Answer:
1,-1,4,-3 so D
Step-by-step explanation:
0 = x^4 - x^3 -13x^2 + x + 12
x = 1,-1,4,-3
The final answer is -3,-1,1 and 4
What is the relation between roots and the biquadratic equation?The biquadratic equation is of the form ax⁴+bx³+cx²+dx+e and hence
The sum of roots is -b/a, the sum of the product of two roots is c/a, the sum of the product of three roots is -d/a, and the product of all four roots is e/a.
Solving the given problemThere is no specific method of solving a biquadratic equation, hence we use the trial and error method and also some form of the root.
So finding f(1) = 1-1-13+1+12 = 0 hence 1 is a root.
finding f(-1) = 1-(-1)-13-1+12 = 0 hence -1 is also a root.
So let other roots be p,q
Now we can use sum of roots formula which is p+q+1-1= 1, hence p+q=1
product of roots p*q*1*-1=12, pq= -12 substituting p = -12/q
-12/q+q = 1, multiplying q on both sides
q²-12=q, q²-q-12=0, q²-4q+3q-12 = 0, q(q-4q)+3(q-4)=0
(q-4)(q+3) = 0 hence the roots are 4,-3 also
Hence 1,-1,4, and -3 are the roots of the equation.
Learn more about the Biquadratic equation here
https://brainly.com/question/27116810
#SPJ2
These cones are similar. Find the surface
area of the smaller cone. Round to the
nearest tenth.
Answer:
33.3
Step-by-step explanation:
help me plx can somewon help me
Move the decimal so that there is one non-zero digit on the left of the decimal point. (The number of decimal spaces you move = exponent on 10) Since the decimal is moving to the left, we know the exponent is positive.
2 + 7 = 9
Answer: 9 * 10^16
Jasmine bought a game system that cost $299 before tax. The sales tax was 0.07 times the price. What was the total cost of the game system including the sales tax?
Answer:
$319.93
Step-by-step explanation:
We can find the total cost of the game system by multiplying the price before tax by 1.07.
299(1.07) = 319.93
= $319.93
Assuming these ratios stay consistent, if each plant recycled 350 total bottles in a day, plant B would recycle_______ more red bottles than plant A. Plant C would recycle________________ more red bottles than plant D.
Answer:
70
80
Step-by-step explanation:
Assuming these ratios stay consistent, if each plant recycled 350 total bottles in a day, plant B would recycle___70____ more red bottles than plant A. Plant C would recycle_____80___________ more red bottles than plant D.
A = We first multiply 150 x 2.333 (2 1/3) = 350 tbottles 60 x 2.333 = 140
B = Then multiply 350/200 = 200 x 1.75 350 tbottles RED = 120 x 1.75=210
First answer = 210-140 = B recycles 70 more than A
C = We first multiply 175 x 2 = 350 tbottles RED = 110 x 2 = 220
D = We first find LCM of 180 and 350
Then find 18x now equals 1/10 x 35x tbottles RED = 72 / 18 = 4 then 4 x 35 = 140
Second answer = 220-140 = C recycles 80 more than D.
Answer:
Plant B would recycle 60 more red bottles than plant A. Plant C would recycle 38 more red bottles than plant D.
Hope this helps!
Sorry for answering so late!
If g (x) is the inverse of f (x) and f (x) = 4 x + 12, what is g (x)
g (x) = 12 x + 4
g (x) = one-fourth x minus 12
g (x) = x minus 3
g (x) = one-fourth x minus
Answer:
[tex]g(x) = \frac{1}{4} x - 3[/tex]Step-by-step explanation:
Since g(x) is the inverse of f (x) to find g(x) must first find f-¹(x)
To find f-¹(x) equate f(x) to y
That's
f(x) = y
y = 4x + 12
Next interchange the terms x becomes y and y becomes x
That's
x = 4y + 12
Next make y the subject
4y = x - 12
Divide both sides by 4
[tex]y = \frac{1}{4} x - 3[/tex]Therefore
[tex]g(x) = \frac{1}{4} x - 3[/tex]Hope this helps you
-32= -7n-12+3n please help thanks
Answer:
5
Step-by-step explanation:
-32=-7n-12+3n
-32=-7n+3n-12
-32=-4n-12
-4n=-32+12
-4n=-20
n=-20/-4
n=5
Answer:
[tex]n=5[/tex]
Step-by-step explanation:
[tex]-32=-7n-12+3n\\\text{Combine Like Terms}\\-32=-7n+3n-12\\-32=-4n-12\\\text{Isolate the Variable}\\-32+12=-4n-12+12\\-20=-4n\\\text{Divide each side by -4}\\n=5[/tex]
If a person earned $32,000 a year and received $800 raise, what was the percent increase in her salary?
Answer:
Hey there!
This would be a 2.5% increase in salary.
Using the percent increase formula we find the answer to be a 2.5% increase.
Let me know if this helps :)
Answer:
2.5%
Step-by-step explanation:
((new - original) / original) * 100
328-320 = 8/320 = 0.025
0.025 * 100 = 2.5
What’s the mass of a liquid if its density is 0.95 G/ml and its volume is 200 ml
Answer:
190 g
Step-by-step explanation:
Mass =Density
Volume
Let the mass be x.
x/200=0.95
x=200 x 0.95
x = 190 g
Thank you!
One of the solutions of the system of equations shown in the graph has an x-value of -4. What is its corresponding integer y-value? -1 -3 0 3
Answer:
Solution: (-4,-3)
Step-by-step explanation:
We need to complete the solution set of given graph.
We are given two graph one straight line and one parabola. We can see in graph both intersect at two points.
At x=-4 and x=-1
We can easily find the value of y corresponding to the value of x using given graph.
At x=-4,
First we draw a vertical line at x=-4 and see where it cut graph. From that point draw a horizontal line and see where y-axis cut.
The value of at x=-4 would be -3
Please see the attachment and see the vertical and horizontal line.
Thus, The Solution is (-4,-3)
Select the correct answer from each drop-down menu.
35
30
25
Number of Roses
20
15
10
5
0
2
1
3
4
5
X
Number of Plants
According to the graph, the relationship between the number of rose plants and the number of roses is
Answer:
I think it is b
Step-by-step explanation:
GUYS PLEASE HELP WILL MARK BRAINLIEST
Answer:
17 in²
Step-by-step explanation:
We can break this figure into two smaller and easier figures:
The top figure (which has side lengths of 3 and 5), and the bottom figure (with sides of 1 and 2.)
Let's find the area of the top figure first. The width is 4 and the length is 5 so:
[tex]3\cdot5=15[/tex] in².
The bottom figure has a length of 2 and a width of 1. So:
[tex]2\cdot1=2[/tex] in².
Now we add these two:
[tex]15+2=17[/tex] in².
Hope this helped!
Answer:
17 square inches
Step-by-step explanation:
We cut the shape in to two bits to make it easier.
5 x 3 = 15 inches
2 x 1 = 2 inches
Now we add these together:
17 square inches.
I know I answered wrong in my first attempt but now I understand the question.
Hope this helps :D
plsssssss help me!!!!!!!!!!!!!!!!!!!!!!! it is recommended that for every 8 square feet of surface, a pond should have 2 fish. a pond that has a surface of 72 square feet should contain how many feet?
3. State the general version of the recursive formula.
72,54, 36, 18,0
Answer:
a(1) = 72
a(n) = a (n-1) - 18
Step-by-step explanation:
This is a simple series of multiplication of 18 . If we divide all the numbers by 18 we get
72/18, 54/18, 36/18. 18/18, 0/18
4 , 3 , 2 , 1 , 0
So we can see that the numbers are in decreasing order as the multiples of 18.
in other words the first term is a= 72
from which we subtract 18 and get 54 and so on.
So the general rule would be
a(1) = 72
a(n) = a (n-1) - 18
Where n and (n-1 ) are subscripts. We are just subtracting 18 from the number to get the answer.
72-18= 54
54-18= 36
36-18= 18
18-18=0
Write the equation for the following table:
X. Y.
0 3
1 7
2 11
3 15
Answer:
[tex] y = 4x + 3 [/tex]
Step-by-step explanation:
The equation of the table of values given can be written as [tex] y = 4x + 3 [/tex] .
When x = 0,
[tex] y = 4(0) + 3 [/tex]
[tex] y = 0 + 3 = 3[/tex] this corresponds with what we have in the table above.
Let's try another.
When x = 2,
[tex] y = 4(2) + 3 [/tex]
[tex] y = 8 + 3 [/tex]
[tex] y = 11 [/tex]
This also corresponds with what we have in the table.
Therefore, the equation of the table given is [tex] y = 4x + 3 [/tex] .
please help real quick
Answer:
B. 945 m^3
Step-by-step explanation:
We just need to find the volume of the big box and the small box and find the difference.
To find the volume of a box, we multiply length, width, and height
Big box:
15.3x7x10=1071
1071
Small box:
4.2x3x10=126
126
1071-126=945
945 m^3
Answer:
b
Step-by-step explanation:
In which situation can a constant of proportionality be identified A. Allison earns $8 per hour for h hours and an $8 bonus for each cell phone plans she sells. B. Ben buys x cans of dog food for $1.25 each and uses a coupon $7 off his entire purchase. C. Claire orders b books online for $4.50 each plus shipping charges $0.30 for each book. D. John runs 3 miles per day for m days in a week and bicyles 20 miles/day the remaining days in the week.
Answer:
C
Step-by-step explanation:
C is the only situation in which there is a clear constant of proportionality and no offset (no initial value). Claires rate is ($4.50 + $0.30)/book, or $4.80/book.
The height of a kicked football can be represented by the polynomial –16t2 + 47t + 3 = 0, where t is the time in seconds. Find the time in seconds of when the football hits the ground.
Step-by-step explanation:
-16t2 + 47t + 3 = 0
-16t2 + 48t - t + 3 = 0
-16t( t - 3) - 1 ( t - 3) = 0
-16t - 1 = 0. t - 3 = 0
-16t = 1 t = 3
t = 1/ - 16.
please help me with this questions. Will Mark brainliest.
Answer: 355
And 33 eggs
Step-by-step explanation:
8 × 40 = 320
7/8 × 40= 35 Add 35+320 = 355
2 × 12= 24 3/4 of 12 = 9
Add 9+24=33
You can also make an improper fraction. Multiply the denominator by the whole number then add the numerator.
2 3/4 becomes 4×2=8
8+3=11 Divide the other factor by the denominator: 12÷4=3
Then multiply by the "improper" numerator 3×11=33
8 7/8 becomes 71/8
40/8=5
5×71=355
Answer:
355
Step-by-step explanation:
So, you first multiply 8 with 8 = 64
Then 64 + 7 = 71
So, 71 is the numerator and 8 stays the denominator.
Now you have 71/8 *40.
You "cut" 40 into five and 8 into 1, Because 40 divided by 8 is 5, so 40 becomes 5 and 8 becomes 1.
Now we have 71 * 5 = 355
hope it helps!
PLEASE brainliest me!
The radius of a circle is 6. Using T, which equation expresses the ratio of the circumference of the circle to the circle's diameter?
Answer:
Option (B)
Step-by-step explanation:
The given question is incomplete; here is the complete question.
The radius of a circle is 6. Using π, which equation expresses the ratio of the circumference of the circle to the circle's diameter?
A) C/6 = π
B) C/12= π
C) C = 6πr
D) C = 12πr
Formula to get the circumference of the circle is,
C = 2πr = π × D
Where C = circumference of the circle
D = Diameter of the circle
By dividing with D on both the sides of the formula,
[tex]\frac{\text{C}}{\text{D}}=\pi[/tex]
Since, diameter 'D' = 2r,
[tex]\frac{\text{C}}{\text{2r}}=\pi[/tex]
[tex]\frac{\text{C}}{2\times 6}=\pi[/tex]
[tex]\frac{\text{C}}{12}=\pi[/tex]
Therefore, equation given in Option (B) will be the correct expression.
What is the value of (-3 + 3) + (-2 + 3)?
0-5 - 61
D-5 + Bi
5 + 61
5-61
Answer:
1
Step-by-step explanation:
(-3 + 3) + (-2 + 3) =
= 0 + 1
= 1
Please answer my question
Answer:
its
1/7
step by step
Answer:
The answer is H because there are 7 balls in total and two of which is red so the possiblity of getting the red ball is 2/7
Need help with this asap.
Which of the following is a graph of f(x) =square root of x +5
Answer:
Step-by-step explanation:
You didn't include any graphs, so I can't tell you which one it is. However, the graph of [tex]f(x)=\sqrt{x+5}[/tex] looks like this:
Hope this helps!
The graph of the function [tex]\rm f(x) = \sqrt{x+5}[/tex] is attached below and this can be determined by using the rules of transformation.
Given :
[tex]\rm f(x) = \sqrt{x+5}[/tex]
The following steps can be used in order to sketch the graph [tex]\rm f(x) = \sqrt{x+5}[/tex]:
Step 1 - The rules of transformation can be used in order to sketch the graph [tex]\rm f(x) = \sqrt{x+5}[/tex].
Step 2 - First draw the graph of [tex]\sqrt{x}[/tex] which is in the shape of a parabola.
Step 3 - Now, translate the graph in the left direction, So the function of the graph obtained is [tex]\rm f(x) = \sqrt{x+5}[/tex].
The graph of the function [tex]\rm f(x) = \sqrt{x+5}[/tex] is attached below.
For more information, refer to the link given below:
https://brainly.com/question/14375099
Find the hypotenuse and the shorter leg of a30°−60°−90° triangle, if the longer leg is 9 in.
Answer:
Since it's a 30-60-90 triangle, the hypotenuse should be
6 √ 3
and the short leg is
3 √ 3
Step-by-step explanation:
Ratio:
Short side: 1
Hypotenuse: 2
Long Side: √ 3
Phillip deposited $5,670 into a savings account 19 years ago. The account has an interest rate of 4.1% and the balance is currently $12,356.04. How often does the
interest compound?
Answer:
$12165.97
Step-by-step explanation:
100 + 4.1 = 104.1%
104.1% = 1.041
$5670 x 1.041^19 = $12165.97
Answer:
daily
Step-by-step explanation:
To answer this try plugging in each type of compund: daily, monthly, quarterly, and annually.
5670(1+0.041/365)^(365*19)
= 12356.04
365= daily
so your answer would be that the interest compounds daily.
How does it do? thank you very much
sorry this subject is physic.
what is x? Please explain how you got it so I can understand for future questions.
Answer:
[tex]\boxed{x = 40}[/tex]
Step-by-step explanation:
Hey there!
Well angles like 142 and 2x + 22 equal each other because they are across from each other.
So we can set up the following,
142 = 3x + 22
Single out x
-22 to both sides
120 = 3x
Divide both sides by 3
x = 40
Hope this helps :)
Answer:
x=40
Step-by-step explanation:
142=3x+22
3x+22-22=142-22
3x=120
120/3=40
Find the slope of this graph
Two cities, A and B, are mapped on the coordinate plane. How far apart are they from each other? A. 145−−−√ units B. 97−−√ units C. 5 units D. 73−−√ units
Answer:
B
Step-by-step explanation:
From the graph we can notice that the coordinates of the cities are:
● A(2,3)
● B(6,-6)
There are many methods to figure out the distance between A and B. We will use the distance formula.
Let d be the distance between A and B.
● d = √[(2-6)^2 + (3-(-6))^2]
● d = √[(-4)^2 + (3+6)^2]
● d = √[ 4^2 + 9^2 ]
● d = √(16+81)
● d = √(97)
Answer:
The answer is B) 97 units
Step-by-step explanation:
From the graph we can notice that the coordinates of the cities are:
● A(2,3)
● B(6,-6)
There are many methods to figure out the distance between A and B. We will use the distance formula.
Let d be the distance between A and B.
● d = √[(2-6)^2 + (3-(-6))^2]
● d = √[(-4)^2 + (3+6)^2]
● d = √[ 4^2 + 9^2 ]
● d = √(16+81)
● d = √(97)
Evaluate 3a2 + 4b2 for a =
2 and b = 3.
O
168
48
O
36
Answer:
48
Step-by-step explanation:
a=2
b=3
3a^2+4b^2
3(2)^2+4(3)^2
3(2)(2)+4(3)(3)
3(4)+4(9)
12+36
48
Hope this helps ;) ❤❤❤
