20. DEPRECIATION Depreciation is the decrease in the value of an item resulting from its age or weac. When an item loses about the same percent of its value each year, an exponential function can be used to model its decreasing value over time. The function g(x)=12,000(0.85)'' can be used to model the value of a $12,000 car as it depreciates at an annual rate of 15% over x years. g(x) is a dilation of the parent function f(x)=0.85*. The graph shows the function g(x).
a. Write the equation of a function h(x) that represents the depreciation of a $20,000 car depreciating at the same rate over x years.
b. Describe h(x) as it relates to the parent function.
c. What is the difference between the values of the $12,000 car and the $ 20,000 car after 5 years?
Answers
a). The equation of a function h(x) as required to be determined is; h (x) = 20,000 (0.85)^x.
b). The function h (x) as required to be described in terms of the parent function f(x) is a dilation of the parent function using a scale factor of 20,000.
c). The difference between the values of the $12,000 and the $20,000 car is; $3549.6.
What is the equation of the function h(x) as required?It follows from the task content that the equation of the function g (x) is given as;
g (x) = 12,000 (0.85)^x.
a). On this note, since the rate of depreciation is same for the $20,000 car too; it follows that the exponential function which represents the situation is;
h (x) = 20,000 (0.85)^x.
b). Also, since the parent function f (x) = 0.85^x, the function g(x) can be described relative to the parent function as a dilation of the parent function using a scale factor of; 20,000.
c). The value of the $12,000 item after 5 years is;
g (5) = 12,000 (0.85)⁵ = $5324.5.
Also, the value of the $20,000 car after 5 years is;
h ( 5 ) = 20,000 (0.85)⁵ = $8874.1.
On this note, the difference between the values of the two items is; 8874.1 - 5324.5 = $3549.6.
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Related Questions
Solve the equation below using factorising. 10y² – 11y − 6 = 0 - Give each answer as an integer or as a fraction in its simplest form.
Answers
Answer:
y = - [tex]\frac{2}{5}[/tex] , y = [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
10y² - 11y - 6 = 0
consider the factors of the product of the y² term and the constant term which sum to give the coefficient of the y - term
product = 10 × - 6 = - 60 and sum = - 11
the factors are - 15 and + 4
use these factors to split the y- term
10y² - 15y + 4y - 6 = 0 ( factor the first/second and third/fourth terms )
5y(2y - 3) + 2(2y - 3) = 0 ← factor out (2y - 3) from each term
(2y - 3)(5y + 2) = 0 ← in factored form
equate each factor to zero and solve for y
5y + 2 = 0 ⇒ 5y = - 2 ⇒ y = - [tex]\frac{2}{5}[/tex]
2y - 3 = 0 ⇒ 2y = 3 ⇒ y = [tex]\frac{3}{2}[/tex]
What’s the correct answer answer asap for brainlist
Answers
Answer:
I hope this will be all right
Answer: I hope this will be right
Firstly, we know that when you rhyme, the ending word must sound the same.
In this case, the most recent word in the poem is "plight"
Let's look at the ending words of choices and see what rhymes with "plight".
A. I hope this will be "right"
B. Why does my teacher deceive "me"
C. I don't know how to write a poem and make it "rhyme"
Here you can see that the only word that rhymes with "plight" is "right".
Second, it has to relate to the poem that is given as much as possible.
The letter "A" both rhymes and relates to the given poem.
The last thing you need to know is the length of the sentence for the poem. In choice "C", it is way too long, making "C" incorrect.
Choice "B" isn't very long, but the number of syllables is also too many.
When writing a poem like this, you want to make the number of syllables as close as you can. In this case, the number of syllables on the bottom sentence is 7, and choice "A", and "I hope I get this right" has 6 syllables, therefore, choice "A" is the correct answer, and it matches all the necessities needed for completing the poem.
Based on the figure on the graph, match the describe transformation with the transformed figures.
Answers
The series of the transformation will be reflected across the x-axis, translating 9 units to the Right and 2 units down. Then the correct options are A and C.
What is a transformation of a shape?A point, line, or mathematical figure can be converted in one of four ways, and each has an effect on the object's structure and/or position. Picture, after translation, refers to the object's ultimate organization and placement.
The translation does not change the shape and size of the geometry. But changes the location.
The reflection does not change the shape and size of the geometry. But flipped the image.
The series of the transformation will be reflected across the x-axis, translating 9 units to the Right and 2 units down. Then the correct options are A and C.
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The complete question is attached below.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Based on the figure on the graph, match the described transformations with the transformed figures.
Reflected across the x-axis
Rotated 180° clockwise
Translated 9 units to the Right and 2 units down
Reflected across the y-axis
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100
POINTS!!!
What is the length of the added metal bar?
Answers
The length of the added metal bar is exactly 5cm.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
In the given cuboid the length is of 4 meters
The height is 3 meters.
We need to find the length of the added metal bar.
We can find this by using pythagoras theorem
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides
In the given figure the added metal bar is the hypotenuse.
4²+3²=d²
25=d²
d=5
Hence, the length of the added metal bar is exactly 5cm.
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One angle of a right triangle measures 69∘. What is the measure of the third angle?
Answers
21°.
In a right-angle triangle, there is always a 90° angle. Because of this, and our knowledge about a 69° angle, when we add 90° + 69° and get 159° as a result, we just subtract this from the area of a triangle, which is 180°. 180° - 159° = 21°, hence the missing and third angle is 21°.
Find the growth/decay rate given the exponential function. *
f(x) = 5(1.34)'
Answers
The growth/decay rate of an exponential function can be found by taking the derivative of the function with respect to the independent variable.
K in terms of growth and decay?
The growth rate is represented by the constant k. When viewed in terms of exponential DECAY, it is NEGATIVE. The length of time since then is t. If the time information is provided as dates, you must convert it to the amount of time that has passed from the starting point.
Given the function f(x) = 5(1.34)^t, the derivative with respect to t is:
f'(x) = 5(1.34)^t * ln(1.34)
The derivative represents the instantaneous rate of change of the function, and it is also the growth/decay rate.
So the growth/decay rate of the function f(x) = 5(1.34)^t is 5ln(1.34) * (1.34)^t.
In this function, the growth/decay rate is directly proportional to the function value, and it is a constant times the function value. This means that the function is growing or decaying at a constant rate, the rate being 5ln(1.34) which is the coefficient of (1.34)^t.
This constant rate of change is the growth/decay rate. In this case it is a growth rate of 5ln(1.34) which is approximately 1.99.
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Calculate (-1 + 3i)^5
Answers
Step-by-step explanation:
you understand how exponents work, right ?
an exponent defines how often its base has to be multiplied by itself.
so,
(-1 + 3i)⁵
means that
(-1 + 3i)
is multiplied 5 times by itself.
and that means we can split this into sub-multiplication groups like
(-1 + 3i)²×(-1 + 3i)²×(-1 + 3i) = (-1 + 3i)⁴×(-1 + 3i)
the advantage is that squares are easily calculated.
(a + b)² = a² + 2ab + b²
so,
(-1 + 3i)² = (-1)² + 2×-1×3i + (3i)² = 1 - 6i - 9 = -8 - 6i
(-1 + 3i)²×(-1 + 3i)² = ((-1 + 3i)²)² = (-8 - 6i)² =
= (-8)² + 2×-8×-6i + (-6i)² = 64 + 96i - 36 = 28 + 96i
(-1 + 3i)⁵ = (28 + 96i)(-1 + 3i) = -28 + 84i - 96i - 288 =
= -316 - 12i
estimate the quotient to the nearest whole number. 45.68 divided by 5.97 PLEASE HELP
Answers
When we divide the given decimal numbers and round off the answer to the nearest whole number, The answer is 8.
What are whole numbers?Whole numbers are the set of non-negative integers including 0, 1, 2, 3, 4, 5, and so on. They are numbers that can be counted and do not have fractions or decimals. Whole numbers are often used to count discrete objects and are an important foundation for many areas of mathematics, including number theory and combinatorics. They are opposite of the negative numbers and called Non-negative integers.
What do you mean by round off ?Round off is a method of approximating a number to a certain number of significant figures or decimal places. It involves replacing the least significant digits in a number with a 0 or a 5, depending on the next digit, in order to make the number simpler or more manageable. This can be done with the help of mathematical functions (e.g. round(), floor(), ceil() etc) in various programming languages. It is used to simplify large and complex numbers for ease of calculation, or to present data in a more readable form.
45.68/5.97
=7.65
rounding off to the nearest whole number , We get 8.
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What is 126²? Show how you got the answer please!
Answers
Answer:
15876
multiply 126 by 126.
this short trick won't be easy for beginners
you need to solve it 6 to 7 times to be a pro in solving square of any three or four digit number less than a 10 seconds
See the Image below.
Answers
Answer:
21 inches
Step-by-step explanation:
The perimeter of a square is given by
P = 4s where s is the side of a square
P = 4 ( 5 1/4)
= 4 * 5 + 4 * 1/4
= 20 + 1
= 21
What is the next step in solving the equation 10x+5=-4x+47 for x after we have combined x variables to one side of the equation?
a. Once x variables have been combined we need to combine the constants using opposite operations.
b. Once x variables have been combined we need to divide the remaining numbers by our new x variable from combining it in step 1.
c. Since we have combined the x variables together we have completed the necessary steps to solve the equation and have the answer.
d. The problem cannot be solved for x.
Answers
The next step in solving the equation 10x+5=-4x+47 for x after we have combined x variables to one side of the equation is once x variables have been combined we need to combine the constants using opposite operations and is denoted as option A.
What is an Equation?This is referred to as a mathematical statement that shows that two mathematical expressions are equal.
The equation 10x+5=-4x+47 is solved by combining x variables to one side of the equation and combining the constants using opposite operations which is denoted below:
10x+5=-4x+47
10x + 4x = 47 - 5
14x = 42
x = 42/14 = 3
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Irsa’s cat catches 9 mice every 3 days. Laiba’s cat catches 21 mice every 7 days. Do the two cats catch mice at the same rate?
Answers
Laiba’s cat catches mice at the rate of 3per day which is the same rate as Irsa’s cat.
What is rate ?Rate is defined as the measurement of a quantity against another to show the difference that exists between the two.
The number of mice caught of Irsa’s cat in 3 days = 9
Therefore in a day = X mice
Make X mice the subject of formula;
X mice = 9/3 = 3
Therefore, Irsa’s cat catches mice at the rate of 3 move per day.
The number of mice caught of Laiba’s cat in 7 days = 21
Therefore in a day = Y mice
Make y mice the subject of formula;
y mice = 21/7 = 3
Therefore, Laiba’s cat catches mice at the rate of 3per day which is the same rate as Irsa’s cat.
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Use 3.14 for the value of , and round your answers to two decimal places, where applicable. A rectangle is 11 inches long and 7 inches wide. What is its area?
Answers
Answer: 77
Step-by-step explanation:
Area of a rectangle is length * width
Area = 7*11 so the answer is 77
which of the following correlation coefficients indicates the strongest relationship between two variables? O -0.98
O 0.90
O 0.00
O 1.20
Answers
The correlation coefficient of 0.90 indicates the strongest linear relationship between two variables. It means that there is a strong positive or negative linear relationship between the two variables.
The correlation coefficient is calculated by finding the covariance of two variables, divided by the product of their standard deviations. The formula is as follows:
Coefficient = Covariance(X,Y) / (Standard Deviation of X * Standard Deviation of Y)
For example, if X and Y have a covariance of 6 and standard deviations of 2 and 3 respectively, then the correlation coefficient is:
Coefficient
= 6 / (2 * 3)
= 0.90
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The correlation coefficients indicates the strongest relationship between two variables is 0.90
The term correlation coefficient in math is defined as the strength of association between two variables.
Here we need to identify the correlation coefficients indicates the strongest relationship between two variables.
As we all know that the value of a correlation coefficient ranges between -1 and 1 and here we also know that the strongest linear relationship is indicated by a correlation coefficient of -1 or 1.
Here the weakest linear relationship is indicated by a correlation coefficient equal to 0.
If there is a positive correlation means that if one variable gets bigger, then the other variable tends to get bigger where as in a negative correlation means that if one variable gets bigger, then the other variable tends to get smaller.
Based on these definition, we have identified that option (b) is correct.
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A factory makes 1,200 shirts every 6 hours. The factory makes shirts for 63 hours each week. What are the fewest number of days the factory will need to make 12,600 shirts?
Answers
Answer: 7
Step-by-step explanation:
Match the inequalities on the left with the correct statement about that inequality on the right.
-4 r ≤ 22
Drop selections here
54 y+-8 ≥ -1
Drop selections here
-7d/4>3
Drop selections here
0>-8 n
Drop selections here
Answers
The statements which happen to be correct about the inequalities in each case as required are as follows;
-4r ≤ 22; Flip the inequality sign.54y + -8 ≥ -1; Do not flip the inequality sign.-7d / 4 > 3; Flip the inequality sign.0 > -8n; Flip the inequality sign.Which statements are correct about the given inequalities?It follows from the task content that the statement which is correct about each of the inequalities is to be matched accordingly.
It is important to know that the underlying rule for solving inequalities at the final stages is such that;
If the coefficient of a variable upon isolation on one side of the inequality is negative, it follows that the inequality sign must be flipped while multiplying or dividing both sides of the inequality by a negative number.
On the other hand, if the coefficient of the variable is positive, the inequality sign is not to be flipped.
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p and q are integers and p*q denotes the remainder when the product pq is divided by 10. Find a value p, greater than 4, such that p*p = (8*p) + 3
Answers
The required value of the given equation is p = √3 + 8.
What is the equation?The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.
If we let x = p - 8, then p = x + 8 and p × p = (x + 8) × (x + 8) = x² + 16x + 64.
We can substitute this expression for p × p in the given equation to get x^2 + 16x + 64 = (8 × (x + 8)) + 3 = 8x + 64 + 3 = 8x + 67.
Subtracting 64 from both sides gives us x² + 16x = 8x + 3, and if we subtract 8x from both sides, we get x² = 3.
The only positive value of x that satisfies this equation is x = √3, so p = √3 + 8.
Since √3 is approximately 1.73, p is approximately 9.73, which is greater than 4.
Therefore, a value of p that satisfies the given equation is p = √3 + 8.
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Mini muffins cost $3.00 per dozen.
Andre says, “I have $2.00, so I can afford 8 muffins.”
Elena says, “I want to get 16 muffins, so I’ll need to pay $4.00."
Do you agree with either, both, or neither of them?
Answers
Which unit would be best for measuring the thickness of a coin?
I
kilometer
meter
millimeter
centimeter
Done
Answers
The thickness of a coin will be measured in millimeters.
What is Units conversion?Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimeter is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.
For the Conversion to Millimeter
1 meter = 1000 millimeter.
1 centimeter = 10 millimeter,
1 kilometer = 1000000 millimeter
We know that the thickness of the coin is too small. To be measured in meters or kilometers of the coin.
Hence, the thickness will be measured in millimeters.
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In kite WXYZ, m < XYW = 23 deg and m < 7WY = 41 deg What is the m < WXY ? Help please help me due tonight
Answers
Answer:
Step-by-step explanation:
118.5
Sum of all angles in the kite is 360.
XYW = 23
XYZ = 46
ZWY = 41
ZWX = 82
We'll make the 2 angles left 2x in the equation because they are congruent.
2x+82+41=360
I got 118.5. This is a weird number, I'm not sure if it's right, but I don't have time to check.
Every pupil in class either swims or dances or both. Three fifths of the class swim and three fifths dance. Five pupil both swim and dance. How many pupils are there in the class?
Answers
Five pupils both swim and dance. Then the number of pupils in the class will be 25.
What are Sets?Sets are groups of clearly specified components. The number of items in a finite set is denoted by a curly bracket.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
Every pupil in class either swims or dances or both. Three-fifths of the class swim and three-fifths dance. Five pupils both swim and dance.
Let 'x' be the total number of pupils. Then the equation is given as,
A∪B = A + B - A∩B
x = (3/5)x + (3/5)x - 5
x = (6/5)x - 5
(1/5)x = 5
x = 25
Then the number of pupils in the class will be 25.
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Calculate the power of a man weight 40m in 15minutes assume G=9.87m~2
Answers
The power of man weight 40 m in 15 min is 394.8 N x distance / 900 seconds the distance is not provided in the question, so it's impossible to calculate the power.
What is the step by step calculation?To calculate the power of a man who weighs 40 kg and walks for 15 minutes, we can use the following formula:Power = Work / TimeWork = force x distancewhereforce = mass x gravity (F = mg)distance = velocity x timeThe force exerted by the man is:force = 40 kg x 9.87 m/s^2 = 394.8 NIf we assume that the man is walking at a constant velocity, we can calculate the distance he travels using the formula:distance = velocity x timeThe power exerted by the man is:Power = (394.8 N x distance) / (15 minutes x 60 seconds/minute) = 394.8 N x distance / 900 secondsThe distance is not provided in the question, so it's impossible to calculate the powerTo learn more about power refer:
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an adult ticket costs 24$ a senior citizen ticket costs 16$ and a students ticket costs 12$. Today only, tickets will cost 3/5 of the original price. what is the discounted price to buy 4 adult tickets, 2 senior citizens ticket, and 3 student tickets?
Answers
Answer:
The total discounted price to buy 4 adult tickets, 2 senior citizen tickets, and 3 student tickets is 96$ + 32$ + 18$ = 146$
Step-by-step explanation:
The discounted price for each ticket type is 3/5 of the original price, so for 4 adult tickets the discounted price is 4 * 24 * 3/5 = 96$, 2 senior citizen tickets is 2 * 16 * 3/5 = 32$, and 3 student tickets is 3 * 12 * 3/5 = 18$. Summing these together gives us 96$ + 32$ + 18$ = 146$.
Hope this helps!
Factor completely using the distributed law 42m+ 56n
Answers
Answer:
14(3m + 4n)
Step-by-step explanation:
Now we have to,
→ factor the given expression.
The expression is,
→ 42m + 56n
Let's factorise the expression,
→ 42m + 56n
→ (14 × 3m) + (14 × 4n)
→ 14(3m) + 14(4n)
→ 14(3m + 4n)
Hence, answer is 14(3m + 4n).
Confused on the answers to #7, #8
Will give votes!
Answers
Question 7
[tex]3(2+x)=-3 \\ \\ 2+x=-1 \\ \\ \boxed{x=-3}[/tex]
Question 8
[tex]4(5+x)=-4 \\ \\ 5+x=-1 \\ \\ \boxed{x=-6}[/tex]
You and your friend each deposit $50 in separate savings accounts. Your account earns 4% simple annual interest. Your friend’s account earns 6% simple annual interest. How long does it take for you to earn $12 in interest? How long does it take for your friend to earn $12 in interest?
I need help! Needs answers quick
Answers
I can earn simple interest $12 in 6 years and My friend can earn simple interest $12 in 4 years.
What is simple interest?
The principal of a loan or the initial deposit into a savings account serves as the foundation for simple interest. Because simple interest doesn't compound, a creditor will only pay interest on the principal sum, and a borrower will never have to pay interest on the interest that has already accrued.
Principle = $50
Rate of Interest I1 = 4%
Interest = $12.
Interest = [tex]\frac{PNR}{100}[/tex]
=> 12 = [tex]\frac{50\times 4\times N}{100}[/tex]
=> N = [tex]\frac{12}{2}= 6[/tex] years.
Rate of Interest I2 = 6%
=> 12 = [tex]\frac{50\times 6\times N}{100}[/tex]
=> N = [tex]\frac{12}{3}[/tex] = 4 years.
Hence I can earn $12 in 6 years and My friend can earn $12 in 4 years.
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Tahlia deposited $6800 into a savings account that earns 3.2% simple
interest each year, calculated annually. What will be the value of Tahlia's
account after 7 years?
OA. $15,232.00
OB. $1523.20
OC. $7017.60
OD. $8323.20
SUBMIT
Answers
Answer:
Simple interest= Principle × Rate× Time then you divide by 100
in this case the principle is $6800, rate is 3.2% and time is 7years
So $6800×3.2×7=152320
then you divide 152320 by 100 to get $1523.20
as the interest
but now to get the value the will be in the account, you will add the principle+ interest that will be gained
$6800+ $1523.20= $8323.20
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100
POINTS!!!
Answers
Answer:
the Pythagorean Theorem
√73 = 8.544
a leg
hypotenuse
√89 ≈ 9.434
Step-by-step explanation:
Use the Pythagorean theorem since you are finding the hypotenuse of a right triangle.
AC = √(8² + 3²) = √73 ≈ 8.544
CG is a leg of right triangle ACG
AG = √(73 + 16) = √89 ≈ 9.434
Use the table below to answer the question. How many more grapes do 8 people eat than 5 people?enter your answer in the box.
Answers
The number of grapes that 8 people eat more than 5 people, given the table attached, is 34 kg of grapes
How to find the amount of grapes ?To find the amount of grapes that 8 people eat more than 5 people, the formula would involve subtracting the amount of grapes eaten by 5 people from the amount of grapes eaten by 8 people.
From the graph, the amount of grapes eaten by 8 people would be 74 kg of grapes. The amount of grapes eaten by 5 people was 40 kg of grapes.
The amount of grapes that 8 people eat more than 5 people, is therefore :
= Grapes eaten by 8 people - Grapes eaten by 5 people
= 74 - 40
= 34 kg of grapes
In conclusion, the amount of grapes that 8 people eat more than 5 people, is 34 kg of grapes.
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If there is 8 apple and 8 oranges how many is in total?
Answers
Answer:
16
Step-by-step explanation:
8+8=16
