Solve this equation and show your work! (1 point for the correct answer and 1 point for showing how to solve the equation) x³ = -2,197
Answers
Here we are given with a equation:
[tex] {x}^{3} = - 2197[/tex]
And we have to solve it with appropriate steps.
So, let's start solving.
Add 2197 to both sides of the equation,
[tex] {x}^{3} + 2197 = - 2197 + 2197[/tex]
[tex] {x}^{ 3} + 2197 = 0[/tex]
Now, using the identity:
a³ + b³ = (a + b)(a² - ab + b²)Let's proceed further.
x³ is the cube of x and 2197 is the cube of 13
[tex](x) {}^{3} + (13) {}^{3} = 0[/tex]
[tex](x + 13)( {x}^{2} - x \times 13 + {13}^{2} ) = 0[/tex]
[tex](x + 13)( {x}^{2} - 13x + 13) = 0[/tex]
Now,
x + 13 = 0x² - 13x + 13 = 0So, x = -13
And, for the second let's use the discriminate formula,
➝ D = b² - 4ac
➝ D = (-13)² - 4(1)(13)
➝ D = 169 - 52
➝ D = 117
Now, using the D. formula,
[tex]x = \dfrac{ - b \pm \sqrt{ D} }{2a} [/tex]
[tex]x = \dfrac{13 \pm \sqrt{117} }{2} [/tex]
[tex]x = \dfrac{13 \pm 3 \sqrt{13} }{2} [/tex]
So the roots of the equation are:
[tex]{ \boxed{ \bf{x = - 1 ,\: \frac{13 + 3 \sqrt{13} }{2} and \: \frac{13 - 3 \sqrt{13} }{2} }}}[/tex]
And we are done !!
#CarryOnLearning
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Related Questions
A class of 128 students from civil, mechanical and electrical engineering backgrounds is divided into 2 sections (sections A and B). Section A contains of 18 civil engineers and a total of 50 students. Section B contains 44 mechanical engineers. There are a total 40 civil engineers and 60 mechanical engineers in the class. What is the probability that a random electrical engineering student is from section A
Answers
Answer:
The probability is 0.5714
Step-by-step explanation:
This is a probability question. We are interested in calculating the probability that a random electrical engineering student is from section A.
Mathematically the probability will be;
Number of electrical engineering students in section A/ Total number of electrical engineering students in both sections
Total number of electrical engineering students = 128 - 60 -40 = 28
Now let’s calculate the number of electrical students from section A
Number of mechanical and electrical = 50-18 = 32
Now, there are a total of 60 mechanical engineers and 44 in B; So the number of mechanical engineers in A = 60-44 = 16
So the number of electrical engineers in A = 32-16 = 16
So the probability will be;
16/28 = 4/7 = 0.5714
Find the value of x that will make A||B.
A
B
4x
2x
X =
?
Answers
Answer:
x = 30
Step-by-step explanation:
Lines A and B are parallel lines and a transverse line is intersecting these lines at two distinct points.
By the definition of interior consecutive angles, sum of the measures of interior consecutive angles is 180°.
4x + 2x = 180°
6x = 180
x = 30
Therefore x = 30 will be the answer.
Find the measures of angles 1 through 5 in the figure shown.
Its 4 PARTS
Answers
Angle 2 = 136
Angle 3 = 44
Angle 4 = 136
Angle 5 = 62
The measure of angle ∠1 is 44 degrees and the measure of angle ∠5 is 62 degrees.
What is an angle?Angle is the space between the line or the surface that meets. And the angle is measured in degree. For complete 1 rotation, the angle is 360 degrees.
Vertically opposite angle - When two lines intersect, then their opposite angles are equal.
Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.
Angle ∠1 and 46° are complementary angles. Then we have
∠1 + 46° = 90°
∠1 = 44°
Angle ∠1 and ∠3 are vertically opposite angles. Then we have
∠1 = ∠3 = 44°
The sum of all the angles of the triangle is 180 degrees. Then we have
∠3 + 74° + ∠5 = 180°
44° + 74° + ∠5 = 180°
∠5 = 62°
More about the angled link is given below.
https://brainly.com/question/15767203
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In the number 4,118, how does the value represented by the 1 in the hundreds place compare with the value represented by the 1 in the tens place?
Answers
Answer:
its 10 times
Step-by-step explanation:
its because the value of 1 in the ten place and multiply by 10 to get the 1 in the hundred place or the 1 in the hundred place divide by 10 to get 1 in the tens place
Find JH
G. H. I. J
2. 12.
Answers
Answer:
JH = 17
Step-by-step explanation:
GH = 2
IJ = 12
GI = 7
find: JH
HI = 7 - 2
HI = 5
JH = 12 + 5
JH = 17
Which is equivalent to (3 + 4i )(3 - 4i )?
Answers
Use the FOIL method to solve.
(3 + 4i)(3 - 4i)
(3 * 3) + (3 * -4i) + (4i * 3) + (4i * -4i)
9 - 12i + 12i - 16i
9 - 16i
Best of Luck!
During a recent beetle infestation, two-thirds of the ash trees in the area were destroyed. If 130 trees were destroyed, how many ash trees were originally in the area?
Answers
set this up as a proportion with 2/3 = 130/x
130 x 3 = 390
390 / 2 = 195
Answer:
195 Trees
Step-by-step explanation:
2/3 is just 2 of 3 parts
2 parts of the trees is 130,
so divide 130 by 2, and that's 65.
Since you know 65 + 65 is the same as 2 out of 3
Then just add 65 one more time to equal 195.
Since, 65*3 is the same as saying 1 * 3 parts
130 is equal to 2/3, so 195 is equal to 3/3.
What is the Domain of the given graph?
(0,2)
(-3,0)
Answers
Answer:
dssds 8900
Step-by-step explanation:
dwdwdmunayaynd
Question 3 of 8
Which of the following are measurements for rectangles that are similar to a
rectangle with a width of 10 and a length of 20? Check all that apply.
A. 17 and 34
B. 2.5 and 6
O C. 15 and 30
0 D. 14 and 30
O E. 5 and 10
Answers
132891 round the nerast hundred
Answers
Chen burns 354 calories in 1-hour swimming. He swam for 28 hours last month. How many calories did Chen burn in all last month from swimming?
Answers
Answer: he burned 9912 calories all last month
Is 5 a solution to 2x + 5 = 15? Yes or No
How do you know?
Answers
Answer:
Yes
Step-by-step explanation:
yes because when you place 5 in the x spot you arrive a final answer of 15=15
(URGENT) Country A produces about four times the amount of diamonds in carats produced in country B. If the total produced in both countries is 20,000,000 carats, find the amount produced in each country.
Answers
Answer:
A: 16,000,000 caratsB: 4,000,000 caratsStep-by-step explanation:
If the ratio is ...
A : B = 4 : 1
Then the ratio to the total is ...
A : total = 4 : (4+1) = 4 : 5
B : total = 1 : (4+1) = 1 : 5
Country A produces (4/5)×20 M carats, or 16 million carats.
Country B produces the remainder, 4 million carats.
A standardized exam's scores are normally distributed. In a recent year, the mean test score was and the standard deviation was . The test scores of four students selected at random are , , , and . Find the z-scores that correspond to each value and determine whether any of the values are unusual.
Answers
Answer:
The following are the solution to this question:
Step-by-step explanation:
In the given question, some of the values are missing which is defined in the attached file please find it.
In this question, the data is used to represent a standardized exam's scores, which is normally spread out into the test score that is 1530 and its standard deviation 316.
Formula:
[tex]\to z=\frac{X- \mu}{\sigma } \\[/tex]
If the value of z-score= 1930
[tex]\to z =\frac{1930- 1530}{316 } \\\\ \to z =\frac{400}{316 } \\\\ \to z = 1.27[/tex]
The z-score is 1.27
If the value of z-score= 1250
[tex]\to z =\frac{1250- 1530}{316 } \\\\ \to z =\frac{-280}{316 } \\\\ \to z = -0.886[/tex]
The z-score is -0.886
If the value of z-score= 2250
[tex]\to z =\frac{2250- 1530}{316 } \\\\ \to z =\frac{720}{316 } \\\\ \to z = 2.27[/tex]
The z-score is = 2.27
If the value of z-score= 1420
[tex]\to z =\frac{1420- 1530}{316 } \\\\ \to z =\frac{-110}{316 } \\\\ \to z = -0.348[/tex]
The z-score is = -0.348
The sum of three consecutive integers is 267. What is the largest integer?
Answers
Answer:
let integers be x,2x, 3x respectively
x+2x+3x= 267
6x= 267
x=267/6= 44.5
2x= 44.5*2= 89
3x= 44.5*3= 133.5
largest integer = 133.5
hope it helps
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Holmes Junior High has 125 more students than Harper Junior High. When the two schools are merged there will be 579 students. How many students currently attend each school?
Answers
Answer: 454
Step-by-step explanation: Holmes has 125, Merged there is 579, 579-125 = 454 :) easy subtraction
A candy store sells mints in 14, 12 , and 34 lb packages. John purchases several packages of each weight.
What is the weight of 6 packages of the 14 lb package?
Answers
Answer:
84 lbs
Step-by-step explanation:
Multiply 14*6 to get the total weight
What is the answer PLEASEE
Answers
Answer:
[tex]3^{-4}[/tex]
Step-by-step explanation:
[tex]3^5\cdot \:3^{-9}=3^{5-9}=3^{-4}[/tex]
Can someone help me with 4?
Answers
Answer:
ok so the answer is 343
Step-by-step explanation:
so for 4) you first use PEMDAS(Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction), and you do what's in the parenthesis first, so 7^4= 2401, that is inside the parenthesis, next you do the exponent outside the parenthesis, so is (2401)^2=5764801, and then you divide the 7^5=16807, so it looks like 5764801/16807=343
hope it helps
Answer:
The Answer is 343.
Step-by-step explanation:
First- We do the parenthesis first according to PEMDAS which is 7 x 7 x 7 x 7 equals 2401.
Next- We do 2401 x 2401 which equals 5764801.
Then- We do the bottom exponent which is 7 x 7 x 7 x 7 x 7 equals 16807.
Last- We divide 5764801 by 16807 and we get 343.
Hope this helps!
Rewrite the quality 827,000,000,000,000 pico second to show :
1sig. Fig.
2sig. Fig.
3sig. Fig.
4 dig. Fig.
5sig. Fig.
Answers
Answer:
a. 1 sig. fig. _800,000,000,000,000 picoseconds (8 x 10^14 picoseconds)
b. 2 sig. figs. 830,000,000,000,000 picoseconds (8.3 x 10^14 picoseconds)
c. 3 sig. figs. 827,000,000,000,000 picoseconds (8.27 x 10^14 picoseconds)
d. 4 sig. figs. 827,000,000,000,000 picoseconds (8.270 x 10^14 picoseconds)
e. 5 sig. figs. 827,000,000,000,000 picoseconds (8.2700 x 10^14 picoseconds)
Step-by-step explanation:
what are strategies to find rational numbers
Answers
functions occur when every x-value is associated with exactly one
Answers
The answer is y-value. A function is formed when one x-value corresponds with one and only one y-value.
Hannah had $237 in her
bank account at the start of
the summer. She worked for four
weeks and now she has $1685
in her bank.how much did Hannah make each week in her summer job
Answers
Answer:
$362
Step-by-step explanation:
Step 1:
$1685 - $237
Step 2:
$1448 ÷ 4
Answer:
362
Hope This Helps :)
Can someone answer this pls?? FAST
Answers
Incorrect answers= 12•-1/2=-6
Answer= 3
There are 48 empty seats and 52 occupied seats on an airplane. What is the ratio of the number of empty seats to the number of occupied seats?
Answers
Answer:
48/52
Step-by-step explanation:
Help me ASAP plssssssssssssssssssssss
Answers
Answer:
the answer is d i think try it.
find the integer that makes this subtraction statement true -3 - ? = -5
Answers
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{2}}}}}[/tex]
Step-by-step explanation:
Let the missing integer be x
Solve for x
[tex] \sf{ - 3 - x = - 5}[/tex]
Move 3 to right hand side and change it's sign
[tex] \dashrightarrow{ \sf{ - x = - 5 + 3}}[/tex]
The negative and positive integers are always subtracted but posses the sign of the bigger integer
[tex] \dashrightarrow{ \sf{ - x = - 2}}[/tex]
Change the signs of both sides
[tex] \dashrightarrow{ \boxed{ \sf{x = 2}}}[/tex]
Hope I helped!
Best regards! :D
What is the value of AB?
Answers
Answer:
use the pythogoras thoerem making aright angled traingle
and multiply the result by 2
ab = 2*8 =16
Step-by-step explanation:
1. The most massive planet in the solar system, Jupiter, has a mass of about 1,898,000,000,000,000,000,000,000,000 kg. Estimate Jupiter's mass using a one-digit whole number times a power of 10. Be sure to include units.
A. 1.9 X 10^18 kg
B. 2 x 10^18 kg
C. 1.9 x 10^27 kg
D. 2x 10^27 kg
Answers
Answer:
D. [tex] 2*10^{27} kg [/tex]
Step-by-step explanation:
Mass of Jupiter is given as 1,898,000,000,000,000,000,000,000,000 kg
Estimating this to the nearest whole number would be = 2,000,000,000,000,000,000,000,000,000 kg (rounding up the the "1,898")
To express this in scientific notation form, simply count how many zeros we have to the nearest whole number, 2.
We have 27 zeros there.
Therefore, we would multiply the whole number, 2, by 10 raise to the power of 27.
An estimate of the mass of Jupiter = [tex] 2*10^{27} kg [/tex]
Find the 9th term of the geometric sequence 4, 16, 64, ...
Answers
Answer: Just keep multiplying by 4 after 64 like multiply 64 times 4 and do that number times and keep doing that until its the 9th answer :)
Step-by-step explanation:
A geometric series is the sum of an unlimited number of terms with a fixed ratio between them. The 9th term of the geometric sequence 4, 16, 64, ... is 262,144.
What is geometrical series?A geometric series is the sum of an unlimited number of terms with a fixed ratio between them.
The first term of the series is 4, while the ratio of the geometric sequence:
[tex]\rm Ratio, r = \dfrac{16}{4} = 4[/tex]
Thus, the 9th term of the geometric series can be written as,
[tex]a_n = a_1 \times r^{(n-1)}\\\\a_9 = 4 \times 4^8\\\\a_9 = 262,144[/tex]
Hence, the 9th term of the geometric sequence 4, 16, 64, ... is 262,144.
Learn more about Geometrical Series:
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