Find the polynomial equation of lowest degree, with real coefficients and leading coefficient 1 1 that has the given roots.
Answer:
x^4 + 2x^3 + 3x^2 + 2x + 2 = 0
Step-by-step explanation:
The computation of the polynomial equation of the lowest degree is shown below
As we know that the complex roots would always arise in the conjucate pairs
As -i is a root, i is also a root
As -1 + i is a root
And, -1 is also a root
Now the polynomial equation would be
(x + i)(x - i)(x + 1 - i)(x + 1 - i) = 0
(x^2 - i^2)[(x + 1)^2 - i^2] = 0
(x^2 + 1)[(x + 1)^2 + 1] = 0
(x^2 + 1)(x^2 + 2x + 2) = 0
x^4 + 2x^3 + 3x^2 + 2x + 2 = 0
Ella invested $4,900 in an account paying an interest rate of 3% compounded monthly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $5,920?
Answer:
It would take 6 years for the value of the account to reach $5,920
Step-by-step explanation:
Principal Amount = $4900
Interest rate r = 3% = 0.03
Compounded monthly = n=12
Time t =?
Future Value = $5920
We can find time using formula: [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Putting values and solving:
[tex]A=P(1+\frac{r}{n})^{nt}\\5920=4900(1+\frac{0.03}{12})^{12t} \\5920=4900(1+0.0025)^{12t}\\5920=4900(1.0025)^{12t}\\\frac{5920}{4900}= (1.0025)^{12t}\\1.21=(1.0025)^{12t}[/tex]
Applying exponent rule; [tex]a=b^c\\c\:ln(b)=ln(a)[/tex]
[tex]12t\:ln(1.0025)=ln(1.21)\\12t\:(0.00249)=0.19062\\t=\frac{0.19062}{12*0.00249}\\t=6.3\approx6[/tex]
So, It would take 6 years for the value of the account to reach $5,920
Plz HELP BRAINLIEST IF CORRECT THANKS
Answer:
5
Step-by-step explanation:
Rise over run... slope formula:
[tex]\frac{y^2-y^1}{x^2-x^1}[/tex]
x=0, y=0
x=1, y=5
[tex]\frac{5-0}{1-0}=\frac{5}{1} =5[/tex]
I need help please:D
Answer:
17 remainder 25
Step-by-step explanation:
due in 40mins help please!!
Answer:
(4,5)
Step-by-step explanation:
what is the value of x??
please help!
Answer:
x=29
Step-by-step explanation:
the degree of a straight line is 180°
180-149
=31
x+2=31
x+2-2=31-2
x=29
Jill works 2.5 hours and earns $37.5. How many hours does she have to work to receive $240?
Order these numbers from least to greatest.
-33, 0.5, -5.87,
17/25
Answer:
-5.87,-33,0.5,17/25
Answer:
-33, -5.87, 0.5, 17/25.
Step-by-step explanation:
Thanks for the points!
Have a great day!
Stay safe and healthy!
Happy holiday seasons!
May I please have brainliest?
(3 x (6 + 4) - 22] x 2 = ?
Answer:
16
Step-by-step explanation:
[3 x (6 + 4) - 22] x 2
[3 x 10 - 22] x 2
[30 - 22] x 2
8 x 2 = 16
Select the correct answer.
Use the inverse matrix to solve this system of equations:
(4x + 3y = 7.5 7x+9z=14. 4y-z=8.3
Answer:
The answer is C.
Step-by-step explanation:
4(.032) + 3(2.458) = 7.502
7(.032) + 9(1.531) = 14.003
4(2.458) - 1.531 = 8.301
The solutions to the system of equation are x = 0.032, y = 2.458, z = 1.531 after using the inverse matrix method option (C) is correct.
What is the matrix?It is defined as the group of numerical data, functions, and complex numbers in a specific way such that the representation array looks like a square, rectangle shape.
We have a system of equations:
4x + 3y = 7.5
7x + 9z = 14
4y - z = 8.3
First we have to write above system of equation in the form of:
AX = B
[tex]\rm X = A^{-1}B[/tex]
Where A, X and B are the matrix such that:
[tex]\rm A = \left[\begin{array}{ccc}4&3&0\\7&0&9\\0&4&-1\end{array}\right][/tex]
[tex]\rm X = \left[\begin{array}{c}x\\y\\z\end{array}\right][/tex]
[tex]\rm B = \left[\begin{array}{c}7.5\\14\\8.3\end{array}\right][/tex]
[tex]\rm \left[\begin{array}{ccc}4&3&0\\7&0&9\\0&4&-1\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] \rm = \left[\begin{array}{c}7.5\\14\\8.3\end{array}\right][/tex]
Now find the determinant of matrix A
|A| = -123
[tex]\rm A^{-1}= \dfrac{Adj(A)}{Det(A)}[/tex]
After calculating, we will get:
x = 0.032, y = 2.458, z = 1.531
Thus, the solutions to the system of equation are x = 0.032, y = 2.458, z = 1.531 after using the inverse matrix method
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Solve for y.
8
= -7
y +7
Simplify your answer as much as possible.
y = 0
No
solution
3
X Х
?
Answer:
y=−1/7
for the picture is y=-57/7
Step-by-step explanation:
1. 8= -7y +7Switch:sides
-7y+7=8
subtract 7 from both sides
-7y=1
divide both sides by -7
y=−1/7
2.so for 8/y+7=-7multiply both sides by (y+7)
8/y+7(y+7)=-7(y+7)
simplify 8=-7(y+7)
flip
-7(y+7)=8
divide both sides by -7
y+7=-8/7
subtract 7 from both sides
and simplify
y=-57/7
Sasha deposited $600 in a simple-interest savings account.In one year the value of the account increased to $621.By what percentage did the value increase?
Answer:
103.5%
Step-by-step explanation:
To find the percent change you will need to divide 621 by 600.
621/600 = 1.035
Multiply 1.035 by 100 to find the percent
(1.035)(100) = 103.5
Therefore, the value increased by 103.5%.
I hope this helps!!
- Kay :)
Answer:
103.5
Step-by-step explanation:
it 30 the answer is 30
Write the equation of the line in slope-intercept form that has a slope of 3 and passes through (5, -1)
Answer:
y = 3x - 16
Step-by-step explanation:
In this question, we have to write an equation in slope-intercept form with the given information.
Slope-intercept form: y = mx + b
We already know our slope: 3
However, we don't know what are y-intercept (b) is.
To find this, plug the given information in the equation and solve for b:
-1 = 3(5) + b
-1 = 15 + b
Subtract 15 from both sides.
-16 = b
This means that our y-intercept will be -16.
Now, plug in our new information to the equation:
y = 3x - 16
The equation y = 3x - 16 will be your answer.
Answer:
y = 3x - 16
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Slope: 3
Points: (5, -1)
y = 3x + b
-1 = 3 ( 5 ) + b
-1 = 15 + b
b = -16
y = 3x - 16
How do you this? Whoever shows full work, I’ll mark brainlist
Answer:
hese angles are supplementary, and x=19 degrees
These two angles are a linear pair, meaning that they are supplementary.
This means that their angles measures must add up to 180 degrees.
65+6x+1=180
6x=114
x=19
Hope this helps!
Step-by-step explanation:
Tyreke can complete 5 problems in 8 minutes.
How long will it take him to complete 30
problems?
Answer:
48 minutes
30/5 = 6
6 x 8 = 48
Answer: 48
Step-by-step explanation:
if Tyreke can solve:
5 problems in 8 minutes
30 problems in ? minutes
(30*8)/5=48
Two angles are supplementary. The measure of the larger angle is 36 degrees less than 8 times
the measure of the smaller angle. Find the measures of both angles.
Answer:
The measures of the angles are 16° and 164°.
Step-by-step explanation:
Let the smaller angle be x and the larger angle be 8x+36.
Supplementary angles add up to 180°.
Small angle + Large angle = 180°
x + 8x + 36 = 180
9x + 36 = 180
9x = 180 - 36
= 144
x = 144 ÷ 9
x = 16
8x+36 = 8(16)+36
= 164
Shelby has x number of clothing items on her bed. She will hang 21 of the items in her closet
and will drop off of the remaining items to a local donation center. Write a function to
represent the number of items Shelby will donate as a function of x, the number of clothing items
on her bed.
Answer:
F(x)1/3x-7
Step-by-step explanation:
f(x)=(x-21)x1/
=/x-21
The number of items Shelby will donate as a function of x is f(x)=x-21.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
A function from a set X to a set Y allocates precisely one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.
Given that Shelby has x number of clothing items on her bed. She will hang 21 of the items in her closet and will drop off of the remaining items to a local donation center. Therefore, we can write,
Total number of clothes = x
Number of clothes she will keep in her closet = 21
Now, the function can be written as,
Function(x) = Number of items Shelby will donate
f(x) = x - 21
Hence, the number of items Shelby will donate as a function of x is f(x)=x-21.
Learn more about Function here:
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What is square root of 16 multiply by 35
A rectangle measures 54 feet by 72 feet. What is the length, in feet, of
the diagonal of the rectangle?
a. 48 ft
b. 90 ft
c. 110 ft
d. 2268 ft
e. 8100 ft
length (l) =54
breath (b) =72
l²+b²= diagonal²..........(Pythagoras theorem) and (all sides of rectangle are 90degree)
(54)²+(72)²=diagonal²
2916+5184=diagonal²
8100=diagonal²
90= diagonal.............(taking square root)
length of diagonal is 90ft
i hope it helps
have a nice day and thanks for asking this question
с
If 2x – 3y = 2 and xy = 8 then find the value of 4x2 +9y2.
(d) If 4x – 5y = 6 and xy = 8 then find the value of 16x2 + 25y2.
Answer:hmmmmm
Step-by-step explanation:
HELP QUICKLY PLEASE Which of these is used to find the estimated age range of a fossil?
Absolute dating
Half-life
Index fossils
Radioactive dating
Answer:
Step-by-step explanation:
Radioactive dating becouse they look how long the fossils were there
what is the product in simplest terms of the mixed number below 2 1/2 × 3 1/2
Answer:
A. 8 3/4
Step-by-step explanation:
2 1/2 x 3 1/2 =
5/2 x 7/2 =
35/4 =
8 3/4
The ration of red marbles to white ones is 13 to 12. If there are 3,081 red marbles how many white ones are there?
Answer:
2844
Step-by-step explanation:
13 is to 12 as 3081 is to x. 13/12 = 3081/x. 12 * 3081 = 13x.
36972 = 13x. divide both sides by 13, you're left with 2844.
If 140 bricks are used to build a wall 20 feet high, how many bricks will you use to build a wall 30 feet high?
Answer:
210
Step-by-step explanation:
The expression on the left side of an equation is shown below.
3(x+1)+9=0
If the equation has no solution, which expression can be written in the box on the other side of the equation?
O 3(x+4)
0 24x+6) + x
O 4(x - 3) - x
O 3(x+1)+9x
Please help with steps??? Question: Find the solution for a system of equations by elimination
2x- 3y=6
5x +7y = -14
Answer:
x = -84, y = -58
Step-by-step explanation:
2x - 3y = 6 --- Equation 1
Equation 1×5: 10x - 15y = 30 --- Equation 2
5x + 7y = -14 --- Equation 3
Equation 3×2: 10x + 14y = -28 --- Equation 4
I will eliminate 10x.
Equation 4-2:
10x - 15y - 10x + 14y = 30-(-28)
-y = 30+28
= 58
y = -58
Substitute y =-58 into Equation 1.
2x - 3y = 6
2x - 3(-58) = 6
2x - (-174) = 6
2x + 174 = 6
Find 2x.
2x = 6-174
= -168
Find x.
x = -168 ÷ 2
x = -84
The elves were busy
planting Christmas trees.
If they planted 51 rows with
14 trees in a row, how many
trees did they plant?
Can anyone please answer?
$1,000 is borrowed at an interest rate of 8% per year.
a. How much is owed at the end of one year if interest is compounded:
i. monthly?
ii. continuously?
b. How much is owed at the end of three years if interest is compounded
continuously?
Answer:
1 (240000)
2 (8000)
3(8160000)
Suppose that y varies directly with x and y = 10 when x = 20. What is y when x = 15?
Given that,
y varies directly with x and y = 10 when x = 20.
To find,
The value of y when x = 15.
Solution,
[tex]y\propto x\\\\y=kx[/tex]
Put x = 20 and y = 10
[tex]k=\dfrac{y}{x}\\\\k=\dfrac{10}{20}\\\\=\dfrac{1}{2}[/tex]
Put k = 1/2 and x = 15 to find the value of y.
[tex]y=\dfrac{1}{2}\times 15\\\\=7.5[/tex]
So, the value of y is 7.5