The formula of P(x) = -0.7 (x-2)²(x+4)
What is a root of a polynomial ?A root of a polynomial is defined as the point or value at which the overall value of the polynomial = 0
It is given that
for a polynomial of degree 3
root x=2, multiplicity 2: (x-2)²
root x= - 4, multiplicity 1: (x+4) ³ ²
P(x) = a(x-2)²(x+4)
here a is constant
y-intercept = -11.2
P(0) = -11.2
a(0-2)²(0+4) = -11.2
a * 4 * 4 = -11.2
16a = -11.2
a = -11.2/(16)
a= -11.2/16
P(x) = -(11.2/16)(x-2)²(x+4)
P(x) = -0.7 (x-2)²(x+4)
Therefore the formula of P(x) = -0.7 (x-2)²(x+4)
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What’s the derivative of the function: A) f(x)= 1/x , in point 2. B) f(x)= 5x^2 , in point 3
Using the power rule, the derivatives are given as follows:
a) [tex]f^{\prime}(2) = -\frac{1}{4}[/tex].
b) [tex]f^{\prime}(3) = 30[/tex].
What is the power rule for a derivative?Suppose we have a power function given by:
[tex]f(x) = x^n[/tex]
The derivative of the function is given by:
[tex]f^{\prime}(x) = n \times x^{n-1}[/tex]
Item a:
The function is:
[tex]f(x) = \frac{1}{x} = x^{-1}[/tex]
Then the derivative is:
[tex]f^{\prime}(x) = -x^{-2} = -\frac{1}{x^2}[/tex]
When x = 2, the derivative is:
[tex]f^{\prime}(2) = -\frac{1}{4}[/tex]
Item b:
The function is:
[tex]f(x) = 5x^2[/tex]
Then the derivative is:
[tex]f^{\prime}(x) = 10x[/tex]
When x = 3, the derivative is:
[tex]f^{\prime}(3) = 30[/tex]
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S
Warm-Up
Determining if a Relationship Is a Function
Determine if each set of ordered pairs represents a function.
(2, 3), (6,-5), (-1, 3)
Function
(1,9), (-3,-2) (1,-4)
(7.-4), (0, 9), (2,-2)
(0, 3), (0, 7), (4,0)
(-6, 5), (-5, 6), (8, 2)
Not a Function
Using it's concept, the set of ordered pairs that represent a function are:
(2, 3), (6,-5), (-1, 3)(7.-4), (0, 9), (2,-2)(-6, 5), (-5, 6), (8, 2)The set of ordered pairs that do not represent a function are:
(1,9), (-3,-2) (1,-4)(0, 3), (0, 7), (4,0)When does a relation represents a function?A relation represents a function if each input X is mapped to only one output Y.
At (1,9), (-3,-2) (1,-4), input 1 is mapped to outputs 9 and -4, hence it is not a function.
At (0, 3), (0, 7), (4,0), input 0 is mapped to outputs 3 and 7, hence it is not a function.
For the other relations, each input is mapped to only one output, hence they are functions.
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Yvonne is solving the quadratic equation 6x2 + 24x + 7 = 0 by completing the square. Her first four steps are shown in the table.
A table listing the first few steps in deriving the quadratic formula
In which step did Yvonne first make an error?
The step in which Yvonne first makes an error while solving the quadratic equation by completing the square in step 1.
What is a quadratic equation?A quadratic equation is an equation in which the highest power of the variable is two.
Yvonne is solving the quadratic equation, which is,
6x² +24x +7 =0
He is solving the above equation by completing the square.
The first step to solving this quadratic equation by completing the square is, Take the constant value 7 at the opposite side of the equation as,
6x² +24x = -7
Here, the number seven was a positive number, which we have changed to negative because this number brings the other side of the equation.
In the image attached below, the first step of the Yvonne while solving the equation by completing the square is,
6x² +24x = 7
Here, Yvonne does not change the sign of the number 7 while taking it to another side of the equation.
Hence, the step in which Yvonne first makes an error while solving the quadratic equation by completing the square is step 1.
The table is attached with the answer below
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Keith tabulated the following values for time spent napping in minutes of six of his friends: 23, 35, 17, 30, 20, and 19. The standard deviation is 7.043.
Keith reads that the mean nap is 22 minutes.
t equals fraction numerator x with bar on top minus mu over denominator begin display style bevelled fraction numerator s over denominator square root of n end fraction end style end fraction
The t-statistic for a two-sided test would be __________. Answer choices are rounded to the hundredths place.
Using the t-distribution, the t-statistic for the two-sided test would be of t = 0.7.
What is the test statistic for a t-distribution hypotheses test?The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the expected value.s is the standard deviation of the sample.n is the sample size.The values of the parameters are given as follows:
[tex]\mu = 22, s = 7.043, n = 6[/tex].
The sample mean is:
[tex]\overline{x} = \frac{23 + 35 + 17 + 30 + 20 + 19}{6} = 24[/tex]
Hence the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{24 - 22}{\frac{7.043}{\sqrt{6}}}[/tex]
t = 0.7.
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#SPJ1You are buying a used car which costs $10,200. You plan to sell the car after keeping it for 5 years. Research shows that this car will lose value at a rate of 8% per year. How much will the car be worth after 5 years?
Answer:
$6,722.63
Step-by-step explanation:
Now: $10,200
In 1 year: 0.92 × $10,200 = $9,384
In 2 years: 0.92 × $9,384 = $8,633.28
In 3 years: 0.92 × $8,633.28 = $7,942.6176
In 4 years: 0.92 × $7,942.6176 = $7,307.208192
In 5 years: 0.92 × $7,307.208192 = $6,722.63
Answer: $6,722.63
Answer:
$6,722.63
Step-by-step explanation:
Using this formula A=P(1-d/100)^n where
A = Amount
P = Principal
d = percent
n = number of year
A=P(1-d/100)^n
A = 10,200(1-8/100)⁵
A = 10,200(1-0.08)⁵
A = 10,200(0.92)⁵
A = 10,200(0.6591)
A= $6,722.63
Geometry
Pls list steps so I can learn :)
(a) The arc length of each of the two smaller semicircles is [tex]4\pi[/tex], and the arc length of each of the two larger semicircles is [tex]15\pi[/tex]. Therefore, the perimeter is [tex]2(4\pi)+2(15\pi)=38\pi[/tex].
(b) The area of each of the smaller semicircles is [tex]\frac{1}{2}(\pi)(4^2)=8\pi[/tex], and the areaof each of the larger semicircles is [tex]\frac{1}{2}(\pi)(15^2)}=\frac{225\pi}{2}[/tex].
So, the combined areas of the four semicircles is [tex]241\pi[/tex].
The area of the rectangle is 60, so the total area is [tex]241\pi+60[/tex].
Find the lengh of AB
Cost of a computer game: $32.00
Markup: 20%
Answer:
38.4
Step-by-step explanation:
32×%20=6.4
32+6.4=38.4 new price
How many cubic meters are in 122047.5 cubic inches (with formula please)
Answer:
2 cubic meters
Step-by-step explanation:
1 Cubic Meter = 61023.7441 Cubic Inch
Sketch the graph by hand using asymptotes and intercepts, but not derivatives. Then use your sketch as a guide to producing graphs (with a graphing device) that display the major features of the curve. Use these graphs to estimate the maximum and minimum values. (Round your answers to three decimal places.)
f(x) = (2x+3)²(x-2)^5/x³(x-5)²
The local minima of [tex]f\left(x\right)=\ \frac{\left(2x+3\right)^2\left(x\ -2\right)^5}{x^3\left(x-5\right)^2}[/tex] are (x, f(x)) = (-1.5, 0) and (7.980, 609.174)
How to determine the local minima?The function is given as:
[tex]f\left(x\right)=\ \frac{\left(2x+3\right)^2\left(x\ -2\right)^5}{x^3\left(x-5\right)^2}[/tex]
See attachment for the graph of the function f(x)
From the attached graph, we have the following minima:
Minimum = (-1.5, 0)
Minimum = (7.980, 609.174)
The above means that, the local minima are
(x, f(x)) = (-1.5, 0) and (7.980, 609.174)
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Factorize this equation:
6=x^2-x
The factored form of the given expression is (x+2)(x-3)
Factorizing equationQuadratic equation are equation that has a leading degree of 2. Given the equation below
6=x^2-x
Equate to zero
x^2-x - 6 = 0
Factorize
x^2 - 3x + 2x - 6 = 0
x(x-3)+2(x-3) = 0
x = 3 and -2
Hence the factored form of the given expression is (x+2)(x-3)
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A system of inequalities is shown.
The graph shows a dashed upward opening parabola with a vertex at negative 2 comma negative 6, with shading inside the parabola. It also shows a dashed line passing through the points negative 3 comma negative 5 and 0 comma 4, with shading below the line.
Which system is represented in the graph?
The required system hence becomes
3x-y+4>0,
y + 6 > (x + 2)²
When the symbols “>”, “<”, “≥”, “≤”, are used to connect two real numbers or algebraic expressions, that relationship is known as an inequality.
The Graph is given below of the given problem statement.
Observe that the parabola y=x² has vertex at (0,0) we can shift the vertex to (-2,-6) to get the parabola
y + 6 = (x + 2)²
And the inequality is
y + 6 > (x + 2)²
Hence, this parabola is as required by the problem.
And the line passing through (-3,-5) and (0,4) is
[tex]\frac{\left(y-4\right)}{\left(-5-4\right)}=\frac{\left(x\right)}{-3}[/tex]
The required inequality hence becomes
3x-y+4>0
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Aaden wants to get a subscription to an online library. There are two subscription options, one of which charges a fixed 96 dollar annual fee and the other which charges 3 dollars per book he borrows.
What does point T represent in this context?
Answer:
A number of books and their costs where the subscription with the annual fee costs less
The first subscription option is given by T = 92 while the second subscription option is given as T = 3x. Where T represent the cost of borrowing x number of books.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let T represent the cost of borrowing x number of books.
For the first subscription option:
T = 92
For the second subscription option:
T = 3x
The first subscription option is given by T = 92 while the second subscription option is given as T = 3x. Where T represent the cost of borrowing x number of books.
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The bookstore sells packages of 15 pens
each and 12 pencils each. They want the
same number of pens and pencils in their
next order. Find the smallest number of
packages of each they can buy.
Considering the definition of least common multiple, this means that smallest number of packages of each they can buy is 60.
Least common multipleA number is a multiple of another when it contains it exactly n times. In other words, the multiples of a number are the ones you get when you multiply one number by another.
The least common multiple allows us to know what is the smallest number that is a multiple of a certain set of numbers.
One procedure for calculating the least common multiple is to break each number into prime factors. Then the common and uncommon factors are raised to the highest exponent, which must be multiplied.
Smallest number of packagesTo calculate the smallest number of packages of each they can buy, you calculate the least common multiple.
First, the decomposition of the numbers into prime factors is carried out:
15= 3×5
12= 2×2×3= 2²×3
Then, the least common multiple is calculated as 2²×3×5
Solving, the least common multiple between 12 and 15 is 60.
Finally, this means that smallest number of packages of each they can buy is 60.
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To be competitive for admission to four-year universities (UCF, UF, FSU, FAU, FIU, UCF, USF, etc.) what courses should you try to have each year of high school no matter the intended college major or current status of high school graduation requirements?
Answer:
Ask your guidance counselor or a college admissions counselor
Step-by-step explanation:
a school district transported a total of 409 students and teachers to a zoo buses and vans
each bus transported a total of 55 students and teachers
each van transported a total of 12 students and teachers there were 5 more buses
what is the total number of students and teachers who rode to the zoo vans
Answer: There are 385 students and teachers who rode to the zoo in buses and 24 students and teachers who rode to the zoo in trains.
Step-by-step explanation:
Since we have given that
Total number of students and teachers = 409
Let the number of vans be x
Let the number of buses be x+5
Number of students and teachers each bus transported = 55
Number of students and teachers each van transported = 12
According to question,
Total number of students and teachers who rode to the zoo in buses will be
Total number of students and teachers who rode to the zoo in vans will be
Hence, there are 385 students and teachers who rode to the zoo in buses and 24 students and teachers who rode to the zoo in trains.
Please solve this question
Using the Poisson distribution, the probabilities are given as follows:
[tex]P(X = 0) = e^{-10.6}[/tex][tex]P(X \geq 1) = 1 - e^{-10.6}[/tex][tex]P(X \leq 2) = 67.78e^{-10.6}[/tex]What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successese = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval.The mean is given as follows:
[tex]\mu = 10.6[/tex]
Hence the probability of no dandelions in an area of 1 m² is P(X = 0), hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-10.6}(10.6)^{0}}{(0)!} = e^{-10.6}[/tex]
The probability of at least one dandelion is:
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - e^{-10.6}[/tex]
The probability of at most two dandelions is:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
Then:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-10.6}(10.6)^{0}}{(0)!} = e^{-10.6}[/tex]
[tex]P(X = 1) = \frac{e^{-10.6}(10.6)^{1}}{(1)!} = 10.6e^{-10.6}[/tex]
[tex]P(X = 2) = \frac{e^{-10.6}(10.6)^{2}}{(2)!} = 56.18e^{-10.6}[/tex]
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = e^{-10.6} + 10.6e^{-10.6} + 56.18e^{-10.6} = 67.78e^{-10.6}[/tex]
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John currently pays $500 monthly towards his minimum payments on his credit cards. , John now pays $350 towards the same credit cards through his debt relief program. How much does John save off his minimums after 3 months
The amount John saves off his minimums after 3 months is $450
Calculating amount savedFrom the question, we are to determine the amount John saves off his minimums after 3 months
The amount John saves off his minimums after 3 months =
($500 - $350) × 3
$150 × 3
= $450
Hence, the amount John saves off his minimums after 3 months is $450
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dexamethasone 4 mg/1 ml is available. the MD orders 6000 mcg. how much will the nurse give? (Round to the tenth)
Answer:
1.5 mL
Step-by-step explanation:
The abbreviation mcg stands for "microgram," or 10^-6 grams. The abbreviation mg stands for "milligram," or 10^-3 grams. The relationship between these is ...
1 mg = 1000 mcg
DoseThe order for 6000 mcg is an order for 6(1000 mcg) = 6(1 mg) = 6 mg. At 4 mg/mL, the quantity of dexamethasone required is ...
(6 mg)/(4 mg/mL) = (6/4) mL = 1.5 mL
The nurse will give 1.5 milliliters of dexamethasone.
math
look at the picture
Answer:
Rational
Step-by-step explanation:
cause I don't know how to explain
Write the equation of the line with a slope of 2/3 and y-intercept of 1. Write your answer in slope-intercept form
B = y - mx = 1 - (2/3)(0) = 1
y = (2/3)x + 1
Find the equations of the following lines.
a) Parallel to 2 + − 3 = 0 and passing through ( −4, 5)
b) Perpendicular to 2 = + 5 and passing through ( −1, 4)
a family has 8 girls and 4 boys. a total of 3 children must be chosen to speak on behalf of their family at a local benefit. what is the probability that no girls and 3 boys will be chosen help quickly someone
Answer:
1/55
Step-by-step explanation:the probability of choosing 3 boys.
The probability of choosing the first boy =4/12
The probability of choosing the second boy =3/11
The probability of choosing the third boy =2/10
The probability of choosing the 3 boys will be,
=4/12×3/11×2/10
=24/1320
what is the value of the expression below when x= 2? for y²-2y+10
Answer:
I think its y = 2.
Then, your answer will be 10.
Step-by-step explanation:
y²- 2y + 10
=2² - 2.2 + 10
=4 - 4 + 10
=10 ans.
Hope its helpful!
Answer:
If y = 2.
Your answer is 10.
Step-by-step explanation:
y²- 2y + 10
=2² - 2.2 + 10
=4 - 4 + 10
=10 ans.
Hope its helpful!
84 2/3% to a fraction in lowest terms
The evaluation of 84 2/3% to a fraction in its lowest term is [tex]\mathbf{ \dfrac{127}{150} }[/tex]
What is a fraction?Fractions are sections or parts of a whole. They are divided into two parts, the numerator, and the denominator.
From the given information, we are to convert a mixed fraction into its lowest terms. By doing that, we are to convert it to an improper fraction.
[tex]\mathbf{= 84 \dfrac{2}{3}\%}[/tex]
[tex]\mathbf{= \dfrac{(84 \times 3)+2}{3} \%}[/tex]
[tex]\mathbf{= \dfrac{254}{3} \%}[/tex]
[tex]\mathbf{= \dfrac{254}{3} \times \dfrac{1}{100}}[/tex]
[tex]\mathbf{= \dfrac{254}{300} }[/tex]
Divide both the numerator and denominator by (2)
[tex]\mathbf{= \dfrac{127}{150} }[/tex]
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find the volume pls
Answer:
i think it is 340
Step-by-step explanation:
what is the answer? PLEASE
Using the combination formula, the probability that Rosa's mom chooses sausage and onion is given by:
B. [tex]\frac{1}{C_{8,2}}[/tex].
The order in which the toppings are chosen is not important, hence the combination formula is used to solve this question.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
2 toppings are chosen from a set of 8, hence the number of options is given by:
[tex]C_{8,2}[/tex].
Sausage and onion correspond to one topping, hence the probability is given by:
B. [tex]\frac{1}{C_{8,2}}[/tex].
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Item cost $430 sales tax was $8.60 what is the percentage of the sales tax rate
Answer:
2%
Step-by-step explanation:
You can write it out as equation first.
430*x%=8.60, leave x% alone, so the equation will change into
x%=8.60/430
8.60/430=0.02=2%
therefore, x%=2%
Which steps would prove the circles similar?
Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 4.
Translate the circles so the center of one circle rests on the edge of the other circle, and dilate circle Y by a scale factor of 4.
Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3.
Translate the circles so the center of one circle rests on the edge of the other circle, and dilate circle Y by a scale factor of 3.
The steps needed is :Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3.
What is dilation?Dilation is a transformation, which is used to resize the object.
As the radius of big circle is 6 then the dilation should be scale factor 3.
As well as they should share the same center.
The radius of circle y being 2, has to increase by 3 times the value to equal the radius of circle x, and hence has to dilate by a scale factor of 3 as to match circle x,
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Find the no. of digits in 9 to the power 33
There are 32 no.of digits in
[tex]9[/tex] to the power of [tex]33 = 9^33 = 30 9031543826 3261236192[/tex]0641803529.
Step-by-step explanation: As the exponent is a positive integer, exponentiation means a repeated multiplication:
9 to the 33rd power =[tex]{9*....*9}[/tex] 33times
The exponent of the number 9, 33, also called index or power, denotes how many times to multiply the base (9).
Thus, we can answer what is 9 to the 33rd power as
[tex]9[/tex] to the power of [tex]33 = 9^33 = 30 9031543826 3261236192[/tex]0641803529.
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There exist 32 digits in 9 to the power [tex]33 = 9^{33}[/tex] of
30903154382632612361920641803529.
How to estimate the power of digits?The power of a numeral stands for how many multiples of the number there exist. The base of the number stands for the number itself and lives in front of the exponent. The exponent stands for the smaller number written above and to the right of the base. Positive exponents result in the base value existing multiplied by itself numerous times.
As the exponent exists as a positive integer, exponentiation signifies repeated multiplication.
9 to the 33rd power [tex]$=9* ........*9*[/tex] 33 times
The exponent of the number 9, 33, even named index or power, indicates how many times to multiply the base (9).
Therefore, we can answer what exists 9 to the 33rd power as 9 to the power of 33 = [tex]9^{33}[/tex] to the power of 30903154382632612361920641803529.
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