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]
Does anyone know how to do it?
Answer:
x = -7º
x+59 = 52º
x+51 = 44º
Step-by-step explanation:
84 + (x+59) + (x+51) = 180º
180 - 84 = 96
x+59 + x+51 = 96
2x + 110 = 96
2x = -14
x = -7
proof:
-7+59 = 52º
-7+51 = 44º
the sum of angles in a triangle must be 180º so:
84 + 52 + 44 = 180
Answer:
∠A = 44°Step-by-step explanation:
84 + x + 59 + x + 51 = 180
2x = 180 - 84 - 59 - 51
x = -14/2
x = -7
∠A = x + 51
∠A = -7 + 51
∠A = 44°
A building has 63 apartments and 70 bathrooms. What is the ratio of apartments to bathrooms in the building?
Answer:
63:70
Step-by-step explanation:
A and B are postive integers such that 1/a + 1/b +1/ab = 1. Find ab
Answer: ab =6
have:
[tex]\frac{1}{a}+\frac{1}{b}+\frac{1}{ab}=1\\\\=>\frac{b}{ab}+\frac{a}{ab}+\frac{1}{ab}=1\\\\<=>\frac{a+b+1}{ab}=1[/tex]
=> a + b + 1 = ab
⇔ a + b + 1 - ab = 0
⇔ b - 1 - a(b - 1) + 2 = 0
⇔ (b - 1)(1 - a) = -2
because a and b are postive integers => (b - 1) and (1 - a) also are integers
=> (b - 1) ∈ {-1; 1; 2; -2;}
(1 -a) ∈ {-1; 1; 2; -2;}
because (b -1).(1-a) = -2 => we have the table:
b - 1 -1 1 2 -2
1 - a 2 -2 -1 1
a -1 3 2 0
b 0 2 3 -1
a.b 0 6 6 0
because a and b are postive integers
=> (a;b) = (3;2) or (a;b) = (2;3)
=> ab = 6
Step-by-step explanation:
an equation of the line that passes through (3, 1) and (0, 10).
Answer:
So the equation of the line that passes through (3, 1) and (0, 10) is y=-3x+10
Step-by-step explanation:
(3, 1) and (0, 10)
m=y²-y¹/x²-x¹
m=10-1/0-3
m=9/-3
m=-3
y=mx+b
y-y=m(x-x1)
y-1=-3(x-3)
y-1=-3x+9
+1 +1
y=-3x+10
Paula has 10 forks and 15 knives to place in silverware holders at the fast food restaurant where she works. She wants to distribute them equally, with no forks or knives left over. What is the greatest number of silverware holders Paula can stock?
Answer:
that answer is 5 hope you get it right
What is the sign of 9(-0.5)
Hi
For a multiplication , law sign state : if the two terms of multiplication are of the same sign, result is positive. Otherwise, it's negative
here 9 is positive, and -0.5 negative. The two terms have contrary signs, then the result will be negative.
Choose all the expressions that are equal to 34 × 8,010.
A. 8,010 × 34
B. 34 × (801 × 102)
C. 30 × 4 × 8,010
D. 34 × (8,000 + 10)
E. (30 + 4) × 8,010
Answer: A. 8,010 × 34
D. 34 × (8,000 + 10)
E. (30 + 4) × 8,010
Step-by-step explanation:
First we need to calculate 34 × 8010 = 272340
A. 8,010 × 34 = 272340
This is equal to 34 × 8010.
B. 34 × (801 × 102)
= 34 × 81702
= 2777868
This is not equal to 34 × 8010.
C. 30 × 4 × 8,010
= 961200
This is not equal to 34 × 8010.
D. 34 × (8,000 + 10)
= 34 × 8010 = 272340
This is equal to 34 × 8010.
E. (30 + 4) × 8,010
= 34 × 8010 = 272340
This is equal to 34 × 8010.
Therefore, the correct options are:
A, D, E.
What is the value of x in the equation x + 10 = 13? (4 points)
a.−3
b.3
c.13
d.23
Answer: B, x=3
Step-by-step explanation: isolate x so 13-10=3
Three friends are starting a new exercise equipment franchise. Their investments are in the ratio of 5:7:11. The smallest investor is contributing $75,000. What is the largest investor contributing?
Given:
Ratio of investments are 5:7:11.
Contribution of smallest investor = $75,000
To find:
The contribution of largest investor.
Solution:
Let the contribution of three friends be 5x, 7x and 11x respectively.
Here, 5x is smallest and 11 is largest.
The smallest investor is contributing $75,000.
[tex]5x=75000[/tex]
Divide both sides by 5.
[tex]x=15000[/tex]
Now,
[tex]\text{Contribution of largest investor}=11x[/tex]
[tex]\text{Contribution of largest investor}=11(15000)[/tex]
[tex]\text{Contribution of largest investor}=165000[/tex]
Therefore, the contribution of largest investor is $165,000.
$97.55 business breakfast, 18% tip
Answer:
115.109 or 115.11 dollars
Step-by-step explanation:
multiply 97.55 by 1.18 to get the amount.
Answer:
$17.60
Step-by-step explanation:
Have an excellent day everyone!
Tre has to pay $180 to book the recording studio plus $30 per hour of recording time. The function c(h)=30h+180 relates the total cost, c(h) of the recording session (in dollars) to the number of hours, (h) needed to record the tracks.
Answer:
1. $3302. 11.5 hoursStep-by-step explanation:
Continuation of the question:
1. Find c (5) and interpret your solution in the context of the problem 2. Find the value of h when c() = 525 and interpret your solution in the context of the problemSolution
c(h) = 30h + 1801 ...............................................
c(5) = 30*5 + 180 = $3302 ...............................................
525 = 30h + 18030h = 525 - 18030h = 345h = 345/30 h = 11.5 hoursMs. Smith bakes 6 cookies in 15 minutes.
will it take her to bake 48 cookies?
How many hours
Answer:
120 minutes or 2 hours I think
Step-by-step explanation:
ok so you want to figure out how many hours it will take for her to bake 48 cookies. It takes 15 minutes to bake 6 cookies.
So 6x8=48 cookies.
Multiply 15 minutes times 8 since one batch of cookies (6) 15 minutes long and she wants to bake 48 cookies.
15x8=120
That's 120 minutes, but you want how many HOURS it takes.
there are 60 minutes on a hour so you will take 120 divided by 60
120/60= 2
To check, multiply 60x2= 120.
Hope this helps!
3x²+5x-10=0 find the values of a,b and c
Answer:
a = 3
b = 5
c = -10
Step-by-step explanation:
ax^2+bx+c
A number line going from negative 1 to positive 1 in increments of 1. There are 4 equal spaces between each number. Is −1 4 < −3 4 ? Use the number line to explain your answer. No, because Negative one-fourth is to the left of Negative three-fourths No, because Negative one-fourth is to the right of Negative three-fourths Yes, because Negative one-fourth is to the left of Negative three-fourths Yes, becauseNegative one-fourth is to the right of Negative three-fourths
Answer:
the answer is option B no because -1/4 is to the right of -3/4
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
The numerator of a rational number is 7 less than the denominator .If the denominator is increased by 9 and the numerator by 2, we again get the same rational number. Find the Number
Answer:
5/3
Step-by-step explanation:
Let
Denominator = x
Numerator = x - 7
New
Denominator = x + 9
Numerator = x - 7 + 2
= x - 5
x / x-7 = x -5 / x + 9
Cross product
x * x + 9 = x-7 * x-5
x² + 9x = x²- 5x - 7x + 35
x² + 9x - x² + 5x + 7x - 35 = 0
21x = 35
divide both sides by 21
x = 35 / 21
= 5 / 3
x = 5/3
The rational number is 5/3
The diagram shows a periscope used to see objects that are behind or under a barrier. What makes it possible to see an object when looking through a periscope? The periscope –
A. contains mirrors that reflect the object
B. magnifies small objects so they can be seen
C. absorbs the light rays passing through it
D. separates the light into different colors
Answer: A. contains mirrors that reflect the object
Step-by-step explanation:
A periscope contains mirrors in it that are on opposite sides and are arranged in a 45° angle to each other. It works by light striking the first mirror which cause its to reflect it at a 45° angle to the next mirror.
Depending on the length of the periscope, this continues until the last mirror reflects the incoming light to the eyes of the person using the periscope thereby allowing them to see objects hidden behind or under a barrier.
help please I don't know how to do this
Answer:
1500 meters
Step-by-step explanation:
At a little-known vacation spot, taxi fares are a bargain. A 14 Mile Taxi ride takes 16 minutes and costs 11.20 you want to find the cost for a 49 mile taxi ride
Answer:
the unit price needed to calculate is $0.8 per mile
Step-by-step explanation:
Here is the complete question:
At a little-known vacation spot, taxi fares are a bargain. A 14 Mile Taxi ride takes 16 minutes and costs $11.20 you want to find the cost for a 49 mile taxi ride . What unit price do you need?
Step-by-step explanation:
To determine the unit price needed to calculate the cost for a 49 mile taxi ride, we will determine the cost of the ride per mile. To do this, let the cost per mile be $x
If it cost $11.20 for a 14 mile ride
Then, it will cost $x for a 1 mile ride
∴ x = (1 × 11.20) / 14 = 0.8
x = 0.8
The taxi ride costs $0.8 per mile.
Hence, the unit price needed to calculate is $0.8 per mile.
If desired,
To find the cost for a 49 mile taxi ride, multiply the distance traveled by the unit price,
Distance = 49 mile
Unit price = $0.8 per mile
∴ Cost for a 49 mile taxi ride = 49 × $0.8
Cost for a 49 mile taxi ride = $39.2
Hence, the cost for a 49 mile taxi ride is $39.2
HELP HELP HELP HELP HELP PLS
Which describes the solution of the inequality y > −15? Select all the points that are part of the solution.
(0, −20)
(−7, −2)
(4, −15)
(−1, −1)
solid horizontal line through (0, −15) with shading below line
dashed vertical line through (0, −15) with shading to left of line
(15, 2)
dashed horizontal line through (0, −15) with shading above line
Answer:
dashed horizontal line through (0, −15) with shading above line
Step-by-step explanation:
Answer:
Dashed horizontal line
Step-by-step explanation:
If its multiple choice and you need help just add a comment
and if you need help with any other math homework assignment or anything just DM me on ig
-Stewart.lil2
sorry me and my friend have matching usernames bc (ion een kno but yea)
Help me with the geometry work
Answer:
Step-by-step explanation:
The thing you have to realize is that the diagonals of a parallelogram bisect each other. So DF = BF. With that fact, you get
4y + 19 = 10y - 11 Add 11 to both sides
4y+19+11 = 10y-11+11 Combine
4y + 30 = 10y Subtract 4y
4y-4y +30 = 10y - 4y Combine
30 = 6y Divide by 6
y = 30/6
y = 5
Muriel says she has written a system of two linear equations that has an infinite number of solutions. One of the equations of the system is 3y = 2x – 9. Which could be the other equation?
2y = x – 4.5
y = x – 3
6y = 6x – 27
y = x – 4.5
Answer: B
Step-by-step explanation: If you divide the 3 Y to get Y by itself, you will divide 3 on both sides. So 2X/3=2X/3 and -9/3=-3
So it will be Y=2X/3-3
Solve the equation 35h+25=40h to find how many hours
__ hour(s)
What is an equation of the line that passes through the points (3, 1) and (4,4)?
Answer:
Step-by-step explanation:
y2-y1
x2-x1=
4-3
4-1 = 1/3
y=1/3x
slove the equation f-(-4)=12.
f =-8.
f =16.
f =8.
f = -9
Step-by-step explanation:
f-(-4)=12(Remove brackets)
f--4=12(Negative and negative is going to give you positive)
f+4=12(Group Like Terms)
f=12-4(Subtract)
f=8
Then that will be the final answer
Answer:
[tex]\huge\boxed{f=8}[/tex]
Step-by-step explanation:
[tex]f-(-4)=12\to f+4=12\qquad|(-)(-)\to(+)\\\\f+4=12\qquad|\text{subtract 4 from both sides}\\\\f+4-4=12-4\\\\f=8[/tex]
Someone please help me:)
Answer: D
Step-by-step explanation:
what is the point do these equation intersect x+4y=15 and 4x+5y=16
plz help An online store advertises 40% off all items and free shipping. Gretta orders a pair of shoes originally priced at $65 and pays an 8% sales tax. How much will Gretta pay in total for this transaction? Show the steps you used to arrive at your solution in a clear, organized response.
Answer:
$42.12
Step-by-step explanation:
The original price of the shoes was $65.
Everything is 40% off. Therefore, the new price of the shoes now will be the original price minus 40% of 65.
40% of 65 is 0.4(65) or $26. So, $26 was deducted.
This means that the new price will be $65-$26 or $39.
There’s also an 8% sales tax that will be applied. So, Gretta’s total will be the new price of the shoes plus the sales tax being applied to the shoes.
The sales tax is 8% of 0.08. So, when applied to the shoes, it will be: 0.08(39) or $3.12.
Therefore, the total sum Gretta will pay is $39 (the new price) + $3.12 (the sales tax) for a grand total of $42.12
The weather forecast calls for a total of 16 inches of snow over the next week. If it is estimated that 2.8 inches of snow will fall on Monday, 3.4 inches of snow will fall on Tuesday, 1.6 inches of snow will fall on Wednesday, 2.1 inches of snow will fall on Thursday, 1.7 inches of snow will fall on Friday, and 2.9 inches of snow will fall on Saturday. How much snow should fall on Sunday?
A.
3.2 inches
B.
3.6 inches
C.
1.5 inches
D.
0.5 inches
The charity gala costs a flat fee of $394, plus an additional $6 per attendee. How many attendees can there be, at most, if the budget for the charity gala is $508?
Answer:
There can be 19 attendees at most, if the budget for the charity gala is $508.
Step-by-step explanation:
From the information given, the cost of the charity gala is equal to the flat fee plus the additional cost per attendee for the number of attendees, which can be expressed as:
C=394+6a, where c is the cost of the charity gala and a is the number of attendees.
Now, you need to replace C with 508 and solve for a that is the number of attendees:
C=394+6a
508=394+6a
508-394=6a
6a=114
a=114/6
a=19
According to this, the answer is that there can be 19 attendees at most, if the budget for the charity gala is $508.
MEANING OF 万華鏡 AND ビアクガン
Answer:
kaleidoscope and Biakgan
Step-by-step explanation: