Answer:
[tex]x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}[/tex]
Step-by-step explanation:
1) Move all terms to one side.
[tex]2x^{3} -x^{2} -3x-210=0[/tex]
2) Factor [tex]2{x}^{3}-{x}^{2}-3x-210[/tex] using Polynomial Division.
1 - Factor the following.
[tex]2x^{3} -x^{2} -3x-210[/tex]
2 - First, find all factors of the constant term 210.
[tex]1,2,3,4,5,6,7,10,14,15,21,30,35,42,70,105,210[/tex]
3) Try each factor above using the Remainder Theorem.
Substitute 1 into x. Since the result is not 0, x-1 is not a factor..
[tex]2*1^{3} -1^{2} -3*1-210=-212[/tex]
Substitute -1 into x. Since the result is not 0, x+1 is not a factor..
[tex]2(-1)^{3} -(-1)^{2} -3*-1-210=-210[/tex]
Substitute 2 into x. Since the result is not 0, x-2 is not a factor..
[tex]2*2^{3} -2^{2} -3*2-210=-204[/tex]
Substitute -2 into x. Since the result is not 0, x+2 is not a factor..
[tex]2{(-2)}^{3}-{(-2)}^{2}-3\times -2-210 = -224[/tex]
Substitute 3 into x. Since the result is not 0, x-3 is not a factor..
[tex]2\times {3}^{3}-{3}^{2}-3\times 3-210 = -174[/tex]
Substitute -3 into x. Since the result is not 0, x+3 is not a factor..
[tex]2{(-3)}^{3}-{(-3)}^{2}-3\times -3-210 = -264[/tex]
Substitute 5 into x. Since the result is 0, x-5 is a factor..
[tex]2\times {5}^{3}-{5}^{2}-3\times 5-210 =0[/tex]
------------------------------------------------------------------------------------------
⇒ [tex]x-5[/tex]
4) Polynomial Division: Divide [tex]2{x}^{3}-{x}^{2}-3x-210[/tex] by [tex]x-5[/tex].
[tex]2x^{2}[/tex] [tex]9x[/tex] [tex]42[/tex]
-------------------------------------------------------------------------
[tex]x-5[/tex] | [tex]2x^{3}[/tex] [tex]-x^{2}[/tex] [tex]-3x[/tex] [tex]-210[/tex]
[tex]2x^{3}[/tex] [tex]-10x^{2}[/tex]
-----------------------------------------------------------------------
[tex]9x^{2}[/tex] [tex]-3x[/tex] [tex]-210[/tex]
--------------------------------------------------------------------------
[tex]42x[/tex] [tex]-210[/tex]
[tex]42x[/tex] [tex]-210[/tex]
-------------------------------------------------------------------------
5) Rewrite the expression using the above.
[tex]2x^2+9x+42[/tex]
[tex](2x^2+9x+42)(x-5)=0[/tex]
3) Solve for [tex]x.[/tex]
[tex]x=5[/tex]
4) Use the Quadratic Formula.
1 - In general, given [tex]a{x}^{2}+bx+c=0[/tex] , there exists two solutions where:
[tex]x=\frac{-b+\sqrt{b^{2} -4ac} }{2a} ,\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]
2 - In this case, [tex]a=2,b=9[/tex] and [tex]c = 42.[/tex]
[tex]x=\frac{-9+\sqrt{9^2*-4*2*42} }{2*2} ,\frac{-9-\sqrt{9^2-4*2*42} }{2*2}[/tex]
3 - Simplify.
[tex]x=\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}[/tex]
5) Collect all solutions from the previous steps.
[tex]x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}[/tex]
What is the slope of the graph?
Answer:
-x
The slope-intercept equation is y = -x + 1
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
The slope is 1 because it goes 2 units down and then 2 units right. So 2 divided by 2 = 1 as slope.
please solve quickly
If a student is selected randomly, the probability that the student is a junior given that the student is male is 14%.
What is the probability?Probability determines the odds that an event would happen. The odds of the event happening lie between 0 and 1.
p (Junior | Males) = number of males that are junior / total number of males
2 / (4 + 6 + 2 + 2 ) = 2/14 x 100 = 14%
To learn more about probability, please check: https://brainly.com/question/13234031
#SPJ1
You spin the spinner once, what is P(not even)
There is three parts to the spinner
Answer:
dad
Step-by-step explanation:
Without using a calculator, determine the value of: sin 60° x tan30° sec45°
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
I've used 'unit triangles' to calculate various trig values without a calculator at all!
Please look at my image that I've attached. It includes all the steps necessary to find the answer to your question.
I've assumed prior knowledge of Pythagoras's Theorem & SOHCAHTOA.
Please give comments if you need further explanation from me!
Best of luck, Kenny!
What is it called when your point is right on the Y axis?
Y Intercept
Slope- intercept
Answer:
y intercept
Step-by-step explanation:
will mark brainiest to whoever gets it right!!!!!!:)
If they are parallel it would be 105
If its right please give brainliest
The width of a 2-by-4 piece of wood is actually 3 1/2 inches. Find the total width of 28 2-by-4s laid side by side. Simplify your answer
Work Shown:
3 1/2 inches = 3.5 inches
total width = 28*3.5 = 98 inches
The required total width of 28 2 - by -4s laid side by side is 98 inches.
Given,
The width of a 2-by-4 piece of wood is actually 3 1/2 inches. to determine the total width of 28 2-by-4s laid side by side.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
The width of a 2-by-4 piece of wood is actually 3 1/2 inches.
Now, the width of 28 2-by-4 woods laid side by side,
= 28 * 3 1 / 2
= 28 * 7 / 2
= 98
Thus, the required total width of 28 2 - by -4s laid side by side is 98 inches.
Learn more about simplification here: https://brainly.com/question/12501526
#SPJ2
A shirt is on sale for 40% off. The sale price is $12. How much was the discount?
Let p = the original price
p - .4p = 12
.96p = 12
p = 12.5
The original price was $12.50
12.5 - 12 = .5
The amount of the discount was $.50
Of the 12 people who have taken their seats at a seminar, 2 have red hair. What is the experimental probability that the next person to take a seat will have red hair? help pls i dont understand this ixl
Answer:
Heyyy!!!!!
I think the answer is 1/6.... Im not really sure...
Step-by-step explanation:
My explanation is that there are twelve people of whom 2 have red hair.
so the probability is 2/12 which simplifies to 1/6.
I really hope this helps!!!
The wind force f on a sail varies jointly as the area a of the sail and the square of the wind speed w.
the force on a sail with area an area of 500 ft2 is 64. 8 pounds when the wind speed is 18 mph. what
would be the force for a sail with an area of 250 ft? with a wind speed of 35 mph.
how would you solve this problem? what would your answer be?
response:
Answer:
122.5 lbs
Step-by-step explanation:
The relation between force, wind speed, and area can be written ...
f = ks²a
for some wind speed s and area a.
__
The constant of proportionality, k, can be found from the given data.
64.8 = k(18²)(500) . . . force in pounds, area in square feet, speed in mph
k = 64.8/(324×500) = 0.0004
__
Using the equation with the second set of data, we have ...
f = 0.0004(35²)(250) = 122.5 . . . . pounds
The force on the 250 square foot sail would be 122.5 pounds.
An Air Force plane flew to the
maintenance facility and back. It took one
hour longer to go there than it did to come
back. The average speed on the trip there
was 256 km/h. The average speed on the
way back was 320 km/h. How many
hours did the trip there take?
Answer:
5 hours
Step-by-step explanation:
Time taken for trip : t + 1
Time taken for return : t
Avg. speed (trip) : 256 km/h
Avg. speed (return) : 320 km/h
The distances covered on both trips are equal.
⇒ Distance (trip) = Distance (return)
⇒ Speed (trip) × time (trip) = Speed (return) × time (return)
⇒ (256)(t + 1) = (320)(t)
⇒ 256t + 256 = 320t
⇒ 64t = 256
⇒ t = 4 hours
Time (trip) = t + 1 = 4 + 1 = 5 hours
Find the surface area of the prism.
10 ft length
1 ft height
5 ft width
Answer:
Surface Area = 130 sq ft
Step-by-step explanation:
If you don't have a picture, draw a picture so you can see what's up. See image. Surface area is the area of all the faces of a 3d shape (a solid) all added up. This solid is a box. It has six faces. Each face is a rectangle. The top and bottom are the same. The front and back are the same. The left and right sides are the same. See image.
Area of a rectangle is:
A = l × w
Area of the top:
5 × 10 = 50
Area of the bottom also 50.
Area of the left side:
1 × 5 = 5
Area of the right side is also 5.
Area of the front:
1 × 10 =10
Area of the back is also 10.
ADD up all 6 areas:
50+50+5+5+10+10
Surface area = 130
Area has square units.
SA = 130 square ft
This is easy for other students in my class just not me lol
Answer:
65
Step-by-step explanation:
Angle FGH = x
Angle FGJ = 25
Angle JGH = 40
Angle FGH = Angle FGJ + Angle JGH
x = 25 + 40
x = 65
The value of x in the diagram is 65.
What is an angle?The angles between two lines are the angles formed by two intersecting lines, measured in degrees or radians.
Several different types of angles can be formed between two lines, including acute angles, right angles, and obtuse angles.
We have,
From the diagram,
∠JGH = 40
∠FGJ = 25
Now,
∠JGH + ∠FGJ = x
So,
40 + 25 = x
Solve for x.
x = 40 + 25
x = 65
Thus,
The value of x in the diagram is 65.
Learn more about angles here:
https://brainly.com/question/7116550
#SPJ7
Version B
We have worked with Ferris Wheels above
ground, but what if a portion of it went
underground and traveled in a clockwise
direction?
Details;
The Ferris Wheel has a diameter of 80
ft
The Ferris Wheel center is 20 feet
below the ground
The Ferris Wheel rotates in a clockwise
direction
The rider enters on ground level on
the right side of the wheel.
It takes 1 minute for 1 ½ rotations.
Your task:
Sketch a diagram that showcases this
scenario with labels and
measurements.
Determine the angular speed.
Develop an equation for the height of
the rider while on the ride.
Construct a graph (height vs. time).
Make sure both axes are labeled with
all landmark points.
Provide a statement, explaining the
relationship between your graph and
the rider's position on the wheel.
When will they be above ground and
below?
Calculate the rider's total distance
traveled from the moment they get on
at ground level on the right to the
other point on ground level on the left
where they get off.
An example of how to sketch the Ferris Wheel diagram is given in the image attached.
What is the angular speed about?To solve for the angular speed, you can use the formula of"
Given that the diameter is 80 feet, so we know the radius will be 40 feet.
The Ferris wheel bottom is 20 feet high, so we add the radius we get that the middle of the Ferris wheel is 60 feet high.
Finally, the Ferris wheel completes 1 ½ rotation (2π radians) in 1 minutes. So we say that the Ferris wheel is said to spins at π rad/min.
Angular velocity ( 1 ½ rev/1min)( 1min/60 sec)
C = 2π(60)
C ≈ 377.04 feet
540 revolution (1 ½ rotations) is 60 seconds, the speed is then
s = d/t
s = 377.06 ft / 60 sec
s = 6.28 ft/sec
To plot the graph, the final equation will be h(t) = 40sin(πt + π/2) + 60.
Learn more about angular speed from
https://brainly.com/question/6860269
#SPJ1
Which is the apparent solution set of the system of equations graphed on the grid? a. {(0,0), (3,0)} b. {(0,-2), (1,0)} c. {(0,0), (1.5,2.25)} d. {(-1,-4), (2,2)}
The apparent solution set of the system of equations graphed on the grid is {(-1,-4), (2,2)}
How to determine the solution?The point of intersection of the curves or lines on a graph is the solution of the system of equations
From the complete question, the lines intersect at approximately
(-1,-4) and (2,2)
Hence, the apparent solution set on the grid is {(-1,-4), (2,2)}
Read more about solution set at:
https://brainly.com/question/1214333
#SPJ4
Answer:
D.
{(-1,-4), (2,2)}
Step-by-step explanation:
This should be the answer for Plato/Edmentum users. (Note: not all answers are in the same position. It might be d for me but the answer might be put under any other letter)
2 similar rectangular pyramids have a similarity ratio of 4:5. What is the ratio of their volumes? Put your answer in the form a:b
Answer:
64:125
Step-by-step explanation:
When you go from a length ratio to an area ratio you need to square the numbers involved: [tex]4^{2} :5^{2}[/tex] = 16 : 25
By the same logic, if you want to go from length to volume you need to cube the numbers involved: [tex]4^{3} :5^{3}[/tex] = 64 : 125
“will give brainliest”
The graph below shows a company's profit f(x), in dollars, depending on the price of erasers x, in dollars, sold by the company:
Graph of quadratic function f of x having x intercepts at ordered pairs 0, 0 and 8, 0. The vertex is at 4, 270.
Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit? (4 points)
Part B: What is an approximate average rate of change of the graph from x = 1 to x = 4, and what does this rate represent? (3 points)
Part C: Describe the constraints of the domain. (3 points)
Answer:
Part A: The x-intercepts represent the prices of the erasers at which the profit will be $0. The function is increasing from [-∞, 4] and decreasing from [4,+∞]. This means that when the price of the eraser is less than 4, the profit will increase until it gets to 4 and decrease for any value greater than 4, where $4 is the price at which the company has the maximum profit.
Part B: From the interval [1,4], the average rate of change is 50.625, which means that for every $1 increase in the price of erasers, the profit goes up by $50.625.
Part C:
The domain of this function is [0,+∞] because this is the only part of the function that is positive. The function cannot have -x-values because it does not make sense to make the price of an eraser 'negative'.
Step-by-step explanation:
The equation of this parabola is [tex]f(x) = -16.875(x-4)^2 + 270[/tex].
Part A:
The x-intercepts represent the prices of the erasers at which the profit will be $0. The function is increasing from [-∞, 4] and decreasing from [4,+∞]. This means that when the price of the eraser is less than 4, the profit will increase until it gets to 4 and decrease for any value greater than 4, where $4 is the price at which the company has the maximum profit.
Part B:
To find the average rate, we can use the slope formula, but first, we must find the y-values at each given x-value. We can plug in 1 and 4. [tex]f(1) = -16.875(1-4)^2 + 270 = 118.125[/tex]. We know that at x = 4, the y-value is 270 because the vertex is at (4,270). Now we can apply the slope formula [tex]\frac{270 - 118.125}{4 - 1} = 50.625[/tex]. This means that from the interval [1,4], the average rate of change is 50.625, which represents that for every $1 increase in the price of erasers, the profit goes up by $50.625.
Part C:
The domain of this function is [0,+∞] because this is the only part of the function that is positive. The function cannot have -x-values because it does not make sense to make the price of an eraser 'negative'.
hope this helped! :)
i'll give brainliest and points to whomever answers these two questions, thank you so much in advance!
Q8- what's the S.S of the inequality: x² + 4 > 2
a) R
b) ∅
c) R-
d) R+
Q9- if x + yi = (1 + i)⁴ , then x + y = ......
a) 4
b) - 4
c) 2
d) - 2
an explanation for future reference would be GREATLY appreciated, thank you again T^T
Answer:
Answer b of the first one
answer of q9
Step-by-step explanation:
(x+iy)(2−3i)=4+i
2x−(3x)i+(2y)i−3yi
2
=4+i
Real
2x+3y
+
Imaginary
(2y−3x)
i=4+i
Comparing the real & imaginary parts,
2x+3y=4--------------------------(1)
2y−3x=1----------------------------(2)
Solving eq(1) & eq(2),
4x+6y=8
−9x+6y=3
13x=5⇒x=
13
5
y=
13
14
∴(x,y)=(
13
5
,
13
14
)
Was this answer helpful?
upvote
196
downvote
23
SIMILAR QUESTIONS
star-struck
If e
x+iy
=α+iβ, then x+iy is called logarithm of α+iβ to the base e.∴log
e
(x+iy)=log
e
(re
iθ
) =log
e
r+iθ where r is modulus value of x+iy & θ be the argument of x+iy If i
α+iβ)
=α+iβ, then α
2
+β
2
equals
Hard
View solution
>
The modulus of (1 + i) (1 + 2i) (1 + 3i) is equal to
Answer:
Q8. a. IR
Q9. b. -4
Step-by-step explanation:
Q8- what's the S.S of the inequality: x² + 4 > 2
x² + 4 > 2
⇔ x² > 2 - 4
⇔ x² > -2
Then the set of solutions is all real numbers because x² is always a positive number which means for all real numbers x² > -2.
……………………………………………………………………………
Q9- if x + yi = (1 + i)⁴ , then
x + yi = [(1 + i)²]² = [2i]² = 2²×i² = 4×(−1) = −4
(Just remember that (1 + i)² = 2i )
somebody please help me with this question!
Answers:
P(A) = 7/12
P(B) = 1/2
=====================================================
Explanation:
To see how I calculated P(A), check out this link to this very similar question
https://brainly.com/question/27669586
--------------------
Now to calculate P(B)
If a number is divisible by 2, then the number is a multiple of 2.
In other words, the number is even.
Counting through the values in the table, you should find that there are 18 sums that are even (2, 4, 6, 8, 10 and 12). Refer to the dice chart below.
Here's a further breakdown
1 copy of "2"3 copies of "4"5 copies of "6"5 copies of "8"3 copies of "10"1 copy of 12Side note: We have nice symmetry going on.
There are 1+3+5+5+3+1 = 18 values total that are even numbers. The other half are odd numbers of course.
P(B) = 18/36 = (1*18)/(2*18) = 1/2
QUICK PLEEEASEEEEEEEEE
Answer:
c) 2
Step-by-step explanation:
By definition The mode is the most repeated number in the data-set.
rashanda claims that she plays roughly 30 hours of golf per week she played 3 hours on monday 9 hours total on tuesday through thursday and 15 hours total over the next five days rashanda plays at a steady rate explain why her claim is or is not accurate
Answer:
Not accurate
Step-by-step explanation:
3+9+9=21
A box is 50 cm long. Which of these is the closet to the length of this box in feet ? (1 inch = 2.54cm)
Answer:
1ft 7.7in/1.64 ft
Step-by-step explanation:
50/2.54=19.69in
12in=1ft
so 1ft 7.7in
19.69/12=1.64
[tex]10/7 + 2/20 + 7-4[/tex]
[tex]\dfrac{10} 7 + \dfrac 2{20} +7 - 4\\\\\\=\dfrac{20(10)+7(2)}{140}+3\\\\\\=\dfrac{200+14+140(3)}{140}\\\\\\=\dfrac{634}{140}\\\\\\=\dfrac{317}{70}[/tex]
Convert the into millimetres.
A. 234cm
B. 15m
C. 25km
A. 234 cm
multiply the given length value ( 234 ) by 10.
[tex]234 \times 10[/tex]
[tex] = 2340 \: mm[/tex]
B. 15m
multiply the given length value ( 15 ) by 1000.
[tex]15 \times 1000[/tex]
[tex] = 15000 \: mm[/tex]
C. 25km
multiply the length value ( 25 ) by 1000000.
[tex]25 \times 1000000[/tex]
[tex] = 25000000 \: mm[/tex]
a)
234 × 10
= 2340 millimeters
b)
15 × 1000
= 15000 millimeters
c)
25 × 1000000
= 25000000 millimeters
Please help! Give detailed answer.
Answer:
C
Step-by-step explanation:
Pythagorean theorem
√25²-20²=15
Answer:
C
Step-by-step explanation:
the figure is a rectangle with opposite equal sides
Consider the upper right triangle
using Pythagoras' identity
p² + 20² = 25²
p² + 400 = 625 ( subtract 400 from both sides )
p² = 225 ( take square root of both sides )
p = [tex]\sqrt{225}[/tex] = 15
_X 11 = 99 what is the missing number ?
Answer:
missing number its 9
Step-by-step explanation:
Ti find the answer you divide 99 by 11 and you find your answer
Two friends each had an auto loan of $20,000. One was repaid at
8% in 3 years at about $625 per month, and the other at 8% in 5
Years at about $405 per month. The total of the payments for the 5-year loan is how much more than the total for the 3-year loan?
Answer:
1,800 more
Step-by-step explanation:
12 × 3 = 36 months
$625 × 36 = $22,500
12 × 5 = 60 months
$405 × 60 = $24,300
$24,300 - $22,500 = $1,800
the interest is paid per month, so we first need to convert the years to months. after that we calculate the total amount of money paid over the specified years. and then we subtract the one from the other to get the difference.
Interior and Exterior Triangle Angles (0/5)
Please full explanation
I will mark brainlist to whoever answers first
Answer:
∠R = 69Step-by-step explanation:
Angle sum propertySum of all angles of triangle = 180
5x - 11 + 3x - 3 + 3x + 18 = 180
5x + 3x + 3x -11 - 3 + 18 = 180
Combine like terms
11x + 4 = 180
11x = 180 - 4
11x = 176
x = 176/11
x = 16
∠R = 5x - 11
= 5*16 - 11
= 80 - 11
= 69
Apply angle sum property
5x-11+3x-3+3x+18=18011x+4=18011x=176x=16m<R
5(16)-1180-1169°I NEED THE ANSWER TO THIS QUESTION ASAP
Answer:
B
Step-by-step explanation:
Add 15,181 and 137 then for part b subtract 15,181 and 4,893 and that's a way higher number than 4,893 and 137
Answer:
Step-by-step explanation:
+ 15,181 ft.
- 137 ft.
d = | 15,181 - ( - 137 ) | = 15,318 ft.
15,318 ÷ 2 = 7,659 ft. > ( 4,893 + 137 ) ft.
⇒ the answer is (B).
Given the function, f(x) = (-3x)2 , evaluate f(4)
Answer:
Step-by-step explanation:
(-3*4)^2 = (-12)^2 = 144