Another term for roots or x intercept is zeroes.
In algebra, a quadratic equation is any equation that can be rearranged in standard form ax^2+bx+c, where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear, not quadratic.)
The numbers a, b, and c are the coefficients of the equation and may be distinguished by respectively calling them, the quadratic coefficient, the linear coefficient and the constant coefficient or free term.
Roots are also called x-intercepts or zeros. A quadratic function is graphically represented by a parabola with vertex located at the origin, below the x-axis, or above the x-axis. Therefore, a quadratic function may have one, two, or zero roots.
Hence , another term for roots or x intercept is zeroes.
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What is the total cost of the rental is Dana drives the car for 15 miles?
The total cost of the rental if Dana drives the car for 15 miles is $90.2
How to determine the total cost?From the question, we have the following parameters that can be used in our computation:
C = 73.25 + 1.13m
Where
m = number of miles
This means that
m = 15
SO, we have the following equation
C = 73.25 + 1.13 * 15
Evaluate
C = 90.2
Hence, the total cost is $90.2
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"Dana and her family are going to Six Flags Great America the sum- mer after her Sophomore year. She is excited, because she will be doing all driving: After doing some complicated analysis, she calcu; lates that it will cost a certain amount per mile to pick up everyone and drive to the park, plus flat amount for everyone's admission tickets. The equation below models the total cost, €,and the variable m represents the number of miles driven: C = 73.25 + 1.13m
write a system of three linear equations with three variables each that has the unique solution . write your equations in standard form. use the variables , , and with non-zero coefficients.
the system of three linear equations with three variables each that has the unique solution is 2x + 3y + 4z = 30, 3x + 4y + 5z = 45 and 5x + 6y + 7z = 75.
2x + 3y + 4z = 30
3x + 4y + 5z = 45
5x + 6y + 7z = 75
The first equation is 2x + 3y + 4z = 30. The coefficients for the variables are 2, 3 and 4 which are all non-zero, meaning that this equation has a unique solution.
The second equation is 3x + 4y + 5z = 45. The coefficients for the variables are 3, 4 and 5 which are all non-zero, meaning that this equation also has a unique solution.
The third equation is 5x + 6y + 7z = 75. The coefficients for the variables are 5, 6 and 7 which are all non-zero, meaning that this equation also has a unique solution.
Therefore, the system of three linear equations with three variables each that has the unique solution is 2x + 3y + 4z = 30, 3x + 4y + 5z = 45 and 5x + 6y + 7z = 75.
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a mistake was made in the steps shown to simplify the expression. which step includes the mistake?
The step in which there is a problem is the operation in step 4. option C
Where is the mistake?In this question, we are expected to solve the problem in a number of steps. We know that in mathematics, the solution to a given problem can only be worked out through a number of steps that can help us to be able to know what the correct solution of the problem ought to be.
In this case we have a simplification problem. It should be know that the acronym of BODMAS has to be called to mind here and that is;
BracketOfDivisionMultiplicationAdditionSubtractionMathematical operations would have to be carried out in this order else there would be a mistake in it. We can see that the addition in step 4 before division did not follow the principle of BODMAS thus that step is wrong.
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What are the domain and range of f (x) = log (x + 6) minus 4?
domain: x > –6; range: y > 4
domain: x > –6; range: all real numbers
domain: x > 6; range: y > –4
domain: x > 6; range: all real numbers
Mark this and return
Domain: x > –6; range: all real numbers are the domain and range of f (x).
What is domain and range ?
The range of values that can be plugged into a function is known as its domain. The x values for a function like f make up this set (x).
The collection of numbers that the function assumes is known as its range. After we enter an x value, the function outputs this sequence of values.
we need to remove all the values of x such that:
x + 6 ≤ 0
Solving for x, we get
x ≤ -6
So the only values of x allowed are the ones that make the next inequality true:
x > -6.
Thus we can write the domain as:
D {x | x ∈ R | x > -6}
Where the second part, x ∈ R, is usually ignored, as we assume that x is a real number .
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Answer:
B
Step-by-step explanation:
The bears in Alaska are limited to a certain area to live due to the resources available for
food and shelter. After years, the number of bears living in the area is modeled by the function below. Using the function, find the number of bears after 17 years.
The number of bears living in the area after 17 years is; 22555
How to solve exponential functions?We are given the function;
f(t) = 103/(1 + 26e^(-0.31t))
Where f(t) is a function that models the number of bears living in the area after t period of years.
Thus, to find the number of bears living in the area after 17 years, we will just substitute 17 for t in the given function to get;
f(17) = 103/(1 + 26e^(-0.31*17))
f(17) = 103/0.00456653759
f(17) ≈ 22555 bears
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Q9.
Rachel, Samina and Tom share £600 between them.
2
Rachel gets 2/5 of the £600
ima
Samina gets 1/4 of the money that is left over.
Tom gets the rest of the money.
Tom says,
"I would have got more money if we had shared the £600 equally between us."
Is Tom correct?
You must show how you get your answer.
No. Tom is not correct.
If the money were split equally everyone would've gotten £200.
But, if everyone went by the mentioned distribution, then,
Rachel would get = 2/5 x 600 = £280
Remainder money = 600 - 280 = £320
Samina would get = 1/4 x 320 = £80
Tom would get the remaining money = 600 - (280 + 80)
= 600 - 360
= £240
Since, £240 > £200, Tom would be incorrect in saying he would have had more money if he had split the money equally.
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the quadtratic expression -3x^2 +6x + 72 will equal zero when x equals
The values of x is x = 6 Or x = - 4 when the expression - 3x² + 6x + 72 will be zero.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Here in the problem, we have to find the roots of the quadratic equation
- 3x² + 6x + 72 = 0.
3x² - 6x - 72 = 0.
x² - 2x - 24 = 0.
x² - 6x + 4x - 24 = 0.
x(x - 6) + 4(x - 6) = 0.
(x - 6)(x + 4) = 0.
x = 6 Or x = - 4 are the values of x when the expression will be zero.
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Erica takes out a loan to purchase a car. She borrows 12,000 at 12% annual percentage rate. Complete the statements. The graph is [Drop Down 1]. Erica's loan is a [Drop Down 2] loan. The equation which models this loan is [Drop Down 3]. If Erica pays off the loan in six years, she will have paid [Drop Down 4].
An increasing exponential function is modeled as follows:
A(t) = A(0)(1 + r)^t.
The parameters of the exponential function are given as follows:
A(0) is the initial value of the exponential function.r is the growth rate of the exponential function, as a decimal.She borrows 12,000 at 12% annual percentage rate, hence the initial value and the growth rate are given as follows:
A(0) = 12,000, r = 0.12.
Then the function that describes her loan is given as follows:
A(t) = 12000(1.12)^t.
After six years, the value of the loan is calculated as follows:
A(6) = 12000(1.12)^6 = $23,686.
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A student claims that the graph shows the player earned more points from Level 2 to Level 3 than from Level 4 to Level 5. Is the student correct?
O No, the player earned 67 points from Level 2 to Level 3 and 69 points from Level 4 to Level 5
O No, the player earned 42 points from Level 2 to Level 3 and 44 points from Level 4 to Level 5.
O Yes, the player earned 67 points from Level 2 to Level 3 and 69 points from Level 4 to Level 5.
OYes, the player earned 42 points from Level 2 to Level 3 and 44 points from Level 4 to Level 5.
x = 7y + 12
2x - 14y = 11
Substitution
The given system of linear equations has no solutions. Thus, they are said to be an inconsistent system of equations.
What is meant by an inconsistent system of equations?The system of equations that has no solution is said to be an inconsistent system of equations.By the substitution method, a system is solved. If the system does not get any values, the system is said to have no solutions.Calculation:The given system of equations is
x = 7y + 12 ...(1)
2x - 14y = 11 ...(2)
Since equation (1) is directly given for the variable 'x', substituting (1) in the (2). So, we get
2(7y + 12) - 14y = 11
⇒ 14y + 24 - 14y = 11
⇒ 24 = 11
This is not possible. So, the system has no solution. Hence it is an inconsistent system.
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Radiocarbon dating is effective on specimens up to 40,000 years old. In 1953, a nuclear chemist was trying to
determine the age of some scrolls that were recently found. Carbon-14 has a half-life of 5730 years. If he found 79.5%
of the original carbon-14 still present, in about what year were the scrolls made?
Radiocarbon dating is effective on specimens up to 40,000 years old. In 1953, a nuclear chemist was trying to determine the age of some scrolls that were recently found. Carbon-14 has a half-life of 5730 years. If he found 79.5% of the original carbon-14 still present, in about 1908 year were the scrolls made.
What is decay constant?Disintegration constant is another name for the decay constant. It is the ratio of the number of radioactive atoms that break down quickly to the number of the same sort of atoms that were there at the beginning.
Given data:
Carbon-14 has a half-life = 5730 years
So, formula for decay constant:
= log 2/half life
= 0.693/5730
=0.0001209
exponential decay equation:
N(t) = N₀[tex]e^{kt}[/tex] ............ (i)
where N₀ is initial amount ;
N(t) = final amount ;
t = time;
k =decay constant
Given that,
N(t) =0.794 N₀
Now, putting the values in equation (i), we get -
0.794 N₀ = N₀ [tex]e^{-0.0001209t}[/tex]
0.794 = [tex]e^{-0.0001209t}[/tex]
take on natural log on both sides:
ln 0.794 = -0.0001209 t
t = 1907.95 years
t = 1908 years
Therefore, it took 1908 years.
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Cuál es la diferencia entre la ley de senos y la ley de cósenos
The law of sines uses only two sides and the angles that are opposite them, while the law of cosines uses all three sides and only one of the sides opposite an angle
What are the laws about?An angle's cosine and sine are equal to each other, with the sine of an angle equal to the cosine of its complementary angle.
The law of cosines uses all three sides and only one of the sides that are opposite an angle, whereas the law of sines only uses two sides and the angles that are opposite them. The sine ratio is used by the law of sines, and the cosine ratio is used by the law of cosines.
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Complete question
What is the difference between the law of sines and the law of cosines
20
Write "less" or "greater" in the blank.
972 is
than 792
Answer:greater
Step-by-step explanation:
Answer:
972 is greater than 792.
An airplane is preparing to land at an airport. It is 55800 feet above the ground and is descending at the rate of 3,500 feet per minute. At the same airport, another airplane is taking off and will ascend at the rate of 2,700 feet per minute. When will the two airplanes be at the same altitude and what will that altitude be? Use pencil and paper. Use two other methods to solve the problem. Explain which methods are easier to use and which are more difficult to use for the situation.
By solving a linear equation, it can be calculated that-
The two planes will be in the same altitude after 9 minutes at an altitude of 24300 feet
What is a linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here, the linear equation is
Let the time taken by the airplane to meet the same altitude be t minutes
An airplane is preparing to land at an airport. It is 55800 feet above the ground and is descending at the rate of 3,500 feet per minute.
So altitude of the first airplane after t minutes = 55800 - 3500t
At the same airport, another airplane is taking off and will ascend at the rate of 2,700 feet per minute.
Altitude of second airplane = 2700t
By the problem,
The linear equation is
55800 - 3500t = 2700t
2700t + 3500t = 55800
6200t = 55800
t = 9 minutes
Altitude = 2700 [tex]\times[/tex] 9 = 24300 feet
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The wholesale price for a chair is $169. A certain furniture store marks up the wholesale price by 16%. Find the price of the chair in the furniture store. Round your answer to the nearest cent, as necessary.
Need Help!
The price of the chair in the furniture store is $94.
How to calculate the price of the chair in the furniture store?Given that the wholesale price for a chair is $169 and that a certain furniture store marks up the wholesale price by 16%.
The price of the chair in the furniture store will be:
= $169 + (16% × $169)
= $169 + $27.04
= $196
The price is $194.
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Write the linear equation in slope intercept form
The given linear equation (1/3)x+ y=2 in the slope-intercept form is
y=(-1/3)x+2.
Explain about slope-intercept form?Where m is the slope and b is the y-intercept, the slope-intercept form is represented as y = mx+ b. By utilizing y=mx+ b, a line is typically simple to graph. The point-slope form and standard form of linear equations are further types. Example 1: A line with a slope of 1/2 and a y-axis crossing at (0, -3). Calculate the line's equation. It is y = x/2 - 3 that determines the line's equation. Example 2: Determine the equation utilizing the y-y-intercept axis's and the horizontal line's slope intercept formula (0, 8).
Finding the slope between two points on a line and then solving for the y-intercept in the slope-intercept equation y=mx+ b allow us to build an equation for that line.
Given linear equation is:
(1/3)x+ y=2
The following is the slope-intercept form of the given linear equation:
y=(-1/3)x+2
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Jaime y rocío están pintando una pared con cubos de pintura idénticos. Si Jaime ha gastado 2/5 de su pintura y rocío,3/5. ¿Quién ha gastado más? ¿Qué cubo de pintura estará más lleno?
Answer:
Step-by-step explanation:
Rocio ha gastado mas. El cubo de Jaime esta mas lleno.
Rocio gasto otro poco mas porque 3 esta mas grande que 2
The radius of a sphere is 4y. Determine its volume, giving the answer as an exact simplified expression in terms of y
Answer:
267.95 y^3 or we can keep it like 85.333πy^3
Step-by-step explanation:
Radius of the Sphere is 4y
Volume of sphere = (4/3)πR^3, where R is the radius of sphere.
Therefore, (4/3) *π*(4y) ^3
= [(256/3) y^3]π
=85.333πy^3
=267.95y^3 (Ans)
one proposed solution to the funding problems faced by social security and medicare is to increase the retirement age from 67 to 70. although this would mean billions of dollars in savings for these federal programs, an unintended consequence may be
An unintended consequence may be an increase in the unemployment rate.
What is Unemployment Rate?
The percentage of workers in the labour force who do not currently have a job but are actively seeking one is measured by the unemployment rate.
The formula for calculating the unemployment rate is: unemployment rate = (Number of jobless people / sums of employed and unemployed people) x 100%.
Example: If there are 500 unemployed persons and 3000 people who are employed, the unemployment rate is calculated as follows: 500/3500 x 100% = 14.29%.
Reason:
When people retire late, new people entering the workforce would have less number of jobs. So, the unemployment rate would increase.
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Which expression is equivalent to 10d+d-2d?
d+8
9d9d
1+8d1+8d
11d11d
pls help
Answer: 9d
Step-by-step explanation:
10d+d-2d = 9d
For one photography session, Dexter earns no less than $50, but no more than $100. Which inequality can be used to represent his earnings, e? e ≥ 50 or e ≤ 100 e > 50 or e < 100 50 < e < 100 50 ≤ e ≤ 100
Answer:[tex]50 \leq e \leq 100[/tex]
Step-by-step explanation:
'No less' corresponds to [tex]\leq[/tex].
'No more' corresponds to [tex]\geq[/tex].
Putting this together, we get [tex]50 \leq e \leq 100[/tex].
Answer:
The Answer is D:50 ≤ e ≤ 100
Step-by-step explanation:) hope this helps:)!.
Brainliest would be very very appreciated.
50 points please help asap
The domain is set of all real numbers and the range is y ≥ -4
How to determine the domain and the range of the function?From the question, we have the following parameters that can be used in our computation:
The equation is given as
g(x) = |x + 4|
The domain
The above equation is an absolute value equation
An absolute value equation can take any value as its input
This means that the domain is the set of all real numbers
When represented as an interval, we have
The domain is (-∝, ∝)
Also, we have
-∝ < x < ∝
Hence, the domain is the set of all real numbers
The range
Here, we have
g(x) = |x + 4|
The above equation is an absolute value function
An absolute value function represented as
y = a|x - h| + k
Where
Vertex = (h, k)
So, we have
Vertex = (-4, 0)
Remove the x value
y = -4
Because the leading coefficient is positive, then the vertex is a minimum
i.e.
[-4, ∝)
Another representation is
y ≥ -4
So, the range is y ≥ -4
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a frequent cause of measurement error in polls is due to a. the increased use of cell phones. b. push polling. c. poorly worded questions. d. too large sample sizes.
Polling mistakes are frequently caused by poorly written questions. People frequently misunderstand questions that are worded strangely and react to the question inaccurately, which leads to an error in the polling data. Due to misinterpretation, people frequently react differently than they would typically say , then option c is correct.
Limited respondent selections, a lack of knowledge, difficulty assessing intensity, and lack of interest in political matters are just a few of the factors that might make a poll unreliable.
Survey mistake, fewer respondent alternatives, a lack of knowledge, problems assessing intensity, and a lack of interest in political matters are some potential polling weaknesses.
The drawback of polling is that if there are too many devices to check, it may take longer to service an I/O device than it does to poll all of the devices.
Instrumental, environmental, procedural, and human errors are frequent causes. Depending on how they affect the outcomes, each of these errors can either be random or systematic.
Therefore,
Polling mistakes are frequently caused by poorly written questions. People frequently misunderstand questions that are worded strangely and react to the question inaccurately, which leads to an error in the polling data. Due to misinterpretation, people frequently react differently than they would typically say , then option c is correct.
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On average, Shandra drinks \frac{3}{5} 5 3 of a 10-ounce glass of water in 1\tfrac{2}{5}1 5 2 hours. How many glasses of water does she drink in one hour? Enter your answer as a whole number, proper fraction, or mixed number in simplest form.
In one hour Shandra can drink [tex]4\frac{2}{7}[/tex] ounces of water.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, On average, Shandra drinks [tex]\frac{3}{5}[/tex] of a 10-ounce glass of water
which is = (3/5)×10 ounces = 6 ounces in [tex]1\frac{2}{5}[/tex] an hour.
[tex]1\frac{2}{5}[/tex] hours is equal to 7/5 hours.
So, 6 ounces of water in 7/5 hours.
Therefore, In one hour Shandra can drink {6/(7/5)} = 6×(5/7) = 30/7 ounces.
= [tex]4\frac{2}{7}[/tex] ounces of water.
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rate change of (0, -9) and (7, 5)
PLEASE HELP WITH THIS PROBLEM
Answer:
y -2 = 2(x +7)y -2 = -1/2(x +7)Step-by-step explanation:
You want equations of lines parallel and perpendicular to y = 2x -1 through the point (-7, 2).
SlopeThe given equation is written in slope-intercept form:
y = mx + b
where m = 2, and b = -1.
The slope of the line is m, the x-coefficient. For the given line, the slope is 2.
A parallel line will have the same slope: 2.
A perpendicular line will have the opposite reciprocal slope: -1/2.
Point-slope equationWhen you have a point and slope, it is useful to use the point-slope form of the equation for a line:
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
For both of the desired lines, the point is (h, k) = (-7, 2). Using this point and the above slopes, we have ...
equation of parallel line: y -2 = 2(x +7)equation of perpendicular line: y -2 = -1/2(x +7)Find the fith term in the sequence.. Pls help!
The fifth term in the sequence is 3
What is a sequence?
Mathematical sequences are lists of elements, usually integers, where the order of the elements is important. Here, the components all fit into a precise pattern. In everyday life, sequences appear frequently. Sequences include, for instance, a row of house numbers, a pay increase each year (by a defined dollar amount or percentage), a book's page numbers, etc.
[tex]a_{n} = 4 + ( -1 )^n[/tex]
Substitute n=5
[tex]a_{5} = 4 + ( -1 )^5[/tex]
= 4 + (-1)
= 4 - 1
= 3
So, the fifth term in the sequence is 3
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the accuracy of a sample is a measure of how closely it reports the true values of the population it represents. true false
A sample's accuracy is determined by how well it captures the genuine characteristics of the population it represents true
Accuracy is a measure of how closely a sample reflects the true values of the population it is representing. A sample that is accurate is one that accurately reflects the characteristics of the population it is representing. For example, if a sample is taken from a population of 1000 people, the sample should represent the diversity of the population, such as age, gender, race, and other characteristics. If the sample accurately reflects these characteristics, then it can be said to be accurate. The accuracy of a sample can be determined by comparing it to the population it is representing, either through surveys, interviews, or other data collection methods. If the sample closely matches the true values of the population, then it can be said to be accurate. If there are discrepancies between the sample and the population, then the sample is not accurate.
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mathematics-help-dilate-
The dilated figure is plotted and attached and the coordinates is written as
preimage image
A (-4, 3) A; (-8, 6)
B (3, 2) B' (6, 4)
C (-4, 0) C' (-8, 0)
How to find the coordinates of the dilationDilation is a method of transformation that magnify or shrink the preimage depending on the scale factor
The transformation rule for dilation is as follows
(x, y) for a scale factor of r → (rx, ry)
following similar procedure for the given problem we have
preimage image
A (-4, 3) → (-4 * 2, 3 * 2) → A' (-8, 6)
B (3, 2) → (3 * 2, 2 * 2) → B' (6, 4)
C (-4, 0) → (-4 * 2, 0 * 2) → C' (-8, 0)
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Select the graph that represents the solution of the compound inequality –6 ≤ 4x + 6 < 14. A number line from negative 5 to 5 in increments of 1. A point is at 0 and a bold line is drawn to the right stopping at the open circle at 2. A number line from negative 5 to 5 in increments of 1. A point is at negative 5 and a bold line is drawn to the right stopping at the open circle at 3. A number line from negative 5 to 5 in increments of 1. A point is at negative 3 and a bold line is drawn to the right stopping at the open circle at 5. A number line from negative 5 to 5 in increments of 1. A point is at negative 3 and a bold line is drawn to the right stopping at the open circle at 2.
The graph that represents the solution to the compound inequality –6 ≤ 4x + 6 < 14 is given as follows:
A number line from negative 5 to 5 in increments of 1. A point is at negative 3 and a bold line is drawn to the right stopping at the open circle at 2.
How to solve the inequality?The inequality for this problem is defined as follows:
–6 ≤ 4x + 6 < 14.
This means that two conditions have to be satisfied.
The first condition is given as follows:
–6 ≤ 4x + 6
That is:
4x + 6 ≥ -6
4x ≥ -12
x ≥ -3.
The second condition is given as follows:
4x + 6 < 14
4x < 8
x < 2.
The intersection of these two conditions is composed by the values between -3 and 2, with a closed interval at -3 and an open interval at 2.
This means that the last option is the correct option.
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