Arianna runs up 4 flights of stairs and then runs down 4 flights of stairs. Does this situation represent additive inverses?
Yes this represents additive inverse,
Since you are subtracting the same number 4 to get to zero.
The additive inverse of a number is simply the negation of the said number.
The given situation is an illustration additive inverse.
Given that:
[tex]Runs \ up = 4\ stairs[/tex]
[tex]Runs \ down = 4\ stairs[/tex]
Let:
[tex]x \to up[/tex]
[tex]y = down[/tex]
When Arianna runs up, we have:
[tex]x = Runs\ up[/tex]
[tex]x = 4[/tex]
When Arianna runs down, we have:
[tex]y = -Runs\ down[/tex] ---- the minus indicates a downward movement
So, we have:
[tex]y = -4[/tex]
The additive inverse of a number n is -n
E.g. The additive inverse of 7 is -7
By comparing x and y, we have:
[tex]y =-x[/tex] and [tex]x = -y[/tex]
Hence, the situation represents additive inverse.
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What is the range for the set of data? 6, 7, 10, 12, 12, 13
For a p-type silicon in which the dopant concentration na = 5x10^18/cm^3
For a p-type silicon in which the dopant concentration N A = 5 × 10^ 18 /cm^3 , find the hole.
For a p-type silicon in which the dopant concentration NA= 5×1018/cm^3, find the hole and electron concentrations
A box with a square base of side z is 9 times higher than it is wide. Express the volume V of the box as a function of z
The value of a collector’s item is expected to increase exponentially each year. The item is purchased for $500. After 2 years, the item is worth $551.25. Which equation represents y, the value of the item after x years?
y = 500(0.05)x
y = 500(1.05)x
y = 500(0.1025)x
y = 500(1.1025)x
Answer: [tex]y=500(1.05)^x[/tex]
Step-by-step explanation:
We know that the general exponential equation to find the value after x years is written as :-
[tex]y=Ab^x[/tex], where A is the initial value and b is the multiplicative rate of change and x is the time period.
Given : The initial amount of a product = $500
After 2 years, the item is worth $551.25.
Substitute A = 500, x=2 and y= 551.25 in the above equation we get
[tex]551.25=500b^2\\\\\Rightarrow\ b^2=\dfrac{551.25}{500}\\\\\Rightarrow\ b^2=1.1025\\\\\Rightarrow\ b=\sqrt{1.1025}=1.05[/tex]
Now, substitute b= 1.05, A = 500 in the general exponential equation, we get the equation represents y, the value of the item after x years as :-
[tex]y=500(1.05)^x[/tex]
draw a rectangle give the length and the width to show that it has an area of 12cm make sure one side is longer than the other to show length and width
What effects does adding a constant have to an exponential function?
In January 2015 the price of gas was on average $2.05 per gallon this was $1.20 cheaper than a year before what is the percent of decrease in price
The percentage decrease in a price is 37 percent.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, in January 2015 the price of gas was on average $2.05 per gallon this was $1.20 cheaper than a year.
Cost of gas per gallon = 2.05+1.20
= $3.25
Now, Percentage decrease = (Original Price - New Price)/Original Price ×100
= (3.25-2.05)/3.25 ×100
= 1.20/3.25 ×100
= 0.3692×100
= 0.37×100
= 37%
Therefore, the percentage decrease in a price is 37 percent.
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The formula f 5280m can be used to convert a measurement of f feet to an equivalent measurement of m miles. If an airplane flies at 21,120 feet above the ground, how much is that in miles?
B) there is a line with positive slope that is tangent to both circles. find the equation of this line, and (c) determine the points at which this tangent line touches each circle
The amount of rhubarb in the original recipe is 31\2 cups. Using what you know of whole numbers and what you know of fractions, explain how you could triple that mixed number
To triple a mixed number, multiply the whole number part by 3 and triple the numerator of the fraction part. For 3 1/2, the result is 9 3/2.
To triple the mixed number 3 1/2:
Multiply the whole number by 3: 3 x 3 = 9.
For the fraction part, triple the numerator: 1 x 3 = 3. The denominator remains the same.
Therefore, tripling 3 1/2 gives 9 3/2.
Suppose a fair die is rolled eight times. find numerical values for the expectation
How to find the slope???
Slope formula: y2-y1/x2-x1
= -3-1/6-0
= -4/6
= -2/3
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Is it possible for a linear function and an exponential funtion to have the indicated number of intersection?
Write a real world situation that can be modeled by the inequality
834 + 14s > 978 - 10s. Then solve the inequality.
The inequality 834 + 14s > 978 - 10s can represent a situation involving saving and spending money over time. To solve it, you perform a series of operations to isolate variable 's', which in this case results in s > 6, indicating more than six weeks required for savings to exceed spending.
Explanation:A real world situation that can be modelled by this inequality 834 + 14s > 978 - 10s could be a scenario involving saving and spending money. Say you start with $834 and each week you save $14 (s represents the number of weeks). On the other hand, you have $978 and you spend $10 each week. You want to figure out how many weeks it will take for the amount you have from saving to be more than the amount left from spending.
Now, to solve the inequality: subtract 834 from both sides which gives 14s > 144 - 10s, then combine like terms to get 24s > 144. Finally, divide both sides by 24 to solve for s: s > 6. Therefore, it will take more than six weeks for the money you save to exceed what remains from your starting amount of $978 after spending $10 each week.
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The repeating decimal, 0.27..., is converted to the fraction 0.27..=3/x
what is the value for x in the fraction
Answer:
The value of x is 11.
Step-by-step explanation:
The given number is 0.27272727..., and it is converted to the fraction as
[tex]0.272727...=\frac{3}{x}[/tex] ..... (1)
Multiply both sides by 100.
[tex]0.272727...\times 100=\frac{3}{x}\times 100[/tex]
[tex]27.272727=\frac{300}{x}[/tex] .... (2)
Subtract equation (1) from equation (2),
[tex]27.272727-0.272727...=\frac{300}{x}-\frac{3}{x}[/tex]
[tex]27=\frac{300-3}{x}[/tex]
Multiply both sides by x.
[tex]27x=297[/tex]
Divide both sides by 27.
[tex]x=\frac{297}{27}[/tex]
[tex]x=11[/tex]
Therefore the value of x is 11.
The value of the variable "x" in the fraction 0.27... = 3/x is x = 11.
To find the value of "x" in the fraction 0.27... = 3/x, we use algebraic techniques to solve for x,
Let us represent the repeating decimal 0.27... as a variable, say y,
y = 0.27...
To eliminate the repeating decimal, we multiply both sides of equation by a power of 10. In this case, we multiply by 100 to shift decimal point two places to right,
100y = 27.27...
Now, we subtract original equation from this new equation to eliminate the repeating part:
100y - y = (27.27...) - (0.27...),
Simplifying the equation:
99y = 27
y = 27/99
The fraction 27/99 is simplified further by dividing both the numerator and the denominator by their greatest common divisor, which is 9,
y = 3/11
Therefore, the required value of "x" is 11.
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Is the product of two mixed number less than, between,or greater than the two factors?explain
The rise and span for a roof are shown. The pitch of a roof is the ratio of the rise to the half-span . If the rise is 8 feet and the span is 30 feet, what is the pitch in simplest form?
a number cube is rolled and a coin is tossed. What is the probability of rolling a 5 and tossing tails
rolling a 5 is a 1/6 probability
tossing tails is a 1/2 probability
doing both is a 1/6 * 1/2 = 1/12 probability
Give your answer as a reduced proper or improper fraction 16/25 +-3/10
Notebooks costs 1.20 each. This weekend they will be on sale for $0.80. What percentage is the sale
write the converse of the conditional statement determine weather the converse is true of false if it is false find a counter example if you are 14 years old then you are a teenager
The converse of the conditional statement "If you are 14 years old then you are a teenager" is true. If someone is a teenager, it implies that they are at least 14 years old.
Explanation:The converse of the conditional statement "If you are 14 years old then you are a teenager" is:
If you are a teenager then you are 14 years old.
The converse statement is true because if someone is a teenager, it implies that they are at least 14 years old. However, it does not guarantee that someone who is 14 years old is necessarily a teenager, as there are other age groups within the teenage years.
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In the first half (distance) of a trip, a truck travels at a speed of 70 km/hr. How fast must it go during the second half of the trip to average 80 km/hr for the entire trip? km/hr
To average 80 km/hr for the entire trip, the truck must go at a speed of 80 km/hr during the second half of the trip.
Explanation:To find out how fast the truck must go during the second half of the trip to average 80 km/hr for the entire trip, we can use the concept of average speed. Average speed is calculated by dividing the total distance traveled by the total time taken.
Let's assume the entire trip is made up of two equal halves. In the first half, the truck travels at a speed of 70 km/hr. So, if we consider the distance traveled in the first half to be 'd', the distance traveled in the second half will also be 'd'.
Therefore, the total distance traveled for the entire trip is 2d. Now, to average 80 km/hr for the entire trip, we can use the formula:Average speed = Total distance / Total time
80 km/hr = 2d / Total time
Since the time taken for the first half is the same as the time taken for the second half, we can represent the total time as '2t', where 't' is the time taken for each half.
Substituting the values, we have:80 km/hr = 2d / (2t)
Cancelling out the common factors, we get:80 = d / t
Since the distance traveled in the first half is 'd' and the time taken for the first half is 't', the speed during the second half must be '80' km/hr to average 80 km/hr for the entire trip.
Approximately 1 million people immigrated to the U.S. from 1850 to 1900.
True
False
help me! need to show work!
Complete the patterns 9430, 94.3, 9.43
Which set of data has the same mode and median?
3, 4, 6, 7, 8
3, 3, 4, 5, 5
6, 7, 7, 8, 9
2, 2, 3, 4, 6
Answer:
6,7,7,8,9 both have 7 for mode and median
Step-by-step explanation:
A factory produces 7,482 widgets per day. It ships these widgets in 2 crates. Each widget sells for $7. How much money does one crate earn?
(4x6) x 3 = 4 x (3x6)
A scuba diver at a depth of −12 ft (12 ft below sea level), dives down to a coral reef that is 3.5 times the diver's original depth. What is the diver's new depth?
Answer:
The diver's new depth is -42 ft.
Step-by-step explanation:
Given : A scuba diver at a depth of -12 ft (12 ft below sea level), dives down to a coral reef that is 3.5 times the diver's original depth.
To find : What is the diver's new depth?
Solution :
A scuba diver at a depth of -12 ft.
Dives down to a coral reef that is 3.5 times the diver's original depth.
So, We have to multiply the original depth by 3.5.
i.e. [tex]d=-12\times 3.5[/tex]
[tex]d=-42[/tex]
Therefore, the diver's new depth is -42 ft.