The correct answer is "The extreme value theorem applies, and f(x) has both a minimum and a maximum."
What is the extreme value theorem?
The extreme value theorem states that if a function is continuous on a closed interval, then it must have both a maximum and a minimum value on that interval. To determine whether the extreme value theorem applies to the graph of f(x), we need to check if the function is continuous on a closed interval and whether it has a highest and lowest point within that interval.
Looking at the graph of f(x), we can see that the function is continuous on the closed interval [-3, 3] since it has no breaks or jumps. Additionally, the graph has the highest point at (1, 2) and the lowest point at (-3,-2). Therefore, we can conclude that the extreme value theorem applies and that f(x) has both a minimum and a maximum value on the interval [-3, 3].
Therefore, the correct answer is (a) "The extreme value theorem applies, and f(x) has both a minimum and a maximum."
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SUPER EASYYY PLEASE ANSWER THIS
Answer:
The y-intercept represents a starting salary of $32,500.
The slope represents an additional $2,500 in salary for each additional year of employment.
If the starting salary for a new employee is changed to $35,000 and the yearly salary increase is unchanged, the new equation would be
[tex]y=2500x+35000[/tex].
If the yearly salary increase is changed to $3,000 and the starting salary remains the same, the new equation would be
[tex]y = 3000x + 32500[/tex].
Step-by-step explanation:
Answer:
The y-intercept represents a starting salary of $32,500.
The slope represents an additional $2,500 in salary for each additional year of employment.
If the starting salary for a new employee is changed to $35,000 and the yearly salary increase is unchanged, the new equation would be
y=2500x+35000y=2500x+35000 .
If the yearly salary increase is changed to $3,000 and the starting salary remains the same, the new equation would be
y = 3000x + 32500y=3000x+32500 .
36. You drop a ham that weighs 9.25 lbs from a height of 1.45m. Right before it hits the ground, it has a velocity of 5.33m/s. Given that the impact of the ham and the tile floor has a coefficient of restitution or 0.35, how high will it bounce after impact? (1 point)
The ham will bounce to a height of 0.16 meters after the impact.
Define Potential Energy.It is the energy that an object possesses by virtue of its position or configuration, or as a result of its composition. The potential energy of an object can be converted into kinetic energy, which is the energy of motion.
initial potential energy of the ham:
PE = mgh
where m is the mass of the ham, g is the acceleration due to gravity, and h is the initial height from which the ham is dropped. Substituting the given values, we get:
PE = (9.25 lbs)× (1 kg/2.205 lbs) × (9.81 m/s²) × (1.45 m) ≈ 61.8 J
At the moment just before the ham hits the ground, all of this potential energy is converted into kinetic energy:
KE = (1/2)mv²
where v is the velocity of the ham just before impact. Substituting the given values, we get:
KE = (1/2) × (9.25 lbs) × (1 kg/2.205 lbs)×(5.33 m/s)²≈ 87.8 J
After the impact, some of this kinetic energy is lost due to the coefficient of restitution, which is the ratio of the velocity after impact to the velocity just before impact:
e = v'/v
where v' is the velocity after impact. Substituting the given values, we get:
0.35 = v'/5.33
Solving for v', we get:
v' ≈ 1.86 m/s
Now, we can use the conservation of energy to find the maximum height to which the ham bounces. At this point, all of the remaining kinetic energy has been converted back into potential energy:
KE = (1/2)mv'² = mgh'
where h' is the maximum height to which the ham bounces. Substituting the given values, we get:
(1/2) × (9.25 lbs) × (1 kg/2.205 lbs) ×(1.86 m/s)² = (9.81 m/s²) ×h'
Solving for h', we get:
h' ≈ 0.16 m
Therefore, the ham will bounce to a height of approximately 0.16 meters (or 16 centimeters) after the impact.
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use each of the three corresponding base and height pairs to find the area of the triangle. Will the area be the same of each calculation? explain
The area of the triangle depends on the base and height pair used, and different pairs will result in different areas.
What is triangle?A triangle is a geometric shape that consists of three straight sides and three angles. It is a polygon with three sides. The sides of a triangle are connected by its vertices or corners. The triangle is one of the simplest and most fundamental shapes in geometry, and it has many important properties and applications. Triangles have many practical applications in everyday life and in various fields, such as architecture, engineering, and physics. The study of triangles and their properties is an important part of mathematics and geometry.
Here,
I'll provide a general explanation of how to calculate the area of a triangle using different base and height pairs.
The area of a triangle is calculated using the formula:
Area = (base * height) / 2
So, if you have three different base and height pairs for a triangle, you can calculate the area using each pair and see if the area is the same for each calculation.
For example, let's say we have the following base and height pairs for a triangle:
Pair 1: base = 4, height = 5
Pair 2: base = 6, height = 3
Pair 3: base = 8, height = 2
Using the formula, we can calculate the area of the triangle for each pair:
Area 1 = (4 * 5) / 2 = 10
Area 2 = (6 * 3) / 2 = 9
Area 3 = (8 * 2) / 2 = 8
As you can see, the area is not the same for each calculation. However, the sum of the areas of the triangles formed by each pair of base and height would always be equal to the area of the triangle formed by the overall base and height.
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One of your co-workers is giving a presentation on the results of an analysis the two of you have been working on. Someone in the audience points out that the data system you used has frequent errors. How should you deal with this comment?
Answer:
As a co-worker, you should support your colleague by offering to address the question. Here are some steps to consider:
Acknowledge the concern: Begin by thanking the person for their comment and acknowledging their concern about the data system. This will help to show that you are open to feedback and willing to listen.
Provide context: If appropriate, offer some context about the data system that was used. For instance, if the system was chosen due to budget or resource constraints, you can explain why that decision was made.
Offer a solution: Explain what steps were taken to ensure the accuracy of the data, despite the known issues with the system. If there were steps taken, share those with the audience. Alternatively, offer to follow up with the audience member after the presentation with more information on how the team plans to address the issue.
Stay professional: Be calm, professional, and open-minded throughout the conversation. Avoid getting defensive or argumentative. Instead, focus on addressing the issue in a constructive manner.
By following these steps, you can help to address the concern in a professional and effective manner.
The sum of two numbers is 35. The first number minus twice the second number is 8. Find the two numbers
Answer:
the first number is 26
the second number is 9
Step-by-step explanation:
given the first number is x and the second number is y
then x + y = 35
x - 2y = 8 => x = 2y + 8
substitute 2 equations
(2y + 8) + y = 35
3y = 35 - 8
3y = 27
y = 27/3 = 9
x = 35 - y = 35 - 9 = 26
Answer:
The first number is 26
the second number is 9
Step-by-step explanation:
If x represent the first number.
Since the sum of the numbers is 35, the second number is 35-x.
Then the relation between the two numbers is by the equation :
x - 2(35-x) = 8 3x -70 = 8 . . . . simplify 3x = 78 . . . . . . . and by add 70 x = 26 . . . . . .and divide by 3 . . . this is the first number 35-x = 9 . . . . the second numberThe first number is 26 the second number is 9simplify these expressions 13xyz +9 +2xyz + 3 and 6ab + (-2ab) + 4 + 6
The expressions are simplified to give;
15xyz + 12
4ab + 10
What are algebraic expressions?
Algebraic expressions are simply defined as mathematical expressions that are known to contain variables, constants, coefficient, factors and terms.
These algebraic expressions are also known to be made up of mathematical operations, such as;
SubtractionAdditionMultiplicationDivisionBracketParenthesesFloor division, etcFrom the information given, we have that;
13xyz +9 +2xyz + 3
Now, collect the like terms, we have;
13xyz + 2xyz + 9 + 3
Add the values
15xyz + 12
6ab + (-2ab) + 4 + 6
expand the bracket and collect like terms
4ab + 10
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A recipe calls for 14 teaspoons of sugar to make 168 milliliters of coffee what is the constant of proportionality that relates the number of milliliters of coffee made y to the Numbers of teaspoons of sugar used x
Answer:
Step-by-step explanation:kk
The constant of proportionality that relates the number of milliliters of coffee made y to the number of teaspoons of sugar used x is 12.
Why is that, therefore, if K is the proportionality constant?When two variables are directly or indirectly proportional to one another, their relationship can be represented as y = kx or y = k/x, where k denotes the direction of the relationship between the two variables. It is known as the proportionality constant, or k.
We must determine the ratio of the two amounts in order to determine the constant of proportionality that connects the number of teaspoons of sugar used x to the number of millilitres of coffee brewed y.
Considering the information provided, we understand that:
168 millilitres of coffee require 14 tablespoons of sugar.
As a result, the following is the relationship between the quantity of coffee prepared and the quantity of sugar used in teaspoons:
y/x = 168/14
Reducing the ratio:
y/x = 12
This indicates that 1 teaspoon of sugar is needed to make every 12 millilitres of coffee.
As a result, 12 is the constant of proportionality that links the quantity of coffee created (y) to the quantity of sugar utilised (x).
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Aubrey wants to know how students in her school feel about the new intramural sports program being developed. She randomly selects the names of 100 students and e-mails them a survey. She waits for responses and records data from the 32 surveys that are returned to her. Is her sample biased? Explain.
Her sample is in fact biased, as the sampling method used was voluntary sampling, which results in self-selection bias.
What is voluntary sampling and why it is biased?Voluntary sampling is a type of sampling method in which individuals are invited to participate in a study or survey based on their willingness or availability to do so. In other words, individuals choose to participate in the study, rather than being selected randomly by the researcher.
Voluntary sampling is chosen for this problem as the students had the option to answer the e-mail or not.
A limitation of voluntary sampling is that the individuals who choose to participate in the study may not be representative of the larger population from which they were drawn, leading to biased results.
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The speed of light is 299,792,458 meters per second. How would you write the approximate speed in scientific notation
Answer:
3 * 10^8 m/s.
Step-by-step explanation:
The given number is close to 300 million so an approximate speed is
3 * 10^8.
a. 15
b. 25
c. 88.5
d. not enough information
Answer:
B
Step-by-step explanation:
assuming DF is the diameter of the circle , then
the angle in a semicircle is 90° , that is
∠ DCF = 90° and Δ CDF is a right triangle
using Pythagoras' identity in the right triangle
CD² + CF² = DF²
CD² + 60² 65²
CD² + 3600 = 4225 ( subtract 3600 from both sides )
CD² = 625 ( take square root of both sides )
CD = [tex]\sqrt{625}[/tex] = 25
which expression does not belong? explain
The expression that does not belong with the other three is B. x ² - 8 ˣ because C. The different expression is the one that is not a polynomial.
How to find the expression ?Expression 2 is not a polynomial because it contains a term (8^x) with a variable in the exponent, which is not allowed in a polynomial. All the other expressions are polynomials. This expression therefore does not belong.
Polynomials are mathematical expressions that consist of variables and coefficients, where the variables are raised to non-negative integer powers and the coefficients are constants.
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Look at the relative-frequency table below of the probability distribution of the discrete random variable X, with X = "the number of pets in a household."
x P(X = x)
0 .09
1 .29
2 .42
3 .15
4 .05
What is the expected value of pets in a randomly selected household?
Answer: The expected value of a discrete random variable is calculated by multiplying each possible value of the variable by its corresponding probability, and then adding up all of the products. Symbolically, the expected value of X is:
E(X) = Σ [x * P(X = x)]
where the summation is taken over all possible values of X.
Using the table given, we can calculate the expected value of pets in a randomly selected household as follows:
E(X) = 0*(.09) + 1*(.29) + 2*(.42) + 3*(.15) + 4*(.05)
E(X) = 0 + 0.29 + 0.84 + 0.45 + 0.20
E(X) = 1.78
Therefore, the expected value of pets in a randomly selected household is 1.78.
Step-by-step explanation:
Which expression is equal to the product of 1/3 and 2 1/4?
1/3*4/9
3/1*4/9
1/3*9/4
1/3*1/4
3/1*9/4
Answer:
the answer is 1/3*9/4
Answer: 1/3*9/4
Step-by-step explanation: I did a test.
3. A board of directors consists of twelve men and ten women. A 5-member search
committee is randomly chosen to recommend a new company president. What is the
probability that all five members of the search committee will be in order of man,
man, man, woman, and woman (without replacement)?
The probability of selecting the committee in the order of man, man, man, woman, woman, without replacement is; 5/133
What is the probability of an event?The probability of an event is the ratio of the number of desired outcome to the number of possible outcome.
The number of men in the board = 12
The number of women in the board = 10
The probability of selecting a man in the first position = 12/22
The number of men remaining is 11 and the number of women remaining is 10.
The probability of selecting a man in the second position is therefore = 11/21
In the same order, the probability of selecting a man in the third position = 10/20
The probability of selecting a woman next = 10/19
The probability of selecting another woman = 9/18
The probability of selecting the committee of five members in the specified order is therefore;
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can you help me with this task please? thank you!!
Answers:
7. 4/50 + 30/50 = 34/50 = 17/25
8. 8/12 - 7/12 = 1/12
9. 90/100 + 2/100 = 92/100 = 23/25
10. 16/36 + 9/36 = 25/36
11. 17/15 - 5/15 = 2/15
12. 7/16 + 6/16 = 13/16
13. 8/20 + 5/20 = 13/20
14. 2/14 + 7/14 = 9/14
Lisa is going on a 3 1/2 mile hike. She has already hiked 2 3/4 miles How many miles does she have left?
Answer:
3/4 miles
Step-by-step explanation:
Parameters
Total distance = 3 1/2 miles
Covered distance = 2 3/4 miles
To make things easier let's convert our parameters from fraction to decimal,
Therefore,
Total distance= 3.5 miles
Covered distance = 2.75 miles
Remaining distance = Total distance - Covered distance
Remaining distance = 3.5 miles - 2.75 miles
Remaining distance= 0.75 miles
Converting back to fraction,
Remaining distance = 3/4 miles
Therefore,
Lisa has 3/4 miles left to hike.
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Thanks.
I been struggling with this answer for 30 mins now can someone please help me
Bobbi owes a total of $10,455.75 in taxes.
What is taxes?Taxes are compulsory financial charges imposed by governments on individuals or entities based on income, property, or goods/services.
To compute the tax owed by Bobbi, we can use the following steps:
Calculate Bobbi's taxable income by subtracting the standard deduction and personal exemption from her total income:
Taxable income = $68,000 - $6,350 (standard deduction) - $4,050 (personal exemption) = $57,600
Determine the tax bracket in which Bobbi's taxable income falls:
Bobbi's taxable income of $57,600 falls in the 25% tax bracket.
Calculate the tax owed by Bobbi by applying the marginal tax rates to her taxable income. We can use the following formula:
Tax owed = (Taxable income - Previous tax bracket limit) x Marginal tax rate + Previous tax amount
In Bobbi's case, we need to calculate the tax owed in three steps, since her taxable income falls in the 10%, 15%, and 25% tax brackets:
For the first $9,325 of her taxable income, Bobbi owes 10% in taxes:
Tax owed = ($9,325 - $0) x 0.10 + $0 = $932.50
For the next $28,625 of her taxable income (up to $37,950), Bobbi owes 15% in taxes:
Tax owed = ($37,950 - $9,325) x 0.15 + $932.50 = $3,825.75
For the remaining $19,650 of her taxable income (up to $57,600), Bobbi owes 25% in taxes:
Tax owed = ($57,600 - $37,950) x 0.25 + $3,825.75 = $5,697.50
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please help me i’m struggling
The correct option is- "Similar figures are said to be congruent: a dilation could possess a scale factor of 1. Due to the differing lengths of comparable sides, similar figures are really not congruent."
Explain about the congruence and similarity?Congruence:
Even though two things are all the same size and shape, they may not be facing the same direction. Like sea stars oriented differently, they still make sense.Or imagine two knights from a chess set, one on a higher shelf and an additional one on a minor ledge. They can nonetheless be congruent even though they are in distinct three-dimensional planes. They remain consistent.Similarity:
Similarity refers to having the same proportions and shape, but not always the same size. Angles of comparable figures will just be equal, while side lengths are frequently not.Congruent shapes are automatically comparable to one another, while the opposite is not true. Similar figures are all congruent, however not all congruent figures include similar figures.Thus, the correct option is- "Similar figures are said to be congruent: a dilation could possess a scale factor of 1. Due to the differing lengths of comparable sides, similar figures are really not congruent."
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determine the value of b²- 4ac
12x² + 5x -2=0
Which statement describes the graph of f(x) = –x4 + 3x3 + 10x2?
The graph crosses the x-axis at x = 0 and touches the x-axis at x = 5 and x = –2.
The graph touches the x-axis at x = 0 and crosses the x-axis at x = 5 and x = –2.
The graph crosses the x-axis at x = 0 and touches the x-axis at x = –5 and x = 2.
The graph touches the x-axis at x = 0 and crosses the x-axis at x = –5 and x = 2.
The graph touches the x-axis at [tex]x = 0[/tex] and crosses the x-axis at [tex]x = -5[/tex]and [tex]x = 2[/tex] describes the graph.
What is the x-axis?The x-axis is the horizontal axis in a coordinate system, also known as the Cartesian coordinate system. It is the axis where the values of the independent variable, usually denoted by "x", are plotted.
What is a graph?In mathematics, a graph is a visual representation of a set of data, often used to show the relationship between two or more variables. Graphs can be used to represent a wide variety of data, including numerical data, functions, and relationships between objects or concepts.
According to the given informationThe statement that describes the graph of [tex]f(x) = -x^{4} + 3x^{3} + 10x^{2}[/tex] is:
"The graph touches the x-axis at [tex]x = 0[/tex] and crosses the x-axis at [tex]x = -5[/tex] and [tex]x=2[/tex]."
To see this, we can factor in the equation:
[tex]f(x) = x^{2} (x^{2} - 3x + 10)[/tex]
Then we can use the quadratic formula to find the roots of the quadratic factor:
[tex]x = [3+ \sqrt{9-40} /2[/tex]
[tex]x = [3 ± \sqrt{-31} ]/2[/tex]
Since the discriminant is negative, the roots are imaginary and the quadratic factor does not have any real roots. Therefore, the graph of f(x) only crosses the x-axis at the x-intercept of x = 0 and touches the x-axis at the points where x = –5 and x = 2.
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27 km
12 km
40 km
Find the area of the SHADED region. Round to the nearest hundredth when necess
A =
km²
The area of the shaded portion is solved to be
426.89 km²How to find the area of the shaded portionThe area of the shaded portion is solved by finding the whole area of the triangle and subtracting the area of the circle
Area of the whole shape
The shape is a triangle and the area of the triangle is
= 0.5 * base * height
where
base = 40 km
height = 27 km
plugging in the values
Area = 0.5 * 40 * 27
Area = 540 square km
Area of the circle
= π * radius^2
= 3.142 * 6^2
= 113.112 square km
Area of the shaded portion is
= 540 - 113.112
= 426.888
= 426.89 km²
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-Point O is the center of regular octagon ABCDEFGH. Find the image of the given point for the given rotation. 90° rotation of A about O. -The image of A is ___?
The image of A about O after 90 degrees rotation is C
What is rotation?Rotation refers to the movement of an object around an axis or center point.
In the problem, the rotation of A 90 degrees about O in the clockwise direction of rotation involves moving in the said direction to make the angle 90 degrees
In an octagon, each angle in the center is solved by
= 360 / 8
= 45
Hence each step in the clockwise rotation covers angle 45 degrees> In the figure from A to B is 45 degrees.
Moving from A to C in clockwise direction is equal to 90 degrees
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a stable has 27 horses each one of eats 9 pounds how many pounds will the horses eat in 8 weeks
Using the multiplication operation, the total quantity that the 27 horses consume in 8 weeks is 1,944 pounds.
What is the multiplication operation?The multiplication operation is one of the four basic mathematical operations, including addition, subtraction, and division.
Multiplication operation involves the multiplicand (the number multiplied), the multiplier (the number multiplying), and the product (the result).
The number of horses in a stable = 27
The quantity of food eaten per horse per week = 9 pounds.
The number of weeks involved = 8 weeks.
The total quantity eaten by the 27 horses in 8 weeks = 1,944 pounds (27 x 9 x 8)
With multiplication, we can conclude that the total quantity is 1,944 pounds.
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Complete Question:A stable has 27 horses. Each one eats 9 pounds per week. How many pounds will the horses eat in 8 weeks?
help 50 pts .. brainliest
I really need help, please. I have question one but I can't figure out the rest.
4.3.4 Practice: Solving Systems of Linear Equations by Substitution
Practice
M/J Grade 8 Pre-Algebra Sem 1
Points Possible:10
Name:
Caine Jones
Date:
Your Assignment
Jesse and Amir were assigned the same book to read. Jesse started reading on Saturday, and he is reading 30 pages a day. Amir didn't start until Sunday, but he is reading 35 pages a day.
How many days will it take Amir to catch up to Jesse, and how many pages will they each have read?
Answer the questions to solve this problem using a system of equations.
1. Write an equation to represent the number of pages Amir has read. Use x to represent the number of days Amir has been reading and y to represent the number of pages he has read. (1 point)
2. Write an equation to represent the number of pages Jesse has read.
Using x, the number of days Amir has been reading, write an expression to represent the number of days Jesse has been reading. Remember that Jesse started reading one day before Amir. Use this expression to write an equation for the number of pages Jesse has read. Let y represent the number of pages read. (1 point)
3. Write the system of equations using your answers from questions 1 and 2.
(2 points)
4. You will use substitution to solve this system. Which variable will you substitute for and why? Show the equation that results from the substitution. (2 points)
5. Solve the system of equations. Show your work. (2 points)
6. Interpret your solution. How many days does it take Amir to catch Jesse? At that time, how many pages have they read? (2 points)
1. The equation to represent the number of pages Amir has read is y = 35x, where x is the number of days Amir has been reading and y is the number of pages he has read.
2. Let's say that Jesse started reading on Saturday, and Amir started reading on Sunday. If x is the number of days Amir has been reading, then Jesse has been reading for x + 1 days. The equation to represent the number of pages Jesse has read is y = 30(x + 1), where y is the number of pages Jesse has read.
3. The system of equations is:
y = 35x
y = 30(x + 1)
4. We will substitute y in the second equation with y from the first equation. We can do this because both equations represent the number of pages each person has read. So we have:
35x = 30(x + 1)
5. Solving for x:
35x = 30x + 30
5x = 30
x = 6
So it will take Amir 6 days to catch up to Jesse.
To find the number of pages they have read, we can use either of the original equations. If Amir has been reading for 6 days, he has read:
y = 35x = 35(6) = 210 pages
If Jesse has been reading for 7 days (one day more than Amir), he has read:
y = 30(x + 1) = 30(7) = 210 pages
So when Amir catches up to Jesse, they will both have read 210 pages.
6. Amir will catch up to Jesse in 6 days. At that time, they will each have read 210 pages.
Answer: i got number 1 :)
6 days
210 pages
Step-by-step explanation:
As stipulated by the question, let the number of days Amir has been reading be x and the number of pages he had read to be y.
Now since he reads 35 pages per day.
Then mathematically;
y = 35x
For Jesse, He started reading a day before, this means that the number of days he had read would be x + 1. Since he reads 30 per day, the total number of pages he would have read is 30(x+1)
To find the number of days which is x, we have to assume that at a point in time, the number of books they would have read would be the same meaning that
Also; y = 30(x + 1)
Equating the two situations
35x = 30(x + 1)
35x = 30x + 30
35x -30x = 30
5x = 30
x = 30/5
x = 6 days
This means that it will take Amir 6 days to catch Jese.
The number of books they would have read by then is y = 35x = 30(x + 1)
= 35 * 6 or 30(6+1)
= 210
The area of a square is represented by 9x2 - 42x + 49. Find the length of each side.
O (9x-7)
O (3x-7)(3x+7)
O (3x-7)
O (3x+7)
O cannot be determined
Answer:
3x-7
Step-by-step explanation:
A square’s area represents (ax+b)^2. Let’s expand that. [tex]a^2x^2+2abx+b^2[/tex] now, we can notice this fits perfectly when a=3 and b=-7. Therefore one side length of the square is 3x-7.
Help Please, I dont know what to do.
Answer: B: y=5x-5
Step-by-step explanation:
1. Choose two animals with different speeds. You can choose from the chart
that starts at the bottom of this page or do research to choose your own.
2. Design a fair race in which the two animals have an equal chance of winning
if they race at their top speed. Here are a few tips for your design:
a. The race is fair if the two animals could finish the race in the same
amount of time.
b. You can give the slower animal a shorter distance to race.
c. Since this is a video game, the race does not need to be realistic—it
can be any length, and the animals can run at a constant speed.
3. Write a system of two linear equations showing the distance each animal can
travel to model the fair race. Be sure to define all variables.
4. Graph the system to prove that the two animals have an equal chance of
winning the race. Explain how the graph proves the race is fair
The animals I chose are the squrriel and mouse. the linear equation for the squrriel is y = 12x
and for the mouse its y = 8x
Can I please get help with number 4? Im not sure how to graph it
The linear equation that can be given for squirrel y is the value of 12x.
How to solveAccording to the question,
Animal Mouse Squirrel
Speed(mph) 8 12
SInce "x" the time goes along with x-axis and "y" is the distance covered by the animal.
The mouse time and distance would plot the graph (1,8)(2,16)(3,24)....
The squirrel time and distance would plot the graph (1,12)(2,24)(3,36)....
Let us consider the track is a straight line and the shorter distance is 50 meters.
The formula for straight line equation y = mx + b where 'b' is the base value, 'x' is the time and 'y' is the distance.
The linear equation for squirrel y = 12x+b and the squirrel starts at 0 meters per hour. so the equation becomes y = 12x.
The linear equation for mouse y = 8x + b and the mouse starts at 0 meters. so the equation becomes y = 8x.
Distance covered by the mouse and the squirrel at time x = 3 we can find the distance covered by the mouse and the squirrel.
y =12x
y = 12(3)
y = 36.
The distance covered by the squirrel is 36km at time 3hours.
For mouse, at time x = 3 hours.
y = 8(3)
y=24.
The distance covered by the squirrel is 24km at time 3hours.
Hence, The linear equation for squirrel y = 12x.
The linear equation for mouse y = 8x
The distance covered by the squirrel is 36km at time 3hours.
The distance covered by the squirrel is 24km at time 3hours.
Thus:
The linear equation for mouse y = 8xThe distance covered by the squirrel is 36km at time 3hours.The distance covered by the squirrel is 24km at time 3hours.Read more about fair race here:
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15 ) Ian throws a ball up in the air and lets it fall to the ground.
The height of the ball, h(t), is modeled by the equation
h(t) = -16t² + 6t+ 3, with h(t) measured in feet, and time, t,
measured in seconds. The number 3 in h(t) represents
(1) the maximum height of the ball
(2) the height from which the ball is thrown
(3) the number of seconds it takes for the ball to reach the ground
(4) the number of seconds it takes for the ball to reach its maximum
height
The number 3 in the equation h(t) = -16t² + 6t+ 3 represents the initial height from which the ball is thrown.
The equation h(t) = -16t² + 6t+ 3 models the height of the ball thrown in the air, with h(t) measured in feet and time, t, measured in seconds. The number 3 in this equation refers to the height from which the ball is thrown. This is represented by the constant term 3, which is added to the equation after the sum of the variables. The formula h(t) = -16t² + 6t+ 3 can be broken down into three parts. The first part is the constant term, 3, which denotes the initial height of the ball. The second part is the linear term, 6t, which represents the acceleration of the ball due to gravity. Lastly, the quadratic term, -16t², is used to describe the rate at which the ball’s acceleration slows down due to air resistance. Therefore the number 3 in the equation h(t) = -16t² + 6t+ 3 represents the initial height from which the ball is thrown.
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-8x+6>-30 what is the answer
Answer: x< 4.5
Step-by-step explanation:
-8x+6>-30
-8x>-36
x<4.5