοsine functiοns:

⇒ \($\mathrm{tan}\,\theta+\mathrm{cot}\,\theta\)

\($\Rightarrow\frac{\mathrm{sin}\ \theta}{\mathrm{cos}\,\theta}+\frac{\mathrm{cos}\,\theta}{\mathrm{sin}\,\theta}$\)

\($\Rightarrow{\frac{\sin^{2}\ \theta+\cos^{2}\!\theta}{\sin\theta.\cos\theta}}$\)

\($={\frac{1}{\sin\theta.\cos\theta}}$\)

= secθ·cscθ

Hence, Proved that tanθ + cotθ = secθcscθ

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Complete question:

Prove that tanθ + cotθ = secθcscθ.

Answer:

Domain: x < 5

Range: all numbers, -∞, ∞

This is because the problem will be able to be solved with multiple solutions as long as there are no specific values assigned to x. The problem will have a solution from a range of negative infinity to infinity, meaning every number or solution you can think of.

Answer:

C

Step-by-step explanation:

im in harvard

the answer is c hope it helps

The function that represents the given equation is:

f(x) = 3x + 8

The equation is -12x + 4y = 32. To solve for y as a function of x, we need to isolate y on one side of the equation.

Adding 12x to both sides, we get 4y = 12x + 32.

To solve for y, we divide both sides of the equation by 4. This gives us y = 3x + 8.

Hence, the function that expresses y as a function of x is:

f(x) = 3x + 8.

Using this function, we can determine the value of y corresponding to any given x value. For example, if we substitute x = 5 into the function, we have f(5) = 3(5) + 8 = 15 + 8 = 23. Therefore, when x is 5, y is 23 according to the function f(x) = 3x + 8.

In summary, the function f(x) = 3x + 8 represents the relationship between x and y in the given equation, allowing us to calculate the corresponding y value for any given x value.

Therefore, the function that represents the given equation is:

f(x) = 3x + 8

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If we solve the given equation for t we get that t=-2

The equation given,

9t+5(t+3) = -(t+13) +t

⇒9t + 5t + 15 = -t -13 +t

⇒14t + 15 = -13                    (∵-t+t=0)

⇒14t = -13-15                       (bringing 15 from left hand side to right hand      side the sign is flipped and 15 becomes -15)

⇒14t = -28

⇒\(t=\frac{-28}{14}\)                            (dividing both sides by 14)

⇒t = -2

Thus on solving the equation we get t = -2

Your question was incomplete but most probably your full question was

Solve for t when this equation is given, 9t+5(t+3) = -(t+13) +t

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Answer:

CD = -2 - (- 5 1/4)

      = 13/4

Answer:

\(Cost= \$47\)

Step-by-step explanation:

Given

Vertices: (−1, 5), (4, 2), and (9, −4)

Cost per foot = $8

Required

Determine the cost of fencing (-1, 5) and (4, 2)

First, we need to determine the distance between (-1, 5) and (4, 2)

Distance, d is calculated as follows:

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

Where

\((x_1,y_1) = (-1, 5)\)

\((x_2,y_2) =(4, 2)\)

So, we have:

\(d = \sqrt{(4 - (-1))^2 + (2 - 5)^2}\)

\(d = \sqrt{(4 +1))^2 + -3^2}\)

\(d = \sqrt{5^2 + -3^2}\)

\(d = \sqrt{25 + 9}\)

\(d = \sqrt{34}\)

\(d = 5.83095189485\)

\(d = 5.831\) -- Approximated;

If the cost of 1 foot is $8.

5.831 feet will cost:

\(Cost= 5.831 * \$8\)

\(Cost= \$46.648\)

\(Cost= \$47\) -- Approximated

Answer:

x- 7.50 i think i hope i helped

Step-by-step explanation: there no explanation

In Prolog, a variable represents a place holder for a value or an expression. Therefore, the correct answer is (d) place holder.

Variables in Prolog are denoted by a capital letter or an underscore (_) followed by a lowercase letter or a sequence of alphanumeric characters. Variables can be used to represent unknown values in queries and clauses, and are used in the process of unification, which is a fundamental operation in Prolog.

When a Prolog query or clause is executed, the system searches for values that satisfy the variable bindings and produce the desired results. Variables are not assigned memory locations or values until they are unified with other terms, and they can be used to represent a wide range of values and expressions, including constants, lists, and complex structures.

In summary, Prolog variables are used as place holders for values or expressions and are an essential part of the logic programming paradigm.

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