[tex]\begin{cases} x = -4\implies &x+4=0\\ x=-2\implies &x+2=0\\ x=1\implies &x-1=0 \end{cases}\qquad \implies (x+4)(x+2)(x-1)=\stackrel{y}{0}[/tex]
now, that's the equation or polynomial in factored form, hmmm we also know that it has a y-intercept of -11, namely, when x = 0 y = -11, well let's plug in a factor to it, that will reflect those values, namely say hmmm factor "a", so
[tex](x+4)(x+2)(x-1)=y\qquad \stackrel{\textit{adding "a" factor for vertical shift}}{a(x+4)(x+2)(x-1)}=y \\\\\\ \stackrel{\textit{we know that when x = 0, y = -11}}{a(0+4)(0+2)(0-1)=-11}\implies -8a=-11\implies a=\cfrac{-11}{-8}\implies a = \cfrac{11}{8} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\mathbb{FOIL}}{\cfrac{11}{8}(x^2+6x+8)}(x-1)=y\implies \cfrac{11}{8}(x^3+6x^2+8x-x^2-6x-8)=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cfrac{11}{8}(x^3+5x^2+2x-8)=y~\hfill[/tex]
Carry out the following integrals, counterclockwise, around the indicated contour
For the first integral, z = π/4 is a pole of order 3 and lies inside the contour |z| = 1. Compute the residue:
[tex]\displaystyle \mathrm{Res}\left(\frac{e^z\cos(z)}{\left(z-\frac\pi4\right)^3}, z=\frac\pi4\right) = \lim_{z\to\frac\pi4}\frac1{(3-1)!} \frac{d^{3-1}}{dz^{3-1}}\left[e^z\cos(z)\right][/tex]
We have
[tex]\dfrac{d^2}{dz^2}[e^z\cos(z)] = -2e^z \sin(z)[/tex]
and so
[tex]\displaystyle \mathrm{Res}\left(\frac{e^z\cos(z)}{\left(z-\frac\pi4\right)^3}, z=\frac\pi4\right) = - \lim_{z\to\frac\pi4} e^z \sin(z) = -\frac{e^{\pi/4}}{\sqrt2}[/tex]
Then by the residue theorem,
[tex]\displaystyle \int_C \frac{e^z\cos(z)}{\left(z-\frac\pi4\right)^3} \, dz = 2\pi j \left(-\frac{e^{\pi/4}}{\sqrt2}\right) = \boxed{-\sqrt2\,\pi e^{\pi/4} j}[/tex]
For the second integral, z = 2j and z = j/2 are both poles of order 2. The second poles lies inside the rectangle, so just compute the residue there as usual:
[tex]\displaystyle \mathrm{Res}\left(\frac{\cosh(2z)}{(z-2j)^2\left(z-\frac j2\right)^2}, z=\frac j2\right) = \lim_{z\to\frac j2}\frac1{(2-1)!} \frac{d^{2-1}}{dz^{2-1}}\left[\frac{\cosh(2z)}{(z-2j)^2}\right] = \frac{16\cos(1)-24\sin(1)}{27}j[/tex]
The other pole lies on the rectangle itself, and I'm not so sure how to handle it... You may be able to deform the contour and consider a principal value integral around the pole at z = 2j. The details elude me at the moment, however.
[tex]{ \color{darkred}{(2+√3)+(4-√3)}} = ?[/tex]
︎︎︎︎︎︎︎︎︎︎︎︎︎︎︎︎︎︎
[tex](2 + \sqrt{3} ) + (4 - \sqrt{3} ) \\ = 2 + \sqrt{3} + 4 - \sqrt{3} \\ = 2 + 4 \\ = 6[/tex]
Answer:
6
Hope you could get an idea from here.
Doubt clarification - use comment section.
[tex]\huge \bf༆ Answer ༄[/tex]
Here's the solution ~
[tex] \sf(2 + \sqrt{3} ) + (4 - \sqrt{3}) [/tex][tex] \sf2 + \cancel {\sqrt{3} } + 4 - \cancel{\sqrt{3} }[/tex][tex] \sf6[/tex]Use the counting techniques from the last chapter. A bag contains three red marbles, three green ones, one fluorescent pink one, two yellow ones, and four orange ones. Suzan grabs four at random. Find the probability of the indicated event.
She gets at least two red ones, given that she gets at least one green one.
Using the combination formula and the probability concept, it is found that there is a 0.1259 = 12.59% probability that she gets at least two red ones, given that she gets at least one green one.
A probability is the number of desired outcomes divided by the number of total outcomes.In this problem, the order in which the marbles are taken is not important, hence, the combination formula is used to solve this question.Combination formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Desired outcomes:
2 red from a set of 3.1 green from set of 3.1 from a set of 1 + 2 + 1 + 2 + 4 = 10.Hence:
[tex]D = C_{3,2}C_{3,1}{C_{10,1}} = \frac{3!}{2!1!} \times \frac{3!}{1!2!} \times \frac{10!}{1!9!} = 90[/tex]
Total outcomes:
Four marbles are taken from a set of 13, hence:
[tex]T = C_{13,4} = \frac{13!}{4!9!} = 715[/tex]
Then, the probability is:
[tex]p = \frac{D}{T} = \frac{90}{715} = 0.1259[/tex]
0.1259 = 12.59% probability that she gets at least two red ones, given that she gets at least one green one.
To learn more about the use of the combination formula and the probability concept, you can check combination formula and the probability concept,
3(y+8)=2y-6 what is y=
Answer:
y = -30
Step-by-step explanation:
3 (y + 8) = 2y - 6
3y + 24 = 2y -6 Distribute the 3
y + 24 = -6 Subtract 2y on both sides
y = -30 Subtract 24 on both sides
Help help help help math math
Answer:
x = 35
Step-by-step explanation:
First, set both equations equal to each other because it is the same angle (congruent)
6x - 20 = 4x + 50
-4x and +20 to both sides of the equation and you end up with:
2x = 70
divide both sides by 2 and:
x = 35
help me please i'll mark as brainliest asap
Answer:
a. A(x) = 3x² - 8x + 5
b. x = ⁸/₃
Step-by-step explanation:
a.
A(x) = shaded area
A(x) = (2x - 3)² - (x - 2)²
= 4x² - 12x + 9 - (x² - 4x + 4)
= 4x² - x² - 12x + 4x + 9 - 4
= 3x² - 8x + 5
b.
ΔABF area = ⁵/₄ cm²
A(x) = 4(⁵/₄)
= 5
Substitution:
3x² - 8x + 5 = A(x) = 5
3x² - 8x + 5 = 5
3x² - 8x = 0
x(3x - 8) = 0
3x - 8 = 0
x = ⁸/₃
x = 0
Since x > 2, x = 0 is not valid;
So, x = ⁸/₃
Can i get some help with this inductive reasoning test, the answer and the explanation please. Thank you.
Answer:
8, 2.
Step-by-step explanation:
2*4 is 8 so I think line them up together and 12/6 is 2
Please hurry and answer!
This graph gives growth of a plant overtime what is the slope of the line, and what does the slope mean in situation
select from the drop down menus to correctly complete the statement
The slope is blank which means that the plant blank by blank everyday
Using the slope of the linear function, it is found that:
The slope is of 0.5, which means that the plant grows by 0.5 inches each day.A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is by how much the output y changes when the input x changes by 1.b is the y-intercept, which is the value of y when x = 0.In this problem:
x is the time in days.y is the height in inches.Two of the points are: (0,0) and (2,1).
The slope is given by change in y divided by change in x, hence:[tex]m = \frac{1 - 0}{2 - 0} = \frac{1}{2} = 0.5[/tex]
Then, applying the interpretation:
The slope is of 0.5, which means that the plant grows by 0.5 inches each day.To learn more about slopes and linear functions, you can take a look at https://brainly.com/question/16302622
Answer:
hes correct. the slope is 0.5 and it grows 0.5 inches everyday
Step-by-step explanation:
c. A square that is 8 inches on a side is placed inside a rectangle that has a length of 24 inches and a width of 20 inches. What is the area of the region inside the rectangle that surrounds the square?
Area = length x width
Area of square = 8 x 8 = 64 square inches
Area of rectangle = 24 x 20 = 480 square inches
Area of rectangle surrounding the square = 480 - 64 = 416 square inches
Answer: 416 square inches
solve the compound inequality 2(x-2)+7>-1 and 5-4x>9
Answer:
1) x > -2
2) x < -1
Step-by-step explanation:
1) 2(x - 2) + 7 > -1
2x - 4 + 7 > -1
2x + 3 > -1
2x > -4
x > -2
2) 5 - 4x > 9
-4x > 4
x < -1
Help help help help math math math math help
Answer:
14
Step-by-step explanation:
because both sides need to be equal so if u plug in the 14 in x it gives you the same number for both sides 107.
Find the median of the following data set. 0.48, 0.66, 1.02, 0.82, 0.7, 0.94 0.44 1.02 0.76
The Hickory Stick has a selection of 3 meats and 6 vegetables. How many different selections of one meat and one vegetable are possible
The different selections of one meat and one vegetable are possible are 18 selections.
Since the Hickory Stick has a selection of 3 meats and 6 vegetables, the number of ways we can select one meat out of 3 is ³C₁ = 3.
Also, the number of ways we can select one vegetable out of 6 is ⁶C₁ = 6.
So, the total number of selections of one meat and one vegetable is ³C₁ × ⁶C₁ = 3 × 6
= 18 selections
So, the different selections of one meat and one vegetable are possible are 18 selections.
Learn more about combination here:
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Elevator 1 in a building moved from ground position to a final position of +13 feet. Elevator 2 in the same building moved from ground to a final position of −10 feet. Which statement best describes the final positions of these two elevators? (5 points)
Question 4 options:
1)
Elevator 1 is 13 feet above ground level, and Elevator 2 is 10 feet below the position of Elevator 1.
2)
Elevator 1 is 13 feet below ground level, and Elevator 2 is 10 feet above the position of Elevator 1.
3)
Elevator 1 is 13 feet below ground level, and Elevator 2 is 10 feet above ground level.
4)
Elevator 1 is 13 feet above ground level, and Elevator 2 is 10 feet below ground level.
Answer:
Elevator 1 is 12 feet above ground level, and Elevator 2 is 15 feet below the position of Elevator 1. We are given that Elevator 1 is "+12 feet" and Elevator 2 is "-15 feet" meaning 15 feet below that of Elevator 1 (because they said it was where it was at Elevator 1 ground level prior), so this should be your answer "A".
Step-by-step explanation:
1 a
Trey wants to earn more than $89 trimming trees. He charges $8 per hour and pays S7 in equipment fees. What are the possible numbers of hours Trey could
trim trees?
Use t for the number of hours.
Write your answer as an inequality solved for t.
Answer:
11 hours
Step-by-step explanation:
8t + 7 > 89
8t > 81 : subtract 7 from both sides
t > 10.125 : divide by 8 for both sides
t = 11 : estimate
Trey has to work 11 hours because 10 hours would only give him $87.
movie theater charges $9 for adults and $7 for senior citizens. On a day when 325 people paid an admission, the total receipts were $2504. How many were seniors and how many were adults?
I will set it up.
Let a = adults
Let s = seniors
The first equation is a + s = 325.
The second equation is 9a + 7s = 2504.
Here is your system of equations:
{a + s = 325
{9a + 7s = 2504
Take it from here.
help me plssssss
ssssssssss
Answer:
The answer is going to be A
Step-by-step explanation:
Factor: 3x4y3 – 48y3
Answer: 4y3(1x1 - 12)
3x4y3 – 48y3
4y3(1x1 - 12)
What is the length of XY?
Answer:
XY = 11.25
Step-by-step explanation:
Corresponding sides of similar triangles are proportional.
XY/5 = 18/8
XY = 5(9/4) = 45/4
XY = 11.25
In a cookie jar,
1
5
of the cookies are chocolate chip and
1
2
of the rest are peanut butter. What fraction of all the cookies is peanut butter?
Which tape diagram shows the cookies that are chocolate chip?
All cookies
Chocolate
chip
All cookies
Chocolate
chip
All cookies
Chocolate
chip
Excellent!
Which tape diagram shows the cookies that are peanut butter?
All cookies
Chocolate
chip
Peanut
butter
All cookies
Chocolate
chip
Peanut
butter
All cookies
Chocolate
chip
Peanut
butter
Good work!
Use the tape diagram to solve.
well, a WHOLE is 1, which we can split in many fractions, say 5/5, 10/10 or 999/999 and so on.
we know 1/5 of the jar is chocolate chip, and there's the rest, well, the Whole jar in 5ths have to be 5/5, if we take away 1/5 from 5/5, the "rest" is 5/5 - 1/5 = 4/5.
now, we also know that 1/2 of the "rest" is peanut butter, or namely that 1/2 of 4/5 is peanut butter, how much will that be? let's divide 4/5 by 2
[tex]\cfrac{4}{5}\div 2\implies \cfrac{4}{5}\div \cfrac{2}{1}\implies \cfrac{4}{5}\cdot \cfrac{1}{2}\implies \cfrac{4}{10}\implies \cfrac{2}{5}[/tex]
Find m< FED Im
giving this question 20 points
Answer:
180° - (61° + 61°) = 58°
Step-by-step explanation:
we can see that two sides of the angle are equilateral making it equiangular therefore the other angle is 61° and solve for <FED
3. Find the total tax using the expanded expression. Did you get the same answer as
you did by evaluating the original expression? (3 points)
Answer:
To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number. To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations
Answer:
To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number. To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations
Step-by-step explanation: Hope it Helpss :D
Read in equality quality for the graph shown below use ask for your beard
Answer:
x<-3
Step-by-step explanation:
Part A: James bought a cake that weighs pounds. How many ounces does the cake weigh? Show your work. (5 points)
[16 ounces = 1 pound]
Part B: A running tap dispenses 0.15 gallons of water every second. How many pints of water is dispensed after 20 seconds? Show your work. (5 points)
[1 gallon = 4 quarts, 1 quart = 2 pints]
Question 4 options:
Answer:
For part a multiply the pound amount by 16. Your work would look something like this... (not actual answer) 10 pounds x 16= 160 ounces. So 10 pounds= 160 ounces!
For part B
0.15 gallons=1.2 pints
Example: .15 x 4= .6
.6 x 2= 1.2 pints
1.2 x 20 seconds= 24 pints!
Hope this helps
Step-by-step explanation:
:)
Answer:
Part A: 52 oz
Part B: 24 pints
Step-by-step explanation:
Part A:
Since 1 pound = 16 ounces, the number of ounces is 16 times the number of pounds. To convert pounds to ounces, multiply the pounds by 16.
3 1/4 lb × 16 oz/lb =
= 13/4 × 16 oz
= 13 × 4 oz
= 52 oz
Answer: 52 oz
Part B:
We need to convert from gallons to pints.
1 gallon = 4 quarts
1 quart = 2 pints
That means that 1 gallon = 8 pints.
0.15 gallon/second × 8 pints/gallon =
= 1.2 pints/second
The tap dispenses 1.2 pints/second.
Now we calculate the number of pints dispensed in 20 seconds.
1.2 pints/second × 20 seconds = 24 pints
Answer: 24 pints
Stacy is selling tickets to the school play. The tickets are $7 for adults and $4 for children she sells twice as many adult tickets as children’s tickets and brings in a total of $270. How many of each kind of ticket did she sell?
Stacy sold 15 children tickets and 30 adult tickets.
The tickets are $7 for adults and $4 for children.
She sells twice as many adult tickets as children tickets and bring in a total of $270.
Therefore,
let
number of children ticket sold = x
number of adult ticket sold = 2x
7(2x) + 4(x) = 270
14x + 4x = 270
18x = 270
x = 270 / 18
x = 15
The number of children ticket sold = 15
The number of adult ticket sold = 15 × 2 = 30
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Which of the following is most likely the next step in the series?
A?
B?
C?
D?
Answer:
c
Step-by-step explanation:
each shape has one more side than the other
the last shape in the pattern so far has 5
the shape at letter c has 6
therefore it is c
I need help with this answer PLEASE I’m stuck
Answer:
40% of airline A's flights were on time
Step-by-step explanation:
0.4=40% .the top row indicates that it was airline A. the left column indicates that it was on time.
Answer:
B
Step-by-step explanation:
happy holidays
find the difderence of 3/4 and 1/28
Answer:
5/7
Step-by-step explanation:
3/4-1/28
21/28-1/28
20/28
simplify
5/7
The figure shown is to be painted on a road sign. Which of the following best describes the two polygons that form the figure?
A. A rectangle and an isosceles trapezoid
B. A rectangle and a rhombus
C. A rectangle and a parallelogram
D. A rectangle and an isosceles triangle
Answer:
D: A rectangle and an isosceles triangle
Step-by-step explanation:
A recangle for the base of the arrow, and an isosceles triangle to form the full arrow.
The answer will be option D which is a rectangle and an isosceles triangle.
What is an isosceles triangle?The triangle in which the two opposite sides are equal and the two opposite angles are equal is called the isosceles triangle.
As we can see in the figure there are one isosceles triangle and a rectangle are joined together to form an arrow.
Thus the answer will be option D which is a rectangle and an isosceles triangle.
To know more about the isosceles triangle follow
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Ann received a $90 gift card for a coffee store. She used it in buying some coffee that cost $8.04 per pound. After buying the coffee, she had $65.88 left on her
card. How many pounds of coffee did she buy?
pounds
5
?
Answer:
3 lbs of coffee
Step-by-step explanation:
$90.00 - $65.88 =$24.12 (spent 24.12 on the coffee)
24.12/8.04 = 3
Answer:
3 ponds of Coffee. take what she spent, and subtract it from the total. Then divide that number by the cost of 1 lb. of coffe. You get 3. 3 pounds.