Which of the following is the correct factorization of the polynomial below?
p3 - 343q3
ANSWER
The correct factorization is
[tex]p^{3} - 343q^{3} = (p - 7q)( {p}^{2} + 7pq + {49q}^{2} )[/tex]
EXPLANATION
The given expression is
[tex] {p}^{3} - 343 {q}^{3} [/tex]
We can write this as difference of cubes.
[tex]{p}^{3} - {7}^{3} {q}^{3} [/tex]
[tex]{p}^{3} - ( {7} {q})^{3} [/tex]
We can now factor using the difference of cube identity:
[tex] {x}^{3} - {y}^{3} = (x - y)( {x}^{2} + xy + {y}^{2} )[/tex]
We substitute x=p and y=7p to get:
[tex]{p}^{3} - ( {7} {q})^{3} = (p - 7q)( {p}^{2} + p \times 7q + ({7q})^{2} )[/tex]
[tex]{p}^{3} - ( {7} {q})^{3} = (p - 7q)( {p}^{2} + 7pq + {49q}^{2} )[/tex]
Final answer:
The polynomial p^3 - 343q^3 is factorized as (p - 7q)(p^2 + 7pq + 49q^2) using the difference of cubes formula.
Explanation:
The correct factorization of the polynomial p3 - 343q3 can be done using the difference of cubes formula, which is a3 - b3 = (a - b)(a2 + ab + b2). Comparing the given polynomial to the formula, we see that a corresponds to p and b corresponds to 7q since 343 is 7 to the power of 3. Therefore, the factorization would be (p - 7q)(p2 + 7pq + 49q2). Always check for the correct signs and coefficients when factoring polynomials, especially when dealing with differences and sums of cubes.
Mike wants to conduct a survey to find how much time the students of his school spent watching television. Which of the following is an appropriate statistical question for this survey?
Who watched television on weekends?
How many hours per week do you watch television?
Who watches television the most on Monday nights?
How many students watch television for an hour every day?
Answer:
How many hours per week do you watch television?
Step-by-step explanation:
In order to conduct a proper survey about a specific topic, it is necessary to be direct and clear. In the case of time spent by students watching TV, asking this question would be effective enought to collect necessary data so as to provide useful and good quality information, which will result in a sucessful survey.
Answer:
B is your answer :D
Step-by-step explanation:
Please help me and please show your answer or explain please
Answer:
31.96
Step-by-step explanation:
The product of 2 numbers is simply one number multiplied by another
6.8 x 4.7 = 31.96
As a sanity check, just round the numbers off to a whole numbers and take a product of those two:
i.e 6.8 rounded off to the nearest whole number is 7 and 4.7 rounded off to the nearest whole number is 5.
7 x 5 = 35
If you look at the possible answers, only 31.96 is anywhere close to 35, hence you can be be more confident that your answer of 31.96 is correct.
Answer:
31.96 is your answer
Step-by-step explanation:
its just like a normal multiplication problem multiply 6.8 and 4.7 and you'll get your answer :))
20 students plays football and 16 students plays hockey.It is found that 10 students plays both game.Find the number of students playing at least one game
A vegetable farmer fills of a wooden crate with of a pound of tomatoes. How many pounds of tomatoes can fit into one crate?
A.
14/15 of a pound
B.
2 1/10 pounds
C.
1 1/14 pounds
D.
10/21 of a pound
To determine how many pounds of tomatoes can fit into one crate, calculate 2/3 of a pound for 1/4 of the crate, and then multiply by 4. The answer is 2 1/10 pounds.
Explanation:A vegetable farmer fills 3/4 of a wooden crate with 2/3 of a pound of tomatoes.
First, find how many pounds of tomatoes are in 1/4 of a crate by multiplying 2/3 pound by 1/4.Then, multiply this result by 4 to find the total pounds of tomatoes that can fill one whole crate.The correct answer is B. 2 1/10 pounds.How are conditional probability and independent events related?
Select the correct phrase or notation from each drop-down menu to complete the explanation.
The notation __A__ reads the probability of Event A given that Event B has occurred. If Events A and B are independent, then the probability of Event B occurring __B__ the probability of Event A occurring. Events A and B are independent if __C__
A.
1. P(B|A)
2.P(A|B)
3. P(A and B)
B.
1. affects
2. does not affect
C.
1. P(A|B) = P(A)
2. P(A|B) = P(B)
3. P(A|B) = P(A and B)
Answer:
1. P(A|B) - option 2
2. does not affect - option 2
3. P(A) - option 1
Step-by-step explanation:
By the definition, the notation P(A|B) reads the probability of event A given that event B has occured. So, for the first gap correct choice is 2 - P(A|B).
If events A and B are independent, then the probability of event B occuring does not affect the probability of event A occuring. So, for the second gap correct choice is 2 - does not affect.
Events A and B are independent, then
[tex]P(A\cap B)=P(A)\cdot P(B)[/tex]
Use formula for the conditional probability:
[tex]P(A|B)=\dfrac{P(A\cap B)}{P(B)}[/tex]
Since events A and B are independent, we get
[tex]P(A|B)=\dfrac{P(A)\cdot P(B)}{P(B)}=P(A)[/tex]
So, for the third gap correct answer is 1 - P(A)
For (A) option (2) is correct, for (B) option (2) is correct, and for (C) option (1) is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
From the basic definitions of the events of probability.
P(A|B) = The probability of Event A given that Event B has occurred
In the independent events, the probability of Event B occurring does not affect the probability of Event A occurring.
P(A|B) = P(A) if events A and B are independent.
Thus, for (A) option (2) is correct, for (B) option (2) is correct, and for (C) option (1) is correct.
Learn more about the probability here:
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70 POINTS!!
14. The population of a town is 18,922 people. Each year the population increases by 3%. What will the town's population be in 17 years? Round your answer to the nearest whole number.
31,275
2,412,376
11,274
70,129
The answer would be: A. 31,275
to solve this you would take the population (18,922) and multiply it as shown below:
18,922(1+0.03)^17
This would equal 31,275 which would be your answer.
Hope this helps! :3
A system of linear equations has infinitely many solutions. Does that mean any ordered pair in the coordinate plane is a solution?
Answer:
Nope, not every ordered pair in the plane is a solution to a system of linear equations.
What is the name of the green line located below the parabola?
A. axis of symmetry
b. asymptote
c. focus
d. directrix
Answer:
d. directrix
Step-by-step explanation:
The name of the green line located below the parabola is directrix.
Hope this helps! Please mark brainliest!
The point stands named the focus of the parabola and the line exists named the directrix.
What is parabola?A parabola exists a plane curve with a U shape which exists mirror-symmetrical.
The directrix exists perpendicular to the axis of symmetry of a parabola and does not feel the parabola. The line (or "axis") of symmetry exists as the y-axis, even comprehended as the line x = 0. This line stands marked green in the picture. The graph exists said to be "symmetric about the y-axis", and this line of symmetry exists even called the "axis of symmetry" for the parabola.
A parabola exists as a set of all points in a plane that exist an equivalent distance away from a given point and given line. The point stands named the focus of the parabola and the line exists named the directrix.
Therefore, the correct answer is option d. directrix.
To learn more parabola
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Find the discriminant of 3x2 - 10X=-2.
Answer:
76
Step-by-step explanation:
Given a quadratic in standard form : ax² + bx + c : a ≠ 0, then
the discriminant Δ = b² - 4ac
Given
3x² - 10x = - 2 ( add 2 to both sides )
3x² - 10x + 2 = 0 ← in standard form
with a = 3, b = - 10 and c = 2
b² - 4ac = (- 10)² - (4 × 3 × 2) = 100 - 24 = 76
Answer:
Discriminant : 74 .
Step-by-step explanation:
Given : 3x² - 10x = -2.
To find : Find the discriminant .
Solution : We have given 3x² - 10x = -2.
On compare with standard form ax² +bx +c = 0.
Where, a =3 ,b = -10 , c = 2.
Discriminant : [tex]b^{2} - 4ac[/tex].
Plug the values of a , b , c .
Discriminant : [tex](-10)^{2} - 4(3)(2)[/tex].
Discriminant : 100 - 24 .
Discriminant : 74 .
Therefore, Discriminant : 74 .
Question 6 of 10
1 Point
81, 77, 94, 50, 97, 68, 98, 55, 70, 58, 68, 58, 56, 98, 70, 61, 99, 94, 97,79
What is the median for the data list above?
O A. 58
O B. 73.5
O C. 76.4
O D. 63
suem
Answer:
73.5
Step-by-step explanation:
Put them in order from greatest to least [or vice versa], find the TWO midst quantities, since we are dealing with an EVEN NUMBER of quantities, then you add & divide [in this order] them by 2⃣, since there are TWO midst quantities.
Jill bought a pound of strawberries for $4.00. What is the price, in dollars, per ounce of strawberries? (1lb = 16 oz)
Answer:
$0.25/lb
Step-by-step explanation:
Convert 1 lb to 16 oz mentally. Then the unit cost of the berries is
$4.00
------------ = $0.25/lb
16 oz
Samuel is running a 3-mile race. He would like to finish the race in under 33 minutes. He has already run for 10.5 minutes. The inequality 10.5 + x < 33 represents the situation. Solve the inequality. How is the solution interpreted in the context of the problem? x < 22.5; Sam has a maximum of 22.5 minutes left to finish running. x < 22.5; Sam has fewer than 22.5 minutes left to finish running. x > 43.5; Sam has at least 43.5 minutes left to finish running. x < 43.5; Sam has no more than 43.5 minutes left to finish running.
Answer: Second Option
x < 22.5; Sam has fewer than 22.5 minutes left to finish running
Step-by-step explanation:
We have the following inequality
[tex]10.5 + x < 33[/tex]
Notice that 10.5 is the amount of time in minutes that Samuel has run.
x represents the amount of additional time it will take to finish the race
33 represents the time limit in which you want to finish the race
The we solve the inequality
[tex]10.5 + x < 33[/tex]
Subtract 10.5 on both sides of the inequality
[tex]10.5 -10.5 + x < 33-10.5[/tex]
[tex]x < 33-10.5[/tex]
[tex]x < 22.5[/tex]
This result means that Samuel must finish the race before 22.5 minutes have elapsed
The answer is the second option
Answer:
X<22.5;sam has fewer than 22.5 left to finish running
Step-by-step explanation:
edgen.
Which types of polygons are the faces of a octahedron?
O A. Equilateral triangles
OB. Regular pentagons
O C. Squares
O D. Regular hexagons
Answer:
Each face of an octahedron is an equilateral triangle. An octahedron is a three-dimensional solid (polyhedron) that has eight faces.
Step-by-step explanation:
Please mark brainliest and have a great day!
The sum of 2 consecutive numbers is 37. Find the numbers
Consecutive numbers means numbers one after another. 1 and 2 are consecutive numbers
The answer would be 18 and 19
18 + 19 is 37
Hope this helped!
~Just a girl in love with Shawn Mendes
Brayden, Howard, and Vincent are on the football team. During a game, Brayden gains 1 less than 5 times the average number of yards gained per play during the game. Howard runs for 1 more than 5 times the average number of yards gained per play during the game. Vincent runs for 5 more than 4 times the average number of yards gained per play during the game.
In this activity, you will write equations to describe this situation and determine whether the equations have one solution, no solution, or infinitely many solutions.
Write an equation to find the average number of yards gained per play if Howard and Vincent gained the same number of yards.
Answer: They are parallel so there is no solution.
Step-by-step explanation:
Brayden- y=5x-1 or y-5x= -1
Howard- y=5x+1 or y-5x= 1
Vincent- y=4x+5 or y-4x= 5
In summary, they are all parallel so there is no solution.
Answer:
5y - 1 = 5y + 1
(Braydon = Howard)
Students from grade 11 and 12
Can you someone please help me with this question?
Tyler is building a fish tank in the shape of a sphere that has a diameter of 18 inches. Based on Tyler's research, it is recommended to have no more than 1 goldfish for every 693 cubic inches of water. How many goldfish should Tyler buy for his fish tank?
The unclear query may pertain to post-high school plans or high school curriculum. The majority of high school graduates in the US tend to pursue higher education immediately after graduating. Similarly, the number of English courses taken by male and female high school students is typically equivalent.
Explanation:The question is somewhat ambiguous as it does not specify a clear query related to students from grade 11 and 12. However, deriving from the provided information, perhaps the student is seeking to understand statistics related to post-high school plans, or is interested in curriculum reviews, or the number of English courses taken by students.
For instance, focusing on life after high school, we know that a significant majority of high school graduates in the US (~69%) begin their college journey immediately following their graduation. This indicates that the orientation towards pursuing higher education is prevalent among recent high school graduates.
On the other hand, if interest lies in the English curriculum, an analysis reveals that the mean number of English courses taken by both male and female high school students over two years generally align with each other.
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a coin is tossed 4 times which of the following represents the probability of the coin landing on heads all 4 times
Answer:
1/16
Step-by-step explanation:
1/2*1/2=1/4*1/2=1/8*1/2=1/16
Answer:1/16
Step-by-step explanation:
what is the domain of f(x)=^3√x
all real numbers
positive numbers and zero
all integers
whole numbers
Answer:
Step-by-step explanation:
^3√x is improperly formed. I'd guess you meant "the third root of x," which looks like ∛x. Note that Brainly's workspace has built-in math symbols. Try them out by clicking on the Greek letter omega (below).
The domain of f(x) = ∛x is "all real numbers."
Answer:
the domain is the "All real numbers"
First option is correct.
Step-by-step explanation:
We have been given the function [tex]f(x)=\sqrt[3]{x}[/tex]
Domain is the set of x values for which the function is defined.
Here, for the given function, we can take any x values. For each real values of x, the cube root function is defined.
Therefore, the domain is the "All real numbers"
First option is correct.
Suppose the times to cook meat on a grill are normally distributed with a mean of 23 minutes and a standard deviation of 1.9 minutes.
What is the difference in times between grilled meat that has a z-score of 2 and another meat that has a Z-score of -1?
• 2.85min
• 4.7min
• 5.7min
• 11.4min
That's a difference of three standard deviations or 3(1.9) = 5.7 minutes.
Answer: 5.7 min, third choice
the first four terms of a sequence are shown below 8,5,2,-1
Answer:
an = 8-3(n-1)
an = 11 - 3n
Step-by-step explanation:
This is an arithmetic sequence which is defined by
an = a1 + d(n-1)
where a1 is the first term of the sequence and d is the common difference
a1 = 8
d = a2-a1
d = 5-8 = -3
an = 8 + -3(n-1)
an = 8-3(n-1)
We can simplify this by distributing the -3
an = 8 -3n +3
an = 11 - 3n
Convert four 4/5 into a percentage
Answer:
Answer is 0.80%
Step-by-step explanation:
Because if you divide the numerator by the denominator, you'll get your answer.
Hope my answer has helped you!
Answer:
80%
Step-by-step explanation:
Divide 4 by 5 to get 0.8
0.8 is the percentage written as a decimal. To write it as a percentage, multiply the decimal by 100.
0.8 x 100 = 80.
So your answer is 80%
what’s the area of a circle with the diameter of 3/4 (0.75)
Answer:
[tex]A=(9/64)\pi\ units^{2}[/tex]
Step-by-step explanation:
The area of a circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=(3/4)/2=3/8\ units[/tex] ----> the radius is half the diameter
substitute
[tex]A=\pi (3/8)^{2}[/tex]
[tex]A=(9/64)\pi\ units^{2}[/tex]
find the equation of the perpendicular bisector of the line segment joining the points (3,8) and (-5,6).
Answer:
y = - 4x + 3
Step-by-step explanation:
The perpendicular bisector is positioned at the midpoint of AB at right angles.
We require to find the midpoint and slope m of AB
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = A(3, 8) and (x₂, y₂ ) = B(- 5, 6)
m = [tex]\frac{6-8}{-5-3}[/tex] = [tex]\frac{-2}{-8}[/tex] = [tex]\frac{1}{4}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{4} }[/tex] = - 4
mid point = [0.5(x₁ + x₂ ), 0.5(y₁ + y₂ ) ]
Using the coordinates of A and B, then
midpoint AB = [0.5(3 - 5), 0.5(8 + 6) ] = (- 1, 7 )
Equation of perpendicular in slope- intercept form
y = mx + c ( m is the slope and c the y- intercept )
with m = - 4
y = - 4x + c ← is the partial equation
To find c substitute (- 1, 7) into the partial equation
Using (- 1, 7), then
7 = 4 + c ⇒ c = 7 - 4 = 3
y = - 4x + 3 ← equation of perpendicular bisector
Answer:
he perpendicular bisector is positioned at the midpoint of AB at right angles.
We require to find the midpoint and slope m of AB
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = A(3, 8) and (x₂, y₂ ) = B(- 5, 6)
m = = =
Given a line with slope m then the slope of a line perpendicular to it is
= - = - = - 4
mid point = [0.5(x₁ + x₂ ), 0.5(y₁ + y₂ ) ]
Using the coordinates of A and B, then
midpoint AB = [0.5(3 - 5), 0.5(8 + 6) ] = (- 1, 7 )
Equation of perpendicular in slope- intercept form
y = mx + c ( m is the slope and c the y- intercept )
with m = - 4
y = - 4x + c ← is the partial equation
To find c substitute (- 1, 7) into the partial equation
Using (- 1, 7), then
7 = 4 + c ⇒ c = 7 - 4 = 3
y = - 4x + 3 ← equation of perpendicular bisector
100 pencils cost 7.00 30 pencil cost
Answer:
2.10.
Step-by-step explanation:
100 costs 7.00
1 costs 7.00 / 100 = 0.07
30 costs 0.07 *30
= 2.10.
Answer:
Step-by-step explanation:
7.00 / 100 = .07
so that makes each pencil worth .07 cent
.07 * 30 = $2.10
so 30 pencils will cost $2.10
is the graph a linear function, non linear function, or relation
a LINEar function has well, the graph of a straight line, so this isn't that.
is it a relation? well, yes, because the y-value correlates with the x-value, so one depends or relates to the other.
is it a non-linear function? well, a function has to pass the vertical line test, meaning if we draw vertical lines they must touch the graph only once on their way down.... and in this case it seems they do, so it is non-linear clearly, and it's also a function.
Helpppppp helpppppppp plssssssssss
Answer:
Its a four sided polygon
Find the dervite of y=X^2 + x + 1
Answer:
2x + 1.
Step-by-step explanation:
y=x^2 + x + 1
Using the algebraic derivative rule, if y = ax^n then y' = anx^(n-1) :
The derivative is 2x^(2 - 1) + 1x^(1-1)
= 2x^1 + x^0
= 2x + 1.
Answer:
y'(x) = 1 + 2 x
Step-by-step explanation:
Find the derivative of the following via implicit differentiation:
d/dx(y) = d/dx(1 + x + x^2)
Using the chain rule, d/dx(y) = ( dy(u))/( du) ( du)/( dx), where u = x and d/( du)(y(u)) = y'(u):
d/dx(x) y'(x) = d/dx(1 + x + x^2)
The derivative of x is 1:
1 y'(x) = d/dx(1 + x + x^2)
Differentiate the sum term by term:
y'(x) = d/dx(1) + d/dx(x) + d/dx(x^2)
The derivative of 1 is zero:
y'(x) = d/dx(x) + d/dx(x^2) + 0
Simplify the expression:
y'(x) = d/dx(x) + d/dx(x^2)
The derivative of x is 1:
y'(x) = d/dx(x^2) + 1
Use the power rule, d/dx(x^n) = n x^(n - 1), where n = 2.
d/dx(x^2) = 2 x:
Answer: y'(x) = 1 + 2 x
For the given image and scale factor, which ordered pair is one of the pre-image vertices if the center of the pre-image is also the origin?
Answer:
Step-by-step explanation:its the first one 3 5ths ,1
i just took the assignment
Answer:
the answer A
Step-by-step explanation:
If anyone could please help me with this I would greatly appreciate it!!
Answer:
The area of the house is approximately 309.54 feet²
Step-by-step explanation:
* Lets describe the figure
- It has a quarter circle with radius = the width of the rectangle
- It has a rectangle with length = 26 - the length of the radius, and
width 10 feet
- It has a triangle with base equal the length of the rectangle and
height 8 feet
- It has a trapezoid, the length of its two parallel bases are 2 , 5 and
height 2 feet
* Lets revise the area of all the shape above
- Area the quarter circle = 1/4 π r²
- Area of the rectangle = length × width
- Area of the triangle = 1/2 × base × height
- Area of the trapezoid = 1/2( the sum of the parallel bases) × height
* Now lets solve the problem
# Area of the quarter circle
∵ The radius of the circle = the width of the rectangle
∵ The width of the rectangle = 10 feet
∴ The radius of the circle = 10 feet
∵ The area of the quarter circle = 1/4 π r²
∴ Its area = 1/4 π (10)² = 25π feet²
# Area of the rectangle
∵ The length of the rectangle = 26 - the length of the radius
∵ the length of the radius = 10 feet
∴ The length of the rectangle = 26 - 10 = 16 feet
∵ The width of the rectangle = 10 feet
∵ The area of the rectangle = length × width
∴ Its area = 16 × 10 = 160 feet²
# Area of the triangle
∵ The base = the length of the rectangle
∵ The length of the rectangle = 16 feet
∴ The base = 16 feet
∵ The height = 8 feet
∵ The area of the triangle = 1/2 × base × height
∴ Its area = 1/2 × 16 × 8 = 64 feet²
# Area of the trapezoid
∵ The length of its two parallel bases are 2 feet , 5 feet
∵ The height = 2 feet
∵ The area = 1/2( the sum of the parallel bases) × height
∴ Its area = 1/2 (2 + 5) × 2 = 7 feet²
- Lets add all of these areas to find the area of the house
∴ The area of the house = 25π + 160 + 64 + 7 = 309.5398 feet²
* The area of the house is approximately 309.54 feet²