Answer:
[tex]x_1=\mathbf{i}\sqrt{6},\ x_2=-\mathbf{i}\sqrt{6},\ x_3=\sqrt{3},\ x_4=-\sqrt{3}[/tex]
Step-by-step explanation:
Biquadratic Equations
Solve:
[tex]x^4 + 3x^2 - 18 = 0[/tex]
The biquadratic equations are equations of degree 4 without the terms of degree 1 and 3.
Solving such equations requires to express the equation as a second-degree equation with [tex]x^2[/tex] as the variable.
Rewriting the equation:
[tex](x^2)^2 + 3(x^2) - 18 = 0[/tex]
The quadratic equation can be factored as:
[tex](x^2+6)(x^2-3)=0[/tex]
It leads to two equations:
[tex]x^2+6=0[/tex]
[tex]x^2-3=0[/tex]
The first equation has imaginary roots. Solving for x:
[tex]x^2=-6[/tex]
[tex]x=\pm\sqrt{-6}[/tex]
[tex]x_1=\mathbf{i}\sqrt{6}[/tex]
[tex]x_2=-\mathbf{i}\sqrt{6}[/tex]
Where
[tex]\mathbf{i}=\sqrt{-1}[/tex]
The second equation has two real roots:
[tex]x^2-3=0[/tex]
[tex]x^2=3[/tex]
[tex]x=\pm\sqrt{3}[/tex]
[tex]x_3=\sqrt{3}[/tex]
[tex]x_4=-\sqrt{3}[/tex]
The roots are:
[tex]\mathbf{x_1=\mathbf{i}\sqrt{6},\ x_2=-\mathbf{i}\sqrt{6},\ x_3=\sqrt{3},\ x_4=-\sqrt{3}}[/tex]
A members-only speaker series allows people to join for $28 and then pay $4 for every event attended. What is the total cost for someone to attend 4 events? Write and solve an equation to find the answer
Given:
Joining fee = $28
Fee of each event = $4
To find:
Total cost for someone to attend 4 events.
Solution:
Let the number of events be x and total fee be y.
Fee for 1 event = $4
Fee for x events = $4x
Joining fee remains constant. So, the total fee is
[tex]y=28+4x[/tex]
Substitute x=4 in this equation.
[tex]y=28+4(4)[/tex]
[tex]y=28+16[/tex]
[tex]y=44[/tex]
Therefore, total cost of 4 events is $44.
Solve for y.
ln(2y−1)=3
Answer y=(e^3+1/2)
for future reference
Answer:
The correct answer should be:
[tex]y=\frac{1}{2}(e^3+1)\text{ or } y=\frac{e^3}{2}+\frac{1}{2}[/tex]
Step-by-step explanation:
We have the equation:
[tex]\ln(2y-1)=3[/tex]
Let’s remove the natural logarithm by raising both sides to e. This yields:
[tex]e^{\ln(2y-1)}=e^3[/tex]
The left will simplify to:
[tex]2y-1=e^3[/tex]
Add 1 to both sides:
[tex]2y=e^3+1[/tex]
Divide both sides by 2. So, the value of y should be:
[tex]y=\frac{1}{2}(e^3+1)[/tex]
Answer:
The correct answer is indeed y = [tex]\frac{e^3+1}{2}[/tex]
Step-by-step explanation:
I also took the test!
solve by factoring x^2 -9 =0
Pls help, I only have ten min
I will give brainliest to right answer
7th grade math
12 = 5/2 b
find the value of b
Answer:
[tex]\huge\boxed{b=\dfrac{24}{5}\to b=4\dfrac{4}{5}\to b=4.8}[/tex]
Step-by-step explanation:
[tex]12=\dfrac{5}{2}b\to\dfrac{5}{2}b=12\qquad|\text{multiply both sides by 2}\\\\2\!\!\!\!\diagup\cdot\dfrac{5}{2\!\!\!\!\diagup}b=12\cdot2\\\\5b=24\qquad|\text{divide both sides by 5}\\\\\dfrac{5b}{5}=\dfrac{24}{5}\\\\b=\dfrac{24}{5}\to b=4\dfrac{4}{5}\to b=4.8[/tex]
William left his house at time zero and drove to the store, which is 8 blocks away, at a speed of 2 blocks per minute. Then he stopped and went into the store for 2 minutes. From there, he drove in the same direction at a speed of 4 blocks per minute until he got to the bank, which is 16 blocks away from the store. He stopped at the bank for 5 minutes. Then he drove home at a speed of 12 blocks every minute. Make a graph showing the number of blocks away from home that William is x minutes after he leaves his house, until he get back home.
Answer:
17 minutes
Step-by-step explanation:
First distance in blocks and time.
x1= 8 b and t1 = 4 min
Second distance in blocks and time.
x2= 8 b and t2 = 6 min
Third distance in blocks and time.
x3= 24 b and t3 = 12 min
Fourth distance in blocks and time.
x4= 24 b and t4 = 17 min
Final distance in blocks and time.
x5= -24 b and t5 = 19 min
The first trap Willian is 8 blocks from home, we know that the speed is 2 b/min (blocks per minute). Using the definition of speed V1 = x1/t1 we can find t1. t1 will be t1 = 8/2 = 4 min.
He spends 2 minutes, so t2 = 6 min.
Now, the new speed is V2=4 b/min and go to the bank that is 16 blocks away from store, so x2 = 16 + 8 = 24 b. Times will be t = 24/4 = 6 min. But we need to add to t2 to get the total time. t3 = 6 + 6 = 12 min.
He spends 5 minutes here, so t4 = 12 + 5 = 17 min.
Finally, he drove home at -12 b/min, so the time to get home will be:
t = 24/12 = 2 min. Therefore, the total time t5 = 17 + 2 = 19 min.
You can learn more about velocity plots here:
https://brainly.com/question/14360042
https://brainly.com/question/18372944
I hope it helps you!
Which is a perfect square
72
81
90
99
Answer:
90
Step-by-step explanation:
90 degree angle is a perfect square
Answer:
B) 81
Step-by-step explanation:
This talented group of dogs has 25 yards of ribbon. They want to cut the ribbon to make bows and awards. If each piece of ribbon needs to be 3/4 of a yard, how many bows will they be able to make?
Answer:
18.75 bows
Step-by-step explanation:
This talented group of dogs has 25 yards of ribbon. They want to cut the ribbon to make bows and awards. If each piece of ribbon needs to be 3/4 of a yard, how many bows will they be able to make?
The total number of yards =25 yards
Each piece of ribbon = 3/4 of a yard
Hence, the number of bows they can make is:
3/4 × 25 yards
= 18.75 bows.
Can someone help me please
If the perimeter of ABC = 9.7cm,
E is the midpoint of AC, and DE||BC, find the length of DE.
Answer:
3.2333 (repeated)
3.23 (rounded
Step-by-step explanation:
ADE is 1/3 of ABC so we just divide the perimeter by 3
9.7cm / 3 = 3.2333
This rounds to: 3.23
What is 3x-4y=10 on a graph
Answer:
Step-by-step explanation:
The 9th and the 12th term of an arithmetic progression are 50 and 65 respectively find the sum of the first 70 terms
Answer:
Sum of the first 70 terms is 12,775
Step-by-step explanation:
For the 9th term, the formula is;
a + 8d = 50
For the 12th
a + 11d = 65
Subtract this from the equation above;
3d = 15
d = 15/3 = 5
To get a, we have a + 8(5) = 50
a = 10
The 70th term
will be
a + 69d
= 10 + 69(5)
= 355
Sum of the first 70
= n/2(a + L)
= 70/2( 10 + 355)
= 35 * 365 = 12,775
Lines j and k are perpendicular. The slope of line j is given. Find the slope of line k. m = 4/5
Answer:
A
Step-by-step explanation:
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{4}{5} }[/tex] = - [tex]\frac{5}{4}[/tex] → A
One lap around a dirt track i 1/3 mile. It takes bryce 1/9 hour to ride one lap. what is bryce's unit rate, in miles, around the track?
Answer:
3 mph
Step-by-step explanation:
To make 1/9 hour to 1 hour, you need to x9.
You can use this way:
Let the speed be x
(1/3)/(1/9)=x/1
1/9x=1/3
x=3
3mph
Hope is this useful :D
There are 40 DuBois students going on a field trip. Each one pays their teacher $8.75 to cover admission to the museum and lunch. Admission for the students is $120 and each one gets an equal amount to spend on lunch. How much will each DuBois student be able to spend on lunch? *
Given :
There are 40 DuBois students going on a field trip.
Each one pays their teacher $8.75 to cover admission to the museum and lunch.
Admission for the students is $120 and each one gets an equal amount to spend on lunch.
To Find :
How much will each DuBois student be able to spend on lunch.
Solution :
Amount they paid for admission :
[tex]P =\$ \dfrac{120}{40}\\\\P=\$3[/tex]
Now, amount of money to spend on lunch is $8.75 - $3 = $5.75 .
Hence, this is the required solution.
The $414 price charges a store for a small refrigerator consists of the refrigerator's original cost to the store plus a profit 15% what was the refrigerator's original cost to the store?
Answer:
$351.9Step-by-step explanation:
the question is not formatted well
A store charges $414 for a small refrigerator, the price consists of the refrigerator's original cost to the store plus a profit 15% what was the refrigerator's original cost to the store?
Step one:
given data
we are told that the price of the small refrigerator contains both the original price and 15% profit
mathematically
$414= original price + 15% profit
Step two:
let us solve for 15% of 414
=(15/100)*414
=0.15*414
=$62.1
This shows that the profit is $62.1
let the original price be x
$414= x + 62.1
solve for x
x=414-62.1
x=351.9
The refrigerator's original cost to the store $351.9
a number b divided by -3 is greater than or equal to 6
b ≤ −18 or (−∞, −18)
44735758 x 46639756-435333 divided by 48883 = what pls help will give brainleist
Answer:
2.0864648e+15
Step-by-step explanation:
Answer:
Ok this is a long one 4,792,801,917.519956
Hope this helps! But is this for a class or were you just wondering?
The top view of a portion of streets in Buffalo, New York is shown. Williams Street runs parallel to Broadway Street and the angle where the Storage is located has a measure of 120 degrees.
Identify other businesses that occupy corners with an angle measure of 120 degrees. Select all that apply.
Answer Choices:
Auto Parts
Charity
Furniture
Pharmacy
Restaurant
Answer:
Auto Parts, Furniture and restaurant.
Step-by-step explanation:
if you add furniture and pharmacy or charity with restaurant, they equal 180. so the bigger one would be 120 as lines are parallel and this is a single straight line passing through.
PLEASE HELP ME
Write the equation from each line
Answer:
1) y = 2x - 2
2) y = - x - 1
3) y = 2/3 x + 1
4) y = 4x - 4
5) y = 3x + 6
6) y = -3x -3
7) y = 3 - x
8) y = 4 - 4x
In AOPQ, OQ is extended through point Q to point R, m PQR = (4x -- 10),
mZOPQ = (x +9)", and mZQOP = (x - 5)°. Find mZPQR.
Answer:
114
Step-by-step explanation:
X + 9 + 4x - 10 + x - 5 = 180
6x - 6 = 180
6x = 186
X = 31
4(31) - 10 = 114
If I parallel m, find the value of x and y
Answer:
x=24 y=9.8
Step-by-step explanation:
5y-23=3x
47+3x+2x+13=180
What is the vertical intercept (or y-intercept) of the line below?
(0,6)
(-3,0)
Answer:
-6 ?
Step-by-step explanation:
Find the greatest common factor of 84 and 36, showing how you got your answer. Then, using complete sentences, explain what your answer means.
The greatest common factor of 84 and 36 will be 2 × 2 × 3 that is 12.
What is the greatest common factor?The term that is common in the given terms.
The terms are given below.
84 and 36
The factor of the 84 will be
84 = 2 × 2 × 3 × 7
The factor of the 36 will be
36 = 2 × 2 × 3 × 3
Then the greatest common factor of 84 and 36 will be 2 × 2 × 3 that is 12.
More about the greatest common factor link is given below.
https://brainly.com/question/282609
#SPJ1
A bus company charges $1.35 a kilometre for chartering a bus. Each bus can transport a maximum of 54 students. Assuming that the a bus is full, how much should each child pay if the distance to be covered is 50 km?
Answer:
$1.25 is the answer in my opinion
Answer:
Each child should pay $1.25
Step-by-step explanation:
$1.35 * 50 = $67.5
$67.5/54 = $1.25
PLEASE ANSWER I WILL GIVE YOU BRANLEST!!!!!!!!!
choose two rules.
Answer:
they both have a pattern and different shapes
Step-by-step explanation:
give me brainlest NOW
13. Jennifer has $900 in a savings account at the beginning of the summer. She wants to have at least $250 in the account by the end of November. She withdraws $35 each week for food and shopping. If w represents the number of weeks, which of the following inequalities could be used to solve for the amount of money she may have by the end of summer?
Answer:
455
Step-by-step explanation:
900-(35×13)=455
Hey everyone! What is -9.56 - (-1.235) = ?
Thanks!
Step-by-step explanation:
-9.56 - (-1.235)
=-9.56+1.235
=-8.325
The 7th-grade class took a survey on their favorite ice cream. 58 people said they prefer vanilla, while 28 people said they prefer chocolate. Write a ratio comparing chocolate to vanilla. (Write it in a :b form)
HELP PLEASE
classify the triangle
Answer:
I believe it would be an acute triangle.