Answers
The expanded equation of the function f(x) = (3x + 2)⁴ is f(x) = 81x + 216x³ + 216x² + 96x + 16
How to expand the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = (3x + 2)⁴
Using the pascal triangle at n = 4, we have the coefficients to be
Coefficient = 1 4 6 4 1
So, when the function f(x) = (3x + 2)⁴ is expanded, we have
f(x) = 1 * (3x)⁴ + 4 * (3x)³ * 2 + 6 * (3x)² * 2² + 4 * (3x) * 2³ + 1 * 2⁴
Evaluate
f(x) = 81x + 216x³ + 216x² + 96x + 16
Hence, the solution is f(x) = 81x + 216x³ + 216x² + 96x + 16
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Related Questions
Tyler is 8 years old. His sister Olivia is 4 years less than twice his age.
Write a numerical expression for Olivia's age in the box below.
Answers
Answer: Olivia is 12 years old.
Step-by-step explanation
Tyler = T
Olivia = O
T=8
O=T*2-4
O=8*2-4
O=16-4
O=12
This is do today Pleaseeee helpppp
Answers
Answer:
A
Step-by-step explanation:
It is A definitely I'm sure
What is the next step for the construction
Answers
Answer:Step 6, put the compass on point L
Step-by-step explanation:
Making a small arc from point L will make a little "X" at the point where you should draw the line through.
Answer:
See the answer above
Step-by-step explanation:
Open your eyes and direct your attention to the answer above.
Find the reciprocal of -1
Answers
The reciprocal value of -1 is 1/-1 which is equal to -1.
What is Fraction?A fraction represents a part of a whole.
We need to find the reciprocal of -1.
The reciprocal (or multiplicative inverse) of a number is whatever value must be multiplied to that number to equal 1.
Let a be a number and b be its reciprocal.
So ab=1
b=1/a
Substitute for a.
b=1/-1
b=-1
Hence, -1 is the reciprocal of -1.
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3 2/5 divided by 4/5
Answers
Answer:
17/4
Step-by-step explanation:
3 2/5 divided by 4/5 =
(3 2/5) / (4/5) =
(3 + 2/5) / (4/5) =
(15/5 + 2/5) / (4/5) =
((15+2)/5) / (4/5) =
(17/5) / (4/5) =
5*(17/5) / (5*(4/5)) = ==> multiply 17/5 and 4/5 by 5 to remove fractions
17/4 ==> simplified form
Carly took a total of 15 quizzes over the course of 5 weeks. How many weeks of school will Carly have to attend this quarter before she will have taken a total of 24 quizzes? Assume the relationship is directly proportional.
Answers
Answer:
Carly will have to attend school for 8 weeks before she takes a total of 24 quizzes.
Step-by-step explanation:
To determine the number of weeks Carly will have to attend school before she takes a total of 24 quizzes, we need to first calculate the proportion of quizzes taken to weeks attended by dividing the number of quizzes taken by the number of weeks attended:
Proportion = Number of quizzes taken / Number of weeks attended
Proportion = 15 quizzes / 5 weeks
Proportion = 3 quizzes / week
Next, we can use this proportion to calculate the number of weeks Carly will have to attend school before she takes 24 quizzes by multiplying the number of quizzes Carly wants to take by the reciprocal of the proportion:
Number of weeks = Number of quizzes / Proportion
Number of weeks = 24 quizzes / 3 quizzes/week
Number of weeks = 8 weeks
Therefore, Carly will have to attend school for 8 weeks before she takes a total of 24 quizzes.
What is 2/5 of 15? help pls
Answers
What is 2/5 of 15?
Answer:
2/5 of 15 is 6.
Answer:
6
Step-by-step explanation:
The word of in math refers to multiplication.
We can convert 15 to a fraction as well so we can use them together (15/1).
[tex]\frac{2}{5}[/tex] x [tex]\frac{15}{1}[/tex]
We can then work diagnolly and reduce the 5 and 15 since they are both divisible by 5- this is also known as the GCF or Greatest Common Factor
[tex]\frac{2}{1}[/tex] x [tex]\frac{3}{1}[/tex]
This is the same as 2 x 3 since both numbers divided by 1 are just themselves.
2x3 = 6
given the vector a⃗ =3.0i^+1.5j^, find a vector b⃗ that is perpendicular to a⃗ .
Answers
1.5i^- 3j^ is the perpendicular vector to the vector 3.0i^+1.5j^
What is perpendicular vector?Whenever there is a 90 degree angle between two vectors, they are said to be perpendicular. Two perpendicular vectors dot product is zero. and dot product is scaler product of 2 vectors.
Let b = xi^+ yj^ be the perpendicular vector to a vector
and we know that 2 vectors are perpendicular if thier dot product is 0
so it implies that
b.a(dot product) =0
=> (3i^+1.5j^) . (xi^+yj^)=0
=> 3xi^.i^+ 3y i^.j^ +1.5xj^.i^+1.5yj^j^=0
=>3x+1.5y=0 ----(i)
becaus i^.j^=0 and j^.i^0
=> x= 1.5 and y=-3 satisfies equation (i).
so the perpendicular vector is 1.5i^- 3j^
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FILL IN THE BLANK. two specific types of ____ are e-commerce systems and point-of-sale (pos) systems.
Answers
Answer:
Order entry systems
Step-by-step explanation:
Two specific types of order entry systems are e-commerce systems and point-of-sale (pos) systems.
it would take charlene and gina 18 minutes to organize charlene’s comic book collection if they work together. if gina works alone, it would take her 15 minutes longer than it would take charlene working alone. when x represents the number of minutes it takes charlene to organize the comic book collection working alone, the situation is represented by this equation: 1/x + 1/x + 15 = 1/18which value is a solution of the rational equation that must be discarded because of the context?a. x = 0 b. x = -9 c. x = -15 d. x = -30
Answers
The value that is a solution of the rational equation that must be discarded because of the context is B. x = 9.
How to illustrate the equation?From the information, it would take Charlene and Gina 18 minutes to organize charlene’s comic book collection if they work together. if gina works alone, it would take her 15 minutes longer than it would take charlene working alone.
The equation can be illustrated as:
1/x + 2/(x + 15) = 1 / 18
The objective is to determine the value which nullify the context. The option will be -9. This is illustrated as:
1 / -9 = 1 / -9 + 15 = 1 / 18
The correct option is B.
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What place value is this
18 thousands x 10 = ?
Answers
if you randomly select a card from a well-shuffled standard deck of 52 cards, what is the probability that the card you select is a heart or 2? (your answer must be in the form of a reduced fraction.)
Answers
Answer:
Step-by-step explanation:
total no of outcome = 52 cards
favorable outcomes = 16 cards
probability of getting a heart or 2 = no . of favorable outcomes
no . of total outcomes
= 16 = 4
52 13
HELPPPP
find three consecutive integers such that the sum of twice the second and three times the third is five less than six times the first.
Answers
Answer:
13, 14, 15
Step-by-step explanation:
The three integers are consecutive so let those integers be x, (x+1), (x+2)
As per the question,
2(x+1) + 3(x+2) = 6x-5
or, 2x+1+3x+6 = 6x-5
or, 8+5 = 6x-5x
or, x = 13
So, x+1 = 13+1 = 14
x+2 = 13+2 = 15
Cian is buying movie tickets for a group. He wants to have at least 30 tickets and spend no more than $400. Adult tickets cost $12.50 and child tickets cost $7.50. Which system of inequalities can be used to find the number of each type of ticket Cian could buy?
A. x + y ≥ 30
7.5x + 12.5y ≤ 400
B. x + y ≤ 30
7.5x + 12.5y ≥ 400
C. x + y ≥ 30
7.5x + 12.5y ≥ 400
D. x + y ≤ 30
7.5x + 12.5y ≤ 400
Answers
The system of linear inequalities for each ticket is (a) x + y ≥ 30, 7.5x + 12.5y ≤ 400
How to determine the system of linear inequality that describes the situation.From the question, we have the following parameters that can be used in our computation:
Budget = No more than $400Tickets = At least 30Children (x) = $7.50Adults (y) = $12.50When the total number of tickets is represented as an equation/inequality, we have
x + y ≥ 30
For the spendings, we have
7.5x + 12.5y ≤ 400
So, we have the following representations (inequality)
x + y ≥ 30
7.5x + 12.5y ≤ 400
Hence, the system of linear inequalities is (a)
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The midpoint of AB is MI(-2, -6). If the coordinates of A are (1, -4), what are
the coordinates of B?
Answers
Can someone help me answer this please?
Answers
Answer:
B
Step-by-step explanation:
When zero is our denominator the graph is undefined at that point. In the case of b, when x = 1 The denominator is o. That is why there is a striped line at x = -1
Y-intercept: (0,2)
X-intercept: (-2,10)
vertical asymptote: x=-1
Since: vertical asymptote: x=-1
The denominator : (x+1)
X-intertent: (-2,0)
The molecule: (x+2)
F(x) = x+2/x+1
It’s a hot summer day. Darius is babysitting and has promised his sweet little sister that he will fill her wading pool. He plans to soak his feet in the water as he sips a cool soda and watch little sister as she plays in the water. Sounds great, right? All he needs to do is get the pool filled. Unfortunately, little sister is impatient and starting to whine. Darius has a hose ready in the backyard to fill the pool, but he decides he will also drag the hose from the front-yard, so the two hoses can work together to fill the pool faster. Nobody wants their darling little sister to be unhappy!
Darius knows from experience that if he only uses one hose at a time, the front-yard hose takes 10 minutes longer to the fill the pool than the back-yard hose. With the two hoses working together, the pool is filled in 12 minutes. Once Darius is comfortable with his toes dangling in the water, he starts to wonder how long it would have taken to fill the pool if he had only used one of the hoses.
Darius thinks, “Hmmm. Usually when I think about how long it takes to do something I have to think about the rate it is going.”
5. Write a function, R(x), that models the combined rate of the two hoses in terms of the time that it takes for the backyard hose to fill the pool alone.
6.a. What is the entire domain of this function, if the context is not considered?
6.b. What is the domain of this function in the context of filling Darius’ pool? Explain your thinking after you submit.
7. Graph R(x). Label all important features and describe them.
Answers
Answer: I can’t help you
Step-by-step explanation:
Calculate the perimeter of the irregular shape please show ur work Bc I have too !!
Answers
The perimeter of the irregular shape would be 34 cm.
What is the perimeter of any shape?
In geometry, the perimeter of a shape is defined as the total length of its boundary. The perimeter of a shape is determined by adding the length of all the sides and edges enclosing the shape.
By using the definition of the perimeter we can compute,
Perimeter = 4 + 2 + 2 + 3 + 3 + 6 + 9 + 5
= 34 cm.
Hence, the perimeter of the irregular shape would be 34 cm.
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need help please thank you
Answers
Answer:
Step-by-step explanation:
They are trying to be tricky :DDD but we got this.
they give you the outside angle at H, but you know both of those two angle also add to 180
180= 131 +∠h
I'm noting that we're solving for the minor angle H of the triangle, the inside angle
49° = ∠h
we also , know that H and J are equal, b/c it's got the red marks , telling us the angles are the same.
use that same strategy to solve,
180 = 2*49 + p
180-98 = p
82 = p
Do you see where I get the equation from? ( 180 = 2*49 + p ) ?
show your work please
Answers
Answer:
Correct Answer is A
Step-by-step explanation:
5×14 = 70
using the addition law of indices
(x¹. x⁷) ( y⁰. y⁵)
Add the powers
Therefore: x^(1+7) = x⁸
y^(0+5) = y⁵
Answer: 70x⁸y⁵
pls do this asap its important
Answers
Answer:
3.1 mm
Step-by-step explanation:
as 1mmx3.14=3.14mm
And then correct it to 1 decimal place =3.1
Formula for circumference
C = 2 x pi x radius
We know the diameter is 1mm so radius is half of that = .5mm
C = (2) (3.14) (.5)
C = 3.14mm
Round to 1 decimal place per question
C = 3.1 mm
Seems to me like a lot of little boys have the name 'Jack' lately. Let's assume it's one in every ten.
What's the probability that my daughter will have at least one Jack on her co-ed soccer team of 12
players, 6 of whom are boys?
O 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10
O 1/10 x 1/10 x 1/10 x 1/10 x 1/10 x 1/10
O 1-(9/10 x 9/10 x 9/10 x 9/10 x 9/10 x 9/10)
O 1/6+1/6 + 1/6 + 1/6 + 1/6 + 1/6
O 6/12 x 5/11 x 4/10 x 3/9 x 2/8 x 1/7
Answers
The probability of at least one boy named Jack is (c) 1 - (9/10 x 9/10 x 9/10 x 9/10 x 9/10 x 9/10)
How to determine the probability of at least one boy named JackFrom the question, we have the following parameters that can be used in our computation:
P(Jack) = 1/10
Number of boys = 6
Using the complement rule of probabilities, we have
P(At least one Jack) = 1 - P(No jack)
Where
P(No jack) = (1 - P(Jack))⁶
So, we have
P(No jack) = (1 - 1/10)⁶
Evaluate
P(No jack) = (9/10)⁶
Substitute the known values in the above equation, so, we have the following representation
P(At least one Jack) = 1 - (9/10)⁶
Evaluate
P(At least one Jack) = 1 - (9/10 x 9/10 x 9/10 x 9/10 x 9/10 x 9/10)
Hence, the probability is (c) 1 - (9/10 x 9/10 x 9/10 x 9/10 x 9/10 x 9/10)
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(T/F) in slicing, if the end index specifies a position beyond the end of the string, python will use the length of the string instead.
Answers
True, If the end index for slicing specifies a location after the end of the alphabet, Python will use the list's length instead.
What is slicing?
In Python, there is a concept of string, list and tuples. Sometimes it is required to access part of those string, list and tuples. This is known as slicing.
In case of slicing, suppose the the end index specifies a position beyond the end of the list, Python will return to the default length of the string. So there will be no error if the end index specifies a position beyond the end of the list.
So the above sentence is a true sentence.
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. about 19% of young adults have high blood pressure. consider the proportion of people with high blood pressure in random samples of 45 young adults. what is the standard deviation of this sample proportion?
Answers
The standard deviation of the sample proportion is 10.
In math standard deviation is defined as the statistical measure of diversity or variability in a data set.
Here we have given that about 19% of young adults have high blood pressure. consider the proportion of people with high blood pressure in random samples of 45 young adults.
And we need to find the the standard deviation of this sample proportion
Let us assume the expected population standard deviation to be 10, and employing t-distribution to estimate sample size, the study would require a sample size of: 44 to estimate a mean with 67% confidence and a precision of 1.5.
Which means that, if you select a random sample of 44 from a population, and determine the mean to be say y, you would be 67% confident that the mean in the population lies somewhere between y - 1.5 and y + 1.5.
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benjamin works as a salesperson at an electronics store and sells phones and phone
accessories. benjamin earns a $10 commission for every phone he sells and a $4
commission for every accessory he sells. On a given day, made a total of
$180 in commission from selling a total of 27 phones and accessories. Graphically
solve a system of equations in order to determine the number of phones sold, x, and
the number of accessories sold, y.
y Click twice to plot each line. Click a line to delete it.
Answers
The required number of phones and accessories sold are x = 12, y = 5,
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Here,
Let the number of phones sold be x and the number of accessories sold be y.
According to the question,
He sold a total of 27 phones and accessories,
x + y = 27 - - - - -(1)
And, made a total of $180 in commission,
10x + 4y = 180 - - - - -(2)
Graph both the equation,
From the graph, the solution of the system of equations is given as,
x = 12, y = 5,
Since, when two intersect each other, is the point of a solution of the system of equation.
Thus, the solutions gives the number of phones and accessories sold as x = 12, and y = 5.
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Marneashia has a total of 14 chickens . If she has 2 times as many chickens as dogs write and solve an equation to determine the number of dogs she has.
Answers
The correct answer is 2x = 14; x = 7
How did we figure this out?For this equation we are going to divide the numbers to find are answer.Divide by 2 on both sides of the equal sign, 14 divided by 2 is 7.Therefore, The correct answer is 2x = 14; x = 7
finish the question
the value of decreasing of 15% from £1200 is equal to....
Answers
Answer: The final value is £1,020
Step-by-step explanation: In order to find the final value, the first step in the process is to multiply 1,200 by 0.15 in order to find out what 15% of 1,200 is. After doing obtaining the answer, which is 180, subtract that from the original answer in order to find out what the final value will be.
The final value is then equal to £1,020
what is the coefficient of x in -3 / 7 x
Answers
Answer:5103
Step-by-step explanation:We only care about 7xy6, cause it's the only term involving x In your example y = −3, thus 7(−3)6x = 7 ⋅ 729x = 5103x The coefficient of x is 5103
2.
12
Bo
5
13
xº
Which measures shown in the triangle are
equivalent to ? (MGSE9-12.G.SRT.6)
5
13
A. sin a Only
B. cos ß Only
C. sin a and cos B
D. sin ß and cos a
Answers
on solving the provided question, we can say that - 5/13 measure shown in the triangle are equivalent to sin [tex]\alpha[/tex] and cos [tex]\beta[/tex].
what are trigonometric functions?Trigonometry uses the first six fundamental trigonometric functions. Trigonometric ratios are these functions. The six fundamental trigonometric functions are the sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function. A right-angled triangle's side ratio corresponds to the trigonometric functions and identities. In order to determine the sine, cosine, tangent, secant, and cotangent values, trigonometric formulae are applied to the perpendicular side, hypotenuse, and base of a right triangle.
as cos x = base/ hypotenuse
and, sin x = perpendicular/ hypotenuse
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Answer this quick please
Answers
The graph of g is the graph of f translated 3 units right. Option C is the answer
How determine how the graphs of f(x) = 2x + 1, and g(x) = 2(x + 3) + 1 compare?In geometry, a translation is a type of transformation that involves moving a geometric figure from one location to another without changing its size, shape, or orientation.
Remember, in the cartesian plane or graph, the movement in x-axis is either to the left (negative) or right (positive).
Since f(x) = 2x + 1, looking at g(x) = 2(x + 3) + 1, you will notice that 3 is added to the value x. This is a movement in the positive x-axis (right translation) and the translation is by 3 units.
Therefore, the graph of g is the graph of f translated 3 units right
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