Answers
Answer:
Part A:
[tex]\left(x + 7\right)^{5}=x^{5} + 35 x^{4} + 490 x^{3} + 3430 x^{2} + 12005 x + 16807[/tex]
Part B:
The closure property describes cases when mathematical operations are CLOSED. It means that if you apply certain mathematical operations in a polynomial it will still be a polynomial. Polynomials are closed for sum, subtraction, and multiplication.
It means:
[tex]\text{Sum of polynomials } \Rightarrow \text{ It will always be a polynomial}[/tex]
[tex]\text{Subtraction of polynomials } \Rightarrow \text{ It will always be a polynomial}[/tex]
[tex]\text{Multiplication of polynomials } \Rightarrow \text{ It will always be a polynomial}[/tex]
But when it is about division:
[tex]\text{Division of polynomials } \Rightarrow \text{ It will not always/sometimes be a polynomial}[/tex]
Example of subtraction of polynomials:
[tex](2x^2+2x+3) - (x^2+5x+2)[/tex]
[tex]x^2-3x+1[/tex]
Step-by-step explanation:
First, it is very important to define what is a polynomial in standard form:
It is when the terms are ordered from the highest degree to the lowest degree.
Therefore I can give:
[tex]x^5-5x^4+3x^3-3x^2+7x+20[/tex]
but,
[tex]x^5+3x^3-3x^2+7x+20-5x^4[/tex] is not in standard form.
For this question, I can simply give the answer: [tex]x^5-5x^4+3x^3-3x^2+7x+20[/tex] and it is correct.
But I will create a fifth-degree polynomial using this formula
[tex]$(a+b)^n=\sum_{k=0}^n \binom{n}{k} a^{n-k} b^k$[/tex]
Also, note that
[tex]$\binom{n}{k}=\frac{n!}{(n-k)!k!}$[/tex]
For [tex]a=x \text{ and } b=7[/tex]
[tex]$\left(x + 7\right)^{5}=\sum_{k=0}^{5} \binom{5}{k} \left(x\right)^{5-k} \left(7\right)^k$[/tex]
[tex]\text{Solving for } k \text{ values: } 0, 1, 2, 3, 4 \text{ and } 5[/tex]
Sorry but I will not type every step for each value of [tex]k[/tex]
The first one is enough.
For [tex]k=0[/tex]
[tex]$\binom{5}{0} \left(x\right)^{5-0} \left(7\right)^{0}=\frac{5!}{(5-0)! 0!}\left(x\right)^{5} \left(7\right)^{0}=\frac{5!}{5!} \cdot x^5= x^{5}$[/tex]
Doing that for [tex]k[/tex] values:
[tex]\left(x + 7\right)^{5}=x^{5} + 35 x^{4} + 490 x^{3} + 3430 x^{2} + 12005 x + 16807[/tex]
Answer:
Ty for the free pointsd!
Step-by-step explanation:
Related Questions
values of r and h, what do you notice about the proportions of the cylinders?
Answers
Answer:
Below
Step-by-step explanation:
r us the radius of the base and h is the heigth of the cylinder.
The volume of a cylinder is given by the formula:
V = Pi*r^2*h
V/Pi*r^2 = h
We can write a function that relates h and r
Answer:
One of the cylinders is short and wide, while the other is tall and thin.
Step-by-step explanation:
sample answer given on edmentum
Help!!!!! Thank you!!!!
Answers
Answer:
97
Step-by-step explanation:
5 * 85 - 4* 82 = 97
Hope u understand
Thanks
Petroleum motor oil does a combination of natural oil and synthetic oil. It contains 5 L of natural oil for every 3 L of synthetic oil. In order to make 768 L of petroleum oil how many liters of natural oil are needed
Answers
Answer:
480 liters of natural oil
Step by step Explanation:
ratio of natural to synthetic oil
= 5:3
If 440 liters have to be made then,
Add 5 + 3 = 8
So, 5/8 of 768 liters will be = 480 liters of natural oil
and, 3/8 of 768 liters will be = 288liters of synthetic oil
Therefore, 480 liters of natural oil will be needed
Circle O below has radius 1. Eight segment lengths are labeled with lowercase letters. Six of these equal a trigonometric function of theta. Your answer to this problem should be a six letter sequence whose letters represent the segment lengths that equal the following functions (in the correct order):
sin(theta),
cos(theta),
tan(theta),
csc(theta),
sec(theta),
cot(theta).
So, for example, you would answer a,k,h,c,b,d if you thought
sin(theta) = a,
cos(theta) = k,
tan(theta) = h,
csc(theta) = c,
sec(theta) = b,
cot(theta) = d.
I was able to come up with:
sin(theta) = d,
cos(theta) = a,
tan(theta) = h,
csc(theta) = f,
sec(theta) = g,
cot(theta) = h.
Answers
Answer:
32
Step-by-step explanation:
Write each of the following expressions without using absolute value. 7m–56|, if m<8
Answers
Answer:
[tex]|7m- 56| = 56 - 7m[/tex]
Step-by-step explanation:
Given
[tex]|7m- 56|[/tex]
[tex]m < 8[/tex]
Required
Rewrite the expression without absolute values
The first step is to check if the expression in |...| is positive or negative;
The question says m < 8,
This means the value of m could be 7, 6 ...
Let's assume m is 7
[tex]7m - 56 = 7 * 7 - 56 = 49 - 56 = -7[/tex]
This means that the expression [tex]|7m- 56|[/tex] will give a negative value if [tex]m < 8[/tex]
So,
[tex]|7m- 56| = -(7m - 56)[/tex]
Open bracket
[tex]|7m- 56| = -7m + 56[/tex]
Rearrange
[tex]|7m- 56| = 56 - 7m[/tex]
The expression can't be further simplified
Example 2
A black die and a white die are thrown at the same
time. Display all the possible outcomes. Find the
probability of obtaining:
a) a total of 5
b) a total of 11
c) a 'two' on the black die and a six' on the white die.
It is convenient to display all the possible outcomes
on a grid. This is called a possibility diagram
It’s example 2 please help:)
Answers
Answer:
Total possible outcomes = 6×6 = 36
a) P(5) = 1/9
b) P(11) = 1/18
c) P(two and six) = 1/36
Step-by-step explanation:
A black die and a white die are thrown at the same time.
Each die has six sides so total possible outcomes are
Total possible outcomes = 6×6 = 36
The possible outcomes are given below:
(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)
a) Find the probability of obtaining a total of 5
Number of ways to get a total of 5 = (1, 4) (2, 3) (3, 2) (4, 1)
Number of ways to get a total of 5 = 4
The probability is given by
P = Number of desired outcomes/total number of outcomes
P(5) = 4/36
P(5) = 1/9
b) Find the probability of obtaining a total of 11
Number of ways to get a total of 11 = (5, 6) (6, 5)
Number of ways to get a total of 11 = 2
The probability is given by
P(11) = 2/36
P(11) = 1/18
c) a 'two' on the black die and a six' on the white die.
There is only one way to get a two on the black die.
Probability of obtaining a two on the black die = 1/6
There is only one way to get a six on the white die.
Probability of obtaining a six on the white die = 1/6
P(two and six) = 1/6×1/6
P(two and six) = 1/36
Which algebraic expression represents the phrase below?
five times the sum of a number and eleven, divided by three times the sum of the number and eight
5(x + 11) + 3(x + 8)
5x+11
3X+8
5(X+11)
3(x+8)
5x + 11 + 3x + 8
Answers
Answer:
[tex] \frac{5x + 11}{3(x + 8)} [/tex]
Step-by-step explanation:
[tex] \frac{5x + 11}{3(x + 8)} [/tex]
Five times the sum of a number and eleven, divided by three times the sum of the number and eight
Five times the sum= 5(_+_)
a number and eleven= x+11
divided= ÷ or /
3 times the sum of= 3(_+_)
the number and eight.
Together it will be
[tex]the \: \: one \: written \: in \: the \: answering \: section[/tex]
Hope this helps ;) ❤❤❤
Help please thanks don’t know how to do this
Answers
Answer:
a = 11.71 ; b = 15.56
Step-by-step explanation:
For this problem, we need two things. The law of sines, and the sum of the interior angles of a triangle.
The law of sines is simply:
sin(A)/a = sin(B)/b = sin(C)/c
And the sum of interior angles of a triangle is 180.
45 + 110 + <C = 180
<C = 25
We can find the sides by simply applying the law of sines.
length b
7/sin(25) = b/sin(110)
b = 7sin(110)/sin(25)
b = 15.56
length a
7/sin(25) = a/sin(45)
a = 7sin(45)/sin(25)
a = 11.71
m
A. not enough information
B. 70
C. 42
D. 38.5
Answers
Answer:
C
Step-by-step explanation:
Using Parts Whole Postulate we can write:
∠LQP = ∠LQR + ∠PQR
We know that ∠LQP = 77° and ∠LQR = 35° so we can write:
77° = 35° + ∠PQR
Therefore the answer is 77 - 35 = 42°.
PLZ HELP WILL GIVE BRAINLIEST
Answers
Answer:
Hey there!
We have the slope is equal to -2.5, and the y intercept is 3.
Thus, the equation is y=-2.5x+3
Hope this helps :)
PLEASE HELP ME ASPA What is the equation of the line that has a slope of -4 and passes through the point (2, 3)? y = -4x + 5 y = -4x – 5 y = -4x + 11 None of these choices are correct.
Answers
Answer:
Third option is the right choice.
Step-by-step explanation:
y = -4x + 11 (Slope = m = -4)
3 = -4(2) + 11
3 = -8 + 11
3 = 3
True.
The function f(t) = -6r+ 11 has the range {- 37. - 25. - 13, -1). Select the domain values from the list
1. 2. 3. 4. 5. 6. 7. 8. Justify your choices by explaining how you determined the domain values.
Answers
answer
-6r+-11=-37
-6r=-37+11
-6r=-48
r=8
Fill in blanks to write the particular equation of this
transformed cosine graph
Answers
Answer:
f ( x ) = -3*cos ( x ) -2
Step-by-step explanation:
Solution:-
The standard generalized cosine function is given in the form:
f ( x ) = a* cos ( w*x - k ) + b
Where,
a: The magnitude of the waveform
w: the frequency of the waveform
k: The phase difference of the waveform
b: The vertical offset of central axis from the origin
To determine the amplitude ( a ) of the waveform. We will first determine the central axis of the waveform. This can be determined by averaging the maximum and minimum values attained. So from graph:
Maximum: 1
Minimum: -5
The average would be:
Central axis ( y ) = [ 1 - 5 ] / 2
= -4 / 2
y = -2
The amplitude ( a ) is the difference between either the maximum value and the central axis or minimum value and the central axis. Hence,
a = Maximum - Central value
a = 1 - (-2)
a = 3
The waveform is inverted for all values of ( x ). That means the direction of amplitude is governed to the mirror image about x-axis. Hence, a = -3 not +3.
The offset of central axis from the x - axis ( y = 0 ) is denoted by the value of ( b ).
b = ( y = -2 ) - ( y = 0 )
b = -2 ... Answer
The frequency of the waveform ( w ) is given as the number of cycles completed by the waveform. The peak-peak distance over the domain of [ 0, 2π ]. We see from the graph is that two consecutive peaks are 2π distance apart. This means the number of cycles in the domain [ 0, 2π ] are w = 1.
The phase difference ( k ) is determined by the amount of "lag" or "lead" in the waveform. This can be determined from the x-distance between x point value of peak and the origin value ( x = 0 ). The peak and the origin coincides with one another. Hence, there is no lag of lead in the waveform. Hence, k = 0.
The waveform can be written as:
f ( x ) = -3*cos ( x ) -2
Explain how to get the volume of this figure
Answers
Answer:
350 meters cubed.
Step-by-step explanation:
If you visualize it, there are two rectangular prisms: one flat one on the top, and one large one on the bottom.
The width of the top one is 5 meters. The length is 7 meters. The height is 8 - 5 = 3 meters. So, one prism has a volume of 5m x 7m x 3m.
The width of the bottom one is 7 meters. The length is 7 meters. The height is 5 meters. So, the bottom prism has a volume of 7m x 7m x 5m.
(5 * 7 * 3) + (7 * 7 * 5)
= (35 * 3) + (49 * 5)
= 105 + 245
= 350
So, the volume of the figure is 350 meters cubed.
Hope this helps!
Solve and CHECK the following: 2(a−3)/3=4
Answers
Answer:
2(a - 3). = 4
_______
3
Cross multiply.
2(a- 3) = 12
2a - 6 = 12
2a = 12 + 6
2a = 18
a = 18 ÷ 2
a = 9
Answer:
a = 9
Step-by-step explanation:
Given
[tex]\frac{2(a-3)}{3}[/tex] = 4 ( multiply both sides by 3 to clear the fraction
2(a - 3) = 12 ( divide both sides by 2 )
a - 3 = 6 ( add 3 to both sides )
a = 9
As a check substitute a = 9 into the left side of the equation and if equal to the right side then it is the solution.
[tex]\frac{2(9-3)}{3}[/tex] = [tex]\frac{2(6)}{3}[/tex] = [tex]\frac{12}{3}[/tex] = 4 = right side
Thus solution is a = 9
2. Global Cable paid dividends of $0.28 and $0.16 per share last year. Given yesterday's closing price was $11.27, determine the current yield on the stock? Round to the nearest tenth.
Answers
Answer:
3.90%
Step-by-step explanation:
Relevant Data provided as per the question below:
Annual dividend = $0.28 and $0.16
Current per share = $11.27
According to the given situation, the calculation of the current yield of the stock is shown below:-
Current yield is
[tex]= \frac{Annual\ dividend}{Current\ share\ price} \times 100\\\\ = \frac{0.28 + 0.16}{11.27} \times 100[/tex]
[tex]= \frac{0.44}{11.27} \times 100[/tex]
= 3.90%
Therefore for computing the current yield of the stock we simply applied the above formula.
PLSSSS HELP The area of a cylinder varies jointly with the radius and the height. When the radius is 3 and the height is 6 the area is 36π. Find the are when the radius is 4 and the height is 5
Answers
Answer:
167.55
Step-by-step explanation:
so it varies jointly so
A-area if cylinder
so
[tex]a \: \alpha \: \pi \: r \: ^{2} h[/tex]
so
[tex]a = k\pi \: r^{2}h[/tex]
where k is the constant
so apply the first set of values to get k=2/3
then substitute the k with the second set of values
Hassan built a fence around a square yard. It took 48 m^2 of lumber to build the fence. The fence is 1.5 meters tall.
Answers
Answer:
Step-by-step explanation:
Please check ones more because this might be incorrect.
The area is in square meters...Let's change it
Square 48= 48*48 =2304
2304 divided by 4( 4 since the formula for the area of a sqaure is s*s and square has 4 sides)
2304 divided by 4 = 576
The formula for area of a square is S*S(side times side)
Let's apply the formula here.
so, 576 times 576
331776 square meters
Hope this is right and helps! :)
( This just my point of view. Please check this onces again)
Answer:
the answer is 64
Step-by-step explanation:
khan
Andrew drives through 5 intersections with stoplights on his way to work. He records that he is stopped by a red light in 2 of the 5 intersections. If he uses this as his general probability of getting stopped at a red light on his way to or from work, how many times can he expect to be stopped at a red light over the next 40 times he drives through an intersection on his route? Andrew should expect to be stopped times.
Answers
Answer:
He should expect to be stopped a total of 16 times
Step-by-step explanation:
What the question is saying is that out of every 5 intersections, he would be stopped at 2.
Now, for forty times in which he passes through an intersection , we want to know the number of times in which he would be stopped
In this case we only need to multiply the probability by the number of times in which he passes an intersection and that would be 2/5 * 40 = 16 times
Answer:
16
Step-by-step explanation:
PLEASE HELP!!!
Rectangle EFGH is reflected across the origin and then rotated 90° clockwise about the origin, forming rectangle E″F″G″H″. What are the coordinates of rectangle E″F″G″H″?
(A.) E″ (1, –5), F″ (1, –1), G″ (4, –1), H″ (4, –5)
(B.) E″ (–1, –5), F″ (–1, –1), G″ (–4, –1), H″ (–4, –5)
(C.) E″ (–1, 5), F″ (–1, 1), G″ (–4, 1), H″ (–4, 5)
(D). E″ (5, 1), F″ (1, 1), G″ (1, 4),
H″ (5, 4)
Answers
Answer:
c.
Step-by-step explanation:
90 degrees clockwise is (x,y)-(y,-x)
Answer:
The answer is A
Step-by-step explanation:
Took the test
Simplify: 14 - 2+ 8 = 2 *3
helppp meeee
Answers
Answer:
20=6?
Step-by-step explanation:
14-2+8=2*3
14-2+8=6
12+8=6
20=6?
Answer:
These to equations aren't equivalent.
Step-by-step explanation:
14-2+8=2*3
12+8=6
20=6
Hope this helps ;) ❤❤❤
The first three steps in determining the solution set of the system of equations algebraically are shown.
y = x2 − x − 3
y = −3x + 5
What are the solutions of this system of equations?
(−2, −1) and (4, 17)
(−2, 11) and (4, −7)
(2, −1) and (−4, 17)
(2, 11) and (−4, −7)
Answers
Answer:
(2, −1) and (−4, 17)
Step-by-step explanation:
I used a graphing tool to graph the systems of equations. The parabola and line pass at points (2, -1) and (-4, 17).
Answer:(2, −1) and (−4, 17) Its C on Edge 2023
Step-by-step explanation: Its (C) after an extensive research
-3 raised to 2 + -3 raised to 2 =
Answers
Answer:
Step-by-step explanation:
(-3)² + (-3)² = (-3)*(-3) + (-3)*(-3)
= 9 + 9
= 18
Answer:
18
Step-by-step explanation:
the constant proportionality of y=5x
Answers
Answer:
k = 5
Step-by-step explanation:
The equation of proportionality is
y = kx ← k is the constant of proportionality
Given
y = 5x , then k = 5
Please answer this question now
Answers
Answer:
d = 8.5
Step-by-step explanation:
The following data were obtained from the question:
Angle D = 100°
Opposite D = d
Opposite E = e = 6
Opposite F = f = 5
Thus, we can obtain the value of d by using the cosine rule as shown below:
d² = e² + f² – 2ef Cos D
d² = 6² + 5² – 2 × 6 × 5 × Cos 100°
d² = 36 + 25 – 60 × Cos 100°
d² = 61 – – 10.419
d² = 61 + 10.419
d² = 71.419
Take the square root of both side.
d = √71.419
d = 8.5
Therefore, the value of d is 8.5
A school has 400 students. They all come to school by bus, and each bus carries the same number of students. How many students might there be on each bus?
Answers
Answer:
100 students on each bus
Step-by-step explanation:
100*4 is 400 so there might be just 4
Answer:
Hey there!
It's possible that there are 200 busses, and each bus carries only 2 people, there are 10 busses and each bus carries 40 people, or there are 5 busses and each bus carries 80 people.
Hope this helps :)
Which equation is perpendicular to y= 3/4x + 4 and passes through the point (0,2)
A. Y= 3/4x + 2
B. Y= -3/4x + 2
C. Y= -4/3x + 2
D. Y= 4/3x + 2
Answers
The function, f(x) = –2x2 + x + 5, is in standard form. The quadratic equation is 0 = –2x2 + x + 5, where a = –2, b = 1, and c = 5. The discriminate b2 – 4ac is 41. Now, complete step 5 to solve for the zeros of the quadratic function. 5. Solve using the quadratic formula. x = StartFraction negative b plus or minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFraction What are the zeros of the function f(x) = x + 5 – 2x2? x = StartFraction negative 1 plus or minus StartRoot 41 EndRoot Over negative 4 EndFraction x = StartFraction 1 plus or minus StartRoot 41 EndRoot Over negative 4 EndFraction x = StartFraction negative 1 plus or minus StartRoot 39 EndRoot Over negative 4 EndFraction x = StartFraction 1 plus or minus StartRoot 39 EndRoot Over negative 4 EndFraction
Answers
Answer:
To solve for the zeros of the function equate f(x) = 0
That's
- 2x² + x + 5 = 0
Using the quadratic formula
[tex]x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
a = - 2 b = 1 c = 5
And from the question
b² - 4ac = 41
So we have
[tex]x = \frac{ - 1± \sqrt{41} }{2( - 2)} = \frac{ - 1± \sqrt{41} }{ - 4} [/tex]
[tex]x = \frac{1± \sqrt{41} }{4} [/tex]
We have the final answer as
[tex]x = \frac{1 + \sqrt{41} }{4} \: \: \: \: or \: \: \: \: x = \frac{1 - \sqrt{41} }{4} [/tex]
Hope this helps you
Answer:
The CORRECT answer is A.
Step-by-step explanation:
just did it.
5.
Which of the following equations has the sum of its roots as 3?
(A) 2x² – 3x + 6 = 0
(B) - x²+ 3x - 3 = 0
(C)√2x²-3/√2x+1
(D) 3x² – 3x + 3 = 0
Answers
Answer:
B
Step-by-step explanation:
Given a quadratic equation in standard form, ax² + bx + c = 0 ( a ≠ 0 )
Then the sum of the roots = - [tex]\frac{b}{a}[/tex]
A 2x² - 3x + 6 = 0
with a = 2 and b = - 3
sum of roots = - [tex]\frac{-3}{2}[/tex] = [tex]\frac{3}{2}[/tex] ≠ 3
B - x² + 3x - 3 = 0
with a = - 1 and b = 3
sum of roots = - [tex]\frac{3}{-1}[/tex] = 3 ← True
C [tex]\sqrt{2}[/tex] x² - [tex]\frac{3}{\sqrt{2} }[/tex] x + 1
with a = [tex]\sqrt{2}[/tex] and b = - [tex]\frac{3}{\sqrt{2} }[/tex]
sum of roots = - [tex]\frac{-\frac{3}{\sqrt{2} } }{\sqrt{2} }[/tex] = [tex]\frac{3}{2}[/tex] ≠ 3
D 3x² - 3x + 3 = 0
with a = 3 and b = - 3
sum of roots = - [tex]\frac{3}{-3}[/tex] = 1 ≠ 3
Thus the equation with sum of roots as 3 is B
49 students choose to attend one of three after school activities: football, tennis or running.
There are 18 boys.
11 students choose football, of which 1 are girls.
29 students choose tennis.
7 girls choose running.
A student is selected at random.
What is the probability this student chose running?
Give your answer in its simplest form.
Answers
49 - 11 - 29 = 9.
The probability that student chose running is 9/49 .
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
Consider the information as that 49 students choose to attend one of three after-school activities: football, tennis, or running.
11 students choose football, 29 students choose tennis.
The students choose running = 49 - 11 - 29 = 9.
The students choose running = 0
This means out of 49 students 9 choose running.
P(E) = 9/49
Hence, the probability that student chose running is 9/49 .
Learn more about probability here;
https://brainly.com/question/9326835
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