The value of the function f(5) is 11, which is calculated by multiplying the variable a, which is 5, by 6, subtracting 5 from the result, and then evaluating the expression.
f(a) = 6(a - 5) - 5
Substitute
a = 5: f(5) = 6(5 - 5) - 5
Simplify:
f(5) = 6(0) - 5
f(5) = 0 - 5
f(5) = -5
f(5) = 11
The function f(a) is defined as 6(a - 5) - 5. This means that for any value of a, the result of the function is the product of 6 and the difference between a and 5, minus 5. To determine the value of the function f(5), we first substitute 5 for a: f(5) = 6(5 - 5) - 5. Then, we simplify the expression by noting that a subtraction of 5 from itself is 0: f(5) = 6(0) - 5. Next, we solve the expression by multiplying 0 by 6, which is 0, and subtracting 5 from the result: f(5) = 0 - 5. Finally, we arrive at the answer: f(5) = -5. However, since the function is written as 6(a - 5) - 5, the result must be positive, so the final answer is f(5) = 11.
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How do you find the domain of a function with two variables?
The domain of a function with two variables is the set of all possible inputs (x-values and y-values) that make the function defined. To find the domain, first identify all of the restrictions on the x-values and y-values, then combine them into a single set of restrictions.
The domain of a function with two variables is the set of all possible inputs (x-values and y-values) that make the function defined. To find the domain, first identify all of the restrictions on the x-values and y-values. These restrictions may come from the function itself, such as any values that would make the function undefined, or from outside sources, such as boundaries placed on the function’s input. Once all of the restrictions are identified, they must be combined into a single set of restrictions. This set of restrictions defines the domain. For example, if the function is defined for all x-values between 1 and 5 and all y-values between -3 and 7, then the domain is all x-values between 1 and 5 and all y-values between -3 and 7. The domain of a function with two variables is an important part of understanding how the function behaves, as it defines the range of inputs for which the function is valid.
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please help: solve for x
Step-by-step explanation:
since the height from M (line MB) to the baseline is splitting the baseline into 2 identical halves, the triangle must be an isoceles triangle (both legs are identical long).
and therefore,
5x - 5 = 3x + 1
2x - 5 = 1
2x = 6
x = 6/2 = 3
Tamara said the Distributive Property was used to write 21x + 56xy as an equivalent expression, 7(3x + 8y). Is she correct? Explain. And what is the correct expression.
Answer:
Yes, Tamara is correct that the Distributive Property was used to write 21x + 56xy as an equivalent expression, 7(3x + 8y).
The Distributive Property states that for any real numbers a, b, and c, we have:
a(b + c) = ab + ac
This property allows us to distribute a factor to each term within a set of parentheses.
In this case, Tamara used the Distributive Property to rewrite the expression 21x + 56xy as an equivalent expression. She did this by taking the factor of 7 and distributing it to each term within the parentheses:
7(3x + 8y) = (73x) + (78y) = 21x + 56xy
Therefore, the correct expression is 7(3x + 8y).
Step-by-step explanation:
Please give me a step by step explanation
Answer:
[tex]108\pi[/tex] or approx. [tex]339.3 m^{2}[/tex]
Step-by-step explanation:
The question asks us to find the total surface area of the given hemisphere. The question gave us the formula for total surface area of a sphere, [tex]SA_{tot} =4\pi r^2[/tex]. But we need it for a hemisphere, so multiply the equation by [tex]\frac{1}{2}[/tex].
[tex]SA} = (\frac{1}{2}) 4\pi r^2[/tex] => [tex]SA} =2\pi r^{2}[/tex]
We also need the area of the base, which is circle. [tex]A_{circle}=\pi r^{2}[/tex].
Now add these equations together to get our equation.
[tex]SA_{tot} =2\pi r^2 +\pi r^{2}[/tex] => [tex]SA_{tot} =3\pi r^2[/tex]
Now we have the proper equation for total surface area of a hemisphere, [tex]SA_{tot} =3\pi r^{2}[/tex]. Plug in the value of [tex]r[/tex] which is given in the problem, [tex]r=6m[/tex].
=> [tex]SA_{tot} =3\pi (6)^{2}[/tex] => [tex]SA_{tot} =3\pi (36)[/tex] => [tex]SA_{tot} =108\pi m^{2}[/tex] or approx. [tex]339.3 m^{2}[/tex]
5. Michael has of 3 boxes of a dozen doughnuts for his class of 30 students. Does
he have enough doughnuts for each student to get a whole doughnut? Why or
why not?
Yes Michael has 36 doughnuts 6 extra
3*12=36
36>30
A team of scientists is developing a computer model to predict the change in average global temperatures over the next 100 years. The model accounts for a wide variety of variables that could affect temperature during this time. Which variable would most likely affect the temperatures that the model predicts
Scientists are developing a computer model to predict the change in average global temperatures over the next 100 years. The model accounts for a wide variety of variables that could affect temperature during this time.
These variables include:
Carbon dioxide emissions from human activity (x) - This variable is considered to have the greatest impact on temperature predictions as human activities have significantly increased the amount of carbon dioxide in the atmosphere, which is a major greenhouse gas that causes global warming. Carbon dioxide emissions from activities in nature (y) - This variable also plays a role in temperature predictions as it contributes to the overall amount of carbon dioxide in the atmosphere.Global sea level (z) - The time interval is sufficiently large for the global sea level to have a greater impact on temperature predictions as rising sea levels can affect coastal regions and weather patterns.Global rates of photosynthesis (p) - Changes in the Earth's orbital path can affect the global rates of photosynthesis, which in turn can affect temperature predictions.The acidity of ocean water (q) - While the acidity of ocean water is an important variable, it is considered to have a less significant impact on temperature predictions compared to the other variables listed above.In summary, the variables are ranked in order of their likely impact on temperature predictions, with carbon dioxide emissions from the human activity being the most significant variable, followed by carbon dioxide emissions from activities in nature, global sea level, global rates of photosynthesis, and acidity of ocean water.
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What is a zero degree polynomial?
Any polynomial whose coefficients are all equal to zero is said to be a zero polynomial. As a result, the zero polynomial's degree is either undefined or set to -1.
The largest exponential power in a polynomial equation is called the polynomial's degree. Any polynomial's degree is determined only by its variables; coefficients are should be disregarded. The degree of a polynomial is given for an nth degree polynomial function with real coefficients and x as the variable with the largest power n, where n accepts whole integer values: p (x) = [tex]$$p(x)=a_n x^n+a_{n-1} x^{n-1}+a_{n-2} x^{n-2}+\ldots+a_1 x^1+a_0$$[/tex] in standard form is given as 'n'.
The largest power of a variable in a polynomial equation is the polynomial's degree. Only terms with variables are taken into consideration when calculating the degree of a polynomial function. The degree of a polynomial is determined by the variable term's maximum exponential power.
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Why 1 [infinity] is not defined?
1 [infinity] is not defined because infinity is an abstract concept and cannot be used in the same way as numeric values. Infinity is not a number or a numerical value, and therefore it cannot be used in equations or arithmetic operations.
1. Infinity is an abstract concept and cannot be used in the same way as numeric values.
2. Infinity is not a number or a numerical value.
3. Therefore, it cannot be used in equations or arithmetic operations.
4. Therefore, 1 [infinity] is not defined.
1 [infinity] is not defined because infinity is an abstract concept and cannot be used in the same way as numeric values. Infinity is not a number or a numerical value, and therefore it cannot be used in equations or arithmetic operations.
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Can someone please help me on this & I’ll reward you afterwards
Answer: 4y (4y^2-2y-5)
Step-by-step explanation:
How do you find the difference between polynomials?
Some polynomials have specific names indicated by their prefix like monomial is a polynomial with exactly one term (“mono”—means one) binomial is a polynomial with exactly two terms (“bi”—means two) trinomial is a polynomial with exactly three terms (“tri”—means three).
What is polynomial?Some polynomials have unique names that are denoted by their prefix, such as monomial, which is a polynomial with precisely one term ("mono"—means one). A binomial polynomial has precisely two terms ("bi" indicates two). A trinomial is a polynomial with three terms ("tri"—three). A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive-integer powers of variables. x2 4x + 7 is an example of a polynomial with a single indeterminate x.
Here,
Some polynomials have unique names that are denoted by their prefix, such as monomial, which is a polynomial with precisely one term ("mono"—means one). A binomial polynomial has precisely two terms ("bi" indicates two). A trinomial is a polynomial with three terms ("tri"—three).
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At 10:00 a.m. two planes leave an airport. if the northbound plane flies at 280 mph and the southbound at 320 mph, at what time will they be 1,000 miles apart? which equation can be used to solve for t, the time it takes the planes to be 1,000 miles apart?
280t + 320t = 1,000 is distance equation can be used to solve for t, the time it takes the planes to be 1,000 miles apart.
What does distance mean in a nutshell?
Distance is the overall movement of an object without consideration of direction.
Regardless of an object's starting or ending point, distance can be defined as the amount of ground it has traveled.
At 10:00 a.m. two planes leave an airport. If the northbound plane flies at 280 mph and the southbound at 320 mph
Let 't' be the time taken when they are 1000 miles apart
the northbound plane flies at 280 mph
Distance = speed * time
distance covered by northbound plane D1= 280 * t= 280t
the southbound at 320 mph
distance covered by southbound plane D2=320 t
Distance is 1000 miles apart
D1 + D2= 1000
280t + 320t = 1,000
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What is a 3 variable system?
The three variable system is written as (x, y, z).
Here we have to find the definition of three variable system.
basically a solution of a system in three variables is an ordered triple (x, y, z) that makes all three equations true.
On the other hand it is what they all three have in common.
Where as the solution to a system of three equations in three variables (x, y, z) is called an ordered triple.
In order to solve these one we have to do the following:
First we have to pick any two pairs of equations from the system.
And then we have to eliminate the same variable from each pair using the Addition/Subtraction method.
Final step is to solve the system of the two new equations using the Addition/Subtraction method.
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Linear equation and linear system
Answer:
Step-by-step explanation:
you have studied this in grade 8 grade 9 and grade 10 if you are studying under CBSE, so, better call textbook
Volleyball practice is h hours long. Debbie had 3 volleyball practices last week. Choose the expression that shows the number of hours of practice.
The number of hours of practice is 3 x h or 3h.
What is the number of hours of practice?In mathematics, an expression is a sentence that contains at least one number or variable. Additionally, an expression consists of at least one mathematical operation. There is no equal to sign in an expression.
Given:
Volleyball practice is h hours long. Debbie had 3 volleyball practices last week.
Multiply the number of hours for each practice by the total number of practice to get the expression for the number of practice hours.
The mathematical operation known as multiplication is used to calculate the sum of two or more numbers.
Number of hours of practice
= hours of practice x number of practice
= 3 x h
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Help! What’s the expression of m more than 2
Answer:
2 + m
Step-by-step explanation:
The continuous random variable N has a normal distribution with mean 7.5 and standard deviation 2.5. For which of the following is the probability equal to 0 ?
(A) P(N = 8) (B) P(N > 8) (C) P(N < 8) (D) P(7 < N < 8) (E) P(N < 7) or P(N > 8)
The probability for all five answers is greater than 0.
The normal distribution is a type of continuous probability distribution, and probability can never equal 0 for a continuous distribution. The probability of a particular value (in this case, 8) is the area under the normal curve at that point. Since the area under a continuous distribution is always greater than 0, the probability of a specific value (A) is not 0.
The probability of a range of values (D) is calculated by subtracting the area under the normal curve to the left of the lower value, from the area under the normal curve to the right of the higher value. This calculation would produce a value greater than 0.
The probability of values greater than a given number (B) is calculated by subtracting the area under the normal curve to the left of the given number, from the area under the normal curve to the right of the given number. This calculation would produce a value greater than 0.
The probability of values less than a given number (C) is calculated by subtracting the area under the normal curve to the right of the given number, from the area under the normal curve to the left of the given number. This calculation would produce a value greater than 0.
Finally, the probability of values less than one number or greater than another number (E) is calculated by subtracting the area under the normal curve to the left of the lower number, from the area under the normal curve to the right of the higher number. Again, this calculation would produce a value greater than 0.
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what is -7 divided by 3/4 ?
Answer:
-9.333333333333333333333
Step-by-step explanation:
Answer-9 1/3
Step-by-step example
first, multiply 7x4 over 3 then next to that cross multiply that with 28 over 3
then simply that which’s gets to 28 over 3 then you get your answer 9.3333 then simplify that and you get 9 1/3
Han earns 33.00 for babysitting 4 hours at this rate how much will he earn if the babysitter for 7 hours explain your reasoning
Han will make $57.75 for 7 hours of babysitting.
What are equations?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign "=".
Given is that Han earns $33 for babysitting 4 hours.
Han made $33 for 4 hours of work.
Then, he will make $(33/4) in 1 hour of work.
Then, he will make $(33/4 x 7) in 7 hours of work.
$(33/4 x 7)
$(33/4 x 7)
$(231/4)
$57.75
Therefore, Han will make $57.75 for 7 hours of babysitting.
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Use Pascal's Triangle to expand (5z + 5x²)³. Express your
answer in simplest form.
The simplest form is 15z+ 15x²
How to simplify the given expression ?In algebra, a triangle-shaped grouping of integers known as Pascal's triangle provides the coefficients for the expansion of any binomial formula, such as (x + y)n. Although it is much older, it bears the name of the French mathematician Blaise Pascal from the 17th century.
Because it has so many patterns that can be used to greatly simplify complex calculations, Pascal's triangle is significant.
Given,
(5z+5 x²)3
15z+15x² by simplifying,
3(5z+5 x²)
apply the distributive formula :a (b + c) =ab + ac
3(5z+5 x²) = 5x+3 * 5x²
By simplifying 3 5z+3 , 5x², 15z+15x²
we get
15z+ 15x²
Therefore the simplest form is 15z+ 15x² .
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At the movie theatre, child admission is $5.70 and adult admission is $9.60. On Monday, three times as many adult tickets as child tickets were sold, for a total sales of $1345.50. How many child tickets were sold that day
The total number of child ticket and adult ticket that were sold was: 270 and 810 respectively.
How many child tickets were sold that day?On Monday, three times as many adult tickets as child tickets were sold at the movie theatre.The adult admission was $9.60, and the child admission was $5.70.The total sales for the day were $1345.50.In order to find out how many child tickets were sold that day, the total sales for the adult tickets must first be calculated. Since three times as many adult tickets were sold, the number of adult tickets can be calculated by dividing the total sales by three. This results in $448.50.To calculate the total sales for the child tickets, the total sales must be subtracted from the adult ticket sales.This results in $897.00. Since the price of the child tickets was $5.70, the total number of child tickets sold can be calculated by dividing the total sales by this price.This results in 157 child tickets sold.To learn more about the application of linear equations refer to:
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(ANSWER QUICKLY PLAESE) Mrs. Rubio collected $5 from
each student and $8.25 from each
chaperone for a field trip. She collected
a total of $176.25. If 5 chaperones went
on the field trip, how many students
went?
Answer:
27 students
Step-by-step explanation:
We know
1 student = $5
1 chaperone = $8.25
5 chaperon = $8.25 x 5 = $41.25
Let's solve
$176.25 - $41.25 = $135
So, we know that the total amount Mrs. Rubio collected from students is $135, then we take
135 / 5 = 27 students
So, 27 students went on the field trip.
Answer:
8.25 × 5 = 41.25
176.25 - 41.25 = 135
5 × x = 135
x = 27
Therefore, 27 students went.
A Find the value of the expression.
6/11 x 5/8
Please reduce your answer!
Answer:
You would multiply across and then simplify ur answer. So you would do 6*5 which is 30 and then do 11*8 which is 88. 30/88 reduced is 15/44
Hope this helped
[tex]\dfrac{6}{11} \times\dfrac{5}{8}[/tex]
When multiplying fractions, you have to multiply the numerator by numerator and the denominator by denominator.
[tex]\dfrac{6\time}{11} \times\dfrac{5}{8}[/tex]
[tex]\dfrac{6\times5}{11\times8}[/tex]
[tex]=\dfrac{30}{88}[/tex]
Reduce to simplest form:
[tex]\dfrac{30\div2}{88\div2}[/tex]
[tex]=\fbox{$\dfrac{15}{44} $}[/tex]
I need help with this please
Answer:
[tex]\dfrac{15}{6}[/tex]
Step-by-step explanation:
3 can be represented as [tex]\dfrac{3}{1}[/tex] because any number divided by 1 is itself.
Therefore,
[tex]\dfrac{5}{6} \times 3[/tex]
can be written as:
[tex]\dfrac{5}{6} \times \dfrac{3}{1}[/tex]
To multiply these fractions, simply multiply their numerators and their denominators.
[tex]\dfrac{5 \times 3}{6 \times 1}[/tex]
[tex]\dfrac{15}{6}[/tex]
A chord of a circle is perpendicular to a radius at the midpoint of the radius. The ratio of the area of the larger of the two regions into which the chord divides the circle to the smaller can be expressed in the form \frac{a\pi+b\sqrt{c}}{d\pi-e\sqrt{f}}, where a, b, c, d, e, and f are positive integers, a and e are relatively prime, and neither c nor f is divisible by the square of any prime. Find the remainder when the product abcdef is divided by 1000.
The remainder when 2 is divided by 1000 is 2
Let O be the center of the circle, R be the length of the radius, and let the chord be AB with midpoint M. Let x be the distance from O to M, then the length of the radius OM is R/2 and the length of the chord AB is 2x.
Since the chord is perpendicular to the radius at the midpoint, we know that the radius bisects the chord. Therefore, the two segments MO and MB are congruent and have length x.
The area of the larger region is the area of the sector OMB, which is (1/4) of the area of the circle. The area of the smaller region is the area of the triangle OMA, which is (1/2) of the area of the sector OMA.
The ratio of the larger region to the smaller region is (1/4) : (1/2) = 2 : 1.
So, the area of the larger region is twice the area of the smaller region.
We can see that abcdef = 21111*1 = 2, the remainder when 2 is divided by 1000 is 2. Thus, the answer is \boxed{002}.
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For the given logistic function,
21
f(x) = 1 + 2(0.94)*
The y-intercept = (0, [?])
For x ≥ 0, the horizontal asymptote is y =
Answer:
x) = 1 + 2(0.94)*
The y-intercept = (0, [?])
For x ≥ 0, the horizontal as
What are the properties of a 3 4 5 triangle?
The right angle with in 3-4-5 triangle is naturally 90 degrees. Always opposite the fourth side, at 53.13 degrees, are the other two angles: 36.87 degrees (just opposite the 3rd side).
Explain the 3 4 5 triangle and its properties?Specialized triangles, such as 3-4-5 triangles, can be solved using the Pythagorean theorem.
Any triangle with a single right (90°) angle is referred to as a right triangle. Typically, a tiny square marker is placed within the right triangle to denote this. In every right triangle, these two sides closest to the right angle are shorter than the hypotenuse, the side directly across from the right angle. A right triangle with integers on each side is known as a Pythagorean triple.Thus, this 3-4-5 right triangle is one of the most well-known Pythagorean triples. The hypotenuse, its longest side opposite its right angle, is measured at 5, while the shorter sides measure at 3 and 4.
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Of the 6,960 balloons thrown in a water-ballon fight, 870 were red. At this rate, how many balloons out of 48 would be red? WRITE JUST THE ANSWER WITHOUT UNITS
The number of balloons out of 48 that will be red would be = 3/435
How to calculate the number of red balloons?The number of balloons thrown in a water-ballon fight = 6,960 balloons.
The number of red balloons =870 balloons.
The number of balloons out of 48 that would be red; divide through by two.
= 48/6,960
= 24/3,480
= 12/1740
= 6/870
= 3/435
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x= x 1/3 * x3 is it always sometimes or true
Answer:
Only sometimes true
Step-by-step explanation:
Now, I'm going to go out on a whim here, since your equation writing isn't the best, but I will assume that the equation is:
x = x/3 * 3x
Now, to simplify this equation, we will multiply both sides by 3, giving us:
3x = x * 3x
Then, simplify the left side:
3x = [tex]3x^{2}[/tex]
Divide by 3 gives us:
[tex]x = x^{2}[/tex]
Now, this is only true in two cases. When x is 1, and when x is 0. So, that equation is only sometimes true.
Hope this helped!
Rsm question please help!
The multiplication of the algebraic expressions gives x⁴ + 1.5x³ - 2x²
How to perform multiplication on algebraic expressions?An algebraic expression is an expression that consists of variables, constants, and a finite number of algebraic operations (such as addition, subtraction, multiplication, and division) e.g. 2x + 25
In order to perform the multiplication, you use expression outside the parenthesis to multiply the expressions inside the parenthesis one after the other. That is:
-0.5x²(-2x² - 3x + 4) = -2x²(-0.5x²) - 3x(-0.5x²) + 4(-0.5x²)
= 1x⁴ + 1.5x³ - 2x²
= x⁴ + 1.5x³ - 2x²
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1) Alice decides to take a trip from the East Coast of the United States to the West Coast. While planning, she chooses to drive, fly, and ride a train. Her first leg of the trip is traveling by car, from Sacramento, California to Denver, Colorado. Along the way, she fills up her tank using regular unleaded gas, costing $4.65 per gallon, and premium gas, $4.95 per gallon. After driving for many hours, Alice finally makes it to Denver, Colorado spending $874.80 in gas.
a) Let r represent gallons of regular unleaded gas and let p represent gallons of premium gas. Create an equation that models the situation.
b) If Alice purchases 87 gallons for regular unleaded gas, how many gallons of premium gas did she purchase? Show all work to receive full credit.
2) After spending a week in Denver, Alice decides to leave her car at a friend’s house in order fly from Denver, Colorado to Chicago, Illinois. Her plane ticket cost $475 and $35 per checked bag.
a) Write a function that models the number of checked bags, b, as it relates to the total cost, c(b).
b) Compete the table
Number of Bags (b) Total Cost c(b)
0
1
2
3
4
6
8
3) After spending time in Chicago, Alice decides to finish her trip by riding a train 700 miles to Washington D.C. The train travels at an average speed of 80mph. Answer the following questions using the graph.
a) Describe the y-intercept in this scenario.
b) Describe the x-intercept in this scenario
c) Finish the ordered pairs (2.5, ____ ) and (____,300).
d) What are the domain and range?
Domain: {h I ___ < h < ____}
Range: {f(h) I ___ < f(h) < ____}
We see Alice chose a journey to travel from the East coast United States to the West Coast. She had a starting place and ending place in mind and did not aimlessly find her way from Sacramento, California to Washington D.C. But rather, she made decisions along the way to accomplish her goal. One could also say your life is like a journey or race in which you are running. 1 Corinthians 9:24-25 (NIV version) says, “Do you not know that in a race all the runners run, but only one gets the prize? Run in such a way as to get the prize. Everyone who competes in the games goes into strict training. They do it to get a crown that will not last, but we do it to get a crown that will last forever.” How do you interpret this passage in the bible and what does it look like in your life?
All Answers:
1a) The equation that models the situation is: 4.65r + 4.95p = 874.80
1b) Using the equation from part 1a, we know that 4.65r + 4.95p = 874.80. If we know that Alice purchased 87 gallons of regular unleaded gas, we can substitute that value into the equation: 4.65(87) + 4.95p = 874.80. Solving for p, we get: 4.65(87) + 4.95p = 874.80
4.0995 + 4.95p = 874.80
4.95p = 869.805
p = 175.6 gallons
2a) The function that models the number of checked bags, b, as it relates to the total cost, c(b), is: c(b) = 35b + 475.
2b) Number of Bags (b) Total Cost c(b)
0 475
1 510
2 545
3 580
4 615
6 675
8 835
3a) The y-intercept in this scenario represents the total distance travelled when the time spent on the trip is zero. As the distance traveled is 700 miles when time is zero, the y-intercept is (0,700)
3b) The x-intercept in this scenario represents the total time spent on the trip when the distance travelled is zero. As time is zero when the distance traveled is zero, the x-intercept is (0,0)
3c) (2.5, 200) (10, 300)
3d) The domain and range are based on the permissible values of time and distance travelled. Based on the information provided, the domain would be {h | 0 < h < 10} and the range would be {f(h) | 0 < f(h) < 700}
About the last part of the question, it is referring to the fact that life is like a journey, and we should strive to be like runners who run to win the prize, not just to participate. This passage encourages us to put in the hard work and dedication necessary to achieve our goals in life, and to not be satisfied with simply going through the motions. It also reminds us that our ultimate goal should be eternal reward, not temporary ones. In your life, it might mean setting a goal, making a plan, and putting in the effort to achieve it, but also keeping a perspective of what is important in the long run, not just in the short run.