The domain and range of the equations for the three cars using the hypothetical condition that x represents additional gas added to the tank are;
Car #1
Domain; 0 ≤ x < ∞
Range; 607.8 ≤ y < ∞
Car #2
Domain; 0 ≤ x < ∞
Range; 568 ≤ y < 0
Car #3
Domain; 0 ≤ x < x
Range; 528.4 ≤ y < ∞
What is an equation?An equation is a statement that indicates that two expressions be equivalent by joining them with an equals sign.
The specified equations for three cars are;
Car #1: y = 28·x + 607.6
Car #2: y = 80·x + 568
Car #3: y = 20·x + 528.4
The domain of a function is the set of possible input values (x-values) of the function
The range is the set of possible output values (y-values) of the function
Let y represent the number of miles driven and let x represent the additional gas added to the car, we get;
The domain of car #1
The additional number of gallons of gas car #1 can drive receive has a domain of 0 ≤ x < ∞
The range for car #1
The total number of miles car #1 can drive = 607.6 ≤ y < ∞
The domain for car #2
The additional amount of gas car #2 receives is; 0 ≤ x < ∞
The range for car #2
The distance car #2 can drive is; 568 ≤ y < ∞
The domain for car #3
The additional volume of gas car #3 receives is; 0 ≤ x < ∞
The range of the function for car #3
The number of miles car #3 can drive is; 528.4 ≤ y < ∞
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Graph the equation
-Show your work
The graph of the equation, y = -50x + 300, is given in the attachment below.
How to Graph the Equation of a Line?The equation of a line, where m is the slope or unit rate, and b is the y-intercept or starting value, is expressed as y = mx + b in the slope-intercept form.
Given the situation above, first determine the value of the starting value / y-intercept (b) and that of the slope / unit rate (m).
The starting value / y-intercept is b = 300.
The slope / unit rate is m = - 50 [this is negative because the distance from home reduces as she drives at the speed of 50 mph]
To write the equation, substitute m = -50 and b = 300 into y = mx + b:
y = -50x + 300.
Thus, the graph of this equation, y = -50x + 300 is shown in the mage attached below.
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find the value of unknown; chapter matrices
please help me out on these questions below! thnak u
with full explanations and working please
Answer:
Step-by-step explanation:
what is the answer i need answers now I'm going to fail
Answer:
3
Step-by-step explanation:
this problem we need to subtract
There is 6 1/2 grape juice and 3 1/3 orange juice
6 1/2 3 1/3
We get common denominators and one is 6
6 3/6 3 2/6
And now we subtract
3 1/6
And rounded down is 3
Hopes this helps please mark brainliest
at a 25% off sale you buy a game for 45$ what was the original price
Answer:
$60
Step-by-step explanation:
Let x = the original cost
x - .25x = 45
.75x = 45 Divide both sides by .75
x = 60
P(x) = 6x³-5x² - 4x + 4;-3
The value of P(-3) =-191 if the given polynomial function is
P(x) = 6x³-5x² - 4x + 4
What is meant by polynomial?A polynomial is an expression made up of exponents, constants, and variables that are combined using addition, subtraction, multiplication, and division in mathematics, according to the definition of a polynomial. Polynomials are frequently employed in both mathematics and science. For example, they are employed to define polynomial functions, which are present in a range of fields ranging from elementary physics and chemistry to economics and social science. From straightforward word problems to intricate scientific conundrums, polynomial equations are utilized to represent a broad variety of topics. In high mathematics, polynomials are used to build algebraic varieties and polynomial rings, which are essential concepts in algebra and algebraic geometry.
Given,
P(x)= 6x³-5x²-4x+4
P(-3)=6(-3)³-5(-3)²-4(-3)+4
=6(-27)-5(9)+12+4
=-162-45+16
=-191
So, the value of P(-3)= -191
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how do you handle data in analytics to gain greater insights into our audience's behaviour? a partition b sample c segment d extract
By using the segment method, you handle data in analytics to gain greater insights into our audience's behavior.
Analytics:
Analytic refers the field of computer science that uses math, statistics, and machine learning to find meaningful patterns in data.
Given,
Here we need to find how do you handle data in analytics to gain greater insights into our audience's behavior.
In order to find the solution for this one, we must know the definition for the terms of the following,
Audience's behavior - attitudes that affect the behavior of an audience towards a brand or category.
Data - information that has been translated into a form that is efficient for movement or processing.
Insights - the capacity to gain an accurate and deep understanding of someone or something.
Here we have divide the full question into segment to solve this.
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3w^2-12w=-12
use quadratic formula to solve
Answer:
To solve the quadratic equation 3w^2 - 12w = -12, we can use the quadratic formula:
x = (-b +/- sqrt(b^2 - 4ac)) / (2a)
In this case, a = 3, b = -12, and c = -12. Plugging these values into the formula, we get:
w = (-(-12) +/- sqrt((-12)^2 - 43(-12))) / (2*3)
Simplifying, we get:
w = (12 +/- sqrt(144 + 144)) / 6
w = (12 +/- sqrt(288)) / 6
w = (12 +/- sqrt(288)) / 6
w = (12 +/- 16.97) / 6
w = (12 +/- 16.97) / 6
w = 28.97/6 or -4.97/6
w = 4.828 or -0.828
Therefore, the solutions to the equation 3w^2 - 12w = -12 are w = 4.828 and w = -0.828.
Answer:
w = 2
Step-by-step explanation:
[tex]3w^{2} -12w=-12\\3w^{2} -12w+12 = 0\\[/tex]
[tex]\frac{-b + \sqrt{b^{2} - 4ac} }{2a}[/tex]
[tex]\frac{-(-12) + \sqrt{(-12)^{2} - 4(3)(12) } }{2(3)} = 2[/tex]
Find the slope of the line that passes through (-21, -47) and (-15,-44).
The slope of the line is 1/2 or 0.5
What is slope of a line ?The slope of a line characterizes the direction of a line.
To find the slope of a line when the coordinates of the two points are given you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points .
Thus if
A ( x1, y1) and B( x2, y2)
The slope of the line is y2 - y1 / x2-x1
Calculations
Given ;
A ( -21, -47)
B(-15, -44)
slope = 3/6
=1/2 or 0.5
The slope of the line is 1/2 or 0.5
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Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answer: x = 25
Step-by-step explanation:
(x-7) = 36/2
x-7 = 18
x = 18 +7
x = 25
Answer: x = 1 and x = 13.
Step-by-step explanation: To solve the equation (x - 7)^2 = 36, we can first rewrite the equation as x^2 - 14x + 49 = 36.
Next, we can rewrite the equation as x^2 - 14x + 13 = 0.
To solve for x, we can then use the quadratic formula:
x = (-b +/- sqrt(b^2 - 4ac)) / (2a)
where a = 1, b = -14, and c = 13.
Substituting these values into the formula, we get:
x = (14 +/- sqrt(14^2 - 4(1)(13))) / 2
x = (14 +/- sqrt(196 - 52)) / 2
x = (14 +/- sqrt(144)) / 2
x = (14 +/- 12) / 2
The values of x are therefore 1 and 13.
Therefore, the correct answer is x = 1 and x = 13.
7. A watch loses 8 seconds every hour. It was set to read the correct time at 1100 h on Sunday. Determine the time, in a 12-hour system, the watch will show on the following Thursday when the correct time is 0500 h.
On Thursday when the correct time is 5:00h, watch shows 4:24h.
What is ratio?Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
The watch is set at 11:00 h on Sunday.
Also, the watch loses 8 seconds in every hour.
To determine the time in watch on Thursday,
In one day total hours = 24 hours.
from Sunday 11:00 to Thursday 11:00
Total hours = 24 x 4 = 96 hours
And 11:00 to 5:00, total = 6 hours
Total hours = 96 + 6 = 102 hours
Since, watch loses 8 seconds in 1 hour
So in 102 hours watch losses = 102 x 8 = 816 seconds
816 seconds = 816/60 minutes = 13.6 minutes
The watch loses 13.6 minutes in 102 hours.
So the exact time will be, 4 : 24.
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What is the equation of the vertical asymptote for the graph of the rational function g(x)=6x−1
Solution n(x), where n(x) is the denominator of the function (notice that this only works if t(x) is not zero for the same value of x).When the denominator is equal to zero, you can solve for x to determine the vertical asymptotes.
How can you locate the graphing formula for a vertical asymptote?By finding the solution to the equation n(x) = 0, where n(x) is the denominator of the function (note that this only works if the numerator t(x) is not zero for the same x value), vertical asymptotes can be obtained. For the function, locate its asymptotes. With the equation x = 1, the graph has a vertical asymptote.When the denominator is equal to zero, you can solve for x to determine the vertical asymptotes. This has previously been factored, therefore reduce each component to zero and get the solution. Since the asymptotes are lines, they are represented mathematically by line equations. X = 3 and X = 1 are the vertical asymptotes.To learn more about Vertical asymptotes refer to:
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A dolphin swims 465,280 feet in 3 hours. Use the formula d = rt, where d represents distance, r represents rate, and t represents time, to answer the following questions. Show your work.
Using distance, rate and time the answer is 155093.3.
What is distance?Distance is the total movement of an object without any regrad to direction. It is the length of the space between two points .
Given question are-
D=rt where d represent distance.
R represent= Rate
T represents= Time
Based on the given conditions formulate :
A dolphin swims= 465,280
Time = 3hour
=465280/3
Evaluate the expression/equation we can get -
155093.3
Thus the answer is
155093.3
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You have 1,312 grams of radioactive kind of lanthanum. If its half-life is 93 minutes, how much will be left after 279 minutes?
If its half-life is 93 minutes, then the amount left after 279 minutes will be equal to 164 grams.
What is Half-life?In radioactivity, the half-life is the amount of time needed for half of a radioactive sample's atomic nuclei to spontaneously decay (convert into different nuclear species by emitter particles and energy) or, alternatively, the amount of time needed for the radioactive material's disintegration rate to drop by half.
As per the given information given in the question,
Initial amount, N₀ = 1312 grams
Time elapsed, t = 279 min
Half-life, [tex]t^1^/^2[/tex] = 93
Then, use the formula of half-life:
N(t) = N₀[tex](\frac{1}{2})^t^/^(^t^)^1^/^2[/tex]
Substitute the values in above equation,
N(t) = 1312[tex](\frac{1}{2})^2^7^9^/^9^3[/tex]
N(t) = 1312(1/2)³
= 1312 × 0.125
N(t) = 164 grams.
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Answer: 164 grams
Step-by-step explanation: I got the answer right on my ixl
Ashley added ice cubes to her iced tea. The change in temperature of her tea was - 15F. If she added 5 ice cubes, what integer represents the change in tea per ice cube?
Answer:
To find the change in temperature per ice cube, you need to divide the total change in temperature by the number of ice cubes. In this case, you would divide -15F by 5 ice cubes to get -3F per ice cube. The negative sign indicates that the temperature of the tea decreased.
Step-by-step explanation:
Using elimination to solve the system of equations.
3x-5y=11
5(x+y)=5
Answer:
3x - 5y = 11
5(x + y) = 5
Expand the second equation:
5x + 5y = 5
Add both equations:
3x - 5y = 11
5x + 5y = 5
8x = 16
Solve for x:
8x = 16
x = 2
Input x in any equation and solve for y:
3(2) - 5y = 11
6 - 5y = 11
-5y = 5
y = -1
A man walked a certain distance at a constant rate. If he had gone 1/2 mile per hour faster, he would have walked the distance in four-fifths the time; if he had gone 1/2 mile per hour slower, he would have been 2 1/2 hours longer on the road. How far did he walk?
Answer:
15
Step-by-step explanation:
15
He walked 15
A freezer in a lab i et o that the temperature change at a rate of -1. 6C every hour. What i the change in the temperature after 4 1/4 hour? Show your work
The change in the temperature after 4 1/4 hour is -6.8 C.
Given :
A freezer in a lab is set so that the temperature changes at a rate of –1.6 C every hour.
Temperature :
Temperature is the degree of hotness or coldness of an object.
The degrees must contain any units like kelvin , centigrade etc .
Change in temperature after 4 1/4 hours = change rate for hour * number of hours.
= -1.6 C * 4 1/4
= -1.6 C * 4.25
= -16 / 10 C * 425 / 100
= -16 * 425 / 10 * 100 C
= -6800 / 1000 C
= -68 / 10 C
= -6.8 C
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the registration fee for a car is 0.9% of the sale price of 5400$ how much is the fee
The registration fee is $60.
Given,
Sale Price = $5400
The value of the registration:
Registration fee = 0.9% of $5,400
= (0.9/100) * 5,400
= 60
Therefore, the registration fee is $60.
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Create a perpendicular bisector of AB and label the intersection point of the lines E. To verify your result, measure AE and EB and the angles between the bisector and AB. Take a screenshot of your work, and paste it below.
The line CD is the bisector line that divides the line segment AB into two equal parts that are AE = EB.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is the m:n ratio, finding the mid-point of the line, etc.
Make an opposite bisector of the Stomach muscle and mark the convergence point of line E. To check your outcome, measure AE and EB and the points between the bisector and Stomach muscle.
The line CD is the bisector line that divides the line segment AB into two equal parts that are AE = EB.
The diagram is given below.
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The number of students who are active in the computer club has jumped from 7 to 19. To the nearest percent, what is the percent increase?
what is the estimated expected (mean) time for activity e? multiple choice 91 days 100 days 99 days 101 days 115 days
The estimate expected mean time for the given activity E from the give table data is equal to 101days.
As given in the question,
Let optimistic time be represented by [tex]T_{o}[/tex]
Most like time be represented by [tex]T_{m}[/tex]
And Pessimistic time be represented by [tex]T_{p}[/tex]
Optimistic time for activity E is equal to [tex]T_{o}[/tex] = 91
Most likely time for activity E is [tex]T_{m}[/tex] = 100
Ans Pessimistic time for activity E is [tex]T_{p}[/tex] = 115
Estimated expected mean time
= [tex]( T_{o} + 4T_{m} + T_{p} ) / 6[/tex]
= [ 91 + 4(100) + 115 ] / 6
= 606/6
= 101
Therefore, option d. 101days represents the estimated expected mean time for the given activity E.
The complete question is:
From the given table:
{ Time estimates (days)}
Activity Predecessor Optimistic Most likely Pessimistic
A A, B, C 30 50 62
B D 90 99 108
C E 85 105 115
D End 19 25 31
E F 91 100 115
F End 62 65 68
What is the estimated expected (mean) time for activity E?
Multiple choice
a. 91 days b. 100 days c. 99 days d. 101 days e.115 days
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Irma wa in charge of keeping attendance for a local ummer camp each year. Summer camp attendance
Year Kid
2018 93
2019 92
2020 78
2021 75
2022 78
According to the table, what wa the rate of change between 2018 and 2021?
The rate of change in the attendance of students between 2018 and 2021 is 1.24.
What is the rate of change?The term "rate of change" (ROC) describes the rate at which something changes over time.
Thus, it is not the number of individual changes themselves but rather the acceleration or deceleration of changes (i.e., the rate).
The rate of change is a tool used in finance to comprehend price returns and spot trend momentum.
Divide the change in y-values by the change in x-values to determine the average rate of change.
Identifying changes in measurable values like average speed or average velocity calls for the knowledge of the average rate of change.
So, according to the given table:
The rates of change between 2018 and 2021 are:
2018/2021
93/75
1.24
Therefore, the rate of change in the attendance of students between 2018 and 2021 is 1.24.
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Please help with the question below
Answer:
A = -5
Step-by-step explanation:
What is the domain and range 5,0, 12,4, 3,-3
Answer:
domain=5,12,3
range=0,4,-3
Simplify: 22-(8-2) + [6 (205) - 11]
Answer: 1,235 is your final answer!
Step-by-step explanation:
First we do what's inside the Parentheses always remember PEMDAS
P-Parentheses
E-Exponent
M-Multiplication
A-Addition
S-Subtraction
So first we do what's inside the brackets!
22-(8-2)+ (1230-11)
22-6+1219
16+1219
1235.
Follow the PEMDAS steps to simplify the answer!
You use a garden hose to fill a wading pool. if the water level rises 17 centimeters every 5 minutes and you record the data point of (15, y), what is the value of y? use slope to justify your answer.
The line has a 17/5 slope and y has a value of 51 which will be (15, 51).
What is the slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
The general equation for every straight line is y = MX + c, where m is the gradient (or degree of steepness) of the line and c is the y-intercept (the point in which the line crosses the y -axis).
So, the water level rises by 17 cm in 5 minutes.
Then in 15 minutes, the water will rise by:
15 * 17/5
3*17
51
Then (x, y) will be (15, 51).
Obtaining the slope as follows:
Formula: m = y1 - y2/x1 - x2
m = y2 - y1/x2 - x1
m = 17 - y/5 - x
m = 17/5
Therefore, the line has a 17/5 slope and y has a value of 51 which will be (15, 51).
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Work out the tax increase on this question!!! Please help
Sales Tax added to the cost of the computer is 178.34 pounds
What is sales tax?
Sales tax is a tax imposed by the government on the price of a commodity for the sale of that commodity. Imposing sales tax on a product increases the price of the product. Nowadays, sales tax has been replaced by Goods and Service Tax (GST).
Here, sales tax is added to increase the price of the computer.
Cost of a computer = 964 pounds
Rate of tax added = 18.5 %
Tax added = [tex]\frac{18.5}{100} \times 964[/tex]
= 178.34 pounds
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COLVE IT PLSS HELP WILL GIVE BRAINLIEST IF THE ANSWER IS RIGHT!
Answer:
degree 5monomialStep-by-step explanation:
You want to know if 5x²y²z +10x²y²z is monomial, binomial, or trinomial, and what its degree is.
DegreeThe degree of a term is the sum of the degrees of the variables in the term:
degree = 2 + 2 + 1 = 5
TermsTwo terms are shown. However, the terms are like terms, so can be combined into one term:
15x²y²z
This tells us the expression is a monomial.
__
Additional comment
The terms of a binomial must be unlike. That is, they don't count as separate terms if they can be combined.
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Is this a function? Explain, why or why not!
X
-2
-4
-6
Y
1
1
1
Edit View Insert Format Tools Table
By using the concept of function, it can be seen that the given table represents a function.
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here the values under x represents the domain and the values under y represents the Range.
From the table it can be seen that
Every point of the domain maps to unique point on the range.
So this is a function.
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Apply the 45°-45°-90° Triangle Theorem to find the length of the hypotenuse of the triangle
If the length of each leg of the triangle is 15√2 in, what is the length of the hypotenuse(c)?
Answer:
30
Step-by-step explanation:
The 45-45-90 Triangle Theorem states that in the isosceles 45-45-90 triangle, if we designate each leg as [tex]a[/tex], the base, or hypotenuse is [tex]a\sqrt{2}[/tex] . Since we know the leg is [tex]15\sqrt{2}[/tex], the hypotenuse would be:
[tex]15\sqrt{2} * \sqrt{2} =\\15 * 2=\\30[/tex]