Answers
Answer:
Multiply the second equation by 2
Solution: \((-\frac{45}{11},\frac{29}{11})\)
Step-by-step explanation:
1) In order to use the elimination method to solve systems of equations, you must first multiply one or both of the equations so that the coefficients of a pair of terms with matching variables share the same number, but have opposite signs.
In this case, the y terms must fit that requirement. The y term in the first equation is 2y and the one in the second equation is -y. They already have opposite signs, one positive and other negative, so we just need -y to be -2y. So, in order to do that, multiply by 2.
2) After multiplying the whole second equation by 2, you will get \(8x - 2y = -38\). Now, add the the two equations together, eliminate the y terms, and isolate x to find its value.
3) Then, substitute that x value back into one of the equations to receive the y-value.
To better explain these steps, I attached pictures below.
Related Questions
PLSSS HELP ANSWER THESE QUESTIONS! WORTH 35 POINTS WILL GIVE BRIANLIEST IF ANWRS ARE CORRECT!
For which value of x do following expressions make sense?
THE FOLLOWING QUESTION HAVE TO BE ANWERED AS X IS LE THAN OR GREATER THAN WHATEVER THE ANWER IS
43a) √x+5 40a) ∛a 44b) √(-5x)^3 47e) √13-(13-2x)
THE NEXT COUPLE OF QUETION HAVE TO ANWERED AS X = WHATEVER THE ANSWER IS.
43b) √|x| + 1 44a) √(-2x)^2
45a) √x-5 = 3 The root is only over x-5
45b) √2x+4 = 2 the root is only over 2x+ 4
45c) √x(x+1) = 0 root is only over x(x+1)
45d) √x+5 = -1 the root is only over x+5
45e) √x + x^2 = 0 the root is only over x
42d) root 5 over x+3 = 17 1
9e) root 4 over x = 1 THE ANSWER IS NOT 1
19f) ∛x - 2 = 0 the root is only over x
THE FOLLOWING QUESTIONS HAVE NUMERICAL ANSWERS
9a) root 0.6 over 36 9h) root (4-10) over 0.01
Answers
The values of the variables and numbers in radical form are presented as follows;
43a) x > -5
40a) a > 0
44b) x < 0
47e) x > 0
43b) x = The set of all real numbers
44a) The set of all numbers
45 a) x = 14
45 b) x = 0
45 c) x = -1
45 d) x = -4
45 e) x = 1
42 d)x = 5/196
9 e) x = 4
9 f) x = 8
9 a) √(0.6/36) ≈ 0.13
9 h) √((4 - 10)/(0.01)) = i·10·√6
What is a radical expression in mathematics?A radical also known as a root is represented using the square root or nth root symbol and is the opposite of an exponent.
43 a) \(\sqrt{x + 5}\)
x + 5 > 0
Therefore, x > -5
40a) ∛a
a > 0
44b) √(-5·x)³
-5·x < 0
x < 0
47e) √(13 - (13 - 2·x))
(13 - (13 - 2·x)) > 0
13 > (13 - 2·x)
0 > -2·x
x > 0
43b) √|x| + 1
x = All real numbers
44 a) √(-2·x)²
√(-2·x)² = -2·x
x = Set of all numbers
45 a) √(x - 5) = 3
(x - 5) = 3² = 9
x = 9 + 5 = 14
45b) √(2·x + 4) = 2
2·x + 4 = 2²
2·x = 2² - 4 = 0
x = 0/2 = 0
45c) √(x·(x + 1)) = 0
(x·(x + 1)) = 0
(x + 1) = 0
x = -1
45 d) √(x + 5) = -1
(x + 5) = (-1)²
x + 5 = 1
x + 5 = 1
x = 1 - 5 = -4
x = -4
45e) √x + x² = 0
√x = -x²
(√x)² = (-x²)² = x⁴
x = x⁴
1 = x⁴ ÷ x = x³
x = ∛1 = 1
x = 1
42d) \(\sqrt{\dfrac{5}{x} } +3= 17\)
\(\sqrt{\dfrac{5}{x} }= 17-3 =14\)
\(\dfrac{5}{x} }=14^2=196\)
\(x = \dfrac{5}{196}\)
9e) \(\sqrt{\dfrac{4}{x} } = 1\)
\(\dfrac{4}{x} } = 1^2\)
x × 1² = 4
x = 4
19f) ∛x - 2 = 0
∛x = 2
x = 2³ = 8
9a) \(\sqrt{\dfrac{0.6}{36} }\)
\(\sqrt{\dfrac{0.6}{36} }\) = \(\sqrt{\dfrac{1}{60} }= \dfrac{\sqrt{15}}{30} \approx 0.13\)
9h) \(\sqrt{\dfrac{4-10}{0.01} }\)
\(\sqrt{\dfrac{4-10}{0.01} }\)= √(-600) = √(-1)·√(600) = i·10·√6
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Initially, there is 70mg of a certain radioactive material present and after two hours, it is observed that the material has lost 10% of its original mass. Find the mass (in mg ) of the material after 9 hours
Answers
The mass of the material after 9 hours would be 34.3 mg.The mass of the radioactive material after 9 hours is approximately 34.3 mg, assuming a 10% loss of mass every 2 hours based on the given information.
To find the mass of the material after 9 hours, we need to calculate the exponential decay of the material based on the given information.
We know that after 2 hours, the material has lost 10% of its original mass, which means it retains 90% of its mass.
Using the formula for exponential decay, which is given by:
M(t) = M₀ * e^(-kt),
where M(t) is the mass at time t, M₀ is the initial mass, k is the decay constant, and e is the base of the natural logarithm.
We can find the value of k using the information given. After 2 hours, the material retains 90% of its mass, so we can set up the equation:
0.9M₀ = M₀ * e^(-2k).
Simplifying the equation, we get:
e^(-2k) = 0.9.
Taking the natural logarithm of both sides, we have:
-2k = ln(0.9).
Solving for k, we find:
k = ln(0.9) / -2.
Now, we can use the value of k to calculate the mass after 9 hours:
M(9) = M₀ * e^(-9k).
Substituting the values, we get:
M(9) = 70 mg * e^(-9 * ln(0.9) / -2).
Calculating this expression, we find that the mass of the material after 9 hours is approximately 34.3 mg.
The mass of the radioactive material after 9 hours is approximately 34.3 mg, assuming a 10% loss of mass every 2 hours based on the given information.
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what is 14 2/7 × 4 3/10
Answers
Answer:
14 2/7 x 4 3/10 is 61 3/7
Step-by-step explanation:
2. a. Find the x-coordinates of all critical points (that is, points that are a possible maximum or minimum) of the function f(x) = 3x + 20 48 x 2. b. One of x-coordinates found in part a. should have been x = -4. Use calculus techniques to determine whether it corresponds to a relative minimum or a relative maximum.
Answers
a) The x-coordinate of the critical point is x = 1/32. and b) x = -4 corresponds to a relative maximum .
a) To find the x-coordinates of the critical points of the function f(x) = 3x + 20 - 48x^2, we need to find the values of x where the derivative of the function is equal to zero.
First, let's find the derivative of f(x) with respect to x:
f'(x) = d/dx (3x + 20 - 48x^2)
The derivative of 3x is simply 3, and the derivative of -48x^2 is -96x.
f'(x) = 3 - 96x
Now, we set f'(x) equal to zero and solve for x:
3 - 96x = 0
96x = 3
x = 3/96
Simplifying the fraction:
x = 1/32
So, the critical point of the function f(x) = 3x + 20 - 48x^2 occurs at x = 1/32.
b) To determine whether x = -4 corresponds to a relative minimum or a relative maximum, we need to analyze the second derivative of the function.
Let's find the second derivative of f(x) by taking the derivative of f'(x):
f''(x) = d/dx (3 - 96x)
The derivative of 3 is 0, and the derivative of -96x is -96.
f''(x) = -96
Since the second derivative f''(x) is a constant value (-96), we can determine the concavity of the function at x = -4 by looking at the sign of the second derivative.
Since the second derivative is negative (-96), this means that the function is concave down at x = -4.
Now, let's determine whether x = -4 corresponds to a relative minimum or a relative maximum. To do this, we can use the first derivative test.
At x = -4, the first derivative is:
f'(-4) = 3 - 96(-4) = 3 + 384 = 387
Since f'(-4) is positive (387), this indicates that the function is increasing to the left of x = -4 and decreasing to the right of x = -4.
Therefore, x = -4 corresponds to a relative maximum for the function f(x) = 3x + 20 - 48x^2.
a) The x-coordinate of the critical point is x = 1/32.
b) x = -4 corresponds to a relative maximum
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You want to buy a new hat that costs $9.20 on the price tag. How much
will you pay at the register if there is an 8.5% tax? Round to the nearest
cent. *
Answers
Answer:
$9.98 :)
Step-by-step explanation:
just multiply the tax (0.085) by the price ($9.20) then add the initial price ($9.20) to that.
The area of a rectangle is given as x2+5x+6. which expression represents either the length or widith of the rectangle. these are the answers, it has to be one of these (x-3) (x+1) (x+3) (x+6)
Answers
The expression which represents either the length or width is (x+3). The correct answer is option (c).
Given that the area of a rectangle which is given as x²+5x+6.
We have to find which expression represents either the length or width.
We are given an expression for the area. But we also know that the area of a rectangle is length times width. So the expression we were given, x²+5x+6 must be equal to the length of the rectangle times its width.
So, will find the factoring the expression we can see expressions for the length and the width.
Factoring x²+5x+6 we get (x+2)(x+3).
One of these factors is the width and the other is the length.
Hence, the expression represents either the length or width of the rectangle when the area of a rectangle is given as x²+5x+6 is (x+3).
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convert 15 into quinary number system
Answers
Answer:
3 is answer .
follow me and help me
1. Sammy lost 2 kg after a week of doing his routine exercise.
A 2
B. 2
C. 2
D 0.2
2. Roby drives 15 meters southward along Cebu City.
A. 15
B. 15
C. 15
D-0.15
3. Mrs. Santos deposits Php20 000 as a savings for her son's education.
A-20 000
B. 20 000
C.-020 000
D. 20 000
4. Rommel graduated from elementary12 years ago.
A 12
B. 12
C. *12
D. - 0.12
5. What do you mean by 25?
A. 25 steps backward B. loss of 25 points C. deposited Php25 D. 25° below
Answers
Answer:
1. A. 2
2. D. 0.15
3. I do not know
4. Nope i dont know
5. C
Step-by-step explanation:
What is equidistant from the angles of a triangle?
Answers
The circumcenter of a triangle is the point in the plane equidistant from the three vertices of the triangle.
In geometry, the circumscribed circle or circumcircle of a polygon is a circle that passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius.
Not every polygon has a circumscribed circle. A polygon that does have one is called a cyclic polygon, or sometimes a concyclic polygon because its vertices are concyclic. All triangles, all regular simple polygons, all rectangles, all isosceles trapezoids, and all right kites are cyclic.
A related notion is the one of a minimum bounding circle, which is the smallest circle that completely contains the polygon within it, if the circle's center is within the polygon. Every polygon has a unique minimum bounding circle, which may be constructed by a linear time algorithm.
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HEEEELP PLEASE
a circle has the following equation
x squared + y squared =25
what's the coordinates of the center of the circle
whats the radius of the circle
Answers
The center of the circle x² + y² = 25 is (0, 0) and the radius is 5 units
Identifying the center and radius of the circleGiven that
x squared + y squared =25
Express properly
x² + y² = 25
The above equation is in its standard form
If not we would have to complete the square
To complete the square, we need to add and subtract a constant to both sides of the equation such that the left side becomes a perfect square trinomial.
So, we have
x² + y² = 25
The equation of a circle is represented as
(x - a)² + (y - b)² = r²
Where
center = (a, b)
radius = r
So the center of the circle is (0, 0) and the radius is √(25) = 5.
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3850 times a 1.3% interest rate for 6 years
Answers
"sam places 3850 in a bank account that pays 1.3% simple interest per year and how much interest will she earn in 6 years | Wyzant Ask An Expert" https://www.wyzant.com/resources/answers/646803/sam-places-3850-in-a-bank-account-that-pays-1-3-simple-interest-per-year-an3850
small brainnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn
Answers
Answer:
combined means to add so you are going to add anything over 1 because it says longer than 1
1 1/4 has 2 marks so you add 1 1/4 + 1 1/4 =
they have like denominators so you can add them together
1 + 1 = 2 and 1/4 + 1/4 = 2/4 which can be reduced to 1/2
so your answer is 2 1/2
order the steps to solve -3x + 2.4 =19.2
Answers
Answer: -5.6
Step-by-step explanation: Subtract 2.4 from both sides
Divide both sides by -3
Write a statistical question that you might ask to gather information about the recycling habits of your neighbors
Answers
Answer:
How often do you recycle?
Step-by-step explanation:
Statistical questions are questions where results may vary meaning that depending on who you ask this question you can get very different but measurable answers.
Archie needs to buy 47 cinema entrance tickets costing £6.85
Answers
The unit price of the 47 entrance tickets is £0.15
How to determine the unit price of the ticketFrom the question, we have the following parameters that can be used in our computation:
Number of cinema entrance ticket = 47
Cost of the total tickets = £6.85
The unit price of the ticket is then calculated using the following equation
Unit price of the ticket = Cost of the total tickets/Number of cinema entrance ticket
Substitute the known values in the above equation, so, we have the following representation
Unit price of the ticket = £6.85/47
Evaluate the quotient
This gives
Unit price of the ticket = £0.15
Hence, the unit price is £0.15
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Complete question
Archie needs to buy 47 cinema entrance tickets costing £6.85
Calculate the unit price of the ticket
in this excerpt from a short story published in 1914, a young
man arrives by train to take a position as an assistant
or secretary, to a certain Mrs. Culme. He di covers that
despite the winter weather, no one from her household has
come to meet him at the station
from "The Triumph of Night"
by Edith Wharton
It was clear that the sleigh from Weymore had
not come; and shivering young traveller
from Boston, who had so confidently counted
on jumping into it when he left the train at
Northridge Junction, found himself standing
alone on the open platform, exposed to the
full assault of nightfall and winter.
1 2 3 4 5 6 7
Toward the end of the story, starting on page 5,
Faxon encounters a man in furs. What function
does Faxon's interaction with this character
serve?
It provides character details that indicate Mrs.
Culme may be an unpleasant person.
It provides setting details that suggest that Faxon
is in danger from the cold.
It provides suspense by implying that the youth
may not be what he seems.
It provides exposition by explaining that Mrs. Culme
will send a sleigh soon.
Answers
It provides character details that indicate Mrs. This function Faxon's interaction with this character serve in the given excerpt. Therefore, the correct option is option A.
An excerpt is indeed a quotation from that other resource that the author introduces with fresh language in a sentence. This phrase is taken from Thomas Jefferson's 1801 inaugural speech: As he warned his audience, "I may often go wrong by defect of judgement," Jefferson admitted the fallibility of human nature. "I shall frequently err through lack of judgement" is the excerpt. It provides character details that indicate Mrs. This function Faxon's interaction with this character serve.
Therefore, the correct option is option A.
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In ΔRST, \overline{RT} RT is extended through point T to point U, \text{m}\angle RST = (3x+17)^{\circ}m∠RST=(3x+17) ∘ , \text{m}\angle STU = (8x+1)^{\circ}m∠STU=(8x+1) ∘ , and \text{m}\angle TRS = (3x+18)^{\circ}m∠TRS=(3x+18) ∘ . What is the value of x?x?
Answers
In ΔRST, the overline{RT} RT is extended through point T to point U, Therefore the value of x = 10.
How do we calculate?The sum of angles in a triangle is 180 degrees, we have:
m∠RST + m∠STU + m∠TRS = 180
We substitute the given values, and have:
(3x + 17) + (8x + 1) + (3x + 18) = 180
We simplify and solve for x, we get:
14x + 36 = 180
14x = 144
x = 10.
A triangle in geometry is descried a three-sided polygon with three edges and three vertices.
The fact that a triangle's internal angles add up to 180 degrees is its most important characteristic.
This characteristic is known as the triangle's angle sum property.
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A law firm is going to designate associates and partners to a big new case. The daily rate charged to the client for each associate is $500 and the daily rate for each partner is $1000. The law firm assigned a total of 8 lawyers to the case and was able to charge the client $6500 per day for these lawyers' services. Determine the number of associates assigned to the case and the number of partners assigned to the case.
Answers
Using a system of equations, it is found that there were 3 associates and 5 partners assigned to the case.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: number of associates.Variable y: number of partners.The firm assigned a total of 8 lawyers to the case, hence:
x + y = 8
x = 8 - y.
The firm was able to charge the client $6500 per day for these lawyers' services, hence, considering the costs:
500x + 1000y = 6500.
Since x = 8 - y, we have that:
500(8 - y) + 1000y = 6500.
500y = 2500
y = 5.
x = 8 - 5 = 3.
The firm assigned 3 associates and 5 partners to the case.
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At a little-known vacation spot, taxi fares are a bargain. A 64-mile taxi ride
takes 72 minutes and costs $57.60. You want to find the cost of a 38-minute taxi ride. What unit price
do you need?
Answers
Answer:
The answer is 34.4
Step-by-step explanation:
Trust me it's correct
Pls mark me as brainliest
Preciso de ajudar nessa questão que segue em anexo.
Answers
Answer: $85
Step-by-step explanation:
Não falo português mas tentarei ajudar.
Multiplique 6 2/3 e 3 1/7.
6 2/3 x 3 1/7 = 20 20/21
Dividir 20 20/21 e 5.
20 20/21 / 5 = 4 4/21.
Precisa de cinco latas de tinta.
5 x $17 = $85
Jake wants to make a garden with a border in the corner of his yard. He has lumber in several different lengths. Which three lengths could NOT be used to make a right triangle to fit into the corner of his yard?
Answers
Answer:
10ft,15 ft, 12ft
Step-by-step explanation:
a sample containing years to maturity and yield for 40 corporate bonds is contained in the excel online file below. construct a spreadsheet to answer the following questions. open spreadsheet a. what is the sample mean years to maturity for corporate bonds and what is the sample standard deviation?
Answers
Use STDDEV.s function to find standard deviation and AVERAGE function to find mean years of maturity.
To answer this question, you would need to open the provided Excel file and input the data into a spreadsheet. Once the data is inputted, you can use Excel's built-in functions to calculate the mean and standard deviation.
To calculate the mean years to maturity, you would use the AVERAGE function and select the column of years to maturity data. The result will give you the average years to maturity for the sample of 40 corporate bonds.
To calculate the standard deviation, you would use the STDEV.S function and select the column of yield data. This will give you the sample standard deviation for the yield data.
Overall, your spreadsheet should have columns for years to maturity and yield, with 40 rows of data for each bond. The mean years to maturity and sample standard deviation for yield can then be calculated using Excel functions.
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The sample mean years to maturity for corporate bonds:
Type the following formula and press Enter:
=AVERAGE(A1 : A40).
The sample standard deviation:
Press Enter: = STDEV.S(A1 : A40).
To calculate the sample mean and sample standard deviation for years to maturity of the 40 corporate bonds, follow these steps:
Open the Excel online file provided.
Assuming that the years to maturity data is in column A, click on an empty cell (let's say B1) to find the sample mean.
Type the following formula and press Enter:
=AVERAGE(A1 : A40).
This will calculate the mean of the years to maturity for the 40 corporate bonds.
To find the sample standard deviation, click on another empty cell (let's say B2) and type the following formula and press Enter:
=STDEV.S(A1 : A40)
This will calculate the sample standard deviation of the years to maturity for the 40 corporate bonds.
Now, you should have both the sample mean years to maturity and the sample standard deviation in cells B1 and B2 respectively.
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Questions are from: Gerald and Wheatly, Applied Numerical Analysis 1) 10. A sky diver jumps from a plane, and during the time before the parachute opens, the air resistance is propor- tional to the power of the diver's velocity. If it is known that the maximum rate of fall under these condi- tions is 80 mph, determine the diver's velocity during the first 2 sec of fall using the modified Euler method with Ar= 0.2. Neglect horizontal drift and assume an initial velocity of zero.
Answers
The diver's velocity during the first 2 sec of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.
Given data: Initial velocity, u = 0 ft/sec
Acceleration, a = g = 32.2 ft/sec²
The maximum rate of fall, vmax = 80 mph
Time, t = 2 seconds
Air resistance constant, Ar = 0.2
We are supposed to determine the sky diver's velocity during the first 2 seconds of fall using the modified Euler method.
The governing equation for the velocity of the skydiver is given by the following:
ma = -m * g + k * v²
where, m = mass of the skydive
r, g = acceleration due to gravity, k = air resistance constant, and v = velocity of the skydiver.
The equation can be written as,
v' = -g + (k / m) * v²
Here, v' = dv/dt = acceleration
Hence, the modified Euler's formula for the velocity can be written as
v1 = v0 + h * v'0.5 * (v'0 + v'1)
where, v0 = 0 ft/sec, h = 2 sec, and v'0 = -g + (k / m) * v0² = -g = -32.2 ft/sec²
As the initial velocity of the skydiver is zero, we can write
v1 = 0 + 2 * (-32.2 + (0.2 / 68.956) * 0²)0.5 * (-32.2 + (-32.2 + (0.2 / 68.956) * 0.5² * (-32.2 + (-32.2 + (0.2 / 68.956) * 0²)))
v1 = 62.732 mph
Therefore, the skydiver's velocity during the first 2 seconds of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.
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Identify which type of sampling is used: random, stratified, cluster, systematic, or convenience.
_________1. A psychologist selects 12 boys and 12 girls from each of 4 Math classes.
_________2. When he made an important announcement, he based conclusion on 10,000 responses, from 100,000 questionnaires distributed to students.
_________3. A biologist surveys all students from each of 15 randomly selected classes.
_________4. The game show organizer writes the name of each contestant on a separate card, shuffles the cards and draws 5 names.
_________5. Family planning polls 1000 men and 1000 women about their views concerning the use of contraceptives.
_________6. A hospital researcher interviews all diabetic patients in each 10 randomly selected hospitals.
_________7. Smart selects every 100th cell phone from the assembly line and conduct a thorough test of quality.
Answers
The type of sampling used in each scenario is as follows:
Stratified sampling, Convenience sampling, Cluster sampling, Random sampling, Convenience sampling, Cluster sampling, Systematic sampling
The psychologist selects a specific number of boys and girls from each math class, which indicates stratified sampling. The population (students) is divided into strata (math classes) and samples are taken from each stratum.
The conclusion is based on responses from questionnaires that were distributed conveniently to students, indicating convenience sampling. The sample is not randomly selected but consists of those who chose to respond.
The biologist surveys all students from randomly selected classes, indicating cluster sampling. The population (students) is divided into clusters (classes), and all members of the selected clusters are included in the sample.
The game show organizer shuffles and randomly selects contestant names, indicating random sampling. Each name has an equal chance of being selected.
Family planning polls a specific number of men and women, suggesting convenience sampling. The individuals surveyed are conveniently selected and may not represent the entire population.
The hospital researcher interviews all diabetic patients in randomly selected hospitals, indicating cluster sampling. The population (diabetic patients) is divided into clusters (hospitals), and all members of the selected clusters are included in the sample.
Smart selects every 100th cell phone from the assembly line, indicating systematic sampling. A sampling interval is used to select samples at regular intervals, ensuring a systematic and consistent approach.
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Why am I using negative numbers in 6th grade science?
Answers
Answer:
Try stopping at nothing to avoid them
It just says to solve for n, anyone able to help me? :,)
Answers
Answer:
n=4
Step-by-step explanation:
n+5{n-2}=14
n+5n-10=14
6n-10=14
+10 +10
6n=24
6/6=1
24/6=
n=4
six distinct positive integers are randomly chosen between and , inclusive. what is the probability that some pair of these integers has a difference that is a multiple of ?
Answers
Answer:
So the probability of this happening is exactly 1 - it must be true
Step-by-step explanation:
If we calculate modulo(5) for each of the six numbers (the integer remainder after dividing by 5), we will get six values from 0 to 4.
By the pigeonhole principle, since there are 6 numbers and only 5 possible values, at least two must share the same value modulo 5. Pick two of those, say x and y, in which case x mod 5 = y mod 5, therefore (x - y) mod 5 = 0. In other words, their difference is a multiple of 5.
So the probability of this happening is exactly 1 - it must be true
Please help I’ll mark brainliest!
Answers
Answer:
Disciminant of f = 0
x-intecept = \((\frac{3}{2}, 0)\)
Step-by-step explanation:
Given the quadratic function, -4x² + 12x - 9
where a = -4, b = 12, and c = -9
The discriminant, b²- 4ac, is the expression inside the radical (numerator) of the quadratic formula:
\(x = \frac{-b +/- \sqrt{b^{2}-4ac} }{2a}\)
The first part of your given problem asks for the discriminant. Substitute the values for a, b, and c:
b²- 4ac = 12² - 4(-4)(-9) = 144 - 144 = 0 → This implies that the quadratic function has one real root.
Therefore, the disciminant of f is 0.
Next, the given problem asks for the x-intercepts. The x-intercept is the point on the graph where it crosses the x-axis. As I mentioned earlier, the function has one real root. Therefore, it means that there is only 1 x-intercept. To find out what the x-intercept is, use the quadratic formula:
\(x = \frac{-b +/- \sqrt{b^{2}-4ac} }{2a}\)
\(x = \frac{-12 +/- \sqrt{12^{2}-4(-4)(-9)} }{2(-4)}\)
\(x = \frac{-12 +/- \sqrt{144 - 144} }{-8}\)
\(x = \frac{-12}{-8} = \frac{3}{2}\)
Therefore, the x-intercept is \((\frac{3}{2}, 0)\).
12)a sample of customers from barnsboro national bank shows an average account balance of $315 with a standard deviation of $87. a sample of customers from wellington savings and loan shows an average account balance of $8350 with a standard deviation of $1800. which statement about account balances is correct? a) barnsboro bank has more variation. b) wellington s
Answers
A sample of customers from barnsboro national bank shows an average account balance of 315 with a standard deviation of 87. a sample of customers from wellington savings and loan shows an average account balance of 8350 with a standard deviation of 1800. Option A: Barnsboro Bank has more variation.So, the correct option is A) Barnsboro Bank has more variation.
The given data is:
A sample of customers from Barnsboro National Bank shows an average account balance of 315 with a standard deviation of 87.
A sample of customers from Wellington Savings and Loan shows an average account balance of 8350 with a standard deviation of 1800.
To compare the variation in the account balances of both banks, we use the coefficient of variation (CV).
CV = Standard deviation / Mean
CV of Barnsboro National Bank = 87/315 ≈ 0.2762
CV of Wellington Savings and Loan = 1800/8350 ≈ 0.2150
The CV of Barnsboro National Bank is greater than the CV of Wellington Savings and Loan.
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Ifa box of apples is distributed among 28 children , each gets 3 . iF 7 children were not present , their share would also ne distriibuted among the others How many apples would each children get
Answers
Answer:
First subtract 28 by 7.
28 - 7 = 21
Then multiply 28 times 3
28 times 3 is 84
Then finally divide 84 by 21
84/21 = 4
Each of the children would get 4 apples
Step-by-step explanation: