Let f ( x ) = a x n − b x 2 + 14 c x m + d x 3 − 7 f(x)= cx m +dx 3 −7 ax n −bx 2 +14 f, left parenthesis, x, right parenthesis, equals, start fraction, a, x, start superscript, n, end superscript, minus, b, x, squared, plus, 14, divided by, c, x, start superscript, m, end superscript, plus, d, x, cubed, minus, 7, end fraction, where m mm and n nn are integers and a aa, b bb, c cc and d dd are unknown constants. Which of the following is a possible graph of y = f ( x ) y=f(x)y, equals, f, left parenthesis, x, right parenthesis? Choose 1 answer:
Answers
The graph in option C is the one that best satisfies the function y = f ( x ) y=f(x)y, equals, f, left parenthesis, x, right parenthesis
How to solveThe ultimate exponent of the equation, [tex]x^n or x^m[/tex], is the key factor that determines the end behavior amid a graph.
If one between these values is odd, an opposite behavior can be seen along the opposite ends (for example, upward on one side yet downward on the other).
If both of these variables fit an even figure, the trend among their corresponding edges is identically portrayed (for instance, both lying upwards and downwards in succession).
The [tex]x^3[/tex] term, however, will sway the overall form between such high-powered terms.
Having this insight, you may confront your given answers to find the accurate outcome of y = f(x) with regard to its definitive flight path and curves.
Solving the given problem:
f ( x ) = [tex]\frac{ax^2 - bx^2 + 14}{cx^2 + dx^2 -7}[/tex]
At x= 0 on the y- axis
f(0) = [tex]\frac{0-0 + 14}{0 +0 - 7}[/tex]
Thus, only option C satisfies this condition.
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Related Questions
The entire graph of the function g is shown in the figure below.
Write the domain and range of g as intervals or unions of intervals.
domain=
range =
Answers
For the given function 'g':
domain = (-4, -2) ∪ (1, 3]
range = (-5, 4]
If the function is defined as f(x) = y, then the values of x for which the value of function exists, the set of that values is said to be the domain of the function f.
If the function is defined as f(x) = y, then the set of all possible values of the function that is the set of all possible values of y is said to be the range of the function f.
Here given the graph of 'g'.
From the graph we can see that for -4 < x < -2 and 1 < x [tex]\le[/tex] 3 the function has graph.
So the domain = (-4, -2) ∪ (1, 3]
And it is clear that the value of y lies between -5 < y [tex]\le[/tex] 4.
So the range = (-5, 4].
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Suppose that $2000 is invested at a rate of 4.6%, compounded quarterly. Assuming that no withdrawals are made, find the total amount after 6 years
Do not round any intermediate computations, and round your answer to the nearest cent.
Answers
Answer:
$2,631.55
Step-by-step explanation:
To find the total amount in the account after 6 years, we can use the compound interest formula.
Compound Interest Formula[tex]\boxed{\sf A=P\left(1+\dfrac{r}{n}\right)^{nt}}[/tex]
where:
A = Final amount.P = Principal amount.r = Interest rate (in decimal form).n = Number of times interest is applied per year.t = Time (in years).Given values:
P = $2,000r = 4.6% = 0.046n = 4 (quarterly)t = 6 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=2000\left(1+\dfrac{0.046}{4}\right)^{4 \cdot 6}[/tex]
[tex]\implies \sf A=2000\left(1+0.0115\right)^{24}[/tex]
[tex]\implies \sf A=2000\left(1.0115\right)^{24}[/tex]
[tex]\implies \sf A=2000\left(1.3157739...\right)[/tex]
[tex]\implies \sf A=2631.54794...[/tex]
Therefore, the total amount after 6 years is $2,631.55 rounded to the nearest cent.
A sample of a radioactive substance has an initial mass of 45.1 mg. This substance follows a continuous exponential decay model and has a half-life of 19
minutes.
(a)let t be the time (in minutes) since the start of the experiment, and
let y be the amount of the substance at time t.
Write a formula relating y to t.
Use exact expressions to fill in the missing parts of the formula.
Do not use approximations.
y = ()e^()t
(b) How much will be present in 9 minutes?
Do not round any intermediate computations, and round your
answer to the nearest tenth.
Answers
a) The formula relating y to t is: y = 45.1 * e^(-0.693/19 * t) b) there will be approximately 30.1 mg of the substance present after 9 minutes.
How to Write a formula relating y to t.(a) The general formula for exponential decay is y = y0 * e^(-kt), where y is the amount at time t, y0 is the initial amount, k is the decay constant, and e is Euler's number.
To find the decay constant, we can use the fact that the half-life is 19 minutes. The formula for half-life is t1/2 = ln(2) / k, where ln(2) is the natural logarithm of 2.
Substituting t1/2 = 19 and ln(2) = 0.693 into the formula gives:
19 = 0.693 / k
k = 0.693 / 19
So the formula relating y to t is:
y = 45.1 * e^(-0.693/19 * t)
(b) To find how much will be present in 9 minutes, we can plug t = 9 into the formula we found in part (a):
y = 45.1 * e^(-0.693/19 * 9) ≈ 30.1 mg
So, there will be approximately 30.1 mg of the substance present after 9 minutes.
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For any positive values x and y, f(xy) = f(x) + f(y). f(1/2021) = 1.
Find f(2021).
I will give BRAINLIEST to correct answer.
Answers
f(1/2021 * 2021) = f(1/2021) + f(2021)
Simplifying the left-hand side gives us:
f(1) = f(1/2021) + f(2021)
Substituting f(1/2021) = 1, we have:
f(1) = 1 + f(2021)
Therefore,
f(2021) = f(1) - 1.
However, we don't know what f(1) is. One way to find it is to let x = y = 1. Then we have:
f(1) = f(1) + f(1),
which implies that f(1) = 0.
Therefore,
f(2021) = f(1) - 1 = -1.
So the answer is -1.
Solve for x. Round to the nearest tenth, if necessary.
Answers
Answer:
x=38.6
Step-by-step explanation:
x=b/cos(alpha)
x=30/cos(39⁰)
x=38.602
can some one help me
Caleb is selecting cards from a set of 12 cards numbered 1-2-4-4-5-5-5-5-6-9-10-13.
What is the probability that Caleb selects a 5 on the first selection, returns the card to the deck, shuffles the cards, and then draws a 5 on the second selection?
Answers
The probability of Caleb selecting a 5 on the first selection and then selecting a 5 on the second selection after returning the card to the deck and shuffling is 1/9.
There are a total of 12 cards, out of which 4 are 5s. Since Caleb returns the card to the deck and shuffles it, the selection of the first card does not affect the probability of selecting a 5 on the second selection.
Therefore, the probability of selecting a 5 on the first selection is 4/12 = 1/3, and the probability of selecting a 5 on the second selection is also 4/12 = 1/3.
Since the events are independent, we can multiply the probabilities to find the probability of both events occurring:
P(selecting a 5 on first selection and selecting a 5 on second selection) = P(selecting a 5 on first selection) x P(selecting a 5 on second selection)
= (1/3) x (1/3)
= 1/9
Therefore, the probability that Caleb selects a 5 on the first selection, returns the card to the deck, shuffles the cards, and then draws a 5 on the second selection is 1/9.
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a2=25 i cant find the ancer to thiss
Answers
The value of the variable a in the equation is 5 from the calculation here.
How to determine the value?We need to square of a number is described as a number that when multiplied by itself give the original number.
Also, index forms are described as those mathematical forms that are used to represent numbers that are too large or small.
From the information given, we have the equation;[tex]a^2[/tex]=25
find the square root of value of 25,
We have;25 = [tex]5^2[/tex]
Substitute the value, we get;[tex]a^2[/tex] = [tex]5^2[/tex]
Take out the similar factor, this is their exponents.
We then have;
a = 5
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Complete question;
Find the value of a in the equation;a² = 25
i need answer please
Answers
The surface area of the rectangular prism is 210 in²
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators.
The surface area of a rectangular prism is the sum of each area for the surface.
Hence:
Surface area = 2(8 in * 5 in) + 2(5 in * 5 in) + 2(8 in * 5 in) = 210 in²
The surface area of the prism is 210 in²
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Which of the following is the graph of the quadratic function y = x² - 4x+4?
A. Graph C
B. Graph B
C. Graph D
D. Graph A
Answers
Answer:
The correct answer is C, Graph D.
x^2 - 4x + 4 = (x - 2)^2.
what's equivalent to x^2-4x-l2
Answers
Answer:
Assuming you meant to write "x^2 - 4x - 12", there are a few equivalent forms that you could use to represent this expression. One common form is:
(x - 6)(x + 2)
Step-by-step explanation:
This is the factored form of the expression, which shows that it can be written as a product of two linear factors. To see why this is true, you can use the distributive property to expand the product:
(x - 6)(x + 2) = x(x + 2) - 6(x + 2) = x^2 + 2x - 6x - 12 = x^2 - 4x - 12
Find the distance from G to S.
Answers
Answer:
i think its b sorry if it's wrong
Step-by-step explanation:
How many quarters do you need to add to 31/4 to get 41/2
Answers
Answer:
51/4 quarters
Step-by-step explanation:
To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator for 4 and 2 is 4x2=8.
So we need to convert both fractions to have a denominator of 8:
31/4 = (31/4) x (2/2) = 62/8
41/2 = (41/2) x (4/4) = 164/8
Now we can add the fractions:
62/8 + x/4 = 164/8
Subtracting 62/8 from both sides:
x/4 = 102/8
Simplifying:
x = 51/4
Therefore, we need to add 51/4 quarters to 31/4 to get 41/2
College Level Trigonometry Question!
Answers
The angle measures for this problem are given as follows:
θ = 150º and θ = 330º.
How to obtain the angle measure?The trigonometric expression for this problem is given as follows:
[tex]\theta = \arctan{\left(-\frac{\sqrt{3}}{3}\right)}[/tex]
The solution to the arctangent function is the angle which has the given tangent value.
The angle on the first quadrant with a tangent value of sqrt(3)/3 is given as follows:
θ = 30º.
The quadrants in which the tangent is negative are given as follows:
2nd and 4th.
Hence the equivalent angles are given as follows:
2nd quadrant: θ = 180 - 30 = 150º.4th quadrant: θ = 360 - 30 = 330º.More can be learned about arctangent at https://brainly.com/question/10061217
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Given that f (x) = StartFraction 120 Over x squared EndFraction , What is the domain of the function f ? a. only positive integers c. only negative integers b. All non zero real numbers. d. All real numbers including zero
Answers
For the function "f (x) = 120/x²", the domain of the function "f" is (b) All non zero real numbers.
The "Domain" of a function is the set of all possible "input-values" for which the function is defined. In this case, the function is defined as:
f (x) = 120/x²
The only restriction on the input values is that the denominator cannot be equal to zero, because division by zero is undefined.
So, the domain of the function f is all non-zero real numbers.
Therefore, the correct option is (b): All non-zero real numbers.
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The given question is incomplete, the complete question is
Given that f (x) = 120/x², What is the domain of the function f ?
(a) only positive integers,
(b) All non zero real numbers,
(c) only negative integers,
(d) All real numbers including zero.
A catering service offers 5 appetizers, 11 main courses, and 4 desserts. A customer is to select 4 appetizers, 9 main courses, and 3 desserts for a banquet. In how many ways can this be done?
Answers
Total number of ways = (Number of ways to select appetizers) x (Number of ways to select main courses) x (Number of ways to select desserts)
Number of ways to select appetizers = C(5,4) = 5
Number of ways to select main courses = C(11,9) = 330
Number of ways to select desserts = C(4,3) = 4
Therefore, the total number of ways the customer can select 4 appetizers, 9 main courses, and 3 desserts is:
Total number of ways = 5 x 330 x 4 = 6,600
So, there are 6,600 ways the customer can select the items for the banquet.
There are 1100 many ways can be done that is when catering service offers 5 appetizers, 11 main courses, and 4 desserts.
Given that,
A catering service offers 5 appetizers, 11 main courses, and 4 desserts. A customer is to select 4 appetizers, 9 main courses, and 3 desserts for a banquet.
We have to find how many ways can this be done.
We know that,
Number of appetizers offered = 5
Number of appetizers customer is to select = 4
Number of main courses offered = 11
Number of main courses customer is to select = 9
Number of desserts offered = 4
Number of desserts the customer is to select = 3
So,
To determine the number of ways this can be selected,
By using the combination formula that is
[tex]^nC_r = \frac{n!}{r!(n-r)!}[/tex]
[tex]^nC_r = ^5C_4\times ^{11}C_9\times^4C_3[/tex]
[tex]^5C_4\times ^{11}C_9\times^4C_3 = \frac{5!}{4!(5-4)!} \times \frac{11!}{9!(11-9)!}\times \frac{4!}{3!(4-3)!}[/tex]
[tex]^5C_4\times ^{11}C_9\times^4C_3 = \frac{5!}{4!1!} \times \frac{11!}{9!2!}\times \frac{4!}{3!1!}[/tex]
[tex]^5C_4\times ^{11}C_9\times^4C_3 = \frac{5!}{4!} \times \frac{11!}{9!(2)}\times \frac{4!}{3!}[/tex]
[tex]^5C_4\times ^{11}C_9\times^4C_3 =[/tex] 5 × 11 × 5 × 4
[tex]^5C_4\times ^{11}C_9\times^4C_3 =[/tex] 1100
Therefore, There are 1100 many ways this can be done.
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Find the slope of the tangent to f(x) = x^2 at the point (-2,4).
Answers
Answer:
f'(x) = 2x, so f'(-2) = 2(-2) = -4.
3⋅f(−4)−3⋅g(−2) = ?
Ayuda por favor
Answers
The value of the 3 × f( - 4 ) - 3 × g( - 2 ) is 40
Given the following expression 3 × f( - 4 ) - 3 × g( - 2 ), to find the required values, we can assume that;
f( - 4 ) = 15
g( - 2 ) = 5
Substitute the given parameters into the expression to have:
3 × f(- 4 ) - 3 × g(- 2) = 3 × 15 - 3 × 5
= 45 - 5
= 40
Hence the value of the 3 × f( - 4) - 3 × g( - 2) is 40
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3^-1/2 x^1/2
express with radical signs instead of fractional exponents. rationalize the denominator.
please help
Answers
Answer:
[tex]\sqrt{x/3}[/tex]----------------------
Use the following identities:
[tex]a^{-b}=1/a^b[/tex][tex]a^{1/2}=\sqrt{a}[/tex][tex]a^bc^b=(ac)^b[/tex]Apply the identities to the given expression:
[tex]3^{-1/2}x^{1/2}=(3^{-1}x)^{1/2}=(x/3)^{1/2}=\sqrt{x/3}[/tex]Drag-and-Drop Technology-Enhanced
An expression is shown.
14a +7+ 5b+ 2a + 10b
Move words into the columns to describe the parts of the expression. Not all words will be used, and each column should
have at least one word to describe it.
14a
sum
term
factor
7
5
product
quotient
coefficient
2a + 10b
Answers
The value of expression 14a +7+ 5b+ 2a + 10b will be 16a + 15b + 7
Since Expression is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We are given the expression as;
14a +7+ 5b+ 2a + 10b
Combine like terms;
14a + 2a + 10b +7+ 5b
16a + 15b + 7
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Solve the equation.
3/4x+3-2x = -1/4+1/2x+5
If necessary:
Combine Terms
Apply Properties:
Add Subtract
Multiply Divide
Answers
The solution of the equation is x = -1.
Given is an equation we need to solve it,
3x/4 + 3 - 2x = -1/4 + x/2 +5
Multiplying the equation by 4 both the sides,
3x + 12 - 8x = -1 + 2x + 20
Combining the like terms,
3x - 8x - 2x = 20 - 1 - 12
3x - 10x = 7
-7x = 7
x = -1
Hence the solution of the equation is x = -1.
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The vertices of AABC are A (-3, -6), B (-3,5), and C (5,5).
What is the area of AABC?
Answers
Answer:
44 units²-----------------------------
AB is vertical with same x-coordinates, and BC is horizontal with same y-coordinates.
Hence this is a right triangle.
Its area is:
A = 1/2 × AB × BCA = 1/2(5 - (-6))(5 - (-3)) = 1/2(11)(8) = 44 units²How many different ways are there to arrange the letters in the word MISSISSIPPI?
Answers
Answer: 34,650 permutations
prove that:
(P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)=-4(2p² + 1)/(p²-4) (p² - 1)
Answers
The given identity (P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)=-4(2p² + 1)/(p²-4) (p² - 1) is proven below
How to prove the given identityGiven the following equation
(P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)=-4(2p² + 1)/(p²-4) (p² - 1)
We start by simplifying the left-hand side of the equation:
(P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)= [(P²+1)/(P(P-1))] + [(P²+1)/(P(P+1))] - [(P²-1)/((P+2)P)] - [(P²+1)/((P-2)P)]
Next, we have the following steps to simplify the expression
= [(P³ + P² + P + 1)/(P(P²-1))] - [(P³ - 3P)/(P(P²-4))]
= [(P³ + P² + P + 1)(P²-4) - (P³ - 3P)(P²-1)]/[(P(P²-1))(P(P²-4))]
= [(P⁵ - 3P³ + P³ - 3P² + P² - 4P + P² - 4P - 4 + P³ - 3P)/(P⁴ - 5P² + 4)]
= [P⁵ - 2P³ - 6P² - 8P - 4]/[(P²-4)(P²-1)]
= -4(2p² + 1)/(p²-4) (p² - 1)
Hence, the given identity is proven.
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for each pair of lines determine whether they are parallel, perpendicular, or neither
Answers
Answer:
All lines are parallel.
Step-by-step explanation:
Get each equation in Slope-Intercept form:
1. Divide both sides by 3: [tex]y=-\frac{4}{3}x+\frac{7}{3}[/tex]
2. No change
3. Subtract 8x and divide by 6 on both sides: [tex]y=-\frac{4}{3}x-\frac{2}{3}[/tex]
Notice:
a. All slopes are -4/3
b. All y-intercepts are different
I would love some help please 18-20
Answers
18. C
(m / 2) - 6 = (m / 4) + 2
---Multiply everything by the LCM of the denominators
---LCM = 4
2m - 24 = m + 8
m - 24 = 8
m = 32
19. A
k / 12 = 25 / 100
---We can simplify 25/100
---We want to simplify enough to where the denominator of 25/100 is a multiple or factor of 12
k / 12 = 1 / 4
---4 x 3 = 12, 1 x 3 = 3
k = 3
20. A
9 / 5 = 3x / 100
---Cross multiply and solve algebraically
(5 * 3x) = (9 * 100)
15x = 900
x = 60
Hope this helps!
19.A
20.A
are the answers
Which linear equation is represented in the graph?
A. y = x – 1
B.y = 2x – 1
C. y = x + 1
D. y = 3x – 1
Answers
help!!!
in the fridge below, m WXZ =72, abs m 1 is 6 degrees more than m 2. find m2
Answers
Step-by-step explanation:
m ∠WXY = 72°
m ∠ 1 = m ∠ 2 + 6°
m ∠WXY = m ∠ 1 + m ∠ 2
72° = (m ∠ 2 + 6°) + m ∠ 2
72° = 2 × (m ∠ 2) + 6°
2 (m ∠ 2) = 72° - 6°
2 (m ∠ 2) = 66°
(m ∠ 2) = 33°
#CMIIWwhich of the following is equivalent to x-5/3?
Answers
The following expression is equivalent to [tex]x^{-5/3}[/tex] as option B that is 1/∛x⁵.
What is fraction?A fraction is a numerical representation of a part or a portion of a whole. It is expressed as one integer (numerator) divided by another integer (denominator), separated by a horizontal line.
Here,
We can rewrite [tex]x^{-5/3}[/tex]as [tex](1/ x^{^(5/3)})[/tex].
The negative exponent in the numerator tells us that we need to move the term to the denominator of a fraction and change the sign of the exponent to make it positive. Similarly, the fractional exponent in the denominator indicates that we need to take the reciprocal of the term and change the sign of the exponent to make it positive.
Therefore, we can rewrite [tex]x^{-5/3}[/tex] as:
[tex](1/ x^{^(5/3)})[/tex]
or
[tex]x^{-5/3}[/tex] = [tex](1/ x^{^(5/3)})[/tex]
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Complete question:
Which of the following is equivalent to [tex]x^{-5/3}[/tex]?
A worker completes a job in a certain number of hours. The standard time allowed for the job is 10 hours, and the hourly rate of wages is Re. 1. The worker earns at the 50% rate a bonus of Rs. 2 under Halsey Plan. Ascertain his total wages under the Rowan Premium Plan.
Answers
Let's assume that the worker completes the job in 'x' hours. So, the Rowan Premium Plan formula to calculate wages is:
Total wages = (time taken / standard time) * standard wages + (time taken - standard time) * hourly rate * premium percentage
Here, the premium percentage is the percentage of time saved, which is given by:
Premium percentage = (standard time - time taken) / standard time * 100
Substituting the given values, we get:
Premium percentage = (10 - x) / 10 * 100
Premium percentage = (100 - 10x) %
Now, substituting this value in the Rowan Premium Plan formula, we get:
Total wages = (x / 10) * 4 + (x - 10) * 1 * (100 - 10x) / 100
Simplifying this expression, we get:
Total wages = (2x + 8 - x^2) / 5
So, the total wages earned by the worker under the Rowan Premium Plan is (2x + 8 - x^2) / 5.
Find the surface area of each composite figure. Use 3.14 for π. Round to the nearest tenth. 12m. 6cm. 6cm. 4cm.
Answers
The Surface area of the composite figure is calculated as approximately: 234 sq. cm
How to Find the Surface Area of a Composite Figure?The surface area of the composite figure is the area surrounding the faces of the solid as a whole. Therefore, we have:
Surface area (SA) = Surface area of the square prism + surface area of the square pyramid - 2(area of base)
Area of base = area of square = 6 * 6 = 36 sq. cm.
Surface area of the square prism = 2a² + 4ah
a = 6 cm
h = 4 cm
Plug in the values:
Surface area of the square prism = 2(6²) + 4*6*4
= 72 + 96
= 168 sq. cm.
Surface area of the square pyramid = 2bs + b²
b = side length = 6 cm
s = slant height = √(8² + 3²) = 8.5 cm
Plug in the values:
Surface area of the square pyramid = 2 * 6 * 8.5 + 6² = 138 sq. cm.
Surface area of the composite figure = 168 + 138 - 2(36) = 234 sq. cm
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