A logarithmic curve is a mathematical function.
A logarithmic curve, also known as a logarithmic function, is a type of mathematical function that describes a relationship between a variable x and a variable y in which the logarithm of y is a linear function of x.
The general form of a logarithmic function is y = logb(x), where b is the base of the logarithm, and x and y are real numbers. The base of the logarithm can be any positive number, but the most common bases used are 10 (common logarithm) and e (natural logarithm).
The graph of a logarithmic function is a curve that starts at negative infinity and increases gradually as x increases. The slope of the curve becomes closer to zero as x increases, and it is undefined for x=0 or x<0.
Logarithmic functions are often used in many areas of science, engineering, and mathematics to model real-world phenomena that exhibit exponential growth or decay, such as population growth, radioactive decay, sound levels and more.
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On Friday, Tyler came up with the expression t= -0.5(1-2h) to represent the temperature change. His math teacher came up with the expression t= 4(2h+2) - 7h - 8.5 for the same day. Are these expressions equivalent or not?
Answer:
no
Step-by-step explanation:
The effect of wearing different types of running shoes on the time it takes to
complete a race is being studied in an experiment. Which of these is most
likely to be an extraneous factor that could also affect the time it takes to
complete the race?
A. Number of people the stadium can hold
OB. Color of the shoes
OC. Day of the week
OD. Type of treads on the shoes
Most likely one of these unrelated factors that could possibly have an impact on how long it takes to finish the race is the environment
What is meant by extraneous solution?An extraneous solution (also known as a spurious solution) is a solution that develops during the problem-solving process but is not a true solution to the issue at hand, such as the answer to an equation. Any variable that you are not researching but that might have an impact on the results of your research study is referred to as an extraneous variable in an experiment. Uncontrolled auxiliary variables can result in conclusions regarding the link between independent and dependent variables that are incorrect. The numbers we obtain when solving equations that aren't actually solutions to the equation are referred to as extraneous solutions. Extraneous variables are anything that could potentially influence the outcomes but is not the independent variable.Therefore the correct option is a) Number of people the stadium can hold
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Please hurry it is timed and i need help!
The best option regarding the solutions of the trigonometric equation presented in this problem is given as follows:
A. 60º + n360º, 300º + n360º.
How to solve the trigonometric equation?The trigonometric equation for this problem is defined as follows:
[tex]\cos{x} - \sqrt{1 - 3\cos^2{x}} = 0[/tex]
Then, isolating the cosine, we have that:
[tex]\cos{x} = \sqrt{1 - 3\cos^2{x}}[/tex]
Applying the square for both sides, we have that:
cos²(x) = 1 - 3cos²(x).
4cos²(x) = 1.
cos²(x) = 1/4
cos²(x) = 0.25.
Applying the square root to both sides, we have that:
cos(x) = 0.5.
Meaning that the angle measures of x with the cosine of 0.5 are given as follows:
x = 60º, x = 300º.
(as the cosine is positive on the first and fourth quadrant).
One entire lap over the unit circle is equivalent to 360º, hence adding 360º n times to any of these solutions is also a solution to the trigonometric equation, meaning that option a is correct.
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What literary device did Oscar Wilde use?
Oscar Wilde creates a hilarious tone by using puns, situational irony, dramatic irony, satire, and epigrams.
Who is Oscar Wilde?Oscar Fingal O'Flahertie Wills, an Irish poet, and playwright, lived from 16 October 1854 to 30 November 1900.
He wrote in a variety of genres throughout the 1880s before becoming one of London's most well-known playwrights in the early 1890s.
The Picture of Dorian Gray, his plays and epigrams, as well as the circumstances surrounding his meningitis-related early death at age 46 and criminal conviction for gross indecency for consensual homosexual activities in "one of the earliest celebrity trials," is what people will remember him for most.
Using puns, situational irony, dramatic irony, satire, and epigrams, Oscar Wilde establishes a humorous tone.
Therefore, Oscar Wilde creates a hilarious tone by using puns, situational irony, dramatic irony, satire, and epigrams.
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What is the y-intercept at 0 4?
The y-intercept of (0,4) is 4.
A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis. This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points satisfy x = 0 because of this.
The y-coordinate of the y-intercept is determined by computing f(0) if the curve in question is supplied as y=f(x), y=f(x), etc. There is no y-intercept for functions that have an value at x = 0.
The constant term a is the y-coordinate of the y-intercept if the function is linear and is written in slope-intercept form as f(x)=a+bx"
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someone pls help
the question is
A jeweler had a fixed amount of gold to make bracelets and necklaces. The amount of gold in each bracelet is 8 grams and the amount of gold in each necklace is 16 grams. The jeweler made a total of 12 bracelets and necklaces using 160 grams of gold. Graphically solve a system of equations in order to determine the number of bracelets made, x, and the number of necklaces made, y.
The number of bracelets is 4.
The number of bracelets is 8.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
Number of bracelets = x
Number of necklaces = y
Amount of gold in each bracelet = 8 grams
Amount of gold in each necklace = 16 grams
Now,
x + y = 12 _____(1)
x = 12 - y ____(2)
8x + 16y = 160 ______(3)
Substituting (2) in (3) we get,
8(12 - y) + 16y = 160
96 - 8y + 16y = 160
96 + 8y = 160
8y = 160 - 96
8y = 64
y = 8
Now,
x = 12 - y
x = 12 - 8
x = 4
Thus,
The number of bracelets and necklaces that were made is 4 and 8.
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Dominic invested $93,000 in an account paying an interest rate of 6. 8% compounded monthly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $202,800?
The standard deviation equation ( 1 + 6.8)% × 93000 > 202800
What is standard deviation?
Your dataset's standard deviation serves as a gauge of its degree of variability. It displays the typical difference between each outcome and the mean.
While a high standard deviation indicates that values are frequently distant from the mean, a low standard deviation indicates that values are typically grouped close to the mean.
( 1 + 6.8)% × 93000
= 202800
Then we get n ≈ 12,
the equation ( 1 + 6.8)% × 93000 > 202800
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How do you find the difference between two different numbers?
Subtract the smaller of the two numbers from the larger of the two numbers to discover the difference between them.
Subtract the smaller of the two numbers from the larger of the two numbers to discover the difference between them. The difference between the two numbers is the sum's product.
Subtracting two integers from each other is a type of subtraction.
The process for determining the difference between two decimals and two whole numbers is the same.
We only add a new step.
Finding the difference between 8.967 and 7.2, for instance, could appear more difficult.
To give them all the same amount of decimal places, we must first convert each decimal.
7.2 becomes 7.200 as a result.
The computation may now be done as before:
8.967 - 7.200 = 1.767
Therefore, there is a 1.767 discrepancy between these figures.
In order to find the difference between two fractions, simplify and find the lowest common denominator of each fraction.
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In in1965 the population of country A wa 2,714,000. In 2015 the population wa 3,663,900. Determine the percentage increae in the population from 1965 to 2015
The percentage increase in the population from 1965 to 2015 is 35 %.
To calculate the population growth rate (PG), take the difference (subtraction) between the original population and the population at time point 1, divide by the original population, and multiply by 100. The population growth rate (PGR) for that period (10 years) was 12%.
Given:
In the year 1965, the population of country A was 2714000.
In the year 2015, the population of country A was 3663900.
Percentage increase in population 50 years
= [tex]\frac{(3663900-2714000)}{2714000}[/tex] × 100
= 35 %
Thus, the percentage increase in the population from 1965 to 2015 , i.e, 50 years is 35%.
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How do you find the missing side of a right triangle without a calculator?
The missing side of a right triangle without using a calculator can be found by using the Pythagoras theorem .
What is Pythagoras Theorem ?
The Pythagoras Theorem states that the square of the hypotnuse (longest side) is equal to the sum of the square of the perpendicular and base .
that means : [tex]Hypotnuse^{2} = Perpendicular^{2} + Base^{2}[/tex] ;
let the missing side of the right triangle be the hypotnuse ;
So , missing side can written as : [tex]Hypotnuse = \sqrt{Perpendicular^{2} + Base^{2}}[/tex] .
For Example : Let the right triangle has sides lengths as perpendicular = 6 and hypotnuse = 10
The length of side "base" is unknown.
So , to find length of side b, we put the known values into theorem:
[tex]10^{2} = 6^{2} + Base^{2}[/tex] ;
[tex]base^{2} = 100 - 36[/tex] ;
So , the missing side "base" = 8 ;
Therefore , the missing side without using calculator can be found by the Pythagoras Theorem .
The given question is incomplete , the complete question is
How do you find the missing side of a right triangle without a calculator when the other two sides are given ?
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How do you solve 2x 3y =- 6?
We can solve this equation using the distributive property. First, we will use the distributive property to multiply the 3y by 2.
What is distributive property?The distributive property is a mathematical rule that allows you to multiply a single number by a group of numbers by multiplying the single number by each number in the group individually. This rule can be expressed in two ways. The first way is a(b + c) = ab + ac. The second way is a(b - c) = ab - ac.
This will give us 2x * 3y = 2(3y). Then, we will subtract 6 from both sides of the equation, which gives us 2x * 3y - 6 = 2(3y) - 6. We can then divide both sides of the equation by 6, which gives us 2x * 3y / 6 = 2(3y) / 6. Finally, we can divide both sides of the equation by 3y, which gives us 2x = -2. Therefore, the solution to 2x 3y = -6 is 2x = -2.
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•25 POINTS•
-A
-B
-C
Answer:
SaS
Step-by-step explanation:
Which problem solving strategy would be best to solve this problem? Avelina earned half as much money as Gus. If Gus earned $125.00, how much money did Avelina earn? A. write an equation B. make a table, chart or list C. compute or simplify D. guess, check and revise
The best approach to solve the problem is writing an equation. Given Avelina earns half of what Gus earns, the equation becomes Avelina's earnings = Gus's earnings / 2. On substituting Gus's earnings with $125, we get Avelina's earnings to be $62.50.
Explanation:The best problem-solving strategy that would be apt to solve this problem, 'Avelina earned half as much money as Gus. If Gus earned $125.00, how much money did Avelina earn?' is to write an equation. We know that Avelina earned half of what Gus earned. This can be represented by the equation: Avelina's earnings = Gus's earnings / 2.
Since we know that Gus earned $125, we can substitute this value into our equation: Avelina's earnings = $125 / 2. Solving this equation gives us the answer: Avelina earned $62.50.
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1/2% in decimal
please give me my answer Also
I AM NOT ASKING for 1/2 in decimal
I am asking for 1/2 percent in decimal
Answer:
Step-by-step explanation:
We know that : Percentage means 'divided by 100'
therefore, 1/2 percent = 1 / 2 ÷ 100 = 0.5 ÷100 = 5÷1000= 0.005
What is the nature of root of equation 2x^2 5x 7 0?
The nature of the roots of the equation x^2 - 5x + 7 = 0 : no real roots
Consider given quadratic equation: x^2 - 5x + 7 = 0
Comparing given quadratic equation with the standard form of quadratic equation i.e., ax^2 + bx + c = 0
a = 1, b = -5, c = 7
First we find the discriminant:
D = b^2 - 4ac
D = (-5)^2 - 4(1)(7)
D = 25 - 4(7)
D = 25 - 28
D = -3
Since, the discriminant D < 0
Therefore, there are no real roots of this equation.
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The mean of 4 5 6 7 8
Answer:
6Step-by-step explanation:
The mean of 4 5 6 7 8
there are 5 numbers in sequence, you can solve at a glance by looking at the number in the middle, or add the numbers and divide them by their number, in any case the answer will be 6
4 5 6 7 8 (6 is central)
or
(4 + 5 + 6 + 7 + 8) : 5 =
30 : 5 =
6
The sequence one-sixth, negative two-sevenths, three eighths, negative four ninths, and so on is given.
Part A: Assuming the pattern continues, list the next four terms in the sequence. Show all necessary math work. (4 points)
Part B: Write the explicit equation for f (n) to represent the sequence. Show all necessary math work. (4 points)
Part C: Is the sign of f (53) positive or negative? Justify your reasoning mathematically without determining the value of f (53). (2 points)
A. 5/10, -6/11, 7/12, -8/13
B. f(n) = n/(n+5)
C. Positive
What is a sequence?A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. It has members, just like a set does. The length of the sequence is determined by the number of items.
Here, we have
A. From inspection of the sequence, the pattern is:
Add 1 to the numerator of the previous term.
Add 1 to the denominator of the previous term.
Make every other term negative.
Hence, assuming the pattern continues, the next four terms in the sequence will be:
5/10, -6/11, 7/12, -8/13
B. An explicit formula for an arithmetic sequence allows you to find the [tex]n^{th}[/tex] term of the sequence.
f(1) = 1/6
f(2) = -2/7
We can see that the numerator is the position of the term (n) in the sequence. So when n = 1 the numerator is 1, when n = 2 the numerator is 2, etc.
The denominator is 5 more than the position of the term in the sequence. So when n = 1 the denominator is 1 + 5 = 6, and when n = 2 the denominator is 2 + 5 = 7.
We observe that if the numerator (the value of n) is odd then the term is positive, and if the numerator (the value of n) is even then the term is negative.
Hence, the rule for the nth term is:
f(n) = n/(n+5)
If n is odd then f(n) is positive.
If n is even then f(n) is negative.
C. 53 is an odd number.
As the function f(n) is positive when n is odd, the sign of f(53) is positive.
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What is a log 10 transformation?
A log 10 transformation is a mathematical operation that is used to change the scale of a variable in a data set. The log 10 transformation is applied to the variable by taking the base-10 logarithm of each value in the data set. The result of this operation is a new variable that is on a different scale than the original variable.
The log 10 transformation is commonly used in statistics and data analysis to normalize data that is on a large scale, such as data that spans several orders of magnitude. By applying the log 10 transformation, the data is transformed into a more manageable scale that is easier to work with and analyze.
The log 10 transformation can also be used to stabilize the variance of a variable, this is particularly useful when the data is positively skewed. The log 10 transformation can also be useful for data that has a multiplicative relationship, for example, population growth or stock prices.
It is important to note that the log 10 transformation can only be applied to data that is positive and greater than zero because the logarithm of zero or a negative number is not defined.
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Rent-A-Car charges $50 to rent a car plus $0.25 per mile. Save-To-Rent charges $25 to rent a car plus $0.41 per
After how many miles will the cost be the same to rent a car?
miles
y = 0.25x + 50 and y = 0.3x + 40 will be the equation to find the cost to rent a car.
Define cost function.A mathematical formula known as a cost function is used to visualize how manufacturing costs will vary depending on the output level. In other words, given a specified quantity produced, it calculates the entire cost of production.
Define cost.Costs are the dollar amount spent on materials, labor, services, goods, equipment, and other items for use by a company or other accounting organization.
y = 0.25x + 50
y = 0.3x + 40
The equations will be written as y = mx + b, or slope-intercept form. You must determine what you have in order to determine what belongs where.
They receive $50 per day plus $0.25 per mile from Rent-A-Wreck. This indicates that the $0.25 per mile is the number that changes daily. Thus, y = 0.25x + 50 will be the equation.
They receive $40 per day with $0.30 per mile from Drive-A-Lemon. This indicates that the $0.30 per mile is the number that changes daily. y = 0.3x + 40 will be the formula.
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Graph the solution to this inequality on the number line.
-4x> 8.4
-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3
The Graph solution to this inequality on the number line is lies between -4 > 8.4 and their numbers are -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3.
How do you graph an inequality's solution on a number line?Draw a circle around the number to indicate an inequality, such as x>3, on a number line (e.g., 3). In case the sign also states equal to, complete the circle (or ). If the sign doesn't include equal to (> or), leave the circle empty.
How would one graph an inequality?When plotting an inequality, use the,, >, or sign as a = sign. If the inequality is either or, graph the equation as a dotted line. If the inequality is either or, graph the equation as a solid line.
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When Souta went to Sweden, 1 Swedish krona was worth about 0. 12 US
dollar. He took d dollars on the trip. Which equation could be used to find
the value in Swedish krona, k, of the dollars?
A
k = 0. 12d
B
d
k=
0. 12
с
0. 12
k=
d
D k= 1. 12d
If 1 Swedish krona was worth 0.12 US dollar , and if he took d dollars for the trip then the equation that is used to find the value in Swedish krona (k) of the dollars is option (a) [tex]k = 0.12\times d[/tex] .
The value of 1 Swedish krona is = 0.12 US dollar ,
the number of dollar that Souta took on the trip is = d dollars ;
we have to find the equation that can be used to find the equation in Swedish krona "k" of the dollars ,
According to the question ,
the equation for Swedish krona can be represented as [tex]k = 0.12\times d[/tex] ;
Therefore , the required equation is [tex]k = 0.12\times d[/tex] .
The given question is incomplete , the complete question is
When Souta went to Sweden, 1 Swedish krona was worth about 0.12 US dollar. He took d dollars on the trip. Which equation could be used to find the value in Swedish krona, k, of the dollars ?
(a) k = 0.12d
(b) dk = 0.12
(с) 0.12k = d
(d) k = 1.12d
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For questions 8 and 9, determine if S could lie on the perpendicular bisector of QR with the
given coordinates.
8. Q(-5, -1), R(3, 7), S(4,-2)
9. Q(-5, 4), R(8. -3), S(-2. -5)
Yes S lies as the perpendicular bisector as asked in the question .
The distance is calculated with the use of distance formula,
d = √( x2 - x1 )² + ( y2 - y1 )²
Now , we are suppose to calculate the distance between the points S and R, given their values are ,
S=(4,-2) and
R=(3,7)
Using distance formula ,
d = √( 3 - 4 )² + ( 7 - (-2))²
d = √ 1 + 81
= √82
Now, the distance between Q and S can be found as ,
Q=(-5,-1)
S=(4,-2)
d = d = √(4 + 5)² + ( -2 + 1)²
d = √ 81 + 1
= √82
As the distance between the two ends of the segment and the point S is the same, the point S must lie on the perpendicular bisector of QR, according to the perpendicular bisector theorem.
For question number 9 the distance between Q and S are,
Q=(-5,4)
S=(-2,-5)
d = √( -2 -5)² + ( 5 - 4)²
d = √ 9 + 1
= √10
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60 workers can complete a work in 21 days. How long will it take to complete the some work if 10 more workers were added?
Answer:
Step-by-step explanation:
set 1 is the work, then 60 works finish 1/21 per day. [tex]\frac{1}{21*60}[/tex] is the work for per workers. so, the days for 70 workers is [tex]\frac{21*60}{70}=18[/tex] days.
it will spend 18 days to complete
can somebody quickly answer this?
Lorraine prepared a 4.5-gallon pot filled with tomatoes to be canned in jars. Each jar will hold 1.25 quarts of tomatoes. If 1 gallon equals 4 quarts, how many jars can Lorraine fill?
Answer:10
Step-by-step explanation:
got the same question
•15 POINTS• don’t need to explain.
a.)
b.)
c.)
Answer: HL
Step-by-step explanation:
HL because the hypotenuse leg theorem shows how a given set of right triangles are congruent if the corresponding lengths of their hypotenuse and one leg are equal.
Can a right triangle with sides 6 and 8 cm and 10 cm be formed give reason?
A right triangle is formed by the provided sides 6 cm, 10 cm, and 8 cm
Given that a triangle has sides measuring 6 cm, 10 cm, and 8 cm.
The question is whether a right triangle is formed by the specified sides.
The Pythagorean theorem states that the sum of the squares of the base and height is equal to the square of the hypotenuse.
Hypothesis 2 Equals Base 2 plus (Altitude)2
Make the hypotenuse 10 cm long.
Specify 6 cm for the base and 8 cm for the perpendicular.
(Hypotenuse)2 LHS (Hypotenuse)
RHS: (Base)2 + (Altitude)2 (Base)2 + (Altitude)2 = (6)2 + 2 = (10)2 = 100 (8)
LHS = RHS: 2 = 36 + 64 = 100
The sides provided meet the requirements for a right triangle.
As a result, a right triangle is formed by the provided sides.
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How do you write an expression in vertex form?
Therefore a quadratic function can be written in vertex form as
y = a(x - h)^2 + k.
Define quadratic function.In mathematics, a polynomial of degree two in one or more variables is referred to as a quadratic polynomial. The polynomial function that a quadratic polynomial defines is known as a quadratic function.
What is a polynomial function?In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.
A quadratic function can be written in vertex form as y = a(x - h)^2 + k
Where (h, k) is the vertex, and a is the leading coefficient.
y = ax^2 + bx + c (standard form)
y = a(x + b/2a)^2 + c - b^2/4a
y = a(x - h)^2 + k where h = -b/2a and k = c - b^2/4a
For example,when y = 3x^2 - 6x - 5
y = 3x^2 - 6x - 5
y = 3(x^2 - 2x) - 5
y = 3(x^2 - 2x + 1 - 1) - 5 = 3(x - 1)^2 - 8
So, the equation is in vertex form y = 3(x - 1)^2 - 8
Note that this only works for parabolas that opens upwards or downwards, if the parabola opens to the sides, the vertex form is y = a(x-h)^2 +k
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Due to delay, a company had to extend a project from 108 day to 137 day. What wa the percentage increae in time to complete the project, round you anwer to the nearet tenth
The percentage increase in project completion time is 26.85%.
What is percent?Percentage is a relative number that represents the hundredth part of any quantity. One percent (symbolized 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount. percentage. Mathematics percentile is a related topic. A percentage is a fraction of a whole represented as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent. To calculate a percentage, divide the share of the total by the total and multiply by 100.
Here,
=(137-108)/108*100
=26.85%
The percentage increase in time to complete the project is 26.85%.
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A fish swims at an altitude of -20. 2 meters. A bird flies at an altitude of 38. 1 meters. Which animal is closer to sea level?
The fish is closer to sea level. Sea level is defined as the mean sea level, which is a fixed point of reference for measuring altitude.
The altitude of the fish is -20.2 meters, which is closer to sea level than the altitude of the bird at 38.1 meters. This means that the fish is closer to sea level than the bird. To explain further, sea level altitude is a point of reference that is used to measure the altitude of other objects. Sea level altitude is defined as the mean sea level which is a fixed point.
Therefore, when trying to determine which animal is closer to sea level, it is important to look at the altitude of both the fish and the bird. The altitude of the fish is -20.2 meters, which is closer to sea level than the altitude of the bird at 38.1 meters. This means that the fish is closer to sea level than the bird.
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helpppppp
math math math math
Answer: 35
Step-by-step explanation:
So first you plug 5 into the equation which is:
10(5)-15
which is 50-15
50-15 is 35
Answer:
35
Step-by-step explanation:
plug 5 in for x and u will get 35