The cubic equation f(x) = x³ + 2 · x² + 4 · x + 8 has one real root and two complex roots.
What kind of roots does have a cubic equation?
In this problem we have a cubic equation and the nature of their roots must be inferred according to a algebraic method.
Cubic equations are polynomials of the form y = a · x³ + b · x² + c · x + d, there is a method to infer the nature of the roots of such polynomials: The discriminant from Cardano's method, an analytical method used to solve polynomials of the form a · x³ + b · x² + c · x + d = 0.
The discriminant is described below:
Δ = 18 · a · b · c · d - 4 · b³ · d + b² · c² - 4 · a · c³ - 27 · a² · d² (1)
Where:
There are three distinct real roots for Δ > 0.Real roots with multiplicity greater than 1 for Δ = 0.A real root and two complex roots for Δ < 0.If we know that a = 1, b = 2, c = 4 and d = 8, then the nature of the roots is:
Δ = 18 · 1 · 2 · 4 · 8 - 4 · 2³ · 8 + 2² · 4² - 4 · 1 · 4³ - 27 · 1² · 8²
Δ = - 1024
The cubic equation f(x) = x³ + 2 · x² + 4 · x + 8 has one real root and two complex roots.
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Find the value of c.
answer choices
A. 26
B. 104
C. 52
D. 93.5
Answer:
option B is the answer of given question
Answer:
D. 93.5
Step-by-step explanation:
Angle Formed by Two Chords= 1/2(SUM of Intercepted Arcs)
The lower arc is twice 52
c = 1/2( 104 +83)
c = 1/2 ( 187)
c =93.5
What is the value of 8x-25 when x is equal to 12?
Answer:
71
Step-by-step explanation:
Evaluate for x=12
(8)(12)−25
(8)(12)−25
=71
Answer:
71
Step-by-step explanation:
To evaluate [tex]8x - 25[/tex] when [tex]x = 12[/tex], we have to replace x with 12 in the expression:
[tex]8x - 25[/tex]
⇒ [tex]8(12) -25[/tex]
⇒ [tex]96 - 25[/tex]
⇒ [tex]\bf 71[/tex]
Karsten is preparing his will. He wants to leave the same amount of money to his two daughters. His elder daughter is careful with money, but the younger daughter spends it carelessly, so he decides to give them the money in different ways. How much must his estate pay his younger daughter each month over 20 years, so that the accumulated present value will be equal to the $50000 cash his elder daughter will receive upon his death? Assume that the younger daughters inheritance earns 6%/a compounded monthly
The amount that Karsten's estate should pay his younger daughter each month over 20 years so that the accumulated present value will be equal to $50,000 is $358.22.
How to calculate periodic payments?The monthly payments out of the present value of $50,000 can be computed using an online finance calculator.
The periodic payment represents the equal amount that can be paid to the daughter monthly so that it equals the PV of $50,000 of the estate share.
Data and Calculations:N (# of periods) = 240
I/Y (Interest per year) = 6%
PV (Present Value) = $50,000
FV (Future Value) = $0
Results:
Monthly Payment = $358.22
Sum of all periodic payments = $85,971.73 ($358.22 x 2400
Total Interest = $35,971.73
Thus, Karsten's younger daughter can be paid $358.22 to equal the accumulated present value of $50,000.
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Question
A scientist needs 60 liters of a 40% solution of alcohol. He has a 30% solution and a 60% solution available.
How many liters of the 30% solution and how many liters of the 60% solution should he mix to make the 40% solution?
Provide your answer below:
30% solution: liters, 60% solution:
4 Previous
liters
ba
77°F 940)
I
9:0
8/2
Answer:
40 liters of 30% solution.
20 liters of 60% solution.
Step-by-step explanation:
Let x = amount of 30% solution.
Let y = amount of 60% solution.
Equation of amounts of solutions.
x + y = 60
Equation of amounts of alcohol in the solutions.
0.3x + 0.6y = 0.4 × 60
x = 60 - y
0.3(60 - y) + 0.6y = 24
18 - 0.3y + 0.6y = 24
0.3y = 6
y = 20
x + y = 60
x + 20 = 60
x = 40
Answer:
40 liters of 30% solution.
20 liters of 60% solution.
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The number of liters of the 30% solution and the number of liters of the 60% solution to mix to make the 40% solution is 40 liters and 20 liters.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 7 is an equation.
We have,
Let 30% solution = m
Let 60% solution = n
Now,
A scientist needs 60 liters of a 40% solution of alcohol.
He has a 30% solution and a 60% solution available.
This means,
m + n = 60 _____(1)
30% of m + 60% of n = 40% of 60
0.30m + 0.60n = 0.40 x 60
0.30m + 0.60n = 24 ____(2)
From (1) and (2) we get,
m + n = 60
m = 60 - n _____(3)
Putting (3) in (2) we get,
0.30m + 0.60n = 24
0.30(60 - n) + 0.60n = 24
18 - 0.30n + 0.60n = 24
18 + 0.30n = 24
0.30n = 24 - 18
0.30n = 6
n = 6/0.30
n = 20
Putting n = 20 in (3) we get,
m = 60 - 20
m = 40
Now,
The number of liters of the 30% solution is 40.
The number of liters of the 60% solution is 20.
Thus,
The number of liters of the 30% solution and the number of liters of the 60% solution to mix to make the 40% solution is 40 liters and 20 liters.
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Find the height (in meters) of a storage tank in the shape of a right circular cylinder that has a circumference measuring 4 m and a volume measuring 36 m3.
Answer:
[tex]h = \bf 28.3 \space\ m[/tex]
Step-by-step explanation:
• We are given:
○ Volume = 36 m³,
○ Circumference = 4 m
• Let's find the radius of the cylinder first:
[tex]\mathrm{Circumference} = 2 \pi r[/tex]
Solving for [tex]r[/tex] :
⇒ [tex]4 = 2 \pi r[/tex]
⇒ [tex]r = \frac{4}{2\pi}[/tex]
⇒ [tex]r = \bf \frac{2}{\pi}[/tex]
• Now we can calculate the height using the formula for volume of a cylinder:
[tex]\mathrm{Volume} = \boxed{\pi r^2 h}[/tex]
Solving for [tex]h[/tex] :
⇒ [tex]36 = \pi \cdot (\frac{2}{\pi}) ^2 \cdot h[/tex]
⇒ [tex]h = \frac{36 \pi^2}{4 \pi}[/tex]
⇒ [tex]h = 9 \pi[/tex]
⇒ [tex]h = \bf 28.3 \space\ m[/tex]
Answer:
9π m ≈ 28.27m
Step-by-step explanation:
The volume of a right cylinder is given by the formula
πr²h where r is the radius of the base of the cylinder(which is a circle), h is the height of the cylinder
Circumference of base of cylinder is given by the formula 2πr
Given,
2πr = 4m
r = 2/π m
Volume given as 36 m³
So πr²h = 36
π (2/π)² h = 36
π x 4/π² h = 36
(4/π) h = 36
h = 36π/4 = 9π ≈ 28.27m
Find a formula for the nth term
of the arithmetic sequence.
First term -2
Common difference 8
an = [? ]n + []
Katrina has the option of an 8-year nonsubsidized student loan of $29,000 at an annual interest rate of 2.5% or an 8-year subsidized loan of $29,000 at an annual interest rate of 4.5%. Determine for which loan Katrina will pay less interest over the term of the loan if she starts making payments 2 years after obtaining the loan. (Assume Katrina makes monthly payments for each loan. Round your answers to the nearest cent, as appropriate.) The total interest paid on the nonsubsidized loan is $
Katrina would pay less amount of interest on the nonsubsidized student loan
The total interest paid on the nonsubsidized loan is $3,860.80
What is monthly compounding?
Monthly compounding means that the interest is computed and added to existing outstanding loan balance at the end of each month.
In this case, the loan would be repaid monthly but the first monthly payment would occur after 2 years of taking out the loans.
In other words, for the first 2 years, the interest would increase the balances with no corresponding reductions by a way of loan repayment, note that interest to be added monthly, as a result, we can compute outstanding balance 2 years for both loans using the future value formula of a single cash flow shown below:
FV=PV*(1+r/n)^(n*t)
FV=balance after 2 years=unknown
PV=loan amount
r=annual interest rate
n=number of times interest is compounded annually=12
t=number of years before repayments commence=2
Non-subsidized loan:
FV=$29,000*(1+2.5%/12)^(12*2)
FV=$30,485.28
Subsidized loan:
FV=$29,000*(1+4.5%/12)^(12*2)
FV=$31,725.71
Having determined the loan balances after 2 years, we can now compute the monthly payments that would be made in the remaining 6 years using the present value formula of an ordinary annuity because monthly payments would occur at the end of each month:
PV=PMT*(1-(1+r)^-N/r
PV=balance of loan after 2 years
PMT=monthly payment=unknown
r=monthly interest rate=annual interest rate/12
N=number of monthly payments in 6 years=12*6=72
Non-subsidized loan:
$30,485.28=PMT*(1-(1+2.5%/12)^-72/(2.5%/12)
PMT=$456.40
total monthly payments=$456.40*72
total monthly payments=$32,860.80
Interest= total monthly payments-loan
interest=$32,860.80-$29,000
interest=$3,860.80
Subsidized loan:
$31,725.71 =PMT*(1-(1+4.5%/12)^-72/(4.5%/12)
PMT=$503.61
total monthly payments=$503.61 *72
total monthly payments=$36,259.92
Interest= total monthly payments-loan
interest=$36,259.92 -$29,000
interest=$7,259.92
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A town has a population of 1.23 x 10 and grows at a rate of 6.7% every year. Which
equation represents the town's population after 4 years?
At the growth rate of [tex]6.7\%[/tex], the population of the town after 4 years can be represented by the equation, [tex]A=1.23\times 10\times(1.067)^4[/tex].
What is the formula for the population?The growth rate of a population is a measure of how fast a population increases.If the initial population is [tex]P[/tex] and the growth rate is [tex]r\%[/tex] every year, then the population after [tex]t[/tex] years will be given by the following formula: [tex]A=P(1+\frac{r}{100})^t[/tex].Here, the initial population is [tex]P=1.23\times 10[/tex] and the growth rate is [tex]r=6.7\%[/tex].
So the population after [tex]t=4[/tex] years will be:
[tex]A=P(1+\frac{r}{100})^t\\\Longrightarrow A=1.23\times 10\times(1+\frac{6.7}{100})^4\\\Longrightarrow A=1.23\times 10\times(1.067)^4[/tex]
Therefore, at the growth rate of [tex]6.7\%[/tex], the population of the town after 4 years can be represented by the equation, [tex]A=1.23\times 10\times(1.067)^4[/tex].
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Please help I need to turn this in by Monday!
Answer: Rational, Irrational, Rational, Natural, Natural, Integer
Step-by-step explanation:
-4.2 is a rational number as it can be converted into a fraction
3√5 is an irrational number as it can't be converted into a fraction
5/3 is a rational number as it is a fraction
9 is a natural number as it is a positive whole number
√16 is a natural number as despite the square root, √16 is 4 which is a natural number
-8/2 is an integer as -8/2 is -4 which is a negative whole number
what is the measure of angle B from the right triangle below ?
Answer:
d
Step-by-step explanation:
using the cosine ratio in the right triangle
cos B = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{2}{10}[/tex] , then
B = [tex]cos^{-1}[/tex] ( [tex]\frac{2}{10}[/tex] ) ≈ 78.46° ( to 2 dec. places )
A COUPLE PLAN TO HAVE THREE CHILDREN.
A) LIST ALL THE POSSIBILITIES FOR THE SAMPLE SPACE.
B) WHAT IS THE PROBABILITY THAT THEY HAVE AT MOST TWO BOYS?
C) WHAT IS THE PROBABILITY THAT THEY HAVE AT LEAST TWO GIRLS?
D) WHAT IS THE PROBABILITY THAT THEY ARE ALL OF THE SAME SEX?
Using the sample space and probability concepts, we have that:
A) All the possibilities for the sample space are: {{G,G,G}, {G,G,B}, {G,B,G}, {G,B,B}, {B,G,G}, {B,G,B}, {B,B,G}, {B,B,B}}.
B) The probability is: 7/8.
C) The probability is: 1/2.
D) The probability is: 1/4.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
The sample space is the set that contains all possible outcomes, hence in this problem, considering G for girl and B for boy, it is given by:
{{G,G,G}, {G,G,B}, {G,B,G}, {G,B,B}, {B,G,G}, {B,G,B}, {B,B,G}, {B,B,B}}.
For item B, 7 outcomes have at most two boys, hence the probability is 7/8.
For item C, 4 outcomes have at least two girls, hence the probability is 4/8 = 1/2.
For item D, 2 outcomes have all the babies with the same sex, hence the probability is 2/8 = 1/4.
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If a certain train fare costs $5.00 for the first
10 miles of service, $0.25 per mile for the next
40 miles, and $0.10 per mile for each additional
mile, what would the train fare be to travel a
total distance of 100 miles?
Answer:
$20
Step-by-step explanation:
$5.00 = 10miles
$0.25(40) = 40 miles
Remaining miles: 100 - (10 + 40) = 50
0.10(50) = 50 miles
5.00 + 0.25(40) + 0.10(50)
5.00 + 10.00 + 5.00
$20.00 for 100 miles
How can 25 e42 n=1 be rewritten?
Answer:
The 'n = 1' below sigma represents the lower bound. meaning the number from which you start adding.
'25' above sigma is the upper bound.
In general it means adding 42 from 1 to 25 times.
so 42(25).
Answer:
C. 42(25)
Step-by-step explanation:
Took the unit test review and this was the correct option choice.
Goodluck on your unit test, I am sure that you will do good :)
Dante is a software salesman. Let represent his total pay (in dollars). Let represent the number of copies of History is Fun he sells. Suppose that and are related by the equation 2400+120x=y
Considering the given linear function, we have that:
The change for each copy that he sells is of $120.If he sells no copies, he makes $2400.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.His payment for x copies bought is:
y = 120x + 2400.
Hence:
The change for each copy that he sells is of $120, as the slope is of $120.If he sells no copies, he makes $2400, which is the y-intercept.More can be learned about linear functions at https://brainly.com/question/24808124
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The set of all triples of real numbers with the standard vector
addition but with scalar multiplication defined by
k(x, y, z) = (k2
x,k2
y,k2
z)
The given operation is not a vector space because it fails axiom 8 ("distributivity of scalar multiplication with respect to field addition").
What is a vector space?A vector space can be defined as a space (set) which comprises vectors, whose elements can be added under the associative and commutative operation, and can be multiplied by scalars under the associative and distributive operation.
This ultimately implies that, a vector space must be comprised of at least one element, which is generally regarded as its zero vector and the smallest possible vector space.
For every element {u, v and w} in vector (V), and element {a and b} in vector (F), this 8th axiom must be satisfied in order to have a vector space:
(k + m)u = ku + mu
Note: The above axiom (k + m)u = ku + mu is generally referred to as the "distributivity of scalar multiplication with respect to field addition."
Given the following vector:
k(x, y, z) = {k²x, k²y, k²z}
If x₁ · x₂ ≥ 0, then, (kx₁) · (kx₁) = k²x₁y₁ ≥ 0 [Closed in scalar multiplication].
If x₁ · x₂ ≥ 0, x₂ · y₂ ≥ 0, then (x₁ + x₂) · (y₁ + y₂):
x₁y₁ + x₂y₂ + x₁y₂ + x₂y₁ < 0
x₁y₁ + x₂y₂ < -(x₁y₂ + x₂y₁) [Not closed in vector addition].
In conclusion, we can infer and logically deduce that the given operation is not a vector space because it fails axiom 8 ("distributivity of scalar multiplication with respect to field addition").
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Complete Question:
Determine whether each set equipped with the given operations is a vector space. For those that are not vector spaces identify the vector space axioms that fail.
The set of all triples of real numbers with the standard vector addition but with scalar multiplication defined by k(x, y, z) = {k²x, k²y, k²z}.
louizah baked 8 dozen muffins and sold them all at the school for R5,50. if louizah bought the ingredients for R12,50. Determine louizahs profit
Answer:
3550
Step-by-step explanation:
C.P=Rs 1250
S.P=8(12)(50)
Rs4800
P=S.P-C. P
=Rs4800-Rs1250
= Rs3550
What is the solution to the system of equations?
y = 2/3 x + 3
X= -2
The solution to the given system of equations is x = -2, y = 5/3. That is (-2, 5/3)
Solving system of equationsFrom the question, we are to determine the solution to the given system of equations
The given system of equation is
y = 2/3 x + 3 ----------- (1)
x= -2 ----------- (2)
The value of x has been given in the second equation of the system of equations.
Now, we will determine the value of y
From the second equation, we have that
x = -2
Substitute the value of x into the first equation,
y = 2/3 x + 3
y = 2/3 (-2) + 3
y = -4/3 + 3
y = 5/3
Hence, the solution to the given system of equations is x = -2, y = 5/3. That is (-2, 5/3)
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To win at LOTTO in one state, one must correctly select 7 numbers from a collection of 61 numbers (1 through 61). The order in which the selection is made does not matter. How many different selections are possible?
Using the combination formula, it is found that 436,270,780 different selections are possible.
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]
In this problem, 7 numbers are taken from a set of 61, hence the number of different selections is given by:
C(61,7) = 61!/(7! x 54!) = 436,270,780
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Function: y=x2+5x−7
Vertex: ( , )
Solutions: ( , ) and ( , )
Answer:
vertex : (-5/2, -53/4)
solutions: (-(5-sqrt53)/2, 0) (-(5+sqrt53)/2, 0)
Step-by-step explanation:
1.The vertex of the function is (-5/2, -53/4).
2.We have two solutions:
x = (-5 + √53) / 2 ≈ 0.73
x = (-5 - √53) / 2 ≈ -5.73
To find the vertex and solutions of the function y = x^2 + 5x - 7, we can use the formula for the vertex and the quadratic formula for finding solutions.
1. Vertex:
The vertex of a quadratic function in the form y = ax^2 + bx + c can be found using the formula:
x = -b / (2a)
y = f(x) = ax^2 + bx + c
Given: a = 1, b = 5, c = -7
x = -5 / (2 * 1) = -5 / 2
Now, substitute the value of x into the equation to find y:
y = (-5/2)^2 + 5 * (-5/2) - 7
y = 25/4 - 25/2 - 7
y = 25/4 - 50/4 - 7
y = (25 - 50 - 28) / 4
y = -53 / 4
So, the vertex of the function is (-5/2, -53/4).
2. Solutions (or roots or x-intercepts):
To find the solutions (x-intercepts) of the function, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Given: a = 1, b = 5, c = -7
x = (-5 ± √(5^2 - 4 * 1 * -7)) / 2 * 1
x = (-5 ± √(25 + 28)) / 2
x = (-5 ± √53) / 2
Now, we have two solutions:
x = (-5 + √53) / 2 ≈ 0.73
x = (-5 - √53) / 2 ≈ -5.73
So, the solutions of the function are approximately x ≈ 0.73 and x ≈ -5.73.
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Slope=-6/5
Y intercept=2
What is the point slope form?
Answer: [tex]\Large\boxed{y-2=-\frac{6}{5} (x-0)}[/tex]
Step-by-step explanation:
Given the requirement of function form
Point-slope form: y - y₁ = m (x - x₁)
m = slope(x₁, y₁) = Any point on the lineGiven information
Slope (m) = -6/5
Y-intercept (x₁, y₁) = 2 = (0, 2)
Substitute values into the required form
y - y₁ = m (x - x₁)
y - (2) = (-6/5) (x - 0)
[tex]\Large\boxed{y-2=-\frac{6}{5} (x-0)}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Amy and Richard each solved an equation using the quadratic formula.
Amy's Equation and Method
Latex: 4x^2+7x-20=0
4
x
2
+
7
x
−
20
=
0
Step 1: Latex: x=\frac{-7\pm \sqrt{7^2-4(1)(20)}}{2(4)}
x
=
−
7
±
√
7
2
−
4
(
1
)
(
20
)
2
(
4
)
Step 2: Latex: x=\frac{-7\pm \sqrt{49-80}}{8}
x
=
−
7
±
√
49
−
80
8
Step 3: Latex: x=\frac{-7\pm \sqrt{-31}}{8}
x
=
−
7
±
√
−
31
8
Step 4: Latex: x=\frac{-7\pm i\sqrt{31}}{8}
x
=
−
7
±
i
√
31
8
Richard's Equation and Method
Latex: x^2-6x+8=0
x
2
−
6
x
+
8
=
0
Step 1: Latex: x=\frac{6\pm \sqrt{(-6)^2-4(1)(8)}}{2(1)}
x
=
6
±
√
(
−
6
)
2
−
4
(
1
)
(
8
)
2
(
1
)
Step 2: Latex: x=\frac{6\pm \sqrt{36-32}}{2}
x
=
6
±
√
36
−
32
2
Step 3: Latex: x=\frac{6\pm \sqrt{4}}{2}
x
=
6
±
√
4
2
Step 4: Latex: x=\frac{6+\sqrt{4}}{2}
x
=
6
+
√
4
2
and Latex: x=\frac{6-\sqrt{4}}{2}
x
=
6
−
√
4
2
Step 5: Latex: x=\frac{6+2}{2}
x
=
6
+
2
2
and Latex: x=\frac{6-2i}{2}
x
=
6
−
2
i
2
Step 6: Latex: x=4
x
=
4
and Latex: x=3-i
x
=
3
−
i
Both students made a mistake.
Describe the mistake each student made.
Explain what each student needs to do to fix their mistake.
Create your own quadratic equation, and explain how to use the quadratic formula to solve it. Be specific, using Latex: a\textsf{, }b\textsf{,} and Latex: c
c
of your equation and giving the solutions to the equation you chose.
Number your responses from 1 to 3 so your instructor can tell which question you're responding to. You may not receive full credit if your teacher cannot determine that you've answered each question.
Search entries or author
The mistake each student made and what each student needs to do to fix their mistake is;
Amy didn't include the negative sign for the 20, so she should include itRichard added a negative sign underneath the radicalQuadratic equationx² - 6x + 8 = 0
x = - b ± √b² - 4ac / 2a
where,
a = 1b = -6c = 8x = - b ± √b² - 4ac / 2a
= -(-6) ± √(-6)² - 4(1)(8) / 2(1)
= 6 ± √36 - 32 / 2
= 6 ± √4 / 2
= 6 ± 2 / 2
x = 6/2 + 2/2 or 6/2 - 2/2
= 3 + 1 or 3 - 1
x = 4 or 2
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ASAP Please help me with this questions ASAP
Answer:
an angle bisector
Step-by-step explanation:
This is showing the construction of the bisector of ∠LNM
hey can anyone give me the answers to the questions that are blank
The value of the rate of change of the function is 14a + 7h
Rate of change of functionThe rate of change of function is also known as the slope expressed according to the equation shown below;
f'(x) = f(a+h)-f(a)/h
Given the function below expressed as:
f(x) =1 + 7x^2
Determine the function f(a)
To determine the function, simply replace x with 'a" to have:
f(a) =1 + 7a^2
Determine the function f(a+h)
f(a+h) = 1 + 7(a+h)^2
f(a + h) = 1 + 7(a^2+2ah+h^2)
f(a + h) = 1 + 7a^2 + 14ah + 7h^2
To determine the rate of change
f'(x) = f(a+h)-f(a)/h
f'(x) = 1 + 7a^2 + 14ah + 7h^2 - 1 - 7a^2/h
f'(x) = + 14ah + 7h^2/h
f'(x) = 14a + 7h
Hence the value of the rate of change of the function is 14a + 7h
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A) AB and BC
B) AC and BD
tell if each pair of segments is congruent
a. Line AB and line BC are not congruent because their distance of separation are not equal
b. Line AC and line BD are not congruent because their distance of separation are not equal
How to proof the statementFrom the number line drawn, we have the following deductions;
Line AB = -5 to -2 = 3
Line BC = -2 to 0 = 2
Line AC = -5 to 0 = 5
Line AD = -5 to 5 = 10
Line BD = -2 to 5 = 7
We can see that;
a. Line AB and line BC are not congruent because their distance of separation are not equal
b. Line AC and line BD are not congruent because their distance of separation are not equal
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If there are 12 donuts per box, which of the following equations will give you the number of boxes, x, that Joe needs to buy?
The equation that would give the number of boxes, x, that Joe needs to buy is 12x = 60. The correct option is c.) 12x = 60
Writing an equationFrom the question, we are to determine the equation that will give the number of boxes, x, that Joe needs to buy
From the given information,
Joe needs 60 donuts to feed his construction crew
Also,
There are 12 donuts per box
This means he needs to buy 60/12 boxes of donut
Since the number of boxes Joe needs to buy is x
∴ 60/12 = x
60 = 12x
12x = 60
Hence, the equation that would give the number of boxes, x, that Joe needs to buy is 12x = 60. The correct option is c.) 12x = 60
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Which is the best approximation of the solutions to the system of equations graphed below?
According to the direct inspection, we conclude that the best approximation of the two solutions to the system of quadratic equations are (x₁, y₁) = (- 1, 0) and (x₂, y₂) = (1, 2.5). (Correct choice: C)
What is the solution of a nonlinear system formed by two quadratic equations?
Herein we have two parabolae, that is, polynomials of the form a · x² + b · x + c, that pass through each other twice according to the image attached to this question. We need to estimate the location of the points by visual inspection on the Cartesian plane.
According to the direct inspection, we conclude that the best approximation of the two solutions, that is, the point where the two parabolae intercepts each other, to the system of two quadratic equations are (x₁, y₁) = (- 1, 0) and (x₂, y₂) = (1, 2.5). (Correct choice: C)
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the five-number summary calculated in part C to create a box plot representing the data. Draw a box plot representing the following data. Be sure to mark the outlier. 10 13 15 12 12 4 12 17 12 13 15 18 10 11 20 19 Lines Shapes Fill: Line: Width: 2 pt
The five-number summary is:
Minimum: 4
Quartile Q1: 11.25
Median: 12.5
Quartile Q3: 16.5
Maximum: 20
The box plot is attached below.
What is the Five-number Summary?The five-number summary of a data that is displayed on a box plot include: minimum and maximum values, lower and upper quartiles, and the median.
Given the data, 10, 13, 15, 12, 12, 4, 12, 17, 12, 13, 15, 18, 10, 11, 20, 19, the five-number summary is:
Minimum: 4
Quartile Q1: 11.25
Median: 12.5
Quartile Q3: 16.5
Maximum: 20
There are no outliers. Thus, the box plot that represents the five-number summary is shown in the image attached below.
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Answer: it is correct i got it from edmentum
Step-by-step explanation:
help me solve this asap
Answer:
a) A = 3, B = 8.
b) C = 2, D = 25
Step-by-step explanation:
See the image below.
f(x)=ax+b/2 then f^-1 (x-1) =2x-5/2 find a and b
From the given inverse function, we have
[tex]f^{-1}(x-1) = 2x - \dfrac52 \\\\ \implies f^{-1}(x) = f^{-1}((x+1)-1) = 2(x+1) - \dfrac52 = 2x-\dfrac12[/tex]
By definition of inverse function,
[tex]f\left(f^{-1}(x)\right) = x[/tex]
so that
[tex]f\left(2x-\dfrac12\right) = x[/tex]
[tex]a\left(2x-\dfrac12\right) + \dfrac b2 = x[/tex]
[tex]2ax - \dfrac a2 + \dfrac b2 = x[/tex]
[tex]\implies\begin{cases}2a=1 \\\\ -\dfrac a2+\dfrac b2 = 0\end{cases}[/tex]
[tex]\implies \boxed{a=\dfrac12}[/tex]
[tex]\implies \dfrac b2 = \dfrac a2 \implies \boxed{b=\dfrac12}[/tex]
EVALUATE THE FOLLOWING:
A) 85!/82!
B) nC0
C) nPn
Answer:
Step-by-step explanation:
85!/82! = 85*84*83 = 592620
n choose 0 is always equals 1
n P n also always equals 1