Using the double-declining-balance method of depreciation, the completion of the table as shown is as follows:
Year Cost Accumulated Book Value Depreciation Accumulated Book
Depreciation B.O.Y Expense Depreciation Value
B.O.Y E.O.Y E.O.Y
1 $29,000 $0 $29,000 $11,600 $11,600 $17,400
2 $29,000 $11,600 $17,400 $6,960 $18,560 $10,440
3 $29,000 $18,560 $10,440 $4,176 $22,736 $6,264
What is the double-declining-balance method?The double-declining-balance method is one of the depreciation methods in use, but it allocates more cost to the earlier years of the asset's life.
This depreciation method uses twice the straight-line rate, which is computed as the product of 100/estimated useful life multiplied by 2.
For each year's depreciation expense, the double rate is applied at the end of the year's balance.
For the last year, the difference between the previous year's ending balance and the residual value is taken as the depreciation expense.
Auto = $29,000
Estimated useful life = 5 years
Residual = $2,000
Depreciable amount = $27,000 ($29,000 - $2,000)
Straight-line depreciation rate = 20% (100/5)
Double-declining depreciation rate = 40% (20% x 2)
Depreciation Expense:1st year = $11,600 ($29,000 x 40%)
2nd year = $6,960 ($17,400 x 40%)
3rd year = $4,176 ($10,440 x 40%)
4th year = $2,506 ($6,264 x 40%)
5th year = $1,758 ($3,758 - $2,000)
Year Cost Accumulated Book Value Depreciation Accumulated Book
Depreciation B.O.Y Expense Depreciation Value
B.O.Y E.O.Y E.O.Y
1 $29,000 $0 $29,000 $11,600 $11,600 $17,400
2 $29,000 $11,600 $17,400 $6,960 $18,560 $10,440
3 $29,000 $18,560 $10,440 $4,176 $22,736 $6,264
4 $29,000 $22,736 $6,264 $2,506 $25,242 $3,758
5 $29,000 $25,242 $3,758 $1,758 $27,000 $2,000
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Find an equation for the perpendicular bisector of the line segment whose endpoints are (4,6) and (8,-6)
The equation of the perpendicular bisector for the line is y = 1/3(x) - 2
How to determine the equation of the perpendicular bisector?
Given: the endpoints of the line (4,6) and (8,-6)
The bisector of the line will divide the line into two i.e. the bisector will be at the point of the line.
The coordinate of the midpoint can be calculated using the formula below:
Xm = (X1 +X2)/2 and Ym = (Y1 +Y2)/2
Where X1 = 4, Y1 =6 and X2= 8, Y2= -6
Xm = (4+8)/ 2 = 12/2 = 6 and Ym = (6+(-6))/2 = 0/2 = 0
Thus, midpoint(6, 0)
slope = y2-y1 / x2-x1
Thus, the slope of the line segment (m₁) = -6-6 / 8-4 = -12/4 = -3
When the two lines are perpendicular, the product of their slope is -1 i.e.
m₁ × m₂ = -1
where m₁ and m₂ represent the slope of the lines
Let the slope of the bisector be m₂
-3 × m₂ = -1
m₂ = 1/3
Equation of perpendicular bisector with coordinate (6,0):
y - 0 = 1/3(x-6)
y = 1/3(x-6)
y = 1/3(x) - 2
Therefore, the equation for the perpendicular bisector of the line segment is y = 1/3(x) - 2
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What is the slope of line KH if H(-4, 2) and K(2, -2)? Remember to reduce!
The slope of a line KH if H(-4, 2) and K(2, -2) is -2/3.
What is a slope?A mathematical word used to define a line's direction and steepness is its slope or gradient.
If a line is rising from left to right, it is growing. The slope is positive, or m>0
If a line decreases from left to right, it is said to be diminishing. The slope is negative, indicating that m < 0
A line has zero slopes if it is horizontal. This function is constant.
The slope of a line is y - y₁ = m(x - x₁)
Slope m = (y₂ - y₁)/(x₂ - x₁)
m = (- 2 - 2)/(2 + 4)
m = - 4/6
m = - 2/3
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ABCDEFGHIJ is a regular decagon. It rotates clockwise about its center to form the polygon A'B'C'D'E'F G'HIJ. Match each angle of rotation to the
point that A' (the image of A) coincides with after that rotation.
252°
108°
135°
180°
288°
324°
A0DO
D after three rotations: 3 × 36° = 108°
F after five rotations: 5 × 36° = 180°
H after seven rotations: 7 × 36° = 252°
I after eight rotations: 8 × 36° = 288°
Given,
In the question:
ABCDEFGHIJ is a regular decagon. It rotates clockwise about its center to form the polygon A'B'C'D'E'F G'HIJ.
To find the each angle of rotation to the point A' coincides with after that rotation.
Now, According to the question:
let's know about Decagon:
A decagon is a ten-sided polygon or 10-gon. The total sum of the interior angles of a simple decagon is 1440°. A self-intersecting regular decagon is known as a decagram.
Every regular polygon with n sides can be divided into n congruent triangles. The angle with vertex the center of the polygon will measure
360 : n degrees. We are given a regular decagon, therefore:
n = 10
α = 360 : n = 36°
We consider that, if the decagon is not rotated, A' coincides with A and the rotation is towards the next letter of the alphabet. This means that after one rotation of 36° A' will coincide with B, after two rotations A' will coincide with C and so on.
A' will coincide with D after three rotations: 3 × 36° = 108°
A' will coincide with F after five rotations: 5 × 36° = 180°
A' will coincide with H after seven rotations: 7 × 36° = 252°
A' will coincide with I after eight rotations: 8 × 36° = 288°
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The formula for simple interest is I=Prt,I=Prt, where II is the interest earned, PP is the principal, rr is the interest rate and tt is the number of years. Solve the formula for PP in terms of r,r, II and t.t.
Answer:
[tex]P=\cfrac{I}{rt}[/tex]----------------------------
GivenI = PrtSolve for P[tex]I = Prt[/tex][tex]\cfrac{I}{rt} = \cfrac{Prt}{rt}[/tex][tex]\cfrac{I}{rt} =P[/tex][tex]P=\cfrac{I}{rt}[/tex]HELP.
This item has two parts: Part A and Part B. Use the function to complete Part A and Part B.
f(x) = (x – 5)(x + 3)(x – 1)2
Which of the following statements CORRECTLY identifies the degree and number of unique zeros of the function?
degree: 3; number of unique zeros: 4
degree: 4; number of unique zeros: 3
degree: 4; number of unique zeros: 4
degree: 3; number of unique zeros: 3
Part B
What is the end behavior of the function?
as x → –∞, f(x) → ∞ and as x → ∞, f(x) → –∞
as x → –∞, f(x) → ∞ and as x → ∞, f(x) → ∞
as x → –∞, f(x) → –∞ and as x → ∞, f(x) → ∞
as x → –∞, f(x) → –∞ and as x → ∞, f(x) → –∞
The degree and number of unique zeros of f(x) = (x – 5)(x + 3)(x – 1)² is:
Degree: 4; number of unique zeros: 3.
The end behavior of the polynomial is:
As x → –∞, f(x) → ∞ and as x → ∞, f(x) → ∞.
How to obtain the degree of the function?The degree of the polynomial function is given by the sum of the multiplicities of the roots.
These roots are given as follows:
x = 5 with a multiplicity of 1.x = -3 with a multiplicity of 1.x = 1 with a multiplicity of 2.Hence the degree is:
1 + 1 + 2 = 4.
The unique zeros are the roots, hence there are three unique zeros, which is the same number of linear factors of the function.
What is the end behavior of the function?The end behavior is the limit of the function as x goes to negative infinity and to positive infinite, hence:
lim x -> -∞ f(x) = lim x -> -∞ x^4 = (-∞)^4 = ∞.lim x -> ∞ f(x) = lim x -> ∞ x^4 = (∞)^4 = ∞.Learn more about the end behavior of a function at brainly.com/question/1365136
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How many reflection symmetry does an eight pointed star have ? How many rotational symmetry does an eight pointed star have ?
An eight pointed star have 8 rotational symmetry and 8 reflection symmetry
What is rotational symmetry?The rotational symmetry of a shape explains why an object's shape remains unchanged when rotated about its own axis.
The eight pointed star while standing on any of the edges will be symmetrical.
What is reflection symmetry?Symmetry with respect to reflections is known as reflection symmetry. Mirror or line symmetry are other names for reflection symmetry.
For a reflection symmetry to be in a figure, the figure must at least have one line dividing it into two parts, one of which is the mirror image of the other,
Each of the peak and crest in the star will make 8 reflection symmetry
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The graph of the absolute value parent function, f(x) = |x), is stretched
horizontally by a factor of 3 to create the graph of g(x). What function is g(x)?
OA. g(x)= x+3|
OB. g(x) = 31x1
C. g(x) = 13x1
OD. g(x)= |||
Option A is the correct answer g(x) = |x+3| by using the relation with the parent function.
Explain absolute value function.
A function that wraps an algebraic expression in absolute value symbols is known as an absolute value function. Remember that a number's distance from 0 on the number line represents its absolute value.
The definition of the absolute value parent function, f(x)=| x |, is as follows:
f(x) = [tex]\left \{ {{x ~, ~ x > 0} \atop {0 ~ , ~x = 0}} \atop {-x ~, ~x < 0} \right.[/tex]
Given parent function is f(x) = |x|
g(x) is obtained by stretching the graph of f(x) by a factor of 3.
Use the function g(x)=f(x−h) to translate the absolute value function f(x)=| x | horizontally.
The graph of f(x) is moved h units to the right to obtain g(x) for h>0
The graph of f(x) is translated h units to the left to obtain g(x) when h>0
Therefore, g(x) = |x+3|
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PLEASE HELP!!!! I WILL GIVE YOU BRAINLIST!! PLEASE ASAP :)
Which graph shows the image of ΔABC after a rotation about the origin?
Answer:
D.
Step-by-step explanation:
just click the rotate button until it matches one of the answers
I need help with an orthocenter of a triangle question. Brainly is having a problem uploading my picture so here is the question: Find the coordinates of the orthocenter of the triangle with the given vertices: P(-1,2), Q(5,2), R(2,1). My Textbook has horrible step by step instructions and I really want to understand this process. Thanks!
The orthocenter of the triangle with vertices P(-1,2), Q(5,2), R(2,1) is
(2, 5)How to find orthocenterOrthocenter is calculated by
finding the slope of a side and the slope of the line perpendicular to the side finding the equation of the perpendicular line passing through the third side of the trianglerepeat step 1 and 2 for another sideWith two equations, solve for the two unknowns (x, y)this gives the coordinate of the orthocenterformula for slope is
m = (y₂ - y₁) / (x₂ - x₁)
slope of the perpendicular = -1/m
Using side PR P(-1,2) R(2,1) ,
m = (1 - 2) / (2 - -1)
m = 1 / 3
slope of the perpendicular = -1/m = - 1 / (1/3) = -3
using point-slope formula for equation of line passing through Q (5, 2)
point slope formula
(y - y₁) = m (x - x₁)
(y - 5) = -3 (x - 2)
y - 5 = -3x + 6
y = -3x + 6 + 5
y = 11 - 3x
Using side PQ P(-1, 2), Q(5, 2)
m = (2 - 2) / (5 - -1)
m = 0
slope of horizontal line is zero for horizontal line the perpendicular is a vertical line
using point-slope formula for vertical line passing through R (2, 1)
point slope formula
(y - y₁) = m (x - x₁)
0 = (x - 2)
x = 2
The two equations are
y = 11 - 3x
x = 2
solving both equations with x already known
y = 11 - 3 * 2
y = 11 - 6
y = 5
Therefore the orthocenter is (2, 5)
The triangle is attached
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algebra help pleaseee
Answer:
3x^2-2x+3+1/x+2
Step-by-step explanation:
Deshaun drove 469 miles in 7 hours.
At the same rate, how long would it take him to drive 335 miles?
We're assuming Deshaun is driving at a constant speed/at the same rate,
He drove 469 miles in 7 hours -> his speed = 469 : 7 = 67 (mph)
Therefore, it would take him 335 : 67 = 5 hours to drive 335 miles.
Pls help I’m failing
Answer:
{-9,-8,7,8,10}
Represent the following expressions as a power of the number a where a ≠ 0.: (a^3)^-2
1/[tex]a^{6}[/tex] is the required number.
What is an expression?Numbers, symbols and operators (such as and times) grouped together that show the value of something.
Given an expression (a³)^-2
(a³)^-2 = [tex]a^{-6}[/tex] = 1/[tex]a^{6}[/tex]
Hence, 1/[tex]a^{6}[/tex] is the value of the expression (a³)^-2
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A dairy farmer wants to mix a 80% protein supplement and a standard 55% protein ration to make 1400 pounds of a high-grade 60% protein ration. How many pounds of each should he use?
If the dairy farmer wants to mix a 80% protein. The amount of pounds of each that he should use is 80% 280 pounds and 55% 1120 pounds.
How to find the number of pounds?Protein I 80% = x pounds
Protein II 55% = 1400 - x pounds
Mixture 60% = 1400
Hence,
80% x + 55% ( 1400 - x ) = 60% × 1400
80 x + 55 ( 1400 - x ) = 84000
80 x + 77000 - 55 x = 84000
Combine like terms
80 x - 55 x = 84000 - -77000
25 x = 7000
Divide both side by 25x
x= 7000/25
x =280 pounds ( Protein I)
Protein II
1400 - x pounds
1400 -280
= 1120 pounds
Therefore the farmer should use 280 pounds and 1120 pounds.
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Two sides are labeled 5,244 feet. The other two sides are labeled 1,495 feet. What is the perimeter to the nearest hundred?
Answer:
Step-by-step explanation:
42feet
A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights is taken. Find the probability that the mean actual weight for the 100 weights is greater than 25.2
The probability that the mean actual weight for the 100 weights is greater than 25.2 is equal to 0.0136%.
How to determine the probability that the mean actual weight for the 100 weights?In order to determine the probability that the mean actual weight for the 100 weights is greater than 25.2, we would have to calculate the mean and standard deviation.
In a uniform distribution, the mean of a data set can be calculated by using this formula:
Mean, E(x) = [a + b]/2
Where:
a is the lowest boundary.b is highest boundary.Substituting the given parameters into the formula, we have;
Mean, E(x) = [24 + 26]/2
Mean, E(x) = 50/2
Mean, E(x) = 25.
For the standard deviation, we have:
Standard deviation, S(x) = √((b - a)²/12)
Standard deviation, S(x) = √((26 - 24)²/12)
Standard deviation, S(x) = √((2)²/12)
Standard deviation, S(x) = √(4/12)
Standard deviation, S(x) = 0.5774.
For the sample standard deviation, we have:
Standard deviation = S(x)/√n
Standard deviation = 0.5774/√100
Standard deviation = 0.5774/10
Standard deviation = 0.05774.
By applying the central limit theorem, we would determine the z-score as follows:
Z-score = (x - μ)/σ
Z-score = (25.2 - 25)/0.05774
Z-score = 0.2/0.05774
Z-score = 3.64
Therefore, the p-value is equal to 0.000136.
Probability (x > z) = 0.0136%.
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Find the distance from the point (1,2) to the line-y= 1/2x-3. Round your answer to the nearest tenth.
Answer:
the graphical explanation please
Please help me with this thank you :)))
Answer:
Step-by-step explanation:
You deposit $500 into a savings account that earns interest annually. The function g(x) = 500(1.06)x can be used to find the amount of money in the savings account, g(x), after x years. What is the range of the function in the context of the problem?
ℝ
[500, ∞)
[0, 500]
[0, ∞)
Omar deposited d dollars into a savings account y years ago. ... following expressions could be used to determine the zeros of the function f (x) when f (x).
Step-by-step explanation:
ax+by=cd
solve for b
Answer:
b=(cd-ax)/y
Step-by-step explanation:
b=(cd-ax)/y
Martin had 6 magazines. Then m more magazines came in the mail. Write an expression that shows how many magazines Martin has now.
Martin had 6 magazines. Then m more magazines came in the mail. Write an expression that shows how many magazines Martin has now.
Martin now has: 6 + m
Fabian has $700 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. He buys a new bicycle for $387.10. He buys 3 bicycle reflectors for $4.43 each and a pair of bike gloves for $12.36. He plans to spend some or all of the money he has left to buy new biking outfits for $45.81 each. What is the greatest number of outfits Fabian can buy with the money that's left over?
Here is the histogram of a data distribution. All class widths are 1
Which of the following numbers is closest to the mean of this distribution?
The number that is closest to the mean of the distribution is 4 (option C)/
What is the mean?A histogram is used to represent data graphically. The histogram is made up of rectangles whose area is the product of the frequency of the rectangle and the width of the rectangle.
Mean is the average of a set of numbers. It is determined by multiplying each bar in the histogram by its height, add the multiplication value for all the bars together and dividing it by the total frequency of the bars.
Mean = [(1 x 1) + (2 x 2) + (3 x 3) + (4 x 4) + (5 x 3) + (6 x 2) + (7 x 1)] / (1 + 2 + 3 + 4 + 3 + 2 + 1)
Mean = (1 + 4 + 9 + 16 + 15 + 12 + 7) / 16
Mean = 64 / 16
Mean = 4
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In a set of eight consecutive integers, the smallest integer is more than $\frac35$ of the largest integer. What is the smallest possible value of the sum of the eight integers?
Answer:
116.
Step-by-step explanation:
Your welcome <3.
Answer:
116
Step-by-step explanation:
Select the expression that is equivalent to (x - 1)².
OA. 2²-2x+1
OB. x² - 2x+2
OC. x²-x+1
OD. x²-x+ 2
SUBMIT
Answer:
hi, I think the answer is x^2-2x+1 I don't see that option there but I'm guessing that was suppose to be option OA.
explanation:
(x-1)^2 is basically
(x-1)×(x-1)
rest of the explanation is in the photo
hope this helps
he residence of a city voted on whether to raise property taxes the ratio of yes votes to no votes was 4 to 7 if there was a 5918 total votes how many yes votes were there
There is a total of 2152 yes votes
How to determine the number of yes votes?From the question, the statement is given as
The ratio of yes votes to no votes was 4 to 7
Mathematically, this can be represented as
Ratio = 4 : 7
Alternatively, we have
Yes : No = 4 : 7
Express the ratio as fraction
Yes = Yes/Yes + No
So, we have
Yes = 4/4 + 7
Evaluate the sum
Yes = 4/11
From the question, we have
Total votes = 5918
So, we have
Yes = 4/11 * 5918
Evaluate
Yes = 2152
Hence, the number of yes votes is 2152
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Which expression can be placed on the right side of the equals sign to form an equation?
2+3³ =
1. O 5³
2. 3 +4:3
3. 10-2-9
4. 52 +4
Expression which placed on the right side of equal sign is,
[tex]2+3^3 =2 +3\times 3\times 3[/tex]
[tex]2+3^3= 2+27[/tex]
[tex]2+3^3= 29[/tex]
What is expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
What do you mean by equation?
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Given, a expression 2 + [tex]3^3[/tex] = ?
what can be placed right side of the expression?
so, first we calculate the [tex]3^3[/tex] which means 3 x 3 x 3 = 27.
then , add 2 and 27 and the answer is 29.
but the answer is not present into the option.
Final answer will be 29 which placed right side of the equation 2 + [tex]3^3[/tex] = 29.
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Which graph represents the polynomial function?
The graph which represents the polynomial function f(x) = x^3 - 2x^2 - 5x + 6 is in option A.
First, let us understand the polynomial function:
A polynomial function is one that uses only non-negative integer powers or positive integer exponents of a variable in an equation such as the quadratic equation, cubic equation, and so on. For example, 9y + 6 is a polynomial with an exponent of 1.
We are given:
f(x) = x^3 - 2x^2 - 5x + 6
We know that, when the graph intersects the x-axis, it satisfies the equation that is f(x) = 0 at that point.
Let us check the points one by one;
Option A;
The graph intersects the x-axis at -2, 1, and 3 it should satisfy the equation f(x) = 0.
Let's put x = -2 in f(x), we will get;
f(-2) = -2^3 - 2(-2)^2 - 5(-2) + 6 = -8 - 8 + 10 + 6 = -16 + 16 = 0
f(-2) = 0.
Let's put x = 1 in f(x), we will get;
f(1) = 1^3 - 2(1)^2 - 5(1) + 6 = 1 - 2 - 5 + 6 = 7 - 7 = 0
f(1) = 0.
Let's put x = 3 in f(x), we will get;
f(3) = 3^3 - 2(3)^2 - 5(3) + 6 = 27 - 18 - 15 + 6 = 33 - 33 = 0
f(3) = 0.
So, the points -2, 1, and 3 satisfy the equation f(x).
Thus, the graph which represents the polynomial function f(x) = x^3 - 2x^2 - 5x + 6 is in option A.
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Which statement is most likely to be true for this distribution?
O A. The mean is less than the median.
• B. The mean is greater than the median.
• C. The mean is the same as the median.
The statement that is most likely correct for the negatively skewed data distribution given is B. The mean is less than the median.
What is a Negatively Skewed Data Distribution?
A negatively skewed data distribution has the tail to the left of the number line, and therefore its median is usually greater than its mean.
The dot plot shows a data distribution that is negatively skewed. Therefore, the statement that is most likely to be true is B. The mean is less than the median.
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His former car was able to travel 20.28 miles per gallon. Is Xavier getting better gas
mileage in his new car?
The Xavier is not getting better mileage with his new car .
In the question ,
it is given that
distance travelled by Xavier's new car in 25 gallons = 528 miles
the mileage can be calculated using the formula = (distance travelled)/( gallons of fuel used) .
So , mileage of the new car = 528/25 = 21.12 miles per gallon ,
the milage of Xavier's former car = 20.28 miles per gallon .
From the above data , we can see that the mileage of former car is greater than new car .
Therefore , The Xavier is not getting better mileage with his new car .
The given question is incomplete , the complete question is
Xavier's new car uses 25 gallons for 528 miles , His former car was able to travel 20.28 miles per gallon. Is Xavier getting better gas mileage in his new car?
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