The answer is 2.1 Km. Hope this helps!
(08.07 MC)
A polynomial function is shown below:
f(x) = x3 − 3x2 − 4x + 12
Which graph best represents the function? (5 points)
Answer:
Graph A (first graph from top to bottom)
Step-by-step explanation:
Given [tex]f(x)=x^3-3x^2-4x+12[/tex], since the degree of the polynomial is 3, the function must be odd and will resemble the shown shape in the graphs. The degree of 3 indicates that there are 3 zeroes, whether distinct or non-distinct. Therefore, the graph must intersect the x-axis at these three points.
Factoring the polynomial:
[tex]f(x)=x^3-3x^2-4x+12,\\f(x)=(x+2)(x-2)(x-3),\\\begin{cases}x+2=0, x=-2\\x-2=0, x=2\\x-3=, x=3\end{cases}[/tex]
Thus, the three zeroes of this function are [tex]x=-2, x=2, x=3[/tex] and the graph must intersection the x-axis at these points. The y-intercept of any graph occurs when [tex]x=0[/tex]. Thus, the y-coordinate of the y-intercept is equal to [tex]y=0^3-3(0^2)-4(0)+12,\\y=12[/tex] and the y-intercept is (0, 12).
The graph that corresponds with this is graph A.
QUESTION 1
Determine the work done by the force
F=31+] + k in moving an object through
displacement T = 7 -7 -K
It's difficult to make out what the force and displacement vectors are supposed to be, so I'll generalize.
Let θ be the angle between the force vector F and the displacement vector r. The work W done by F in the direction of r is
W = F • r cos(θ)
The cosine of the angle between the vectors can be obtained from the dot product identity,
a • b = ||a|| ||b|| cos(θ) ==> cos(θ) = (a • b) / (||a|| ||b||)
so that
W = (F • r)² / (||F|| ||r||)
For instance, if F = 3i + j + k and r = 7i - 7j - k (which is my closest guess to the given vectors' components), then the work done by F along r is
W = ((3i + j + k) • (7i - 7j - k))² / (√(3² + 1² + 1²) √(7² + (-7)² + (-1)²))
==> W ≈ 5.12 J
(assuming F and r are measured in Newtons (N) and meters (m), respectively).
the value of 456×6+35×2 is
Answer:
2806
Step-by-step explanation:
→ First complete the multiplication
456 × 6 = 2736 and 35 × 2 = 70
→ Add the totals
2736 + 70 = 2806
Answer:2806
Step-by-step explanation:
^﹏^
Which points in the graph are in Quadrant II?
Answer:
A, L, F
Step-by-step explanation:
Quadrant ll (2) is the top left one so points A, L, F are in it. Hope this is correct!
Answer: AL
Step-by-step explanation: THE OTHER ARE ON THE AXIS AND NOT NEITHER QUADRANTS
Find the volume of the cylinder pictured below. What is the exact volume in terms of pi?
Help? write down the answer with an explanation I give brainiest!!!!
Answer:
Step-by-step explanation:
Let the amount Emily started with be 100x
Amount spent at grocery 1/2 of the money:
[tex]\frac{1}{2} \ of \ 100x = 50x[/tex]
Remaining amount
[tex]=100 x - 50x = 50x[/tex]
Amount spent at the Bakery 1/2 of what is left :
[tex]\frac{1}{2} \ of \ 50x = 25x[/tex]
Remaining amount
[tex]= 50x - 25x = 25x[/tex]
Amount spent on CD , 1/2 of what is left :
[tex]=\frac{1}{2} \ of \ 25x = \frac{1}{2} \times 25x = 12.5x[/tex]
Remaining amount
[tex]= 25x - 12.5x = 12.5x[/tex]
But given the amount left is $6
That is ,
[tex]12.5x = 6\\\\x = \frac{6}{12.5} = 0.48[/tex]
Therefore amount Emily had in beginning = 100 x = 100( 0.48) = $48
9.5 sq. miles = _____ acres
2 acres = _______ square yards
Answer:
frist answer is
6080
second answer is 72 square yard
what are functions in math
The set of ordered pairs (–1, 8), (0, 3), (1, –2), and (2, –7) represent a function. What is the range of the function?
Answer:
8 3 -2 -7
Step-by-step explanation:
becoz the y values are the ranges of the function
Answer:
{y: y = –7, –2, 3, 8}
This is a 30-60-90 triangle. What is the measure of x? rationalize the denominator.
Answer:
[tex] x=\frac{[2] \sqrt {[21] }}{[3] }[/tex]
Step-by-step explanation:
Since, given is a 30°-60°-90° triangle.
[tex] \therefore \sqrt 7 = \frac{\sqrt3}{2} \times x[/tex]
[tex] \therefore 2\sqrt 7 = \sqrt3 \times x[/tex]
[tex] \therefore x=\frac{2\sqrt 7}{\sqrt 3}[/tex]
[tex] \therefore x=\frac{2\sqrt 7(\sqrt 3)}{\sqrt 3(\sqrt 3)}[/tex]
[tex] \huge \therefore x=\frac{[2] \sqrt {[21] }}{[3] }[/tex]
Consider the random experiment of tossing 3 fair coins and observing how many of them come to rest with the heads side of the coin facing upwards. (Assume that each of the coins comes to rest with either its heads side or its tails side facing upwards (i.e., none of the coins comes to rest balanced on its edge).) Letting A denote the event that at least 1 of the coins comes to rest with its heads side upwards, B denote the event that none of the coins comes to rest with its heads side upwards, and S denote the sample space, which of the following statements does not include an abuse of notation?
a. S = 16
b. S = AUB
c. S - 4
d. S = 3
e. P(B) = φ
Answer:
b. S = AUB
Step-by-step explanation:
Since the coins are tossed 3 times and each coin has head, H and tail, T(2 sides), the sample space is S = 2 × 2 × 2 = 2³ = 8
All the possible outcomes are HTT, HHT, HHH, THH, TTH, HTH,THT and TTT
Since S denote the sample space
S = {HTT, HHT, HHH, THH, TTH, HTH,THT, TTT}
Since A denote the event that at least 1 of the coins comes to rest with its heads side upwards, the possible outcomes are HTT, HHT, HHH, THH, TTH, HTH and THT
So, A = {HTT, HHT, HHH, THH, TTH, HTH,THT}
Also B denote the event that none of the coins comes to rest with its heads side upwards, that is no heads. The possible outcome is TTT
So, B = {TTT}
Since S denote the sample space
S = {HTT, HHT, HHH, THH, TTH, HTH,THT, TTT}
So, A ∪ B = {HTT, HHT, HHH, THH, TTH, HTH,THT} ∪ {TTT} = {HTT, HHT, HHH, THH, TTH, HTH,THT, TTT} = S
So, S = A ∪ B
So, S = A ∪ B does not denote an abuse of notation.
The answer is b.
4x^2 + 4y^2 - 24x - 32y + 72 = 0 is a circle. What is the radius of the cirlce?
Answer:
√7
Step-by-step explanation:
(4x²-24x)+(4y²-32y)= -72
(4x²-24x+36)+(4y²-32y+64)= -72+36+64
4(x-3)²+4(y-4)²= 28
(x-3)²+(y-4)²=7
The radius of the circle 4x² + 4y²- 24x - 32y + 72 = 0 is √7.
CircleWe know that the general equation for a circle is ( x - h )² + ( y - k )² = r², where ( h, k ) is the center and r is the radius.
How to find the radius of the circle?The given equation is 4x² + 4y²- 24x - 32y + 72 = 0
Simplify the given equation in general equation for a circle.
(4x²-24x)+(4y²-32y)= -72
Add 100 on both side of equality
(4x²-24x)+(4y²-32y)+100= -72+100
(4x²-24x+36)+(4y²-32y+64)= 28
4(x-3)²+4(y-4)²= 28
(x-3)²+(y-4)²=7
(x-3)²+(y-4)²=(√7)²
Hence the radius of the circle is √7.
Learn more about radius here: https://brainly.com/question/24375372
#SPJ2
the distance between a number and 2 on the number line
Answer:
2
Step-by-step explanation:
f(1,2)=(3,5) , f(0,2)=(4,-6) tìm ma trận của f đối với cơ sở của R^2 lả B={u=(1,1), v=(3,1)}
Answer:
yeet
Step-by-step explanation:
What is the 13th term of 5,15,45,135
Answer:
2657205.
Step-by-step explanation:
This is a Geometric Sequence with common ratio 3.
13th term = 5*(3)^(13-1)
=5(3)^12
= 2657205.
Answer:
2657205.
Step-by-step explanation:
Consider the frequency distribution below, which has single values as classes: Value Frequency 10 11 12 13 14 15 16 17 18 19 20 21 1 3 7 18 10 4 2 7 16 10 6 2 Construct a new frequency distribution for this data with 4 classes.
The original table (attached to this response) shows single values as classes.
To construct a new frequency distribution for this data with 4 classes, follow these steps:
i. Starting from the least value (which is 10) create groups each of 4 values. For example, the first group will contain 10, 11, 12 and 13. Therefore, we have a class of 10 - 13.
The second group will contain 14, 15, 16 and 17. Therefore, we have a class of 14 - 17
The third group will contain 18, 19, 20 and 21. Therefore, we have a class of 18 - 21
ii. Get the frequency of these classes, we add the frequencies of the members of the class.
For example,
Class 10 - 13 will have a frequency of (1 + 3 + 7 + 18) = 29
Class 14 - 17 will have a frequency of (10 + 4 + 2 + 7) = 23
Class 18 - 21 will have a frequency of (16 + 10 + 6 + 2) = 34
The new table has been attached to this response.
Calculate the mean and the standard deviation of the age of individuals that purchased skateboarding shoes. Use 10 as the midpoint of the first class. (Do not round intermediate calculations. Round your answers to 2 decimal places.)
Answer:
Mean = 19.84
Standard deviation = 11.12
Step-by-step explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question. See the attached pdf file for the complete question.
The explanation of the answer is now given as follows:
Note: See the attached excel file for the calculation of the total of fx and total of f*x^2.
N = Number of individuals sampled = 200
From the attached excel file, we have:
Total of fx = 3,967
Total of f*x^2 = 103,425.50
Therefore, we have:
Mean = Total of fx / N = 3,967 / 200 = 19.84
Variance = (Total of f*x^2 / N) - Mean^2 = (103,425.50 / 200) - 19.84^2 = 517.13 - 393.43 = 123.70
Standard deviation = Variance^0.5 = 123.70^0.5 = 11.12
A circle is centered at the point (-3, 2) and passes through the point (1, 5) what is the radius of the circle
Answer:
5 units
Step-by-step explanation:
Center of the circle = (-3, 2)
Point on the circle = (1, 5)
Radius of the circle will be equal to the distance between the points (-3, 2) & (1, 5)
[tex] \therefore \: radius \: of \: the \: circle \\ = \sqrt{ {( - 3 - 1)}^{2} + {(2 - 5)}^{2} } \\ = \sqrt{ {( - 4)}^{2} + {( - 3)}^{2} } \\ = \sqrt{16 + 9} \\ = \sqrt{25} \\ \therefore \: radius \: of \: the \: circle = 5 \: units[/tex]
The area of a rectangular wall of a barn is 175 square ft.it’s length is 6feet longer than twice its width.find the length and width of the wall barn.
Answer:
[tex]L =21.945[/tex] --- Length
[tex]W = 7.9725[/tex] --- Width
Step-by-step explanation:
Given
Let
[tex]L \to Length[/tex]
[tex]W \to Width[/tex]
So:
[tex]Area = 175[/tex]
[tex]L = 6 + 2W[/tex]
Required
The dimension of the rectangle
The area is calculated as:
[tex]Area =L*W[/tex]
This gives:
[tex]175 =L*W[/tex]
Substitute: [tex]L = 6 + 2W[/tex]
[tex]175 =(6 + 2W)*W[/tex]
Open bracket
[tex]175 =6W + 2W^2[/tex]
Rewrite as:
[tex]2W^2+ 6W -175 = 0[/tex]
Using quadratic formula:
[tex]W = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]
This gives:
[tex]W = \frac{-6 \± \sqrt{6^2 - 4*2*-175}}{2*2}[/tex]
[tex]W = \frac{-6 \± \sqrt{1436}}{2*2}[/tex]
[tex]W = \frac{-6 \± 37.89}{4}[/tex]
Split
[tex]W = \frac{-6+ 37.89}{4}, W = \frac{-6- 37.89}{4}[/tex]
[tex]W = \frac{31.89}{4}, W = \frac{-43.89}{4}[/tex]
The width cannot be negative;
So:
[tex]W = \frac{31.89}{4}[/tex]
[tex]W = 7.9725[/tex]
Recall that:
[tex]L = 6 + 2W[/tex]
[tex]L =6 + 2 * 7.9725[/tex]
[tex]L =21.945[/tex]
. Hannah is selling slices of pie at the bake sale. The pie has 8 slices. She has sold 1/4 of the slices. What fraction with a denominator of 8 is equal to 1/4?
Answer:
2/8 because each 1/4 0f the 8 slices is equal to 2/8 by multipliction or you can say 1/4 of 8
Answer:
2/8
Step-by-step explanation:
1/4
times everything by 2 as 8 / 4 = 2
2/8
A customer buys a different book that has an original selling price of $38. The book is discounted 25%. The customer must pay a 6% sales tax on the discounted price of the book.
What is the total amount, in dollars, the customer pays for the discounted book? Explain and SHOW how you arrived at your answer.
Answer:
$30.21
Step-by-step explanation:
100% -25%= 75%
Discounted price of the book
= 75% ×$38
= $28.50
Since the customer must pay an additional 6% of the discounted price,
percentage of discounted price paid
= 100% +6%
= 106%
Total amount paid
= 106% × $28.50
= $30.21
_________________________________
Alternative working:
Original selling price= $38
Since the book is discounted 25%,
100% ----- $38
1% ----- $0.38
75% ----- 75 ×$0.38= $28.50
Since the sales tax is based on the discounted price, we let the discounted price be 100%.
100% ----- $28.50
1% ----- $0.285
106% ----- 106 ×$0.285= $30.21
∴ The total amount the customer pays for the discounted book is $30.21.
there is 300ml of oil in the small bottle there is six times as much in the big bottle how much oil is in the big bottle?
Answer:
1800 ml of oil
Step-by-step explanation:
300*6
Ethan and his friends went to a movie on Thursday afternoon. They left at 1:00 P.M. It took 1 hour and 5 minutes to drive to the theater. They arrived at the theater 1 hour and 10 minutes before the movie started. Once it started, the movie lasted for 1 hour and minutes. What time was it when the movie ended?
Spanish: Ethan y sus amigos fueron al cine el jueves por la tarde. Salieron a la 1:00 p.m. Tardaron 1 hora y 5 minutos en llegar al teatro. Llegaron al cine 1 hora y 10 minutos antes de que comenzara la película. Una vez que comenzó, la película duró 1 hora y minutos. ¿A qué hora terminó la película?
Answer:
4:15 p.m.
Step-by-step explanation:
There's something missing in this:
Once it started, the movie lasted for 1 hour and minutes. What time was it when the movie ended?
What is the minutes because thats missing.
Also can I get Brainliest please
the sum of a number squared and 12 is identical to four added to the same number
Answer: x^2+12=x+4
Step-by-step explanation:
What is a formula for the nth term of the given sequence?
36, 24, 16...
Answer:
The formula to find the nth term of the given sequence is 54 · [tex]\frac{2}{3} ^{n}[/tex]
Step-by-step explanation:
The formula for nth term of an geometric progression is :
[tex]a_{n} = \frac{a_{1}(r^{n})}{r}[/tex]
In this example, we have [tex]a_{1}[/tex] = 36 (the first term in the sequence) and
r = [tex]\frac{2}{3}[/tex] (the rate in which the sequence is changing).
Knowing what the values for r and [tex]a_{1}[/tex] are, now we can solve.
[tex]a_{n} = \frac{a_{1}(r^{n})}{r}[/tex] = [tex]\frac{36 (\frac{2}{3} ^{n}) }{\frac{2}{3} }[/tex] = 54 · [tex]\frac{2}{3} ^{n}[/tex]
Therefore, the formula to find the nth term of the given sequence is
54 · [tex]\frac{2}{3} ^{n}[/tex]
Given the functions:
g(n) = 3n - 5
f(n) = n2 + 50
Find:
(g+f)(8)
Answer:
[tex](g + f)(8) =133[/tex]
Step-by-step explanation:
Given
[tex]g(n) = 3n - 5[/tex]
[tex]f(n) = n^2 + 50[/tex]
Required
[tex](g + f)(8)[/tex]
This is calculated as:
[tex](g + f)(n) =g(n) + f(n)[/tex]
So, we have:
[tex](g + f)(n) =3n - 5 + n^2 +50[/tex]
[tex]Substitute[/tex] 8 for n
[tex](g + f)(8) =3*8 - 5 + 8^2 +50[/tex]
[tex](g + f)(8) =24 - 5 + 64 +50[/tex]
[tex](g + f)(8) =133[/tex]
If the coordinates of a point p(m-3 , -6) = p(-7 , -6), then find the value of m .
Answer:
[tex]m =-4[/tex]
Step-by-step explanation:
Given
[tex]p(m-3 , -6) = p(-7 , -6)[/tex]
Required
Find m
[tex]p(m-3 , -6) = p(-7 , -6)[/tex]
By comparison:
[tex]m-3 = -7[/tex]
Add 3 to both sides
[tex]m = -7+3[/tex]
[tex]m =-4[/tex]
You are building a door frame. Both sides are 80.5 in long, and the top and bottom are both 36.5 in wide. Which additional statement does not give enough information to conclude that the door frame forms a rectangle
a) the door frame has a right angle
b) the diagonals of the door frame are congruent
c) The door frame has a pair of congruent, opposite angles
d) the door frame has a pair of congruent adjacent angles
I think the answer is number three but Im not sure why pls help ASAP.
Answer:
The answer is A.
Step-by-step explanation:
Rectangles is a quadrilateral shape that has four sides, two pairs of parallel lines, and all the corners MUST be right angles for it to be a rectangle. :)
I hope this helps :DD
Besties I'm..WELL I'M ME AND I NEED HELP
Answer:
h = 30°
Step-by-step explanation:
All angles in a triangle add up to 180°, so:
60° + 90° + h° = 180°
Solving for h, we should get 30 as our answer.
Help plsss !!!!!!Trying to get my grade up
Work Shown:
area of the triangle on the left = base*height/2 = 0.75*2/2 = 0.75
area of the triangle on the right = base*height/2 = 0.5*4/2 = 1
total area = 0.75+1 = 1.75 square feet