The area of a rectangular carpet is given by the quadratic function A(x) = x(x + 30), where A(x) is the area and x is the width of the carpet in feet. What are the restrictions on the domain of the function and its inverse?
Answers
The inverse of the function is; f⁻¹(x) = - 15 ± √(x + 225)
What is the Inverse of the Function?We have been given a quadratic function f(x) = x(x + 30) and we need to restrict the domain such that it becomes a one to one function.
Now, the given function can also be written in vertex form as;
f(x) = (x + 15)² - 225
We know that vertex of this quadratic function occurs at (-15, -225).
Further, we know that range of this function is (-225, ∞).
If we restrict the domain of this function to either (-∞, -225) or (-225, ∞) , it will become one to one function.
Let us know find its inverse;
y = (x + 15)² - 225
Upon interchanging x and y, we get:
x = (y + 15)² - 225
Solving for y gives;
y = - 15 ± √(x + 225)
Thus, the inverse of the function is;
f⁻¹(x) = - 15 ± √(x + 225)
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Related Questions
help..564 patrons can borrow up to 6 books. If all the patrons are currently holding on to 6 books each, how many books are left in the library?
Answers
Answer:
3,384
Step-by-step explanation:
So this is a classic multiplication problem. If each patron has 6 books, and there's 564 patrons, you multiply:
564 x 6 = 3,384
hope this helps:D
'Do you believe the quarantine crisis will leave no scars'?'.... , I believe we
will feel its bite for years'.
A. By contrast
B. On the contrary
C. O Instead
Answers
Answer:
B .on the contrary...........
A 20 foot ladder liens against a building and must just reach a window that is 8 feet of the level ground the latter will be unstable if the base is more than 15 feet from the bottom of the building will the ladder be unstable
Answers
Answer:
the ladder will be unstable because it is 18.33ft from the bottom of the building
Use this calculator for problems like this
https://www.calculator.net/triangle-calculator.html
The length of the base is 18.33 feet greater than 15 feet then the ladder will be unstable.
What is a Pythagorean theorem?Pythagorean theorem states that in the right-angle triangle the hypotenuse square is equal to the sum of the square of the other two sides.
Given that a 20-foot ladder is placed against a building and must just reach a window that is 8 feet of the level ground the latter will be unstable if the base is more than 15 feet from the bottom of the building.
Calculate the base of the triangle by using the Pythagorean theorem:-
H² = P² + B²
B² = H² - P²
B² = 20² - 8²
B = √( 400 - 64 )
B = √336 = 18.33 feet
Therefore, the length of the base is 18.33 feet greater than 15 feet then the ladder will be unstable.
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If x= -4 find 3x^2+2x
Answers
Answer:
40
Step-by-step explanation:
3(-4)^2 + 2(-4)
3(16) - 8
48-8
40
15 POINTS!
What is the correct answer for Landon's problem? Explain where he went wrong.
Answers
A rain gutter is made from aluminum sheets that
28 cm wide. The first step in forming a rain gutter is to lift the edges of the aluminum sheet to form right angles, as show in in the illustration below. The cross-section
area formed by the raised edges affects the water flow. This cross-section area, A, can be represented by the function A = x(28-2x) where x
represents the height of the raised edges.
1. To the nearest centimetre, determine the height of the raised edge, x cm, which will maximize the
transverse area.
Answers
Answer:
7 cmStep-by-step explanation:
For any quadratic function f(x)=ax²+bx+c given in form f(x)=a(x-h)²+k, where:
h=-b/2a and k=f(h) the point (h, k) is vertex of the function graph.
It means that k is maximum (if a<0) or minimum (if a>0) value of function and x=h is the x which will maximize function.
A(x) = x(28-2x) = 28x - 2x² = - 2x² + 28x ⇒ a = -2 , b = 28
h = -28/[2•(-2)] = 7
What are the lengths of sides kn and nm of the kite? kn = units nm = units
Answers
the lengths of sides KN and NM of the kite KN = 15 units and NM = 20 units
What is quadrilateral?
Quadrilaterals are typically four-sided closed shapes, and there are numerous varieties of them. Square, rectangle, rhombus, kite, and trapezoid are the most typical shapes. Four closed sides make up a quadrilateral. Quadrilaterals are the following figures: a four-sided figure. The form features a single set of parallel sides and no right angles.
Given that KLMN is a kite
According to the given figure KN = KL and LM=NM
we have the equation y+10=2y+5
y = 5
So KN = KL =15
On putting x =7 for LM and MN we get
LM = MN = 20
Hence, the lengths of sides KN and NM of the kite KN = 15 units and NM = 20 units
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Which line plot shows sonia's data? 241/4 243/4 24 241/2 241/4 241/4
Answers
The line plot that shows Sonia's data will be line plot A.
How to explain the line plotA line plot, also known as a dot plot or a scatter plot, is a graphical representation of data that displays individual data points as dots or markers on a number line. The line plot is used to show the distribution of a set of data and to identify any patterns or trends that may be present.
Line plots are particularly useful for displaying small to medium-sized data sets with discrete values. They are commonly used in the fields of statistics, mathematics.
In this case, the correct option is A.
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What is the center of the circle given by the equation x2 + y2 + 18x – 32y +4= 0?
Answers
Answer:
Center: (-9,16)
next time try using a app called math_way
Answer: the center is (-9,16)
a large population of mice in a laboratory has an average weight 32 grams with a standard deviation of 4 grams. a scientist weighs a random sample of 25 mice for an experiment. if the sample mean of the 25 mice is 30.4 grams, would this be significant evidence, at the 5 percent level of significance, against the hypothesis that the average weight of all mice is indeed 32 grams?
Answers
We REJECT the null hypothesis that these rats came from a population with a mean of 32 in favour of the alternative that they were selected in a way that the mean was different from 32 because our test statistic is bigger than this (in absolute value).
In the given question,
The population mean is 32g with a st. dev. of 4g.
We collect a sample of n=25 mice with a sample average of 30.4g.
We wish to test the hypothesis that these were drawn randomly from the population.
So our null hypothesis is
H0: mean = 32
Our alternative hypothesis is
HA: mean ≠ 32.
This is a two-sided test.
A sample mean should have the same mean as the population mean, and the sample st. dev. should be (pop st. dev./√n).
In this case, under the null hypothesis, the sample mean should be distributed with an average of 32 and a st. dev. of 4/√25 = 4/5 = 0.8.
To test this hypothesis, we need to calculate a test statistic and compare it to a critical value of the standard normal distribution.
Our test statistic is:
z = (Observed value - hypothesized value) / (st. dev. in sample mean)
z = (30.4-32)/0.8
z = -1.6/0.8
z = -2.
The critical value of the z-distribution with α/2 = 0.05/2 = 0.025 is 1.96.
We REJECT the null hypothesis that these rats came from a population with a mean of 32 in favour of the alternative that they were selected in a way that the mean was different from 32 because our test statistic is bigger than this (in absolute value).
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The right answer is:
A colony of laboratory mice consists of several thousand mice. The average weight of all the mice is 32 grams with a standard deviation of 4 grams. A laboratory assistant was asked by a scientist to select 25 mice for an experiment. However, before performing the experiment the scientist decided to weigh the mice as an indicator of whether the assistant’s selection constituted a random sample or whether it was made with some unconscious bias (perhaps themice selected were the ones that were slowest in avoiding the assistant, which might indicate some inferiority about this group). If the sample mean of the 25 mice was 30.4, would this be significant evidence, at the 5 percent level of significance, against the hypothesis that the selection constituted a random sample?
Write an equation of a line that is perpendicular to
the line y = 2/3x+5 and that passes through the
point (0,4).
Answers
Answer:
y = (-3/2)x + 4
Step-by-step explanation:
The slope of the given line is 2/3. The slope of any line perpendicular to the given line is the negative reciprocal of 2/3, which comes out to -3/2.
Now we have the slope of the new line and know that it passes through (0, 4). (0, 4) happens to be the y-intercept, b, in y = mx + b:
Substituting -3/2 for m and 4 for b, we get y = (-3/2)x + 4.
*4) The image of the origin under a certain translation is (5,-6). The
image of point (-4,2) under the same translation is which?
(1) (1,-4)
(3) (-5,6)
4).
(2) (9,8)
(4) (-9,8)
Answers
The origin is located at (0,0). Point (5, -6) is a positive x coordinate and negative y coordinate (x,y). This means, on a graph, from 0 to 5, you move 5 units to the right on the x-axis (horizontally). Then, 0 to -6 means you move 6 units down on the y-axis (vertically).
5 right and 6 down.
This translation on point (-4, 2) can be represented by (-4 + 5, 2 -6), which is the point (1, -4).
When 2(3/5x+2 3/4 is simplified what is the resulting expression
Answers
Answer:
A. 1 7/10x+2 1/2y+6
B. 7/10x+2 1/2y+6
C. 7/10x+8 1/2y+6
D. 1 7/10x+4 1/4y+3
Part 1:
Jeff and Donald are the partners in a company. They invested $72,000. to start the business. They invested in the ratio 7:11, respectively. How much did Jeff invest?
Part 2:
Jeff and Donald are the partners in a company. They invested $72,000. to start the business. They invested in the ratio 7:11, respectively. How much did Donald invest?
Answers
18x = 72,000
x = 4,000
Now multiply the ratio
4,000 * 7 = 28,000
4,000 * 11 = 44,000
Solution; Jeff invested 28,000
Donald invested 44,000
(Assuming Jeff is the 7 part while Donald is the 11 part)
The height at time t (in seconds) of a mass, oscillating at the end of a spring, is s(t) = 300 + 16 sin t cm. Find the velocity and acceleration at t = pi/3 s. v(pi/3) = a(pi/3) =
Answers
The height at time t (in seconds) of a mass, oscillating at the end of a spring, is s(t) = 300 + 16 sin t cm. We have to find the velocity and acceleration at t = π/3 s.
Let's first find the velocity of the mass. The velocity of the mass is given by the derivative of the position of the mass with respect to time.t = π/3 s
s(t) = 300 + 16 sin t cm
Differentiating both sides of the above equation with respect to time
v(t) = s'(t) = 16 cos t cm/s
Now, let's substitute t = π/3 in the above equation,
v(π/3) = 16 cos (π/3) cm/s
v(π/3) = -8√3 cm/s
Now, let's find the acceleration of the mass. The acceleration of the mass is given by the derivative of the velocity of the mass with respect to time.t = π/3 s
v(t) = 16 cos t cm/s
Differentiating both sides of the above equation with respect to time
a(t) = v'(t) = -16 sin t cm/s²
Now, let's substitute t = π/3 in the above equation,
a(π/3) = -16 sin (π/3) cm/s²
a(π/3) = -8 cm/s²
Given, s(t) = 300 + 16 sin t cm, the height of the mass oscillating at the end of a spring. We need to find the velocity and acceleration of the mass at t = π/3 s.
Using the above concept, we can find the velocity and acceleration of the mass. Therefore, the velocity of the mass at t = π/3 s is v(π/3) = -8√3 cm/s, and the acceleration of the mass at t = π/3 s is a(π/3) = -8 cm/s².
At time t = π/3 s, the velocity of the mass is -8√3 cm/s, and the acceleration of the mass is -8 cm/s².
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Suppose that a test for a disease correctly gives positive results for 95% of those having the disease and correctly gives negative results for 90% of those who don't have the disease. Suppose also that the incidence of the disease is 1%. If a person tests positive for the disease, what is the chance that they have the disease
Answers
If the test gives positive results for 95% of those having disease and correctly gives negative results for 90% of those who don't have disease and the incidence of the disease is 1% then the chance of having disease is 0.0105.
Given that a test for a disease correctly gives positive results for 95% of those having the disease and correctly gives negative results for 90% of those who don't have the disease.
We have to calculate the chance of having disease.
Probability that test is correct in determining the disease when person is suffering from it is 0.95.
Probability that test is not correct in determining the disease when person is suffering from it is 1-0.95=0.05.
Probability that test is correct in determining that the person is not suffering from disease when person is not suffering from it is 0.90.
Probability that test is not correct in determining that the person is not suffering from disease when person is not suffering from it is 1-0.9=0.10.
The chance of having disease is equal to incidence of disease multiplied by probabilities that the test has corectly determined disease when personis suffering from it and when test is not able to determine the disease when person is suffering from it.
Chance=0.01*0.95+0.01*0.10
=0.0095+0.001
=0.0105.
Hence the chance of having disease is 0.0105.
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Can someone please help me with this one
Answers
Answer:
The answer is - 7.95
Step-by-step explanation:
\(15.9x + c = 5.3(3x - 1.5) \\ 15.9x + c = 15.9x - 7.95 \\ c = - 7.95\)
Sketching a Function from its Derivatives A In this post, you will use the first and second derivatives of a function (along with a few other pieces of information) to sketch the graph of a function. Sketch the graph of a single function f (x) that satisfies all of the following conditions. Use the techniques that we have learned in this course to do so. f'(x)= 16(x + 2) (6 - x) ³ 32(x + 6) f"(x) = (6 x - x) 4 The domain of fis (-[infinity], 6) U (6,[infinity]) x = 6 is a vertical asymptote of f lim f(x) = 1, lim f(x) = 1 x→→[infinity]0 f(2)= 1 8个
Answers
Here, x = 6 is a vertical asymptote of f, so the function approaches infinity as x approaches 6 from both sides.
Let's start by integrating f'(x) to get f(x). We have:
f'(x) = 16(x+2)(6-x)³ - 32(x+6)
Integrating both sides with respect to x:
f(x) = ∫[16(x+2)(6-x)³ - 32(x+6)] dx
Simplifying the integral, we get:
f(x) = -2(x+2)²(6-x)⁴ + 16(x+6) + C
where C is the constant of integration.
Next, we can find the critical points of f(x) by setting f'(x) = 0:
f'(x) = 16(x+2)(6-x)³ - 32(x+6) = 0
Solving for x, we get x = -2 and x = 6 as critical points.
Now, we can use the second derivative f''(x) to determine the concavity of the function. We have:
f''(x) = (6x-x)⁴ = x⁴
Since the second derivative is always positive for x > 0, the function is concave up on the interval (6, ∞).
Similarly, since the second derivative is always negative for x < 0, the function is concave down on the interval (-∞, -2).
At x = -2 and x = 6, the function has an inflection point.
Finally, we know that x = 6 is a vertical asymptote of f, so the function approaches infinity as x approaches 6 from both sides.
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simplify the expression by combining like terms
-4f-9-1f+15
Answers
Answer:
-5f+6
Step-by-step explanation:
-4f-9-1f+15
-4f-1f-9+15
-5f-9+15
-5f+6
!PLEASE HELP!
Find the length of the missing side. Round your answer to the nearest tenth.
A) 2.8
B) 6.5
C) 4.7
D) 8.2
Answers
Answer: B) 6.5
Step-by-step explanation:
We will use the Pythagorean theorem to solve. The "c" variable is the hypotenuse and the other variables are the legs.
a² + b² = c²
3.6² + b² = 7.4²
12.96 + b² = 54.76
b² = 41.8
b = \(\sqrt{41.8}\)
b ≈ 6.5
The length of the missing side is about B) 6.5.
Answer:
B)6.5
Step-by-step explanation:
H²=P²+B²
7.4²=3.6²+B²
B=√41.8
B=6.465≈ 6.5
Given 2x²=-8, x is
DONE ✔
Answers
\(2x {}^{2} = - 8 \\ x {}^{2} = \frac{ - 8}{2} \\ x {}^{2} = - 4 \\ x = ± \sqrt{ - 4} \\ x_{1} = 2i \: \: \: \: \: \: x_{2} = - 2i\)
Use the given values of n and p to find the minimum usual value - 20 and the maximum usual value y + 20. Round to the nearest hundredth unless otherwise noted. n = 100; p = 0.26 O A. Minimum: 21.61; maximum: 30.39 OB. Minimum: 17.23; maximum: 34.77 OC. Minimum: -12.48; maximum: 64.48 OD. Minimum: 34.77; maximum: 17.23
Answers
The answer is OC. Minimum: -12.48; maximum: 64.48.
The minimum usual value - 20 and the maximum usual value y + 20 for the given values of n and p, n = 100; p = 0.26 are found below.
Minimum usual value = np - z * sqrt(np(1 - p)) = 100 × 0.26 - 1.645 × sqrt(100 × 0.26 × (1 - 0.26))= 26 - 1.645 × sqrt(100 × 0.26 × 0.74) = 26 - 1.645 × sqrt(19.1808) = 26 - 1.645 × 4.3810 = 26 - 7.2101 = 18.79 ≈ 18.80
Maximum usual value = np + z * sqrt(np(1 - p)) = 100 × 0.26 + 1.645 × sqrt(100 × 0.26 × (1 - 0.26))= 26 + 1.645 × sqrt(100 × 0.26 × 0.74) = 26 + 1.645 × sqrt(19.1808) = 26 + 7.2101 = 33.21 ≈ 33.22
Therefore, the minimum usual value - 20 is 18.80 - 20 = -1.20.The maximum usual value y + 20 is 33.22 + 20 = 53.22.
Hence, the answer is OC. Minimum: -12.48; maximum: 64.48.
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im not sure of my answer so can anyone help me out on this
Answers
question b: 8cm
question c: 12cm
(could be wrong)
Answer:
6 cm
13 cm
14 cm
Step-by-step explanation:
a) length of AC
= 3² + 5²
= √36
= 6 cm
b) length of BG
= 5 cm + 8 cm
= 13 cm
c) length of BF
= 6 cm + 8 cm
= 14 cm
The chance that two people have four repeats in location A is 1 in 100. The chance that two people have eight repeats in location B is 1 in 50. The probability that two people have three repeats in location C is 1 in 200. What is the probability that two people would have matching DNA fingerprints for these three locations by chance
Answers
The chances that two people would have matching DNA fingerprints for these three locations is 1/1,000,000
According to statement
In location A the chance that two people have four repeats is 1 in 100.
In location B the chance that two people have eight repeats is 1 in 50.
In location C the chance that two people have three repeats is 1 in 200.
So, to find the probability that two people would have matching DNA fingerprints for these three locations
Multiply the all chances in these locations:
1/100 x 1/50 x 1/200 = 1/1,000,000
So, The chances that two people would have matching DNA fingerprints for these three locations is 1/1,000,000
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How many solutions does an equation have? Is there always a solution?
Answers
BODMAS
Step-by-step explanation:
brackets,of,dividing, multiplication, subtraction
For every dollar the United States spends on health care, it spends an additional 90 cents on social services. For every dollar peer countries spend on health care, how much do they spend on social services
Answers
For every dollar peer countries spend on health care, they spend an additional 55 cents on social services.
According to the data provided, the United States spends an additional 90 cents on social services for every dollar it spends on health care. On the other hand, peer countries spend an additional 55 cents on social services for every dollar they spend on health care. This means that peer countries allocate a greater proportion of their resources towards social services as compared to the United States. Social services refer to a wide range of public services designed to support the well-being of individuals and communities. Examples of social services include education, housing, food assistance, and job training.
calculate how much peer countries spend on social services for every dollar they spend on health care, we can subtract 1 from 1.55 (the total amount spent on health care and social services) and then multiply the result by 1 dollar. This gives us the amount spent on social services, which is 55 cents for every dollar spent on health care.
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1. A multi-cab starter motor has a current of 60.0 A and a voltage of 12 V. What is
the resistance of the starter motor?
А
Given: Current (1)
Voltage (V)
Required: Resistance (9)
V
Formula:
R= voltage
curent
Solution:
V - IR
Answer:
Resistance -
92, the resistance of the electric motor.
Answers
Answer: 0.20 Ω
Step-by-step explanation:
From the question, we are informed that a multi-cab starter motor has a current of 60.0 A and a voltage of 12 V. The resistance of the starter motor will be calculated thus:
Current (I) = 60.0A
Voltage (V) = 12V
Resistance = Unknown
Since Voltage = Current × Resistance
Therefore, Resistance = Voltage / Current
= 12/60
= 0.20 Ω
The resistance of the motor is 0.20 Ω
The resistance of the starter motor if a multi-cab starter motor has a current of 60.0 A and a voltage of 12V is 0.2 ohms
Based on the given question, for us to get the resistance of the starter motor, we will need to use Ohm's law.
According to the law, the current I passing through a conductor at constant temperature is directly proportional to the voltage "V". Mathematically;
V = IR
V is the voltage = 12V
I is the current = 60.0A
R is the resistance
Substitute the given parameters into the formula as shown:
12 = 60 R
R = 12/60
R = 1/5
R = 0/2
Hence the resistance of the starter motor if a multi-cab starter motor has a current of 60.0 A and a voltage of 12V is 0.2 ohms
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help me I need help on this
Answers
Answer:
It is 1.
Step-by-step explanation:
Hope this helped have an amazing day!
I’ll mark brainliest again to the first answer
Answers
Answer:
Yes i am pretty sure it is 3/5
Step-by-step explanation:
BEcause y is always over x in this kind of math
Ramon drew boxplots to summarize the number of pages in each chapter of two books. The values of the interquartile ranges for these boxplots are the same. Which boxplot could represent this data?
Answers
Answer
look at the ss i sent to see the answer
Step-by-step explanation:
