The solution of the linear inequality 2x + 8 > x + 10 > 3x + 9 is:
X>2 and X<1/2
What is linear inequalities?When two mathematical expressions or two numbers are compared in an unequal way, it is called an inequality in mathematics. Inequalities can generally be classified as either numerical, algebraic, or a combination of the two. A polynomial of degree 1 is compared to another algebraic expression of degree less than or equal to 1, which is the case in a linear inequality, which is an inequality involving at least one linear algebraic expression.
step1:
2x + 8 > x + 10 > 3x + 9
2x+8>x+10 and x+10>3x+9
2x + 8 > x + 10 :X>2
X+10>3X+9:X<1/2
Step2:
X>2 and X<1/2
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A large church has a niche in one wall. On the floor plan it appears as a semicircular indentation of radius 2.60 m. A worshiper stands on the center line of the niche, 1.70 m out from its deepest point, and whispers a prayer. Where is the sound concentrated after reflection from the back wall of the niche
40m is the sound concentrated after reflection from the back wall of the niche.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
with radius 2.60m , the cylindrical wall is a highly efficient mirror for sound , with focal length
f = R/2 = 2.60/2 = 1.30
in a vertical plane the sound disperses as usual butthat radiated in a horizontal plane is concentrated in a soundimage at a distance q from the back of niche ,
so 1/p+1/q = 1/f
so 1/1.70 +1/q = 1/1.3
1/q = 1/1.3 - 1/1.70
q = 40m
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Please help find the variable in both triangles.
Step-by-step explanation:
these are projections from V and W to the same projection "screen" (SU and YX).
since the angles are equal, the ratio between projection beam length and screen length must be the same.
so,
6.
24/14 = 48/x
48/28 = 48/x
x = 28
7.
besides the projection principle, we have a basic triangle situation :
the bisector of the angle W is also bisecting the opposing side YX. that means that this is an isoceles triangle (both legs are equally long).
therefore,
y = 4×sqrt(2)
Answer:
[tex]\textsf{6.} \quad x = 28[/tex]
[tex]\textsf{7.} \quad y = 4\sqrt{2}[/tex]
Step-by-step explanation:
What is an angle bisector?An angle bisector is a line that divides an angle into two equal parts.
Angle Bisector TheoremAn angle bisector in a triangle divides the opposite side into two segments which are in the same proportion as the other two sides of the triangle.
Question 6Applying the Angle Bisector Theorem:
[tex]\implies \dfrac{UT}{TS}=\dfrac{VU}{VS}[/tex]
[tex]\implies \dfrac{x}{14}=\dfrac{48}{24}[/tex]
Cross multiply:
[tex]\implies 24 \cdot x=48 \cdot 14[/tex]
[tex]\implies 24x=672[/tex]
Divide both sides by 24:
[tex]\implies \dfrac{24x}{24}=\dfrac{672}{24}[/tex]
[tex]\implies x=28[/tex]
Question 7Applying the Angle Bisector Theorem:
[tex]\implies \dfrac{XZ}{ZY}=\dfrac{WX}{WY}[/tex]
[tex]\implies \dfrac{4}{4}=\dfrac{y}{4\sqrt{2}}[/tex]
Carry out the division on the left side:
[tex]\implies 1=\dfrac{y}{4\sqrt{2}}[/tex]
Multiply both sides by 4√2:
[tex]\implies 1\cdot 4\sqrt{2}=\dfrac{y}{4\sqrt{2}}\cdot 4\sqrt{2}[/tex]
[tex]\implies 4\sqrt{2}=y[/tex]
[tex]\implies y=4\sqrt{2}[/tex]
The following curve passes through (3,1). Use the local linearization of the curve to find the approximate value of y at x
m = the slope of the curve at x=3 and b = the y-intercept at x=3. Therefore, the approximate value of y at x=2
We can use the local linearization of the curve to approximate the value of y at x=2.
The local linearization of the curve is given by the equation y = mx + b, where m is the slope of the curve at x=3 and b is the y-intercept at x=3.
Let m be the slope of the curve at x=3 and b be the y-intercept at x=3.
The slope of the curve at x=3 can be found by calculating the derivative of the curve at x=3.
The y-intercept at x=3 can be calculated by substituting x=3 into the equation of the curve and solving for y.
Therefore, m = the slope of the curve at x=3 and b = the y-intercept at x=3.
Substituting the values of m and b into the equation of the local linearization, we get the equation y = mx + b.
Substituting x=2 into the equation, we get y ≈ 0.5 + 1 = 1.5.
Therefore, the approximate value of y at x=2
The local linearization of the curve can be used to approximate the value of y at x=2. Substituting x=2 into the equation, we get y ≈ 1.5, which is the approximate value of y at x=2.
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The following scatter plot shows the billions of dollars spent by travelers in the United States since 1993.
Write an equation for the line of best fit and then predict how much money travelers will spend in 2008.
A.y=2x+380 travelers will spend about $410 billion in the year 2008.
B.y=2x+320 travelers will spend about $350 billion in the year 2008.
C.y=20x+320 travelers will spend about $620 billion in the year 2008.
D.y=20x+380 travelers will spend about $680 billion in the year 2008.
The equation for the line of best fit that predicts how much money travelers will spend in 2008 is y = 20x + 320.
What is the equation of the line?
The equation y = mx + c is the general equation of any straight line where m is the gradient of the line (how steep the line is) and c is the y-intercept (the point at which the line crosses the y -axis).
This is a linear function,
let's say the equation is y =ax + b,
the points (1.5, 350) and (4, 400)
a = (400-350) /(4 - 1.5)
= 50/2.5
= 20
y = 20x + b,
350 = 20(1.5) + b
350 = 30 + b
350 -30 = b
b = 320
y = 20x + 320
so, in 2008,
x =15,
y = 20(15) + 320 = 300 + 320 = 620
Hence, the equation for the line of best fit that predicts how much money travelers will spend in 2008 is y = 20x + 320.
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Suppose a student named Marcus wants to learn about the sleeping habits of students in his class. Marcus wants to collect data from his classmates to learn how many hours of sleep his classmates get. He then wants to process this data with a computer and visualize it in a Histogram. Which of the following would be the best technique for Marcus to collect this data
From the above given options by using app is more accurate and reliable so option b is correct
The question is incomplete the options are not given the options are:
a. Marcus should ask each of his classmates to write down on a piece of paper how many hours of sleep they get per night and hand the paper to him.
b. Marcus should have them download an app that tracks their phone geolocation and activity so he can see when their phones are in their rooms and not being used. From this data he can figure out how long each student sleeps.
given that
Marcus wants to learn about the sleeping habits of students in his class.
Marcus wants to collect data from his classmates to learn how many hours of sleep his classmates get.
He then wants to process this data with a computer and visualize it in a Histogram
survey can be done in different ways:
1. by asking question
2. survey
3. observation
From the above given options by using app is more accurate and reliable so option b is correct
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Mary and Ryan each have some sweets.
The ratio of the number of sweets Mary has to the number Ryan has is 3:2
If Mary gave 5 sweets to Ryan they would have the same number of sweets.
Work out how many sweets Mary and Ryan have altogether.
Answer:
Let x be the number of sweets that Ryan has.
Since the ratio of the number of sweets Mary has to the number Ryan has is 3:2, we can say that Mary has 3/2*x sweets.
We know that if Mary gave 5 sweets to Ryan they would have the same number of sweets, so we can write the following equation:
3/2*x -5 = x
By solving this equation, we can find that x = 10. So, Ryan has 10 sweets
Therefore, Mary has 3/2*10 = 15 sweets.
Altogether, Mary and Ryan have 15+10 = 25 sweets.
Answer: 25
Step-by-step explanation:
3x - 5 = 2x, so
x = 5.
And 5x = 5*5 = 25
what are the four conditions necessary for x to have a binomial distribution? mark all that apply.
Characteristic of binomial distribution Mean should be n *p n is the number of trials p is the successful outcome of the process
a set number of trials, such as three rolls of the dice or five flips of the coin.Each trial can either be successful or unsuccessful. Note that the example with the die seems to have six possible outcomes. We must take into account options like "get a 6" (success) or "not obtain a 6." (failure).The likelihood of success must be constant (equal for every try). P(6) = 1/6 for each roll of the die in the example.The trials are separate. The likelihood of success in future trials is unaffected by the outcome of the first.Know more about binomial at:
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Simplify using order of
operations.
3.10(9 + 1)² 2
PEMA
MD
AS
The value of the expression 3.10(9 + 1)²2 is 620.
What is PEMDAS?The abbreviation PEMDAS is used to indicate the sequence of steps to be taken when resolving expressions with multiple operations. P is for "parentheses," E is for "exponents," M is for "multiplication," D is for division, A is for addition, and S is for subtraction.
Given:
An expression,
3.10(9 + 1)²2.
Solving the expression by the help of PEMDAS,
First, we solve the parenthesis,
3.10(10)²2
= 3.10 x 100 x 2
Now, applying multiplication,
3.10 x 100 x 2,
= 620
Therefore, the value is 620.
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Can someone help me with this? I need an equation and the cup of nuts. It’s due tmr
Answer:
Step-by-step explanation:
I assume that the amount of peanut butter chips in original recipe is [tex]1\frac{1}{2}[/tex] c (the picture isn't clear!)
2( [tex]1\frac{1}{2}[/tex] + x ) = [tex]4\frac{1}{2}[/tex]
[tex]1\frac{1}{2}[/tex] + x = [tex]4\frac{1}{2}[/tex] ÷ 2
[tex]1\frac{1}{2}[/tex] + x = [tex]2\frac{1}{4}[/tex]
x = [tex]2\frac{1}{4}[/tex] - [tex]1\frac{1}{2}[/tex] = [tex]1\frac{5}{4}[/tex] - [tex]1\frac{2}{4}[/tex] = [tex]\frac{3}{4}[/tex]
There is [tex]\frac{3}{4}[/tex] of a cup of nuts in original recipe.
Use the distributive property to remove the parentheses
(-4+v+4x)(-6)
By distributive property for real numbers, the expression (- 4 + v + 4 · x) · (- 6) is equivalent to the expression 24 - 6 · v - 24 · x.
How to use distributive property
In real algebra, distributive property is an algebraic property where a real number is "distributed" on every term of a sum of real numbers. This property is described below:
c · (a + b) = a · c + b · c
Where a, b, c are real numbers.
Now we proceed to use distributive property in the following case. First, write the entire expression:
(- 4 + v + 4 · x) · (- 6)
Second, apply distributive property:
(- 6) · (- 4) + (- 6) · v + (- 6) · (4 · x)
Third, use associative property:
(- 6) · (- 4) + (- 6) · v + [(- 6) · (4)] · x
Fourth, use sign laws and multiply on each term:
24 - 6 · v - 24 · x
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1. please help me. 3 divide 255 2. 16 divide 368 3. 65 divide 2 210
The answer of the given conditions is 255/3 =83, 368/16 = 23 and 2 210/65 = 34.
What are the numerator and denominator?
For example, 4/5 is a fraction, and the line separating the numbers 4 and 5 is the fraction bar. Here the number above the fraction bar is the numerator, and the one below the fraction bar is the denominator. A numerator represents the number of parts out of the whole, which is the denominator.
3 divided by 255 is equal to 3/255.
16 divided by 368 is equal to 16/368.
65 divided by 2 210 is equal to 65/2210.
Note that for 2 and 3 the numerator and denominator have been swapped and the division is not correct, it should be 368/16 = 23 and 2 210/65 = 34
Hence, the answer of the given conditions are 255/3 =83, 368/16 = 23, and 2 210/65 = 34.
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Flu is spreading exponentially at a school. The number of new flu patients can be modeled using the
equation F=10e^0. 12d, where d represents the number of days since 10 students had the flu.
(a) How many days will it take for the number of new flu patients to equal 50? Determine your answer
algebraically using the natural logarithm. Round your answer to the nearest day
If the number of flu patients at the school is modelled by the equation [tex]F=10e^{0. 12d}[/tex] , then the number of days that it will take for the number of patients to reach 50 is 13 days .
The Exponential Growth equation is given as : [tex]F=10e^{0. 12d}[/tex] ;
We have to find How many days will it take for the number of new flu patients to equal 50 .
So , we substitute the value [tex]F=50[/tex] in the model equation ;
we get ;
⇒ [tex]50 = 10e^{0. 12d}[/tex] ;
dividing both side by 10 ,
we have ;
⇒ [tex]5=e^{0. 12d}[/tex] ;
taking [tex]\ln[/tex] on both sides ,
⇒ [tex]\ln 5 = 0.12d(\ln e)[/tex] ,....we know that [tex]\ln e = 1[/tex] ;
⇒[tex]d= \frac{\ln 5}{0.12}[/tex] ⇒ 13.41198 ;
≈ 13 days .
Therefore , it will take 13 days for the number of patients to reach 50 .
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what is the positive and negative to this question
The positive and negative roots of the given quadratic graph are; -2 and 4.
What are the roots of the quadratic graph?We want to find the positive and negative roots of the quadratic graphs. Now, the general form of quadratic equations is expressed as;
y = ax² + bx + c
Now, for a quadratic graph, the roots are defined as the value of x where the curve crosses the x-axis.
In this given graph, we can see that the y-intercept which is the point at which the curve crosses the y-axis is at y = -8. We also see that the points at which the graph crosses the x-axis are at x = -2 and x = 4. This clearly shows that one root is positive and one root is negative.
Therefore from the two x-intercept values above as well as the y-intercept we got and when considering the type of roots that are being looked for, we can easily conclude that the positive and negative roots are as gotten above.
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The mean number of accidents a week at a company is 6. 4 with a standard deviation of 1. 5. What proportion of weeks would you expect to have more than 7 accidents?
The mean number of accidents that would be expected to be more than 7 accidents is 0.6554.
What is mean?By dividing the sum of the given numbers by the entire number of numbers, the mean—the average of the given numbers—is determined.
What is z-score?A statistical measurement known as the Z-score indicates how closely a value relates to the mean of a collection of values. The Z-score is calculated using standard deviations from the mean. When a data point's Z-score is 0, it means that it has the same score as the mean. One standard deviation from the mean would be indicated by a Z-score of 1.0.
Given that mean is 6.4 and the standard deviation is 1.5.
The z score is used to determine the accidents:
z = 7 - 6.4 / 1.5
z = 0.4
Using the table of normal distribution we have, P(x > 7 ) = P(z > 0.4) = 0.6554
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What is no solution called?
An inconsistent system is a set of equations that have no solution.
Consider the following as the lines' equation:[tex]p_1x+q_1y+a_1=0 , p_2x+q_2y+a_2=0[/tex]
We can start analyzing the equations of lines and evaluating their various properties now that we understand how to display points on a coordinate plane and graph linear equations. The common forms for writing linear equations and the characteristics of lines that can be inferred from their equations are covered in this section.
If both lines are parallel to one another, there is no answer because the lines never cross.
In such a circumstance, the pair of linear equations in two variables is considered to be inconsistent because algebraically, [tex]\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}[/tex].
For example, line of equations are
[tex]2x-y=4\\\\4x-2y=8[/tex]
[tex]\frac{a_1}{a_2}=\frac{2}{4}=\frac{1}{2}\\\frac{b_1}{b_2}=\frac{1}{2}\\\frac{c_1}{c_2}=\frac{4}{8}=\frac{1}{2}[/tex]
Here, both equation has no solution so equation are called inconsistent equation.
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14. Katherine jogs 6m. The distance she
h
travels in x hours is represented by
mi
k(x) = 6x. Julio jogs 4-
h
he travels in x hours is represented by
j(x) = 4x.
a. Graph and label k(x) = 6x, and
j(x) = 4x.
Distance (mi)
AY
24
The distance
16
0
2
Time (h)
X
b. Who travels further in 4 hours, and
how far does this person travel?
c. Which function has a greater slope?
Answer: ANSWERS BELOW
Step-by-step explanation:
Part A.
At time = 1 hour, k(x) = 6 and f(x) = 4.
At time = 2 hours, k(x) = 12 and f(x) = 8.
At time = 3 hours, k(x) = 18 and f(x) = 12.
At time = 4 hours, k(x) = 24 and f(x) = 16.
- - -
Part B.
Katherine travels farther within 4 hours. She travels 24 miles in 4 hours, which is 8 more than Julio travels.
- - -
Part C:
The function k(x) has a greater slope. It has a slope of 6, while k(x) has a slope of 4.
What is the value of 1 − 2 × 3 + 4 ÷ 5 ?
Answer: -4.2
Step-by-step explanation:
=1-6+0.8
=-4.2
Please math is rally hard can someone help me? I’m struggling so bad right now
Explanation:
The two interior angles 55 and 6x+8 add to the exterior angle 14x-1; this exterior angle is not adjacent to the interior angles mentioned.
Refer to the Remote Interior Angle Theorem for more information.
So,
55+(6x+8) = 14x-1
6x+63 = 14x-1
6x-14x = -1-63
-8x = -64
x = -64/(-8)
x = 8
Then we can determine angle T
angle T = 6x+8 = 6*8+8 = 56 degrees
2. is line parallel to line ? choose the best justiication. a. line is parallel to line because triangle is a dilation of triangle by a scale factor of 3 from point . b. line is parallel to line because triangle is a dilation of triangle by a scale factor of 2 from point . c. line is parallel to line because triangle is a dilation of triangle by a scale factor of from point . d. line is not parallel to line because there is no dilation that sends triangle to triangle .
Line is not parallel to line because no scaling from point can transform triangle into triangle.
Line is not parallel to line because there is no transformation that can send triangle to triangle. A transformation is a function that changes the location, size, or orientation of an object. A dilation of a shape is a transformation that changes its size, either making it larger or smaller, but does not change its orientation. To determine if two lines are parallel, one must consider if a dilation from a point can send one line to the other. In this case, there is no dilation from point that can send triangle to triangle, so line is not parallel to line.
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3. Apply Math Models The height of a flag
pole is 20 feet. The distance from the top of
the flag pole to a point that is 21 feet from
the base of the pole is 28.9 feet. Does the
flag pole form a 90° angle with the ground?
No, the flag pole does not form a 90° angle with the ground.
We can use the Pythagorean theorem to find the length of the flag pole, which states that in a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side (the hypotenuse).
Let x be the length of the flag pole. Then, we have:
x² = (20 - x)² + 28.9²
Expanding and solving for x, we get x = 30.8.
Therefore, the length of the flag pole is 30.8 feet, which is greater than the height of 21 feet. This means that the angle between the flag pole and the ground is not 90°, but rather less than 90°.
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What is 2 and 3 over 4 times 5 and 1 over 3?
The answer to the word problem is 14 2/3.
What is a fraction?A fraction shows part of a whole. This whole can be a region or a collection. The word fraction is derived from the Latin word "fractio" which means 'to break'. fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
Expressing the word problem into an expression;
2 3/4 x 5 1/3
= 11/4 x 16/3
= 44/3
= 14 2/3
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The answer and explanation
The requried value of 'a' in the given expression is a = -12.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
8⁻⁵⁵ / 8ᵃ = 8⁻⁴³
8ᵃ = 8⁻⁵⁵ / 8⁻⁴³
8ᵃ = 8 ⁻⁵⁵ ⁺ ⁴³
8ᵃ = 8⁻¹²
Taking logs on both sides
a ln 8 = -12 ln 8 [lnbˣ = x lnb]
a = -12
Thus, the requried value of 'a' in the given expression is a = -12.
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For each sequence find the first 4 terms and the 10th term.
A)n^2+6
B)3n^2
The first 4 terms and the 10th term of the sequences are listed below
How to determine the terms of the sequenceFrom the question, we have the following parameters that can be used in our computation:
Calculate the first 4 terms and the 10th term.
A)n^2+6
Here, we have
First = 1^2 + 6 = 7
Second = 2^2 + 6 = 10
Third = 3^2 + 6 = 15
Fourth = 4^2 + 6 = 24
Tenth = 10^2 + 6 = 106
B)3n^2
Here, we have
First = 3 * 1^2 = 3
Second = 3 * 2^2 = 12
Third = 3 * 3^2 = 27
Fourth = 3 * 4^2 = 48
Tenth = 3 * 10^2 = 300
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Type the correct answer in each box. Spell all words correctly, and use numerals instead of words for numbers.
Leslie and Joanne are in the same class. Their school day is 6 hours long. Joanne said that she was in school for 360 minutes. Leslie said she was in school for 320 minutes. Complete the table below to see who is correct.
Answer:
.
Step-by-step explanation:
I just need to know the which one is the answer out of (1-4) questions. Please help??
Answer:
1/ 14^4
Step-by-step explanation:
Rules of Exponents
We know that a^-b = 1/a^b
14^-4 = 1/ 14^4
Answer:
[tex]{14}^{ - 4} = \frac{1}{ {14}^{4} } [/tex]
Step-by-step explanation:
To find the answer for this, you have to follow the negative rule of exponents.
That is,
1) If the number with a negative power is in it's numerator, the number with a negative exponent should be put to the denominator and make the power positive.
2) If the number with a negative power is in it's denominator, the number with a negative exponent should be put to the numerator and make the power positive.
Here, we have follow the rule 1.
Ex:
[tex] {a}^{ - n} = \frac{1}{ {a}^{n} } [/tex]
Accordingly, let us find the answer for the question.
[tex] {14}^{ - 4} = \frac{1}{ {14}^{4} } [/tex]
Find the values of the variables. Then find the side lengths of the square.
X=?
y=?
Answer:
multiply 16-y this is correct
Step-by-step explanation:
it is a square.
so, all sides are equally long.
that means e.g.
y - 3 = 2y - 11
-3 = y - 11
8 = y
and then
3x - 10 = 3y - 19 = 3×8 - 19 = 24 - 19 = 5
3x = 15
x = 15/3 = 5
so the length of all 4 sides is by using e.g.
y - 3 = 8 - 3 = 5
each side is 5 units long.
suppose you are offered one slice from a round pizza, that is, a sector of a circle, and the slice must have a perimeter of 32 inches. what diameter pizza will produce the largest slice?
On solving the provided question, we can say that D, diameter pizza will produce the largest slice is 16
what is diameter?Any straight line segment with an endpoint on the circle and that travels through its center is considered a circle's diameter in geometry. The longest chord of a circle is another way to describe it.
Let r be the radius and be the angle of a circle.
According with the graph, the area of the sector is given by
A = 1/2r^2∅
The arc length of a circle with radius r and angle∅ is r∅
The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length
The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches.
Thus the perimeter has length
2r + r∅ = 32 in
r∅ = 32 - 2r
∅ = 32- 2r / r
Now,
A = 1/2r^2[32- 2r / r]
A = 16r - r^2
A' = 16 - 2r 16 -2r = 0
r = 8
A" = -2
so, D, diameter pizza will produce the largest slice is 16
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a cyclist rides at a average speed of 18km/h for 9 minuets. work out the distance traveled by the cyclist in km
Answer: d=162km
Step-by-step explanation:
the equation of this question is:
speed = distance / time
s=d/t
18=d/9
d=18*9
d=162km
what is the area of a triangle if the legs ar5e x and y long. if the first leg of the triangle is x and the length of the second leg is y, the formula
The area of a triangle is Area = sqrt(s(s-x)(s-y)(s-c)).
The area of a triangle can be found using the Heron's formula if we know the lengths of all three sides, or using the formula (1/2) * x * y if we know the lengths of two legs and the triangle is a right triangle.
In the case where the legs of the triangle are x and y long, if we don't know if the triangle is a right triangle, we can't use the formula (1/2) * x * y. However, we can use Heron's formula to calculate the area. Heron's formula states that the area of a triangle is equal to the square root of s(s-a)(s-b)(s-c), where s is the semi-perimeter of the triangle and a, b, and c are the lengths of the three sides.
In this case, since we know the lengths of the two legs x and y, we can find the area of the triangle using Heron's formula as follows:
s = (x + y + c)/2
Area = sqrt(s(s-x)(s-y)(s-c))
Where c is the length of the hypotenuse of the triangle, this information is not provided, so we cannot calculate the area of the triangle.
Therefore, The area of a triangle is Area = sqrt(s(s-x)(s-y)(s-c)).
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20 children lineup to ride go carts.The go cart operator collects two dollars from each child in order from the first to the 20th in line. do the ordered pairs (child number, amount paid) represent a function? explain your reasoning.
Yes, the ordered pairs (child number, amount paid) represent a function.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Number of children = 20
Cost per children = $2
Now,
The ordered pairs are:
(1, 2), (2, 4), (3, 6), (4, 8), (5, 10), (6, 12), (7, 14), (8, 16), (9, 18), (10, 20),
(11, 22), (12, 24), (13, 26), (14, 28), (15, 30), (16, 32), (17, 34), (18, 36), (19, 38), (20, 40)
The ordered pairs are a function.
A function can be one-to-one or many-to-one but not one-to-many.
We see that the ordered pairs are one-to-one.
Thus,
The ordered pairs are functions.
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