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Short explanation:
Plug z = 2 into the equation and you'll find that
z^3 + 8 = 2^3 + 8 = 8+8 = 16
but the result should be 0 since the original equation has 0 on the right side. Therefore, z = 2 is not a solution.
------------------------------------
Longer explanation:
Solve the equation for z to find the three roots.
z^3 + 8 = 0
(z+2)(z^2 - 2z + 4) = 0 ... sum of cubes factoring rule
z+2 = 0 or z^2 - 2z + 4 = 0
z = -2 or z^2 - 2z + 4 = 0
We see that z = -2 is one root. To find the other two roots, use the quadratic formula to solve z^2 - 2z + 4 = 0 for z
[tex]z = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\z = \frac{-(-2)\pm\sqrt{(-2)^2-4(1)(4)}}{2(1)}\\\\z = \frac{2\pm\sqrt{-12}}{2}\\\\z = \frac{2\pm\sqrt{-1*4*3}}{2}\\\\z = \frac{2\pm\sqrt{-1}*\sqrt{4}*\sqrt{3}}{2}\\\\z = \frac{2\pm i*2*\sqrt{3}}{2}\\\\z = \frac{2\pm 2i*\sqrt{3}}{2}\\\\z = \frac{2(1\pm i*\sqrt{3})}{2}\\\\z = 1\pm i\sqrt{3}\\\\z = 1+ i\sqrt{3} \ \text{ or } \ z = 1- i\sqrt{3}\\\\[/tex]
Therefore, the three roots of z^3+8=0 are [tex]z = -2, \ z = 1+i\sqrt{3}, \ z=1-i\sqrt{3}[/tex]
The value z = 2 is not part of the list of solutions.
We can verify each solution by plugging it back into the original equation. For instance, with z = -2, we get
z^3 + 8 = 0
(-2)^3+8 = 0
-8+8 = 0
0 = 0 ... solution is confirmed.
I'll let you check the other solutions.
Hello
does anyone need any help, im really good at math and i would love to help someone
Answer:
Yes please
Step-by-step explanation:
what is
8+1/2(12)=x
Thank you!!!
√(25 - 10 √(3) + 3)
(not as a decimal)
Answer:
[tex]\huge\boxed{\sqrt{25-10\sqrt3+3}=5-\sqrt3}[/tex]
Step-by-step explanation:
[tex]\sqrt{25-10\sqrt3+3}=(*)\\\\25=5^2\\3=(\sqrt3)^2\\10\sqrt3=(2)(5)(\sqrt3)\\\\(*)=\sqrt{5^2-(2)(5)(\sqrt3)+(\sqrt3)^2}\\\\\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\=\sqrt{(5-\sqrt3)^2}\\\\\text{use}\ \sqrt{a^2}=|a|\\\\=|5-\sqrt3|=5-\sqrt3\\\\^{\text{because}\ 5>\sqrt3\to5-\sqrt3>0}[/tex]
Use the sequence below
to complete each task.
-6, 1, 8, 15, ...
a. Identify the common difference (a).
b. Write an equation to represent
the sequence.
C. Find the 12th term (22)
Answer:
d=7, b -13+7n c 71
Step-by-step explanation:
a= - 6
2nd term=a+(n_1)d
a+d
1+6
=7
b tn a-(n_1)d
_6+(n_1)d
_6 +7n_7
_13+7n
tn a+11d
6+11(7)
6+77
=83
Which function has the smallest x-intercept value, if it exists?
Answer:
x intercept. The x intercept is the point where the line crosses the x axis. At this point y = 0. y intercept. The y intercept is the point where the line crosses the y axis.
Answer:
f(x)=x+1 or C on edge
Step-by-step explanation:
Evaluate 3|-3|
if you could do it step by step I’d appreciate
Answer:
9
Step-by-step explanation:
the absolute value of -3 is 3
so; 3*|-3| =3*3 =9
The height of trapezoid VWXZ is 8 StartRoot 3 EndRoot units. The upper base,VW, measures 10 units. Use the 30°-60°-90° triangle theorem to find the length of YX.
Once you you know the length of YX, find the length of the lower base, ZX.
A.14 units
B.10 + 4 StartRoot 3 EndRoot units
C.18 units
D.10 + 8 StartRoot 3 EndRoot units
Answer:
C. 18 units.
Step-by-step explanation:
The value of the length of YX is, 8 units
And, The lower base will be 18 units.
Since, The tangent of an angle is the ratio between the opposite side of the angle and the adjacent side of the angle.
⇒ tanθ = opposite side/adjacent side
So according to asked question;
In the trapezoid VWXZ,
VW || XZ
Height of trapezoid= VZ = WY = 8√3
VW = 10
∠YWX = 30°
∠WXY = 60°
In triangle ΔWYX,
∠WYX = 90°
ΔWYX is a right angle triangle
So, tan ∠YWX= XY/WY
⇒ tan30° = XY/8√3
⇒ 1/√3 = XY/8√3
⇒ XY = 8√3/√3
⇒ XY = 8 units
Thus, The length of the lower base is,
ZX = ZY + XY = VW + XY = 10 + 8 = 18units
Therefore, The lower base will 18 units.
Learn more about trapezoid visit:
brainly.com/question/15439615
#SPJ7
What type of correlation is shown in the graph?
A) Positive
B) negative
C) no correlation
Answer:
No correlation
Step-by-step explanation:
This is because they are all spread out and aren't all consistently going up or down.
Answer:
C
Step-by-step explanation:
I will give you brainliest if you answer pleaseee
Answer: The area of the banner is 100 in^2
Step-by-step explanation:
so let say the banner was still a rectangle with the triangle still attached to it so if we needed to find the area of the whole rectangle we will need to multiply the length times the width
so 14 * 8 = 112
But now a triangle is being cut out of the rectangle so we need to find the area of the triangle being cut out and subtract it from the area of the whole rectangle. But first we need to find the base and the base is 8 since the other side base is 8 too and the height will be 3 since 14- 11= 3
Now find the area of the triangle by multiplying the base times the height and divide it by 2.
8 * 3= 24
24/2= 12
subtract 12 from 112
112- 12 = 100
Solve the equation for x : x3=64
Answer:
x=21.3333
Step-by-step explanation:
its right
Answer:
X=4
Step-by-step explanation:
Hope I helped:)
Write and solve a proportion to answer the question.
120% of 10 is what number?
Answer:
12
Step-by-step explanation:
the proportion is 120/10=1200%
I'm sorry if this is wrong
PLZ help I don't understand!!!!
Answer:
The answer is 24.4.
Step-by-step explanation:
You use tan to figure it out as we they have given us the opposite value and we need to find out the adjacent value. and tan tan(x) = opposite over adjacent.
x is the value we need to find
tan(16) =7÷x
xtan(16) = 7
x= 7 ÷ tan(16)
x = 24.4
Hope this helped!
I need help finding the area of the polygons.
Answer:
hope it helps
Step-by-step explanation:
1. area = 15*15 - 5*6 = 195
2. area = (8+16)*8 /2 - 5*3 = 96 - 15 = 81
3. area = 12*3 + 9 * (12 - 4 - 4) = 36 + 9*4 = 36+36 = 72
4. x = 6-3 = 3
y = 3- (-1) = 4
z = 7-3 = 4
area = 2*x*y/2 + y*z = 2*3*4/2 +4*4 = 12+16 = 28
Heyguys can soeom plzz help meee?? IDK how to do this!! 20 Points? plz write all details of the problem plzz!
Math problem: An airplane traveled 5.7 x 102 miles per hour for 1.4 x 101 hours. How far did the airplane travel?
Answer:
The distance travelled is 7.98×10³ miles.
Step-by-step explanation:
Given that the formula to find distance is Distance = Speed×Time. Then you have substitute the values into the formula :
[tex]distance = speed \times time[/tex]
Let speed = 5.7×10²,
Let time = 1.4×10¹,
[tex]d = (5.7 \times {10}^{2} ) \times (1.4 \times 10)[/tex]
[tex]d = (5.7 \times 1.4) \times ( {10}^{2} \times 10)[/tex]
[tex]d = 7.98 \times {10}^{3} miles[/tex]
Determine if a linear, exponential, or quadratic function is the best model for the data given in the table below.
Answer:
linear
Step-by-step explanation:
yes it is linear since I did this question and got it right
Maria is four times as old as Frank. In two years Maria will be 3 times as old as Frank. Find their present ages?
Answer:
Maria is 16 and Frank is 4
Step-by-step explanation:
HELPPPPPPPPPPPPPPP MEEEEE
Answer:
-2
Step-by-step explanation:
Answer:
the number is the third one -2
Which operations could you use to solve this word problem? Check all that
apply
STEP 2: PLAN
The entire school, 250 students, went to the soap
box derby. The Math Club went in 2 vans, and
each van held 6 students. How many students
from the Math Club went to the soap box derby?
O
A. Multiplication
B. Subtraction
C. Division
D. Addition
Answer:
A and D
Step-by-step explanation:
if each van held 6 students and the math club went in two vans, then you can use multiplication to figure it out. each van held 6 students, the math club went in two vans, so the equation can be 6 x 2. BUT you can do addition as well. because 6 plus 6 will give you the same answer as 6 x 2 because each van holds six students, there were two vans so 6 plus 6 is another way to solve this problem.
Find the Lateral AND Total Surface Area of a pyramid with slant height 6.8mi whose triangular base measures 11mi on each side. Each altitude of the base measures 9.5mi.
Answer:
Step-by-step explanation:
The given pyramid is a square based pyramid. The formula for determining the lateral surface area of a square base pyramid is expressed as
Lateral surface area = 1/2 × perimeter × slant height
From the information given,
Length of each side = 11 miles
Perimeter of base = 4 × 11 = 44 miles
Slant height = 6.8 miles
Lateral surface area = 1/2 × 44 × 6.8 = 149.6 miles²
The formula for determining the total surface area of a square base pyramid is expressed as
Total surface area = base area + (1/2 × perimeter × slant height)
Base area = 11² = 121
Total surface area = 121 + (1/2 × 44 × 6.8) = 270.6 miles²
percentage increase from 14 to 40
Answer:
185.714% increase
Step-by-step explanation:
To find the percentage increase, take the new amount and subtract the original amount
40-14 = 26
Divide by the original amount
26/14
1.857142857
Multiply by 100% to change to percent form
185.714%
Answer:
185.714%
Step-by-step explanation:
Jaylen rents bowling shoes for $6 and pays $5 per bowling game. Is the relationship a proportional relationship? Explain
Answer:
yes
Step-by-step explanation:
the easy explanation is that the graph is straight so it means its proportional. the more detailed one is that you don't care about those 6$, cause its only says to you where the graph starts from (if you'll see it isn't from 0 there its from 6). you do care about the 5$ detail. and they say its for every game which is the definition of proportional (for every *blank amount of x* youll need *blank amount of y* ) you can see that after 1 game youll pay 5$ and then 10$ and so on....
Robert wants to put lights around the edge of his deck.the deck is 46 feet long and 29feet wide .how many yards of lights does he needs.
Answer:
1334feet
Step-by-step explanation:
46x29
Lines r and a are parrallel.if m<2=110,what is m<7?
Answer:
m< 7 = 70
Step-by-step explanation
m< 2 + m< 1 = 180
180 - 110 = 70
m< 1 = 70
because the lines are parallel m< 1 = m< 7
so m< 7 = 70
Please help me with this question i am struggling
Answer:
x would be 7 units because 4 × 7 = 28 And 28 + 10 = 38
Step-by-step explanation:
Determine between which consecutive integers the real zeros of f(x) = x2 – 3x + 1 are located.
between -1&0,0&1 and 2&3
between -1&0,0&1 and 1&2
between -28-1,0&1 and 1&2
between -2&1, 0&1 and 1&2
Answer:
between -2&1,0&1 and 1&2
Reading a Bar Graph Worksheet
Answer:
1. 80 students
2. 45 students
3. i believe that its 25 dollars
4. i dont know sorry
5. i dont know sorry
Step-by-step explanation:
Hello there tiny humans can any you answer this pls for me
Answer:
1) B
2) a. 5x-7 b. 15b + 25 c. 16x^2 + 4x d. 13g -20. e. 6h + 23
Step-by-step explanation:
I’m sorry if any of them are wrong but I believe they’re right, most of it was distribution
Answer:
28. B
29:
A. 5x-7
B. 15b+25
C. 16x^2+4x
D. 13g-20
E. 6h+23
30:
A. Constant = 103, Coefficient= 94, Variable= w
B. Constant= -3, coefficient= 18, variable= x
C. Constant= -7, coefficient = -5, variable = y
D. Constant = 16, coefficient = -24, variable = z
31:
A. x+10
B. 13-9/x
C. 9x+4
D. 4+11x
What is the formula for a line that passes through point (6,5) and runs perpindicular to a line with a slope of 1/2
Using THIS formula:
(y-y₁) = m(x-x₁)
PLUGGING IT IN:
(y-5) = 1/2(x-6)
Is this what your teacher is looking for?
An aircraft carrier left Port 35 traveling north five hours before a container ship. The container ship traveled in the opposite direction going 8 km/h faster than the aircraft carrier for seven hours after which time the ships were 303 km apart. What was the aircraft carrier's speed ?
Answer:
Aircraft carrier speed = 4.97 km/h
Step-by-step explanation:
Given that the time taken by the aircraft = 5 hours
Let the distance covered = X
Speed = V
Time taken by the ship = 7 hours
Let the distance covered = Y
Speed = 8V
Since it is 8 km/h faster than the aircraft carrier.
Using the speed formula
Speed = distance/time
Distance = speed × time
For the aircraft;
X = 5V
For the ship:
Y = 7 × 8V = 56V
Since they are 303km distance apart,
X + Y = 303
5V + 56V = 303
61V = 303
V = 303/61
V = 4.97 km/h
Aircraft carrier speed = 4.97 km/h
Mathematics question
So the answer of question no 4 is 2
The answer of question no 5 is 5
Look at the attached picture
Hope it will help you
Good luck on your assignment
Answer:
Step-by-step explanation:
number 4 : x=2
number 5: x=5
John and David have a rectangular piece of property. The length is 8 more miles than the width, the perimeter is 60. What are the possible dimensions?
Answer:
Length: 19
Width: 11
Step-by-step explanation:
19 miles is 8 miles longer than 11 miles.
With these dimensions, the perimeter is equal to 60 miles.