Hey! i've been working on these questions but I have no idea how to solve this one, could anybody help me? Thanks in advance!
Answers
Answer:
1) [tex]\boxed{p(x) = x^3-x^2+x-1}[/tex]
2) [tex]\boxed{p(x) = x^2+x-2}[/tex]
3) [tex]\boxed{p(x) =- 2x^2+2x+4}[/tex]
4) [tex]\boxed{p(x) = 2x^2+x-4}[/tex]
Step-by-step explanation:
Part (1)
[tex]p(x) = x^3-x^2+x-1[/tex]
As we have to determine it by ourselves, this is the polynomial having a degree of 3. p(x) with a degree of 3 means that the highest degree/exponent of x should be 3.
Part (2)
[tex]p(x) = x^2+x-2[/tex]
This can be the polynomial having the factor x-1 because if we put:
x - 1 = 0 => x = 1 in the above polynomial, it gives us a result of zero which shows us that (x-1) "is" a factor of the polynomial.
Part (3)
[tex]p(x) = -2x^2+2x+4[/tex]
This can be the polynomial for which p(0) = 4 and p(-1) = 0
Let's check:
[tex]p(0) =- 2(0)^2+2(0)+4\\p(0) = 0 + 0+4\\p(0) = 4[/tex]
[tex]p(-1)= -2(-1)^2+2(-1)+4\\p(-1) = -2(1)-2+4\\p(-1) = -2-2+4\\p(-1) = 0[/tex]
So, this is the required polynomial determined by "myself".
Part (4):
[tex]p(x) = 2x^2+x-4[/tex]
This is the polynomial having a remainder 6 when divided by (x-2)
Let's check:
Let x - 2 = 0 => x = 2
Putting in the above polynomial
[tex]p(x) = 2(2)^2+(2)-4\\Given \ that \ Remainder = 6\\6 = 2(4) +2-4\\6 = 8+2-4\\6 = 10-4\\6 = 6[/tex]
So, Proved that it has a remainder of 6 when divided by (x-2)
Related Questions
What is the equation of the parabola that has its vertex at (8,-1) and a y-intercept of (0,-17)?
Answers
y = a(x + 1.5)^2 - 12.5
y intercept is (0,-8) so:-
-8 = a(0+1.5)^2 - 12.5
-8 = 2.25a - 12.5
a = 4.5/ 2.25 = 2
so we have
y = 2 ( x +1.5)^2 - 12.5
solving for x when y = 0:-
(x + 1.5)^2 = 12.5/2 = 6.25
taking sqrt's x + 1.5 = +/- 2.5
x = -4, 1
so the x intercepts are (-4,0) and (1,0)
Answer:
y = –1∕4(x – 8)^2 – 1
Step-by-step explanation:
I took the exam and got it right.
If the nth term is , then the (n+1)st is: Please make sure you check the image :)
Answers
Answer:
( n+1) /2 *( 3n+2)
Step-by-step explanation:
n/2 * ( 3n-1)
We want the n+1 term
Replace n with n+1
( n+1) /2 *( 3( n+1) -1)
Distribute
( n+1) /2 *( 3n+3 -1)
( n+1) /2 *( 3n+2)
Answer:
[tex]\large \boxed{\sf C. \ \frac{n+1}{2} (3n+2)}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{n}{2} (3n-1)[/tex]
To find the (n+1)st term, replace the n variable with n+1.
[tex]\displaystyle \frac{n+1}{2} (3(n+1)-1)[/tex]
Expand brackets.
[tex]\displaystyle \frac{n+1}{2} (3n+3-1)[/tex]
Subtract like terms in brackets.
[tex]\displaystyle \frac{n+1}{2} (3n+2)[/tex]
the grasshopper population in Georgia is currently 4,000. It's growing by 2.3% each year. Write an equation that models the situation.
Answers
Answer:
[tex]4000(1.023)^t\\\\[/tex]
Step-by-step explanation:
Using this exponential growth equation we can get an equation that models the situation.
A= Principal Amount
R= Rate of Growth
T= Amount of time
[tex]A=4000\\R=2.3/100=.023\\T= Non[/tex]
[tex]A(1+R)^t\\4000(1+0.23)^t\\4000(1.023)^t\\\\[/tex]
Which phrase describes the algebraic expression 8f+7?
the product of 8 and 7 more than a number
the quotient of 8 and 7
8 times the sum of a number and 7
8 times a number plus 7
Answers
Answer:
8 times a number plus 7
Step-by-step explanation:
Let the number be f.
Simply, 8 f+7 is the expression.
Thank you!
The sum of 8 times a number and 7 equals 9!
Answers
Answer:
0.25*8+7=9
Step-by-step explanation:
8x+7=9
2/8=x
0.25=x
A certain game involves tossing 3 fair coins, and it pays .14 for 3 heads, .06 for 2 heads, and .01 for 1 head. The expected winnings are?
Answers
Answer:
Total expected amount = $0.04375
Step-by-step explanation:
We need to calculate probability of getting heads on every combination of coin tosses
HHH = 1/8 = 3 heads
HHT = 1/8 = 2 heads
HTH = 1/8 = 2 heads
HTT = 1/8 = 1 head
THH = 1/8 = 2 heads
THT = 1/8 = 1 head
TTH = 1/8 = 1 head
TTT = 1/8 = 0 head
So the probability of 3 heads is 1/8 and the amount is (1/8)* 0.14 = $0.0175
Probability of 2 heads is 3/8 and the amount is (3/8) * 0.06 = $0.0225
Probability of 1 head is 3/8 and amount is (3/8) * 0.01 = $0.00375
Total expected amount = 0.00375 + 0.0225 + 0.0175
Total expected amount = $0.04375
What is the 25th term in the following arithmetic sequence? -7, -2, 3, 8, ...
Answers
Answer:
108.
Step-by-step explanation:
-7, -2, 3, 8 is an arithmetic sequence with a1 (first term) = -7 and common difference (d) = 5.
The 24th term = a1 + (24 - 1)d
= -7 + 23 * 5
= -7 + 115
= 108.
If the weight (in grams) of cereal in a box of Lucky Charms is N(470,5), what is the probability that the box will contain less than the advertised weight of 453 g?
Answers
Answer:
The probability that the box will contain less than the advertised weight of 453 g is 0.00034.
Step-by-step explanation:
Let X represent the weight (in grams) of cereal in a box of Lucky Charms.
It is provided that X follows a Normal distribution with parameters, μ = 470 and σ = 5.
Compute the probability that the box will contain less than the advertised weight of 453 g as follows:
[tex]P(X<453)=P(\frac{X-\mu}{\sigma}<\frac{453-470}{5})[/tex]
[tex]=P(Z<-3.4)\\=0.00034[/tex]
*Use the z-table.
Thus, the probability that the box will contain less than the advertised weight of 453 g is 0.00034.
Use the dot product to determine whether v and w are orthogonal.
v=-i-j, w=-i+j
Select the correct choice below and fill in the answer box to complete your choice.
O A. The vectors v and w are not orthogonal because their dot product is ___
O B. The vectors v and w are orthogonal because their dot product is ___
Answers
Answer:
B. The vectors v and w are orthogonal because their dot product is 0
Step-by-step explanation:
Given that :
v= - i - j
w= - i + j
Therefore;
vw = ( - i - j ) ( - i + j )
Taking each set of integer of the vector into consideration:
vw = ( -1 × - 1) ( -1 × 1)
vw = 1 - 1
vw = 0
Hence, we can conclude that :
The vectors v and w are orthogonal because their dot product is 0
Identify the recursive formula for the sequence given by the explicit formula f(n) = 20 – 4(n − 1).
Answers
Answer:
[tex]\huge\boxed{f(n)=\left\{\begin{array}{ccc}f(1)=20\\f(n)=f(n-1)-4\end{array}\right}[/tex]
Step-by-step explanation:
[tex]f(n)=20-4(n-1)=20+(n-1)(-4)\\\\\text{It's an explicit formula of an arithmetic sequence:}\\\\f(n)=a_1+(n-1)(d)\\\\a_1-\text{first term}\\d-\text{common difference}\\\\\text{Conclusion:}\\\text{Next term}=\text{previous one}\ -4\\\\\text{The recursive formula:}\\\\\huge\boxed{f(n)=\left\{\begin{array}{ccc}f(1)=20\\f(n)=f(n-1)-4\end{array}\right}[/tex]
Answer:
Step-by-step explanation:
someone answered already
2. Write the equation of the circle in general form. Show your work.
Answers
Answer:
[tex] {(x + 1)}^{2} + {(y - 1)}^{2} = 9[/tex]
[tex] {x} ^{2} + {y} ^{2} + 2x - 2y - 7 = 0 [/tex]
Enclosing the Largest Area The owner of the Rancho Grande has 3,052 yd of fencing with which to enclose a rectangular piece of grazing land situated along the straight portion of a river. If fencing is not required along the river, what are the dimensions (in yd) of the largest area he can enclose
Answers
Answer:
the shorter side = 1526
the longer side = 763
area = 1164338
Step-by-step explanation:
lets say
a=length
b = width
a + 2b = 3052
this is the perimeter
such that
a = 3052 - 2b
the area of a rectangle is a*b
= (3052 - 2b)b
= 3052b - 2b²
we differentiate this to get:
= 3052 - 4b
such that
3052 = 4b
divide through by 4, to get b, the width
3052/4 = 763
b = 763
put the value of b into a
a = 3052 - 2b
a = 3052 - 2(763)
a = 3052 - 1526
a = 1526
therefore
the shorter side = 1526
the longer side = 763
area = a x b
area = 1526 x 763
area = 1526 x 763
= 1164338
Use the frequency distribution, which shows the number of American voters (in millions) according to age, to
find the probability that a voter chosen at random is in the 18 to 20 years old age range
Ages
18 to 20
21 to 24
25 to 34
35 to 44
45 to 64
65 and over
Frequency
4.2
7.8
20.8
23.7
50.1
28 2
Date
07/2
3:29
The probability that a voter chosen at random is in the 18 to 20 years old age range is 0.0311
(Round to three decimal places as needed.)
07/2
8:52
Question Viewer
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8:03
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Question is complete. Tap on the red indicators to see incorrect answers.
07/1
12:00
Answers
Answer:
The probability that a voter chosen at random is in the 18 to 20 years old age range is = 4.2/ 134.8= 0.0311572
Step-by-step explanation:
We can find the probability by simply dividing the frequency of the ages range of 18-20 by the total frequency.
Ages Frequency
18 to 20 4.2
21 to 24 7.8
25 to 34 20.8
35 to 44 23.7
45 to 64 50.1
65 and over 28.2
∑ 134.8
The probability of an event is given by the occurrence of an event by the total occurrences .
So
Here the occurrence of ages 18-20 is given by 4.2
and the total frequency is 134.8
The probability that a voter chosen at random is in the 18 to 20 years old age range is = 4.2/ 134.8= 0.0311572
A publishing company claims that in fall 2019, the average price of college textbooks for a single semester is $385. Suppose you decide to collect data from a random sample of students to assess whether the publisher's claim is reasonable, and you find that in a random sample of 22 college students, the mean price of textbooks for the fall 2019 semester was $433.50 with a standard deviation of $86.92. At the 0.01 significance level, is there sufficient evidence to conclude that the mean price of college textbooks for a single semester is different from the value claimed by the publisher?
Answers
Answer:
We accept H₀ . We don´t have enough evidence to express the publisher claim is not true
Step by Step explanation:
We must evaluate if the mean of the price of college textbooks is different from the value claimed by the publisher
n < 30 then we must use t - distrbution
degree of freedom n - 1 df = 22 - 1 df = 21
As the question mentions " different " that means, a two-tail test
At 0,01 significance level α = 0,01 α/2 = 0,005
and t(c) = 2,831
Test Hypothesis
Null Hypothesis H₀ μ = μ₀
Alternative hypothesis Hₐ μ ≠ μ₀
To calculate t(s)
t(s) = ( μ - μ₀ ) /σ/√n
t(s) = ( 433,50 - 385 ) / 86,92 / √22
t(s) = 2,6171
Comparing t(c) and t(s)
t(s) < t(c)
Then t(s) is in the acceptance region we accept H₀. We don´t have enough evidence to claim that mean price differs from publisher claim
a company should stop making a part internally and buy externally when
Answers
Answer:
Make-or-Buy Decision
Step-by-step explanation:
Joey’s pizza sells large cheese pizzas for $12.00. Each additional topping costs $0.50. Basketball Boosters bought 12 large pizzas, each with 3 toppings. There are 8 slices per pizza. How much does it cost per slice? Round to the nearest cent.
Answers
Answer:
So first you do $0.50 x 3 = 1.5
then you add that to $12.00
$12.00 + 1.5 = 13.5
13.5 is the cost of one pizza.
Since they bought 12:
The total cost of the 12 pizza is $162 <== not important
13.5 divided by 8 is 1.687
round 1.56875 to the nearest cent 1.7 = $2
so each slice costs $2
Billy has x marbles. Write an expression for the number of marbles the following have… a) Charlie has 5 more than Billy b) Danny has 8 fewer than Billy c) Eric has three times as many as Billy
Answers
Answer:
Charlie: 5 + xDanny: x - 8Eric: x × 3the bold answer is incorrect. what is the right answer?
Answers
Explanation:
A complementary angle are two angles add up to 90 degree
Can I have somebody answer a few more of the questions that I need please and this one too?
Answers
Answer:
x > 22
Step-by-step explanation:
Hey there!
Well to solve,
52 - 3x < -14
we need to single out x
52 - 3x < -14
-52 to both sides
-3x < -66
Divide both sides by -3
x > 22
The < changes to > because the variable number is a - being divided.
Hope this helps :)
Answer:
x > 22
Step-by-step explanation:
First, rearrange the equation
52 - 3 × x - (-14) < 0Then, pull out the like terms:
66 - 3xNext, apply algebra to the equation by dividing each side by -3. It should now look like this: x > 22.
Therefore, the solution set of the inequality would be x > 22.
If there are 80 students in a class and 20 are seniors, what proportion of students are not seniors?
Answers
Answer:
3/4
Step-by-step explanation:
First find the number that are not seniors
80 -20 = 60
60 are not seniors
The ratio of not seniors to total
60/80
Divide top and bottom by 20
3/4
Answer:
60 students
Step-by-step explanation:
80 -20 = 60
How long will it take $3800 to grow into $5700 if it’s invested at 6% interest compounded continuously?
Answers
Answer: 25 years
Step-by-step explanation:
t = I / Pr
t = 5700 / ( 3800 × 0.06 ) = 25
t = 25 years
If the sum of the daily unpaid balances is $7,812 over a 31-day billing cycle, what is the average daily balance?
Answers
Answer:
252
Step-by-step explanation:
Divide 7812 by 31 and we get the average daily answer... Hope this helps!!
HELP PLZ A circle inscribed in a triangle:
Answers
Answer:
The answer is the second photo.
Step-by-step explanation:
It's literally a circle in a triangle. So, it's the second one.
Which of the following is the correct notation of the complex number?
Answers
Answer:
-84 + 10i
Step-by-step explanation:
Standard Complex Form: a + bi
Step 1: Evaluate
√-100 = √-1 x √100 = i x 10 = 10i
-84 = -84
Step 2: Combine
10i - 84
Step 3: Rearrange
-84 + 10i
Answer:
Last Option
Step-by-step explanation:
√-100 - 84
(√(100×-1)) - 84
(√100)(√-1)-84
√-1 = i
10i - 84 or -84 + 10i
Rational equation of 3/x+1=2/x-3
Answers
Answer:
x = 11
Step-by-step explanation:
3/x+1=2/x-3
Solve by using cross products
2 (x+1) = 3 (x-3)
Distribute
2x+2 = 3x-9
Subtract 2x
2x+2-2x = 3x-2x-9
2 = x-9
Add 9 to each side
2+9 =x-9+9
11 =c
Ava placed the point of her pencil on the origin of a regular coordinate plane. She marked a point after moving her pencil 4 units to the left and 7 units up. Which ordered pair identifies where Ava marked her point?
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[tex] \Large{ \boxed{ \bold{ \color{lightgreen}{Solution:}}}}[/tex]
So, Let's solve this question by using cartesian plane.
Here, Origin is shown by (0, 0)Ava moves 4 units left from origin. On the left side of origin, negative x axis begins. So, she reached (-4, 0) now.Then, from that point she moved 7 units upwards. On the upper side, there is positive y axis. So, Finally she will reach point (-4, 7).(-4, 7) is the coordinate of point which is 4 units left from y axis and 7 units up from x axis.It lies on the second quadrant.Well, What is cartesian plane?
A - A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a set of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length.
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The following is the number of minutes to commute from home to work for a group of 25 automobile executives. 35 36 39 43 37 35 34 30 36 34 30 39 37 40 38 33 31 28 39 35 35 36 41 24 36 How many classes would you recommend? What class interval would you suggest? (Round up your answer to the next whole number.) Organize the data and plot a frequency distribution on a piece of paper. Comment on the shape of the frequency distribution. It is not symmetric. It is fairly symmetric, with most of the values between 24 and 43. It is not very symmetric, but most of the values lie between 24 and 43.
Answers
Answer:
It is not symmetric, but skewed left. Data appears more to be on the left side.
Step-by-step explanation:
The smallest value is 24 and the largest is 43 . The difference between these two values is 19 which can be divided into into intervals of 4.
19/4= 4.75 It will be rounded to 5.
The class interval can of 5. Starting from 20 we get class intervals and frequency distribution as
Class Intervals Data Frequency
20-24 24 1
25- 29 28, 1
30-34 34,30,34,30,33,31, 6
35-39 35,36,39,37,35,36,39,37, 14
38,39,35,35,36,36
40-44 43,40,41 3
The class intervals are inclusive of both upper and lower limits. The difference between the lower limits of two consecutive classes or upper limits of two consecutive classes must be the same.
As we see the difference here is that of 5 between the two upper or lower limits of consecutive classes.
The histogram is attached which shows the class intervals along x- axis and data frequency along y- axis.
PLEASE HELP QUICK!!!!!!! Find the length of a rectangle that has one side of length 8 and area 32
Answers
Answer:
4
Step-by-step explanation:
Length of one side=8
Area=32
Length of another side=x
8 into x = 32
X=32/8
=4
I need help ? which linear function is represented by the graph?
Answers
=================================================
Explanation:
The diagonal line passes through 1 on the vertical y axis. So the y intercept is b = 1. This means the location of the y intercept is (0,1).
Start at (0,1) and move down 1 and to the right 2 to arrive at (2,0). This is another point on the diagonal line. The motion of "down 1 and right 2" is effectively the slope
slope = rise/run = -1/2
rise = -1, run = 2
The rise being negative means we have gone downhill as we move to the right.
With m = -1/2 as the slope and b = 1 as the y intercept, we go from y = mx+b to y = (-1/2)x+1
The last thing to do is replace y with f(x) to get f(x) = (-1/2)x+1 as the final answer.
Answer:
it's b
Step-by-step explanation:
b
What is the volume of a square pyramid whose length of one side of its base is 9cm and whose height is 15cm. Show your work
Answers
Answer:
The answer is 405cm³Step-by-step explanation:
Volume of a pyramid is given by
[tex]V = \frac{1}{3} \times area \: of \: base \: \: \times height[/tex]
height = 15cm
From the question the pyramid is a square pyramid which means it's base is a square
Area of a square = l²
where l is the length of one side
l = 9cm
Area of square = 9² = 81cm²
So the volume of the pyramid is
[tex]V = \frac{1}{3} \times 81 \times 15[/tex]
[tex]V = 27 \times 15[/tex]
We have the final answer as
V = 405 cm³
Therefore the volume of the pyramid is
405cm³Hope this helps you
