Answer:
Part A:
To determine whether a linear or exponential function can be used to describe the value of each house after a fixed number of years, we need to examine the change in the value of the houses over time. If the change is constant, a linear function can be used. If the change is proportional to the current value, an exponential function can be used.
Looking at the data in the table, we can see that the value of House 1 is increasing by a relatively constant amount each year, whereas the value of House 2 is increasing by a proportional amount. Therefore, a linear function can be used to describe the value of House 1, and an exponential function can be used to describe the value of House 2.
Part B:
For House 1, we can use the formula y = mx + b, where y is the value of the house in dollars, x is the number of years, m is the slope or rate of increase, and b is the initial value. Using the data from the table, we can find the slope and initial value:
m = (264240.79 - 253960) / 2 = 5140.395
b = 253960
So the function to describe the value of House 1 after x years is:
y = 5140.395x + 253960
For House 2, we can use the formula y = ab^x, where y is the value of the house in dollars, x is the number of years, a is the initial value, and b is the growth factor. Using the data from the table, we can find the initial value and growth factor:
a = 256000
b = (270000 / 256000)^(1/3) = 1.02905
So the function to describe the value of House 2 after x years is:
y = 256000(1.02905)^x
Part C:
To determine which house will have the greatest value in 45 years, we can plug in x = 45 into the functions we found in Part B and compare the results. Using a calculator, we get:
House 1: y = 5140.395(45) + 253960 = 472 339.25
House 2: y = 256000(1.02905)^45 = 798 825.85
Therefore, House 2 will have a significantly higher value after 45 years.
Step-by-step explanation:
On a coordinate plane, a curved line labeled f of x with a minimum value of (1.9, negative 5.7) and a maximum value of (0, 2), crosses the x-axis at (negative 0.7, 0), (0.76, 0), and (2.5, 0), and crosses the y-axis at (0, 2).
Which statement is true about the graphed function?
F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) > 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) < 0 over the intervals (-0.7, 0.76) and (2.5, ∞).
F(x) > 0 over the intervals (-0.7, 0.76) and (0.76, ∞)
The correct statement is that F(x) < 0 over the intervals (-0.7, 0.76) and (2.5, ∞).
What is value?Value of subjective concept that refers to the word of important that an individual group of people places on the something it is often associated with principal beliefs and the standard that are accepted by society when you can be seen as a matter of how important something is true person of organization it is often seen as a reflection of funds for view and can help to save decision.
This can be seen by looking at the function's minimum and maximum values and its points of intersection with the x- and y-axes. The minimum value of (1.9, negative 5.7) is to the left of the x-axis, indicating that the function is negative over the interval (-0.7, 0.76). The maximum value of (0, 2) is above the x-axis, indicating that the function is negative over the interval (2.5, ∞).
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an instrument used to measure the air taken in by and expelled from the lungs is the __________.
The instrument used to measure the air taken in by and expelled from the lungs is called a spirometer. It measures lung volumes and capacities.
Which are important indicators of lung function and respiratory health. Spirometry is a common test used to diagnose and monitor respiratory diseases such as asthma, chronic obstructive pulmonary disease (COPD), and pulmonary fibrosis.
air that a person inhales and exhales. It measures several lung volumes and capacities, including:
Tidal Volume (TV): This is the amount of air that is inhaled or exhaled during normal breathing.
Inspiratory Reserve Volume (IRV): This is the additional amount of air that can be inhaled after a normal inhalation.
Expiratory Reserve Volume (ERV): This is the additional amount of air that can be exhaled after a normal exhalation.
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What is multiplicative property of equality?
According to this property, when both sides of an equation are multiplied by the same real number, both sides of the equation always remain the same. The formula for this property can be expressed in real numbers a, b and c. If a × c = b × c.
Property of Equality:
The equivalence property describes the relationship between two equal quantities. If you apply a math operation to one side of the equation, you must also apply it to the other side of the equation to maintain balance.
That is, a property that does not change the truth value of an equation or does not affect the equivalence of two or more quantities is called an equality property. These equality properties help solve various algebraic equations and define equivalence or equilibrium relationships.
Multiplicative Property of Equality:
According to this property, when both sides of an equation are multiplied by the same real number, both sides of the equation always remain the same.
The formula for this property can be expressed as for the real numbers a, b, and c.
If a × b, then, a × c = b × c.
In algebra, the multiplicative property of an equation helps extract unknown terms from an equation. Because multiplication and division are opposites of each other.
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Toby goes on holiday to Geneva, Switzerland. In Geneva, Toby sees a watch costing 193. 75 CHF (Swiss Francs). In Manchester, an identical watch costs £145. Given that £1 = 1. 55 CHF
a) In which city is the watch cheaper?
b) By how much is it cheaper (in £)?
To answer this question, we will need to convert the price of the watch in Geneva to pounds and compare it to the price of the watch in Manchester.
First, let's convert the price of the watch in Geneva from CHF to pounds:
193.75 CHF ÷ 1.55 CHF/£ = 125 pounds
Now, we can compare the price of the watch in Geneva to the price of the watch in Manchester:
125 pounds (Geneva) < 145 pounds (Manchester)
Therefore, the watch is cheaper in Geneva.
To find out by how much it is cheaper, we can subtract the price of the watch in Geneva from the price of the watch in Manchester:
145 pounds - 125 pounds = 20 pounds
So, the watch is 20 pounds cheaper in Geneva.
In conclusion, the watch is cheaper in Geneva by 20 pounds.
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Determine whether the relation is a function. Find the domain and the range. 10, 2, -10, 2, 6, 4, 5, 3, -6, 7
Therefore , the solution of the given problem of domain comes out to be The range is {-10, 2, 3, 4, 5, 6, 7} and The domain is {-10, -6, 2, 3, 4, 5, 6, 7, 10}
Explain a domain.The domain of a function is the range of possible arguments that it can accept. The cross of the an f-like functional is represented by these numbers (x). The range of potential values to which a function can be applied is known as its domain. The value that the procedure returns after inserting the x value is part of this set. An equation for a function is Y = f, where y and x are predictor variables (x). When a given value of x can produce a single value of y, a parameter is said to be in the scope of a function.
Here,
To determine if the relation is a function, we need to check if each input value (the "x" value) corresponds to exactly one output value (the "y" value).
Looking at the relation {10, 2, -10, 2, 6, 4, 5, 3, -6, 7}, we can see that the input value 2 corresponds to two different output values, 2 and 4. Therefore, the relation is not a function.
To find the domain, we simply list all the input values in the relation. The domain is:
{-10, -6, 2, 3, 4, 5, 6, 7, 10}
To find the range, we list all the output values in the relation.
The range is:
{-10, 2, 3, 4, 5, 6, 7}
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1. Is 26,341 divisible by 3? If it is, write the number as the product of 3 and another factor. If not, explain. 2.
The required sum of digits is 16 which is not divisible by 3, so 26,341 is not divisible by 3.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
To determine if 26,341 is divisible by 3, we can add up the digits of the number and see if the result is divisible by 3.
2 + 6 + 3 + 4 + 1 = 16
16 is not divisible by 3, so 26,341 is not divisible by 3.
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Norman is 12 years older than Michael. In 6 years, he will be twice as old as Michael. How old is Michael now?(A) 3(B) 6(C) 12(D) 18(E) 24Spoiler: OA
Answer:
Choice (C) 6
Step-by-step explanation:
We know that Norman is currently 12 years old, and in 6 years he will be twice the age of Michael. Using the two numbers, we can divide 12 by 2 and evaluate.
[tex]\frac{12}{2}=6[/tex]
So Michael is 6 years old.
Don’t know answer can u please help me understand this and give me the answers
The value of the expression is 1/c - 5
How to simply the expressionNote that algebraic expressions are described as expressions that are composed of terms, variables, coefficients, factors and constants.
From the information given, we have that;
c/ c² - 7c + 10 - (2/ c² - 7c + 10)
Find the lowest common factors
c - 2/ c² - 7c + 10
solve the quadratic equation
c - 2/ c² - 5c - 2c + 10
Factor the expression, we get;
c- 2/c(c - 5) - 2(c - 5)
Factor the terms
c-2/(c-2)(c-5)
Divide the values
1/c - 5
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In AKLM, m = 63 inches, m/K=24° and m/L-42°. Find the length of 1, to the
nearest inch.
Answer:Using sine law, the value of k in the triangle KLM to the nearest tenth is 2.0 inches.
How to use sine law to find sides of a triangle?
Using sine law,
k / sin K = m / sin M
Therefore,
k = ?
K = 21 degrees
M = 180 - 21 - 88 = 71 degrees
m = 5.3 inches
Hence,
k / sin 21 = 5.3 / sin 71°
cross multiply
5.3 sin 21 = k sin 71°
5.3 × 0.35836794954 = 0.94551857559k
1.89935013259 / 0.94551857559 = k
k = 2.00846113168
k = 2.0 inches
Step-by-step explanation:
the usual price of a bag of oranges was $4. during a promotion, two bags of oranges were sold for $5.99. find the percentage decrease in the price of the two bags of oranges. give your answer correct to 1 decimal place.
The percentage decrease in the price of the two bags of oranges is 25.1 %.
We have been told that the usual price of a bag of oranges was $4 and during the promotion, it became $5.99 for two bags of oranges. We need to find the percentage decrease here.
We can calculate that two bags before the promotion cost = $4 × 2 = $8
As we already know, the two bags during the promotion cost = $5.99
The decrease in price can be calculated as well = $8 - $5.99 = $2.01
Percentage decrease = ($2.01 / $8) * 100 %
Percentage decrease = 25.1 %
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NEED HELP ASAP:In the year 2000, a person bought a new car for $15000. For each consecutive year
after that, the value of the car depreciated by 11%. How much would the car be worth
in the year 2004, to the nearest hundred dollars?
The car would be worth $9400 in the year 2004.
How to determine the worth of the car?If the car depreciates by 11% each year, then its value at the end of each year will be 89% of its value at the beginning of the year (100% - 11% = 89%). Therefore, the value of the car after 1 year will be:
$15000 * 0.89 = $13350
The value of the car after 2 years will be:
$13350 * 0.89 = $11881.50
The value of the car after 3 years will be:
$11881.50 * 0.89 = $10576.77
The value of the car after 4 years (in the year 2004) will be:
$10576.77 * 0.89 = $9422.19
Therefore, the car would be worth $9400 in the year 2004.
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How do you remember greater than less than?
The usual sign for greater than and less than is "<", the pointed side is always towards the smaller quantity.
When we compare two quantities in mathematics we us the sign"<".
Now, let us say that there are two quantities a and b, and a is greater than b. So, we can write the relation as, a > b. So, we see that b is less than as a and a is greater than b.
Now, to remember this, the pointed side of the sign will be always towards the quantity that is smaller.
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I Need help on number 15 pls
Using the fact that the figures are similar, we will get z = 4.
How to find the value of z?We know that the two figures are similar, then the correspondent quotients between sides must be equal.
That means that we can write the equation:
10/15 = z/6
And we can solve that equation for z, we will get:
z = 6*(10/15) = 4
That is the value of z.
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