Answer:
Step-by-step explanation:
complex roots always occur in pairs.
roots are 1,2-2i,2+2i
P(x)=a(x-a)(x-b)(x-c)
P(x)=1(x-1)[x-(2-2i)][x-(2+2i)]
=1(x-1)[(x-2)+2i][(x-2)-2i]
=(x-1)[(x-2)²-(2i)²]
=(x-1)[(x-2)²-4i²]
=(x-1)[x²-4x+4-4(-1)]
=(x-1)[x²-4x+4+4]
=(x-1)[x²-4x+8]
=x³-4x²+8x-x²+4x-8
=x³-5x²+12x-8
find the original price given the total amount and the tip rate if the total amount is $51.84 and the tip is 20%
Answer: $41.472 or $41.50
Step by step solving: First convert 20% to a decimal which is .20 now multiply that by $51.84 which equals 10.368 now subtract that number from 51.84 which equals 41.472
If you are allowed to round to the nearest hundreth then that would be $41.50 before the tip.
Please help!!!! I'll give you 15 points!!
Step-by-step explanation:
the answer is C
2/5(2x+3)
I hope it helps
Astronomers treat the number of stars X in a given volume of space as Poisson random variable. The density of stars in the Milky Way Galaxy in the vicinity of our solar system is one star per 16 cubic light-years, on average. NOTE: Light-years is a distance measure. 7. What is the probability of exactly two stars in 16 cubic light-years? 8. What is the probability of three or more stars in 16 cubic light-years? 9. How many stars would be expected in 4 cubic light years? 10. How many stars would be expected in t cubic light years? 11. How many cubic light-years of space must be studied so that the probability of one or more stars exceeds 0.95? HINT: let `t' represent the unknown region of space, then nd the `t' that gives you the relevant probability.
Answer:
Explained below.
Step-by-step explanation:
The random variable X is defined as the number of stars in a given volume of space.
[tex]X\sim \text{Poisson}\ (\lambda=1)[/tex]
The probability mass function of X is:
[tex]p_{X}(x)=\frac{e^{-\lambda}\lambda^{x}}{x!}[/tex]
(7)
Compute the probability of exactly two stars in 16 cubic light-years as follows:
[tex]P(X=2)=\frac{e^{-1}\times 1^{2}}{2!}=\frac{e^{-1}}{2}=\frac{0.36788}{2}=0.18394\approx 0.184[/tex]
(8)
Compute the probability of three or more stars in 16 cubic light-years as follows:
[tex]P(X\geq 3)=1-P(X<3)\\\\=1-P(X=0)-P(X=1)-P(X=2)\\\\=1-\sum\limits^{2}_{x=0}[\frac{e^{-1}\times 1^{x}}{x!}]\\\\=1-0.36788-0.36788-0.18394\\\\=0.0803[/tex]
(9)
In 16 cubic light years there is only 1 star.
Then in 1 cubic light years there will be, (1/16) stars.
Then in 4 cubic light years there will be, 4 × (1/16) = (1/4) stars.
(10)
In 16 cubic light years there is only 1 star.
Then in 1 cubic light years there will be, (1/16) stars.
Then in t cubic light years there will be, [t × (1/16)] stars.
Finding Decimal Products Which statements are true for the product of 0.2 and 0.2? Check all that apply. The product will be smaller than both the factors. ✓ There will be a zero in the tenths place, There will be a zero in the hundredths place. The answer is 0.4. ✓ The answer is 0.04.
Answer:
0 The product will be smaller than both the factors.
0 There will be a zero in the tenths place.
0 The answer is 0.04.
Use the zero product property to find the solutions to the equation x2 + x – 30 = 12.
Answer:
x= 6, -7
Step-by-step explanation:
What is five times the difference of a number and three?
Btw I need answer immediately
Answer:
t=x+3
y = (x+3)^2 + 5
y = x^2+6x + 9 + 5
y= x^2 + 6x + 14
Answer:
5 times x-3?
Step-by-step explanation:
Sorry if its wrong i didn't really understand what you wanted.
The graph of y = -3x + 4 is:
Answer:
(0,4)
Step-by-step explanation:
Mary has 96 muffins which she needs to box up, 5 of which are blueberry, into dozens. How many boxes dose he need
Answer:
8
Step-by-step explanation:
Mary needs 8 boxes to put 96 muffins in dozens so 96÷12 gives you 8
i need help on this stuck on it
Answer:
5=148 and 8=32
Step-by-step explanation:
For this equation we know since the lines are parelle that they will produce the same angle degrees.
so 2,4,6,and 8 are all 32
if we subtract 180 (the dregree of a stright line) from 32 we get 148
so 148 is for 1,3,5, and 7
Suppose tan(b) = –2, and the terminal side of b is located in quadrant II. What is cot(b)?
Answer:
- 1/2
Step-by-step explanation:
Just took the test
The value of cot (b) using trigonometry is -1/2 when tan b = -2.
Since we are given that tan(b) = -2 and the terminal side of angle b is in quadrant II, determine the value of cot(b).
In quadrant II, the sine and cosine values are positive, while the tangent and cotangent values are negative.
Given:
tan(b) = -2
The cotangent (cot) of an angle is the reciprocal of the tangent:
cot(b) = 1 / tan(b)
Now, substituting the given value of tan(b):
cot(b) = 1 / (-2)
cot(b) = -1/2
So, the value of cot(b) is -1/2.
Learn more about Trigonometry here:
https://brainly.com/question/11016599
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h(x)=x^2-4x-12 in factored form?
k(x)=x^2-4x+8 in factored form?
Answer:
h(x) = (x-6)(x+2)
k(x) is not further factorable
Step-by-step explanation:
h(x) = x²-4x-12
= (x-6)(x+2)
k(x) = x²-4x+8
not further factorable
3. f(x) = x2 + 4x - 2
Answer:
f(x)= -(x-2)^2+2
Step-by-step explanation:
the same valuve needs the be added to both sides
f(x)+?= -x^2+4x+?-2
to complete the square -x^2+4x-4= -(x-2)^2 add the -4 to the expression
f(x)+?= -x^2+4x-4-2
since -4 was added to the right side, also add -4 the the left side
f(x)-4= -x^2+4x+?-2
now factor out the negative sign from the expression
f(x)-4= -(x^2-4x+4)-2
using a^2-ab+b^2=(a-b)^2
f(x)-4= -(x-2)^2-2
move the constant the the right side and change its sign
f(x)= -(x-2)^2-2+4
now calculate the sum
f(x)= -(x-2)^2+2
how many decimal places would the answer have when you find the product of 43.09281×5.092?
Answer:
219.42858852
Step-by-step explanation:
At sunrise on monday the temperature in new haven, ct is -5f. By noon the temperature is 14 degrees warker and by sunset the temperature is 9 degrees colder than it was noon
Answer:
0 degrees faranhiet
Step-by-step explanation:
when you add 14 and -5 you get 9 then the question says 9 degrees cooler so that would translate to the problem 9 - 9 which you get zero.
Question 9 of 10 What is the scale factor of ABC to DEF?
An AutoCAD drawing has a scale of inches to 3 ft. If a piece of a bridge measures 17 feet, how long is that piece in the AutoCAD printout?
Answer:
D
Step-by-step explanation:
Answer:
2.83 inches
Step-by-step explanation:
Let y equal the length of the drawing in inches. Use a proportion to solve for the missing length.
what is -1 as a decimal
Answer:
-1.0
Step-by-step explanation:
I need these graphed, they’re easy but I don’t have time to do them since it’s late. Excuse the bad handwriting
Answer:
For #5 all you have to do is set down to points in order for it to count. The answer is: (0,2) and (3,6)
Step-by-step explanation:
In order to find where exactly you must plot the points, we plug in what we know. In our equation, the 2 is our y intercept, this means that the point is (0,2) (Side Note: here's another example, (0,6) the 6 would be our y intercept)
From the point (0,2) we use the other value given. The other value given in this case, is our slope. When dealing with slope, we use Rise over Run or Rise/Run. This means that from the 2 on the graph, you rise 3 which would be 5 and you run to the right for 4. This now gets you the points (3,6)
Hope this helps with plotting the other questions! :)
(SIDE NOTE: IF THEY GIVE THE VALUE WITH X AS JUST A NUMBER, YOU CAN PLACE A 1 UNDER IT TO TURN IT INTO A FRACTION. FOR EXAMPLE 3X CAN BE TURNED INTO 3/1 WHICH WOULD THEN BE RISE 3 AND RUN 1.
(sooory about the caps, it's just to get your attention.)
The total sales tax in a certain city is 8.75%. The state sales tax rate is 7.25%, and the county adds an additional sales tax of 0.5%. How much in sales tax is added by the city?
a.) 0.1%
b.) 0.25%
c.) 1%
d.) 2.5%
Answer:
C.1%
Step-by-step explanation:
HELP ASAP!!!! simplify 3^2-4/5
Answer:
9-4/5
5/5 = 1
Step-by-step explanation:
Answer:
1
9-4/5 is equal to 5/5 which is equal to 1
I need help with 35-38 please!!!
Answer:
-3
Step-by-step explanation:
Odd number between 3 and 19
Answer:
11, there both 8 away so its right in ze middle :D
Step-by-step explanation:
Reese wants to organize a party and decides to save money for it.He calculates that he needs $420 in 9 weeks.He already has $60
Solve.
2x + 4 3
B) x < 3
B) x 1/3
D) x < 1/3
Answer:
c
Step-by-step explanation:
Please help being timed for test !
Last week's and this week's low temperatures are shown in the table below.
Low Temperatures for 5 Days This Week and Last Week
Low Temperatures
This Week (F)
4 10 6 9
Low Temperatures
Last Week (OF)
13 9 5 8
6
5
Which measures of center or variability are greater than 5 degrees? Select three choices
the mean of this week's temperatures
the mean of last week's temperatures
the range of this week's temperatures
the mean absolute deviation of this week's temperatures
the mean absolute deviation of last week's temperatures
Answer:
I think it B or C but hope I can help :)
Step-by-step explanation:
7.5 more than the quotient of h and 3 is w
Answer: h/3 + 7.5 = w
8
Write the equation of the line through the
points (-8, -2) and (-4,-3) in POINT-SLOPE
FORM
Answer:
Y=-1/4x-4
Step-by-step explanation:
To find the slope, you would need to use the equation y2-y1/x2-x1 by the coordinates. You would get -3-(-2)/-4-(-8). This would result in -1/4. Now that you have your slope, you plug in one of the coordinates. If you used (-8,-2), you would get -2=-8(-1/4)+b. Simplify the equation to get -2=2+b, which simplifies to -4=b, and b is the y intercept.
Is Triangle B a rotation of Triangle A?
Explain How u know
Answer:
No, triangle B is a reflection of triangle A.
Step-by-step explanation:
The points of triangle A are reflected across the dotted line. So as a result triangle B is a reflection of triangle A.
Answer:
No
Step-by-step explanation:
Its a reflection because even if you did rotate it it would never be in that orientation.
What is the slope of the line through the points (-4, 2) and (-16, -6)
Answer:
[tex]m = \frac{2}{3}[/tex]
Step-by-step explanation:
Use the following equation:
slope [tex](m) = \frac{y^2 - y^1}{x^2 - x^1}[/tex]
Set the variables with the points:
[tex](x_1 , y_1) = (-16 , -6)\\(x_2 , y_2) = (-4 , 2)\\[/tex]
Plug in the corresponding numbers to the corresponding variables in the equation:
[tex]m = \frac{2 - (-6)}{-4 - (-16)}[/tex]
[tex]m = \frac{2 - (-6)}{- 4 - (-16)} = \frac{2 + 6}{16 - 4} = \frac{8}{12}[/tex]
slope [tex]m = \frac{8}{12}[/tex] [tex]= \frac{2}{3}[/tex] (simplified)
~
Answer:
2/3
Step-by-step explanation:
2. Find the distance between (-2,1) and (3,4).