Find tan theta if theta is an angle in standard position and the point with coordinates (4,3) lies on the terminal side of the angle

1.The beginning balance should be $4,000

2.The amount to be adjusted is $2554

3.The ending balance of the account after the adjustment $2554

4. Office Supplies Account is $14846

An adjusting entry is an additional journal entry that is made at the end of the month or year. When any financial transaction is incurred for which the amount is not accrued yet or no financial transaction incurred for the accrued amount and in such case the adjusting entry is made to know the actual amount accrued in the month or year.

The adjustment entries are the additional entries to the recorded journal entries.

"Information available from the question"

The Office Supplies account started the year with a $4,000 debit balance

The company purchased supplies for $13,400,

The inventory of supplies available at the end of the year totaled $2,554.

Now, According to the question:

1. The beginning balance should be $4,000

2.The adjusted amount is

Opening balance = 4000

Add: New purchases = 13400

Balance after Purchase = 17400

Less: Year end balance = 2554

3. The ending balance is $2,554

4. The adjusting journal entry is

Dr. Supplies Expense Account is 14846

Adjustment in the year = Cr. 14846 (subtracted from the balance)

Office Supplies Account is 14846

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From the question above, we can know the groups of 2 customers that are possible to be chosen to receive a special gift is 1,275 groups.

How to find possibility of combination?

To find possibility of combination like in the question above, we can use  binomial coefficient formula. The binomial coefficient is about two things with two result. The formula of binominal coefficient is  \(\binom{n}k} = \frac{n!}{k! (n - k)!}\)

Anyone of the 51 can be chosen first and any of the remaining 50 can be chosen second. Or in which 2 of the 51 can be chosen ⇒ 51 x 50

But, for any given group of 2, the number of different orders in which they could have been chosen is 2 x 1.

So, the numbers of different combination of 2 chosen from 51 is:

\(\binom{51}2} = \frac{51 x 50}{2 x 1}\)

\(\binom{51}2} = \frac{2,550}{2} = 1,275\)

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Answer:

25%

Step-by-step explanation:

30/120 = 1/4

1/4 = 25%

The value of x is after solving the logarithm equation logx⁽⁵¹²⁾ = 3 is 8.

A logarithmic equation is an equation that involves the logarithm of an expression containing a variable.

To solve the logarithm equation, we follow the steps below.

Given:

Step 1:

Therefore,

Step 2:

Convert 512 to index form. (i.e 8³)

Comparing both side of equation 1,

Hence, the value of x is 8.

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Answer:

Step-by-step explanation:

Susan has a collection of 98 nickels and dimes. If the number of nickels is six times the number of dimes, how many nickels and how many dimes does she have?

nickels = x

dimes = 6x

6x + x = 7x

98 : 7 = 14   (nickels)

14 x 6 = 84 (dimes)

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

14 + 84 = 98 (the answer is good)

The perimeter of the triangle is the sum of the lengths of its sides, which is: 12.24

Explanation:

To show that the given points form an isosceles right angled triangle, we first need to find the lengths of the sides of the triangle using the distance formula.

Let the given points be A(4, 9, 6), B(-1, 6, 6), and C(0, 7, 10).

The distance between points A and B is given by:

AB = sqrt((4 - (-1))^2 + (9 - 6)^2 + (6 - 6)^2) = sqrt(5^2 + 3^2 + 0^2) = sqrt(34)

The distance between points A and C is given by:

AC = sqrt((4 - 0)^2 + (9 - 7)^2 + (6 - 10)^2) = sqrt(4^2 + 2^2 + 4^2) = 2*sqrt(6)

The distance between points B and C is given by:

BC = sqrt((-1 - 0)^2 + (6 - 7)^2 + (6 - 10)^2) = sqrt(1^2 + 1^2 + 4^2) = sqrt(18)

Now, we can see that the triangle ABC is not isosceles since all three sides have different lengths.

To check if the triangle is right-angled, we can use the Pythagorean theorem. If the square of the length of the longest side is equal to the sum of the squares of the other two sides, then the triangle is right-angled.

Here, the longest side is AC with length 2*sqrt(6), so we need to check if:

AC^2 = AB^2 + BC^2

4*6 = 34 + 18

24 = 52

This equation is not true, so the triangle ABC is not a right-angled triangle.

Therefore, the given points do not form an isosceles right angled triangle.

The perimeter of the triangle is the sum of the lengths of its sides, which is:

AB + AC + BC = sqrt(34) + 2*sqrt(6) + sqrt(18) ≈ 12.24

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The number of contestants in round 5 is 128.

The formula used to calculate the number of contestants in round N is:  

Number of contestants in round N = (Number of contestants in round N-1)^((N-1)/N), rounded to the nearest integer.

Given that the number of contestants in round 2 is 243, then the number of contestants in round 5 can be calculated as follows:

Number of contestants in round \(5 = 243^((5-1)/5)\), rounded to the nearest integer

Therefore, the number of contestants in round 5 = 128.

To summarize, the number of contestants in round 5 is 128, which is calculated by raising the number of contestants in the previous round (round 2) to the ((N-1)/N)-th power and rounding the result to the nearest integer.

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Answer:

15 degrees

Step-by-step explanation:

Answer:

\(2 \frac{2}{9} + 1 \frac{4}{9} \\ = \frac{20}{9} + \frac{13}{9} \\ = \frac{33}{9} \\ = 3 \frac{2}{3} \\ \\ { \underline{ \blue{ \tt{⚜becker \: jnr}}}}\)

Answer:

sqrt of 2 is between 1 and 2

The square root of 2 is in between the square of one and the square of 2.

Answer:

8 digit smallest number is 10000000. 7 digit largest number is 9999999.

Step-by-step explanation:

The solid has a 62.5 cubic unit volume. Finding the volume of a solid with a circular base of radius 5 units is the task at hand.

The following formula can be used to determine how much of the magical potion is left after a specific period of time:

Let h represent the solid's height. The volume can therefore be stated as follows:

V = (12.5 dh from 0 to h)

Combining, we obtain:

V = 12.5h

The height of the solid is equal to the radius of the circle, which is 5 units, because the slices are perpendicular to the base. Therefore:

V=12.5h=12.5(5)=62.50 cubic metres

Thus, the solid has a 62.5 cubic unit volume.

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To find the slope of the line given, we write the equation in slope-intercept form:

For the equation,

subtracting 3x from both sides gives

Finally, dividing both sides by 8 gives

which can be rearranged and written as

Hence, the slope of the line parallel to the given line is -3/8.

To find the slope of the perpendicular line, we have to remember that

Since m = -3/8, the above gives

Simplifying the above gives

Hence, the slope of the perpendicular line is 8/3.

Answer:

5/3

Step-by-step explanation:

The partners have a total profit of $2000. Since there are only 2 partners, then the average profit each one makes is $2000/2 = $1000.

The difference between the 2 amounts is half of the average, so it is $1000/2 = $500.

One amount is x.

The other amount is x + 500

The sum is 2000

x + x + 500 = 2000

2x + 500 = 2000

2x = 1500

x = 750

x + 500 = 750 + 500 = 1250

The partners had profit of $1250 and $750.

The ratio is 1250/750 = 125/75 = 5/3

Answer: 5/3

The ratio of the larger to the smaller amount will be 5 : 3

A ratio says how much of one thing there is compared to another thing. We can write the ratio as -

x : y

{x/y} = k

x = ky

[k] is called the scale factor.

Given is that two partners divide a profit of $2,000 so that's a difference between the two amounts is half of their average.

Assume that the amount with partner [1] is $[x] and with partner [2] is $[y]

. So, we can write according to the question as -

x + y = 2000      ......Eq [1]

x - y = {1/2 x (x + y)/2}     ......Eq [2]

Now -

x - y = {1/2 x (2000/2)}

x - y = {1/2 x 1000}

x - y = 500

x = 500 + y

So, we can write the equation [1] as -

x + y = 2000

500 + y + y = 2000

2y = 1500

y = 750

So, [x] will be equivalent to -

x = 2000 - 750

x = 1250

The ratio of the larger to the smaller amount will be -

x/y = 1250/750 = 250/150 = 50/30 = 5/3

Therefore, the ratio of the larger to the smaller amount will be 5 : 3.

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Answer:

(−3, −9)

Step-by-step explanation:

(−4, −11)

y=6x+9

-11 = 6(-4) + 9

-11 = -15

False

(−3, −9)

y=6x+9

-9 = 6(-3) + 9

-9 = -9

True

(−2, −7)

y=6x+9

-7 = 6(-2) + 9

-7 = -3

False

(−1, −5)

y=6x+9

-5 = 6(-1) + 9

-5 = 3

False

Answer:

b) 2/6

Step-by-step explanation:

0, 1/6, 2/6, 3/6, 4/6, 5/6, 1

Hope this helps!

In the Histogram the horizontal line (dimension) represents the value of the selected collection plan element. The vertical line (dimension) represents the count or sum of occurrences of the primary collection element on the horizontal line.

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Answer:

y = (-1/3)x + 3.

Step-by-step explanation:

To find the equation of a line perpendicular to a given line, we need to take the negative reciprocal of the slope of the given line.

The slope of the given line Y=3x-5 is 3. Therefore, the slope of a line perpendicular to this line would be -1/3.

Now, using the point-slope form of a line, we can write the equation of the line passing through (-9,6) and having a slope of -1/3:

y - 6 = (-1/3)(x - (-9))

Simplifying:

y - 6 = (-1/3)x - 3

y = (-1/3)x + 3

Therefore, the equation of the line that passes through (-9,6) and is perpendicular to the line Y=3x-5 is y = (-1/3)x + 3.

Step-by-step explanation:

15x^5 +10x^4+25x^3

5x³(3x²+2x+5)

Answer:

5x^3

Step-by-step explanation:

I have no idea how to explain this but here we go

If we were to factor, we first look at all the numbers, not the variables and their exponents.

So we have: 15, 10, and 25, and the greatest common factor is 5

So 5 is going to be part of our final answer.

Then, we look at all the x's and the exponents on them

So we have: x^5, x^4, x^3,

The smallest out of all of them is x^3.

So that's going to be part of your answer

and since it's multiplication

bam, you join them together to make it 5x^3

I hope this helped, let me know if you have any questions

I need help with this question too but less hope we get a answer

Answer: To find the moment of inertia of multiple bodies, we need to use the parallel axis theorem. The parallel axis theorem states that the moment of inertia of a body about any axis parallel to its centroidal axis is equal to the moment of inertia about the centroidal axis plus the product of the body's mass and the square of the distance between the two axes.

Here are the steps to find the moment of inertia of multiple bodies:

Find the moment of inertia of each body about its centroidal axis using the appropriate formula for that body. For example, the moment of inertia of a solid cylinder about its central axis is 1/2MR^2, where M is the mass of the cylinder and R is the radius of the cylinder.

Determine the centroid of the system of bodies. This is the point through which the axis of rotation passes and is the point about which the moment of inertia is calculated.

Calculate the distance between the centroid and each body's centroidal axis.

Use the parallel axis theorem to find the moment of inertia of each body about the axis passing through the centroid of the system. Add up all the moments of inertia of each body about the centroid of the system to get the total moment of inertia.

The formula for the parallel axis theorem is:

I = I_cm + md^2

where I is the moment of inertia about the axis passing through the centroid of the system, I_cm is the moment of inertia about the centroidal axis of the body, m is the mass of the body, and d is the distance between the two axes.

By using this formula, we can find the moment of inertia of any system of bodies with respect to any axis parallel to the centroidal axis.

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

d=34

r=17

Im just gonna use the picture to help explain

to get AP we can use the pythagoras theorem

\( {17}^{2} - {15}^{2} = {ap}^{2} \)

\(289 - 225 = {ap}^{2} \)

\(64 = {ap}^{2} \)

Therefore AP =8

AB=AP+PB

AP=PB. (line perpendicular to chord bisects chord)

Therefore AB=16

Answer:

  2)  c)  (x-3)² + (y+2)² = 25

  5)  x^2 +y^2 -8x -16y +54 = 0

  6)  x^2 +y^2 -10x -12y +36 = 0

Step-by-step explanation:

2) The standard form equation for a circle is ...

  (x -h)^2 +(y -k)^2 = r^2

You are given the center: (h, k) = (3, -2) and a point on the circle. So, the equation will be ...

  (x -3)^2 +(y +2)^2 = r^2

Since we know a point on the circle we know that ...

  (7 -3)^2 +(1 +2)^2 = r^2 = 16 +9 = 25

So, the circle's equation is ...

  (x -3)^2 +(y +2)^2 = 25 . . . . . matches choice C

__

5) As in the previous problem, the standard form equation is ...

  (x -4)^2 +(y -8)^2 = (-1-4)^2 +(7-8)^2 = 25+1 = 26

To put this in general form, we need to subtract 26 and eliminate parentheses.

  x^2 -8x +16 +y^2 -16y +64 -26 = 0

  x^2 +y^2 -8x -16y +54 = 0

__

6) A circle tangent to the y-axis will have a radius equal to the x-value of the center point.

  (x -5)^2 +(y -6)^2 = 5^2

  x^2 -10x +25 +y^2 -12y +36 = 25

  x^2 +y^2 -10x -12y +36 = 0

To find the dimensions of the second rectangular prism that will have the same surface area as the first one, we can use the formula for the surface area of a rectangular prism which is:

Surface Area = 2lw + 2lh + 2wh

where l is the length, w is the width, and h is the height of the rectangular prism.

For the first rectangular prism, we have:

l = 3 m w = 7 m h = 4 m

Surface Area = 2lw + 2lh + 2wh Surface Area = 2(3)(7) + 2(3)(4) + 2(7)(4) Surface Area = 42 + 24 + 56 Surface Area = 122 m²

To find the dimensions of the second rectangular prism that will have the same surface area as the first one, we can use this formula again and solve for one of the variables. Let’s solve for l:

Surface Area = 2lw + 2lh + 2wh 122 = 2l(w+h) + 2wh 122 = 2l(w+h) + w(4) 122 = 2l(w+h) + 4w 118 = l(w+h)

Now we can choose any value for w and h and solve for l. Let’s choose w=1 and h=1:

118 = l(1+1) 118 = l(2) l = 59

So the dimensions of the second rectangular prism that will have the same surface area as the first one are:

l = 59 m w = 1 m h = 1 m

"A number" means the unknown.

"Difference" means to subtract.

We already know two numbers, 8 and 14, but we don't know "A number."

We can put v as our variable. You can put any type of letter.

Therefore, the answer is: v - 8 = 14

The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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Answer:

Bisector

Step-by-step explanation:

Brainliest pls

Answer:

the answer is the bisector

The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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