Answer:
[tex]\large \boxed{\sf \bf \ \ f(x)=(x-4i)(x+4i)(x+3)(x-5) \ \ }[/tex]
Step-by-step explanation:
Hello, the Conjugate Roots Theorem states that if a complex number is a zero of real polynomial its conjugate is a zero too. It means that (x-4i)(x+4i) are factors of f(x).
[tex]\text{Meaning that } (x-4i)(x+4i) =x^2-(4i)^2=x^2+16 \text{ is a factor of f(x).}[/tex]
The coefficient of the leading term is 1 and the constant term is -240 = 16 * (-15), so we a re looking for a real number such that.
[tex]f(x)=x^4-2x^3+x^2-32x-240\\\\ =(x^2+16)(x^2+ax-15)\\\\ =x^4+ax^3-15x^2+16x^2+16ax-240[/tex]
We identify the coefficients for the like terms, it comes
a = -2 and 16a = -32 (which is equivalent). So, we can write in [tex]\mathbb{R}[/tex].
[tex]\\f(x)=(x^2+16)(x^2-2x-15)[/tex]
The sum of the zeroes is 2=5-3 and their product is -15=-3*5, so we can factorise by (x-5)(x+3), which gives.
[tex]f(x)=(x^2+16)(x^2-2x-15)\\\\=(x^2+16)(x^2+3x-5x-15)\\\\=(x^2+16)(x(x+3)-5(x+3))\\\\=\boxed{(x^2+16)(x+3)(x-5)}[/tex]
And we can write in [tex]\mathbb{C}[/tex]
[tex]f(x)=\boxed{(x-4i)(x+4i)(x+3)(x-5)}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Find an equation in slope-intercept form of the line that has slope –9 and passes through point A(-9,-1)
Answer:
y = -9x - 82
Step-by-step explanation:
Line with slope m=-9 passing through A(x1, y1) =A(-9,-1)
y-y1 = m(x-x1)
Substitute values
y-(-1) = -9(x-(-9)
y+1 = -9x -81
y = -9x - 82
Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer. [Start 4 By 4 Matrix 1st Row 1st Column 4 2nd Column 5 3rd Column 7 4st Column 5 2nd Row 1st Column 0 2nd Column 1 3rd Column 4 4st Column 6 3rd Row 1st Column 0 2nd Column 0 3rd Column 3 4st Column 8 4st Row 1st Column 0 2nd Column 0 3rd Column 0 4st Column 1 EndMatrix ]
Answer:
Yes, it is invertible
Step-by-step explanation:
We need to find in the matrix determinant is different from zero, since iif it is, that the matrix is invertible.
Let's use co-factor expansion to find the determinant of this 4x4 matrix, using the column that has more zeroes in it as the co-factor, so we reduce the number of determinant calculations for the obtained sub-matrices.We pick the first column for that since it has three zeros!
Then the determinant of this matrix becomes:
[tex]4\,*Det\left[\begin{array}{ccc}1&4&6\\0&3&8\\0&0&1\end{array}\right] +0+0+0[/tex]
And the determinant of these 3x3 matrix is very simple because most of the cross multiplications render zero:
[tex]Det\left[\begin{array}{ccc}1&4&6\\0&3&8\\0&0&1\end{array}\right] =1 \,(3\,*\,1-0)+4\,(0-0)+6\,(0-0)=3[/tex]
Therefore, the Det of the initial matrix is : 4 * 3 = 12
and then the matrix is invertible
If a dog has 2,000,000 toys and he gives 900,000 away. Then gets 2,000 more, also looses 2,000,000. He's sad but then also got 5,000,000,000 more and gives 1,672,293 out. How much does he have now? And how much he gave away. And how much he got.
Answer:
See below.
Step-by-step explanation:
He does not have enough to loose 2,000,000 at that point, so this whole problem is nonsense.
Find the area of the shape shown below.
3.5
2
2
Answer:
26.75 units²
Step-by-step explanation:
Cube Area: A = l²
Triangle Area: A = 1/2bh
Step 1: Find area of biggest triangle
A = 1/2(3.5)(2 + 2 + 5)
A = 1.75(9)
A = 15.75
Step 2: Find area of 2nd biggest triangle
A = 1/2(5)(2)
A = 1/2(10)
A = 5
Step 3: Find area of smallest triangle
A = 1/2(2)(2)
A = 1/2(4)
A = 2
Step 4: Find area of cube
A = 2²
A = 4
Step 5: Add all the values together
A = 15.75 + 5 + 2 + 4
A = 20.75 + 2 + 4
A = 22.75 + 4
A = 26.75
Please help with this
Answer:
A
Step-by-step explanation:
● first one:
The diagonals of a rhombus are perpendicular to each others wich means that they form four right angles.
STP is one of them so this statement is true.
● second one:
If ST and PT were equal this would be a square not a rhombus.
● third one:
If SPQ was a right angle, this woukd be a square.
● fourth one:
Again if the diagonals SQ and PR were equal, this would be a square.
Simply this question and get marked branlist
Answer:
72/n^5r
Step-by-step explanation:
Answer:
Below
Step-by-step explanation:
13)
● 2d^3 × c^6 × 8d^5 × c^2
Isolate the similar terms
● (2×8)× (d^3 × d^5)×(c^6×c^2)
● 16 × d^(3+5) × c^(6+2)
● 16 × d^8 × c^8
● 16 × (dc)^8
● 16(dc)^8
■■■■■■■■■■■■■■■■■■■■■■■■■■
● 8n×r^(-4) ×9×n^(-6)×r^3
Isolate the similar terms
● (8×9)× (r^(-4)×r^3) × (n×n^(-6))
● 72 × r^(-4+3) × n^(1-6)
● 72 × r^-1 × n^(-5)
● 72 ×(1/r) × (1/n^5)
● 72/(r×n^5)
Records indicate that x years after 2008, the average property tax on a three bedroom home in a certain community was T(x) =20x^2+40x+600 dollars.
Required:
a. At what rate was the property tax increasing with respect to time in 2008?
b. By how much did the tax change between the years 2008 and 2012?
Answer:
a) 40 dollars
b) 480 dollars
Step-by-step explanation:
Given the average property tax on a three bedroom home in a certain community modelled by the equation T(x) =20x²+40x+600, the rate at which the property tax is increasing with respect to time in 2008 can be derived by solving for the function T'(x) at x=0
T'(x) = 2(20)x¹ + 40x° + 0
T'(x) = 40x+40
At x = 0,
T'(0) = 40(0)+40
T'(0) = 40
Hence the property tax was increasing at a rate of 40dollars with respect to the initial year (2008).
b) There are 4 years between 2008 and 2012. To know how much that the tax change between the years 2008 and 2012, we will find T(4) - T(0)
Given T(x) =20x²+40x+600
T(4) =20(4)²+40(4)+600
T(4) = 320+160+600
T(4) = 1080 dollars
Also T(0) =20(0)²+40(0)+600
T(0) = 0+0+600
T(0)= 600 dollars
T(4) - T(0) = 1080 - 600
T(4) - T(0) = 480 dollars
Hence, the tax has changed by $480 between 2008 and 2012
Try to get to every number from 1 to 10 using four 4's and any number of arithmetic operations (+, −, ×, ÷). You may also you parentheses.
Answer:
Step-by-step explanation:
1. 4/4+4-4=1
2. 4/4+4/4=2
3. 4+4/4-4=3
4. 4 × (4 − 4) + 4=4
5. (4 × 4 + 4) / 4=5
6. 44 / 4 − 4=6
7. 4+4-4/4=7
8. 4+4+4-4=8
9. 4+4+4/9=9
10. 44 / 4.4=10
Answer:
1 = (4 x 4)/(4 x 4) or (4 + 4)/(4 + 4) or (4 / 4) x (4 / 4) or (4 / 4)/(4 / 4)
2= (4 x 4)/(4 + 4) or 4 / ((4+4)/4)
3= (4 + 4 + 4)/4 or (4 x 4 - 4)/4
4 = 4 - (4 - 4)/4
5 = (4 x 4 + 4)/4
6 = 4 + (4 + 4)/4
7 = 4 - (4/4) + 4
8 = 4 + (4 x 4)/4
9 = 4 + 4 + (4/4)
10 - I tried the best. You might need ! or sqrt operator to get 4.
Updated:
I forgot we could use 4, 44, 444, or 4444, so that 10 could be expressed as:
10 = (44 - 4)/4
The function fix) = (x - 4)(x - 2) is shown.
What is the range of the function?
8
all real numbers less than or equal to 3
all real numbers less than or equal to -1
all real numbers greater than or equal to 3
all real numbers greater than or equal to - 1
6
2
16
2
14
COL
40
8
G D
Answer:
The range of the function f(x)= (x-4)(x-2) is all real numbers greater than or equal to -1
Step-by-step explanation:
Randy is walking home from school. According to the diagram above, what is his total distance from school to home? Show your work and include units. If he had a jet pack, would you use distance or displacement? Why?
Answer:
if he needs to walk, we can see that between the street and his house he must walk 4 times a distance of 0.5km, so this is a total of 4¨*0.5km = 2km.
Now he has a jet-pack, he can ignore the buildings and just travel in the shorter path, so we can draw a triangle rectangle, in such a way that the hypotenuse of this triangle is the distance between the home and the school.
One of the cathetus is the vertical distance, in this case, is 1km, and the other one is the horizontal distance, also 1km.
So the actual distance is given by the Pythagorean's theorem:
A^2 + B^2 = H^2
Where A and B are the cathetus, and H is the hypotenuse, then:
H^2 = 1km^2 + 1km^2
H = (√2)km = 1.41km.
Now, in the case that he has a jet-pack, he can actually go to the school using this hypotenuse line as his path, so in this case the distance and the displacement would be the same.
Distance: "how much ground an object has covered"
Displacement: "Difference between the final position and the initial position"
When he walks, the distance is 2km, but the displacement is 1.41km
When he uses the jet-pack, both the distance and the displacement are 1.41km
Answer and Step-by-step explanation:
The first thing is we can see in the image, when he walks, that between the house and his school he has to walk four times a distance of 0.5 km. The result of this is a total of 4¨*0.5 km = 2 km. The second thing is that he must walk 2 kilometers. On the other hand, if he has a jetpack, he can simply take the shorter path by ignoring all the buildings. This idea is where we can draw a triangular rectangle on the map in a way so that the hypotenuse of the triangle is the distance between the school and the home. As for the Catheti, it is a vertical distance which in this case is two blocks of 0.5 km. The result is that these catheti have a length of 2*0.5 km = 1 km. The other is the distance of the horizontal line, which is 1 km. The absolute distance of this path is given by Pythagorean's theorem, which is A^2 + B^2 = H^2. Here, A and B are the cathetus, and H is the hypotenuse, then, H^2 = 1 km^2 + 1 km^2. As well, H = (√2)km = 1.41 km. Currently, in the situation where he has a jetpack, he can literally fly to the school utilizing this hypotenuse line for the path he would need to follow. For this specific situation, the displacement, and the distance would be the exact same. The reason for this is that the definitions of displacement and distance are displacement is the difference between the final position and the initial position and distance is how much area an item has covered. Also, when he walks, the distance is 2 km and the displacement is 1.41 km. Also, when he utilizes the jet pack, the distance is equal to the displacement. Both of these are 1.41 km.
Timothy invested $2,000 in an account earning 3.5% annual interest that is compounded continuously. How long will it take the investment to grow to $3,500?
Answer: 16 years
Step-by-step explanation:
The exponential function for continuous growth is given by :-
[tex]P=Ae^{rt}[/tex]
, where A = initial amount, r= rate of growth and t = time.
As per given , we have
A= $2,000, =r 3.5%=0.035 and P= $3500
put these vales in equation , we get
[tex]3500=2000e^{0.035t}\\\\\Rightarrow\ \dfrac{3500}{2000}=e^{0.035t}\\\\\Rightarrow\ 1.75=e^{0.035t}[/tex]
Taking log on both sides , we get
[tex]\ln 1.75=0.035t\\\\\Rightarrow\ t=\dfrac{\ln1.75}{0.035}=\dfrac{0.560}{0.035}=16[/tex]
Hence, it will take 16 years to grow to $3,500.
Last Sunday, the average temperature was 8\%8%8, percent higher than the average temperature two Sundays ago. The average temperature two Sundays ago was TTT degrees Celsius. Which of the following expressions could represent the average temperature last Sunday?
Work Shown:
T = average Celsius temperature two Sundays ago
8% = 8/100 = 0.08
8% of T = 0.08T
L = average Celsius temperature last sunday
L = 8% higher than T
L = T + (8% of T)
L = T + 0.08T
L = 1.00T + 0.08T
L = (1.00 + 0.08)T
L = 1.08T
The 1.08 refers to the idea that L is 108% of T
Answer:
b and d
Step-by-step explanation:
khan
How to graph the line y=4/3x
Answer:
make a table of values
Step-by-step explanation:
then plot using those values
The required graph has been attached which represents the line y = 4/3x
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
We have been given the equation of a line below as:
y = 4/3x
Rewrite in slope-intercept form.
y = (4/3)x
Use the slope-intercept form to discover the slope and y-intercept.
Here the slope is 4/3 and y-intercept = (0, 0)
Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y values.
When substitute the value of x = 0, then the value of y = 0, and When substitute the value of x = 3, then the value of y = -4,
Hence, the graph represents the line y = 4/3x
Therefore, the required graph of the line y=4/3x will be shown in the as attached file.
Learn more about the graphs here:
brainly.com/question/16608196
#SPJ2
0 = -12 + 4y - 3x whats the slope
Answer:
3/4 is the slope
Step-by-step explanation:
We want to put this in slope intercept form
y = mx+b where m is the slope and b is the y intercept
0 = -12 + 4y - 3x
Subtract 4y from each side
-4y = -3x-12
Divide each side by -4
-4y/-4 = -3x/-4 -12/-4
y = 3/4 x +3
Answer:
Slope=3/4
Step-by-step explanation:
0=-12+4y-3x (Add 12 on the other side)
12=4y-3x (Add 3x on the other side)
3x+12=4y (Divide by 4)
y=3/4+3
a) which function has the graph with the greatest y intercept?
b) which functions have graphs with slopes less than -3
c) which functions graph is the least steep?
Answer:
a =4,b=2, c=3
Step-by-step explanation:
Solve x/5 - 1/2 = x/6 (make sure to type the number only)
X/5 -1/2 = x/6
Find the least common denominator of the 3 denominators:5,2,6
The limited is 30
Multiply all 3 fractions by 30:
6x -15 = 5x
Subtract 6x from both sides:
-15 = -x
Multiply both sides by -1:
X = 15
. Simplify the sum. (2u3 + 6u2 + 2) + (7u3 – 7u + 4)
Answer:
9u^3 + 6u^2 - 7u + 6
Step-by-step explanation:
Select the correct answer from each drop-down menu.
The function f is given by the table of values as shown below.
x 1 2 3 4 5
f(x) 13 19 37 91 253
Use the given table to complete the statements.
The parent function of the function represented in the table is
.
If function f was translated down 4 units, the
-values would be
.
A point in the table for the transformed function would be
.
Answer:
3^x9, 15, 33, 87, 249(4, 87) for exampleStep-by-step explanation:
a) First differences of the f(x) values in the table are ...
19 -13 = 6, 37 -19 = 18, 91 -37 = 54, 253 -91 = 162
The second differences are not constant:
18 -6 = 12, 54 -18 = 36, 162 -54 = 108
But, we notice that both the first and second differences have a common ratio. This is characteristic of an exponential function. The common ratio is 18/6 = 3, so the parent function is 3^x.
__
b) Translating a function down 4 units subtracts 4 from each y-value. The values of f(x) in the table would be ...
9, 15, 33, 87, 249
__
c) The x-values of the function stay the same for a vertical translation, so the points in the table of the transformed function are ...
(x, f(x)) = (1, 9), (2, 15), (3, 33), (4, 87), (5, 249)
Answer: I think this is it:
The parent function of the function represented in the table is exponential. If function f was translated down 4 units, the f(x)-values would be decreased by 4. A point in the table for the transformed function would be (4,87)
Step-by-step explanation: I got it right on Edmentum!
A waiter earns $11.00 an hour and approximately 10% of what he serves in a shift. If he works a 6 hour shift and takes $425 in orders, his total earnings for the six hours would be:
Answer:
108.50
Step-by-step explanation:
First find the wages
11* 6 = 66 dollars
Then figure the commission
10% of 425
.10 * 425
42.5
Add the two amounts together
42.5+66
108.50
An oblique cylinder is shown.
An oblique cylinder is shown. It has a radius of 5, a height of 12, and a slant length of 13.
Which represents the volume of the cylinder, in cubic units?
120π
130π
300π
325π
Answer:
The volume in terms of Pi is 300πStep-by-step explanation:
This problem is on the mensuration of solid shapes, an oblique cylinder.
the expression for the volume of an oblique cylinder is given as
[tex]volume= \pi r^2h[/tex]
Given data
radius r= 5
height h= 12, and
slant length of 13.
Substituting the given data into the expression we can solve for the volume below
[tex]volume= \pi* 5^2*12\\\ volume= \pi*25*12\\\ volume= \pi*300\\\ volume= 300\pi[/tex]
Answer:
300
Step-by-step explanation:
Combine like terms to create an equivalent expression. 1/7 - 3 (3/7n - 2/7)
━━━━━━━☆☆━━━━━━━
▹ Answer
1 - 9/7n
▹ Step-by-Step Explanation
1/7 - 3(3/7n - 2/7)
Remove the parentheses (Distribute -3 among the parentheses):
1/7 - 9/7n + 6/7
Calculate:
1 - 9/7n
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Answer:
1-9/7n
Step-by-step explanation:
[tex]\frac{1}{7}-3(\frac{3}{7}n-\frac{2}{7} ) \\=\frac{1}{7}-\frac{9}{7}n +\frac{6}{7} \\=\frac{1-9n+6}{7} \\=\frac{7-9n}{7}\\=1-\frac{9}{7}n[/tex]
Monique makes $11 per hour delivering pizzas. Monique works Monday
through Friday, and on average she earns $20 a day in tips. If Monique
made no less than $450 for one week, find an inequality for the number
of hours she worked
Answer:
x > 39 hours
Step-by-step explanation:
Let x be the number of hours she worked.
11x - is how much she would get paid for working for x hours
11x + 20 > 450
11x > 430
x > 39 hours
Hope that helped!!! k
Evan’s dog weighs 15 3/8 pounds. What is this weight written as a decimal? A. 15.125 Ib B. 15.375 Ib C. 15.385 Ib D. 15.625 Ib Please include ALL work!
Answer:
ok as we know 15 is a whole number by itself and 3/8 is the decimal part
so we know it is 15. something
that something is 3/8 to find decimal you do 3/8
3/8 is = .375
so 15.375 is the answer
hope it helps
brainliest give me pls
Sarah has $30,000 in her bank account today. Her grand-father has opened this account for her 15 years ago when she was born. Calculate the money that was deposited in the account 15 years ago if money has earned 3.5% p.a. compounded monthly through all these years.
Answer:
Deposit value(P) = $17,760 (Approx)
Step-by-step explanation:
Given:
Future value (F) = $30,000
Number of Year (n) = 15 year = 15 × 12 = 180 month
rate of interest (r) = 3.5% = 0.035 / 12 = 0.0029167
Find:
Deposit value(P)
Computation:
[tex]A = P(1+r)^n\\\\ 30000 = P(1+0.0029167)^{180} \\\\ 30000 = P(1.68917) \\\\ P = 17760.2018[/tex]
Deposit value(P) = $17,760 (Approx)
Zamba has found a little black dress on sale for 50% off the original price of $239.99. She also has a coupon offering free shipping and an additional 10% off of her entire online purchase. If she buys the dress and a pair of shoes costing $34.70, how much will she pay for her ensemble?
$108.00
$104.70
$94.23
$139.23
Answer:
$139.23
Step-by-step explanation:
50% off the original price of $239.99
= $239.99-(0.5*239.99)
= 239.99-119.995
= $119.995
She purchase a pair of shoes also worth $34.70
Total cost now= $119.995 + $34.70
Total cost now= $154.695
But she has a coupon that gives her 10% off her total sales
Now she wants pay
= $154.695 - 0.1(154.695)
= $154.695-15.4695
= $139.2255
Approximately $139.23
What is the solution to this system of linear equations?
y-x = 6
y + x = -10
(-2,-8)
(-8.-2)
(6.-10)
(-10.6)
Answer:
The correct answer is A
Step-by-step explanation:
Answer:
(-8, -2)
Step-by-step explanation:
y-x = 6
y + x = -10
Add the two equations together to eliminate x
y-x = 6
y + x = -10
--------------------
2y = -4
Divide by 2
2y/2 = -4/2
y = -2
Now find x
y+x = -10
-2+x = -10
x = -8
he sum of two nonnegative numbers is 300. What is the maximum value of the product of these two numbers?
Answer:
[tex]\boxed{22,500}[/tex]
Step-by-step explanation:
Hey there!
Well, half of 300 is 150, and 150•150 = 22500
So 150 and 150 are it's highest numbers.
Hope this helps :)
(Algebra) PLZ HELP ASAP!
Answer: Rational, integer, whole, natural, real
So basically everything but irrational
====================================================
Explanation:
109 is a rational number because 109 = 109/1. Any rational number is a fraction of two integers. Because of this, it cannot be irrational as "irrational" means "not rational".
An integer is anything that does not have a fractional or decimal part. So it involves the set of positive and negative whole numbers, and zero as well. So we can see that 109 is an integer.
A whole number is very similar to an integer, but we're referring to the set {0, 1, 2, 3, ..} meaning we ignore the negative integers. This makes 109 a whole number as well.
A natural number is from the set {1, 2, 3, ...}. We've kicked 0 out from the set of whole numbers. This is the set of counting numbers. So 109 is also a natural number.
A real number is any number you have encountered so far assuming your teacher has not introduced complex and imaginary numbers yet. Effectively a real number is any number that can be written as decimal. This makes 109 to be a real number.
A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. When he started his diet, he weighed 79.5 kilograms. He gained weight at a rate of 5.5 kilograms per month. Let y represent the sumo wrestler's weight (in kilograms) after x months. Which of the following could be the graph of the relationship? graph of an increasing linear function in quadrant 1 with a positive y-intercept (Choice B) B graph of an increasing linear function in quadrants 1 and 4 with a positive x-intercept and negative y-intercept (Choice C) C graph of a decreasing linear function in quadrants 1 and 4 with a positive x-intercept and positive y-intercept (Choice D) D graph of a decreasing linear function in quadrant 4 with a negative y-intercept
Answer:
(Choice A) A graph of an increasing linear function in quadrant 1 with a positive y-intercept.
Step-by-step explanation:
The weight of the sumo wrestler starts at a positive value of 79.5 kilograms, and we are given that the sumo wrestler gains a linear amount of weight per month at 5.5 kilograms per month.
If we were to graph this relationship, the sumo wrestler's weight would be represented on the y-axis, and the amount of time on the x-axis.
So the initial weight would occur at (0, 79.5) which is the positive y-intercept.
And since his weight is increasing at 5.5 kilograms per month, the slope of the linear function is positive.
Hence, the graph of the linear increasing function in quadrant 1 with a positive y-intercept.
Cheers.
Lena is comparing offers from two banks on checking accounts that include debit cards. Bank A charges $20 monthly fee for a checking account and debit card, with unlimited transactions. Bank B charged a $5 monthly fee for a checking account and debit card, plus
$ 0.50 for each transaction.
Suppose Lena makes 35 transactions in a given month.
How much would she pay at each bank for the given month?
Bank A
Bank B
For the given month, which bank is cheaper and by how much?
Bank A. is cheaper than Bank B by $
or
Bank B is cheaper than Bank A by $
Answer:
Bank A spending= $20
Bank B spending= $22.5
Bank A is cheaper with $2.5
Step-by-step explanation:
Bank A charges $20 monthly fee for a checking account and debit card, with unlimited transactions.
Sheade 35 transactions.
Total charges from bank A
= $20 monthly
Bank B charged a $5 monthly fee for a checking account and debit card, plus
$ 0.50 for each transaction.
She made 35 transactions.
Total charges on bank B= $5 + (0.5)35
Total charges on bank B= $5+17.5
Total charges on bank B= $22.5
