write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. Write the function in standard form. -2,3,6
Answer:
A polynomial function f of least degree = f = x³ - 7x² + 36
The function in standard form = f = x³ - 7x² + 36
Step-by-step explanation:
As given, Leading coefficient of polynomial function = 1
Also given, zeroes of the function = -2, 3, 6
for root -2 : (x - (-2)) = (x + 2)
for root 3 : ( x - 3)
for root 6 : (x - 6)
Therefore, the polynomial function becomes -
f = 1(x+2)(x-3)(x-6)
⇒f = (x+2)(x² - 6x - 3x + 18)
⇒f = (x+2)(x² - 9x + 18)
⇒f = x³ - 9x² + 18x + 2x² - 18x + 36
⇒f = x³ - 7x² + 36
The polynomial function in standard form is [tex]f(x) = x^3 - 8x^2 +9x +18[/tex]
The zeros of the polynomial are given as:
[tex]Zeroes = -2,3,6[/tex]
Rewrite as:
[tex]x= -2,3,6[/tex]
Express the zeroes as an equation
[tex]x= -2[/tex], [tex]x =3[/tex] and [tex]x =6[/tex]
Equate to 0
[tex]x + 2 = 0[/tex], [tex]x -3 = 0[/tex] and [tex]x -6 = 0[/tex]
Multiply the equations
[tex](x + 1) \times (x - 3) \times (x - 6) = 0 \times 0 \times 0[/tex]
[tex](x + 1) \times (x - 3) \times (x - 6) = 0[/tex]
Expand
[tex](x^2 - 3x + x - 3) \times (x - 6) = 0[/tex]
[tex](x^2 - 2x - 3) \times (x - 6) = 0[/tex]
Expand
[tex]x^3 - 2x^2 - 3x -6x^2 +12x +18 = 0[/tex]
Collect like terms
[tex]x^3 - 2x^2 -6x^2 - 3x +12x +18 = 0[/tex]
[tex]x^3 - 8x^2 +9x +18 = 0[/tex]
Express as a function
[tex]f(x) = x^3 - 8x^2 +9x +18[/tex]
Hence, the function in standard form is [tex]f(x) = x^3 - 8x^2 +9x +18[/tex]
Read more about functions at:
https://brainly.com/question/20510856
A series of books is published at 4-year intervals. When the fifth book is issued, the sum of the publication’s years will be 10,020. When was the first books published?
Answer:
The first book was published in 1816.
Step-by-step explanation:
A series of books is published at 4-year intervals.
This means that:
The first book is published at year x.
The second book is published at year x + 4.
The third book is published at year x + 4 + 4 = x + 8
The fourth book is published at year x + 8 + 4 = x + 12
The fifth book is published at year x + 12 + 4 = x + 16
When the fifth book is issued, the sum of the publication’s years will be 10,020.
This means that:
[tex]x + x + 4 + x + 8 + x + 12 + x + 16 = 10020[/tex]
[tex]5x + 40 = 10020[/tex]
When was the first books published?
This is x. So
[tex]5x + 40 = 10020[/tex]
[tex]5x = 9080[/tex]
[tex]x = \frac{9080}{5}[/tex]
[tex]x = 1816[/tex]
The first book was published in 1816.
Shawn bought fruit last week, consisting of 2.26 pounds of bananas, 1.5 pounds of grapes,and a watermelon that weighed 6.78 pounds.
What is the total weight, in pounds, of the fruit that Shawn bought last week?
Answer:
not sure but i think it should be 10.54
Can somebody plz help!!
Answer:
A
Step-by-step explanation:
there are 4 columns and 1 drama so it equals 1/4
Use the exchange rate £1 = $1.38 to convert $276 into £.
Answer:
£200
Step-by-step explanation:
Traditionally, the earth's surface has been modeled as a sphere, but the World Geodetic System of 1984 (WGS-84) uses an ellipsoid as a more accurate model. It places the center of the earth at the origin and the north pole on the positive z-axis. The distance from the center to the poles is 6356.523 km and the distance to a point on the equator is 6378.137 km.
A) Find an equation of the earth's surface as used by WGS-84.
B) Curves of equal latitude are traces in the planes z = k. What is the shape of these curves?
C) Meridians (curves of equal longitude) are traces in planes of the form y=mx. What is the shape of these meridians?
Answer: You are smart, figure it out yourself
Step-by-step explanation:
What is 3/5 times 6/5
Answer is 0:72
hope it is helpful
Answer:
18/25
Step-by-step explanation:
pls help solve question 3
Answer:
If m is the midpoint of ab it means am is equal to mb
am = 3x + 8 and mb = 6x-4
and ab = am + mb
first find the value of x by using am = mb
3x + 8 = 6x - 4
8 + 4 = 6x - 3x
12 = 3x
x = 4
ab = 3 (4) + 8
= 12 + 8 = 20 = mb
ab = am + mb
= 20 + 20
40
so, the value of ab is 40
You have two cats. Each cat has a litter of K kittens. Write an expression that describes a total number of cats and kittens you have.
What percent of 40 is 14?
First translate the question into an equation.
"What percent" means x/100, "of 40" means times 40, "is 14" equals 14.
So we have (x)(40) = 14 or 40x = 14.
Dividing both sides by 40, we find that x = 0.35.
Now, we want to write our answer as a percent.
So we move the decimal 2 places to the right and we have 35%.
33/50
13/20
18/25
51/75
3/5
least to greatest
Answer:
3/5, 13/20, 33/50, 51/75, 18/25
least greatest
Step-by-step explanation:
in decimal form:
.6 .65 .66 .68 .72
least greatest
PLEASE HELP FOR 20 POINTS, Yesterday, Chang planted 6 trees that were each 8 feet tall in his yard. Chang projects the trees to grow at the following annual rates over the next 5 years. Assume that x represents the amount of years from when Chang planted the trees. Which of the following equations represent the height of each of the trees in 5 years? Select all that apply.
Answer:
Its oka linden
Step-by-step explanation:
Just cause
In the geometric sequence below, what is the common ratio?
80, 40, 20, 10...
121/2% in to a fraction
9514 1404 393
Answer:
1/8
Step-by-step explanation:
You can replace % with /100 to make it a fraction.
12 1/2% = (12 1/2)/100 = (25/2)/100 = 25/200 = 1/8
__
Or, you can reduce the decimal fraction.
12.5% = 12.5/100 = 0.125 = 125/1000 = 1/8
2. Identify the Formula for finding the nth term of an Arithmetic Sequence, where A(n) is the nth term of an Arithmetic Sequence, is the first term, n is the term number and d is the common
difference
A(n) = 2 - 1 + (n - 1)d
A(n) = a + (n - 1)d
A(n) = a + (n)(d - 1)
O A(n) = a + (n + 1)d
Answer:
A(n) = a + (n - 1)d is the correct formula for an arithmetic sequence.
Step-by-step explanation:
- 1/2 + (3/4 X 4/9) =
Answer:
= 0.16666666666, hope it helps
Answer:
you can use fac caul the answer i got was 1/6 and decemal format is 0.1666667
a car can drive 165 miles in 5 hours.
how many yards can thee car travel in a hour
Answer: 58,080 yards in one hour.
Step-by-step explanation:
1. 165 miles ÷ 5 = 33 miles per hour
2. 1 mile = 1760 yards
3. 1760 x 33 = 58,080 yards.
4. 58,080 yards per hour.
Therefore the car travels 58,080 yards in 1 hour.
Happy black history months!!!!!!!
Answer:
Thank You!
Step-by-step explanation:
Answer:
Happy black history months!!!!!!!
to you too
Step-by-step explanation:
3x - 2(6 - x) = 7x + 2(5 + x) - 6
What is the answer
Answer:
x= -4
Step-by-step explanation:
Answer: x = -4
Step-by-step explanation:
first, we remove the parentheses.
3x - 12 + 2x = 7x + 10 + 2x - 6
then, we cancel equal terms.
3x - 12 = 7x + 10 - 6
then, we calculate.
3x - 12 = 7x + 4
next, we move the terms.
3x - 7x = 4 + 12
then, we collect like terms and calculate.
-4x = 16
finally, we divide both sides.
x = -4
Which statement best describes the area of Triangle ABC shown below? A triangle ABC is shown on a grid. The vertex A is on ordered pair 4 and 6, vertex B is on ordered pair 6 and 1, and the vertex C is on ordered pair 2 and 1. It is twice the area of a rectangle of length 4 units and width 5 units. It is one-half the area of a rectangle of length 4 units and width 5 units. Correct Answer It is twice the area of a square of side length 5 units. It is one-half the area of a square of side length 5 units.
Answer:
Hello there! This answer would be.. It is one-half the area of a rectangle of length 4 units and width 5 units.
Answer:
What Livv said :)
Step-by-step explanation:
10. Sarah finances $549,000 with a 30/6 balloon mortgage at 5.35%. How much will she pay for principal and interest over the life of the loan? (3 points)
$715,175.04
O $713,297.14
O $717,393.12
O $719,607.40
Answer:
$717,393.12
Step-by-step explanation:
The 30/6 balloon mortgage means that she would make monthly payments for the first six years, while the balance outstanding after 6 years is paid by making one large payment.
The 30 implies that monthly payment should be computed on the basis it is a 30-year mortgage.
Loan amount=monthly payment*(1-(1+r)^-n/r
loan amount=$549,000
monthly payment=the unknown
r=monthly interest rate=5.35%/12=0.004458333
n=number of monthly payments in 30 years=30*12=360
549000=monthly payment*(1-(1+0.004458333)^-360/0.004458333
549000=monthly payment*(1-0.201607475)/0.004458333
549000=monthly payment*0.798392525/0.004458333
monthly payment=549000*0.004458333/0.798392525=$ 3,065.69
Total monthly payments for6 years=$ 3,065.69*12*6=$220,729.68
The ballon payment is the present value of monthly payments for 24 years remaining
Financial calculator:
N=288(24*12)
PMT=3065,69(monthly payment)
I/Y=5.35/12(monthly interest rate)
FV=0(balance after payments is nil)
CPT PV=$496,663.41
Total payments=$496,663.41 +$220,729.68=$717,393.09
If 4 dollars can be exchanged for 114.12 Russian rubles, how many Russian rubles can be obtained for 1500 dollars?
Answer:
42,795
Step-by-step explanation:
114.12/4=28.53
28.53x1500=42,795
Jermey swims 10 laps in 15 minutes. How many minutes per lap is that?
Answer:
1,5
Step-by-step explanation:
Answer:
1.5 minutes
Step-by-step explanation:
If he swims 10 laps in 15 minutes, then the answer can be found with the ratio 15 : 10. Simplifying the ratio, it becomes 1.5 : 1, or 1.5 minutes per 1 lap
Need help ASAP highschool level math
Answer:
The solution for the system of equations is (2, 4). This means that for February, both the number of imports and the number of exports was 4.
Step-by-step explanation:
Again, remember that the solutions for a system, in this case two charts, are where the outputs (exports) are the same.
We can see that the exports for both f(x) and g(x) are the same for the month of February (second month).
This means that the solution to our system of equations is (2, 4).
So, the solution means that for the second month February, the number of imports was equivalent to the number of exports: both are 4.
(And lastly, out of the four months given, only February had the same number of imports and exports.)
125% • n=45..............
Answer:
125% = 1.25 x 45 = 56.25
Step-by-step explanation:
First 125% as a decimal is 1.25 and the . means multiply if n=45 so 1.25 x 45 = 56.25
Which is the better buy 30lb 25.20 20lb 17.20
Answer:
depends on what your using it for but i think the 2 one
Step-by-step explanation:
50 points! Due in 20 minutes! So hurry ! no random answers please. Will mark brainliest:)
y = (x – 6)2 - 4
Find the inverse
Answer:
y = (x + 16)/2
Step-by-step explanation:
y = (x - 6)2 - 4 Switch the x and y variables
x = (y - 6)2 - 4 Solve the (y - 6)2
x = 2y - 12 - 4 Combine like terms
x = 2y - 16 Isolate the y variable
x + 16 = 2y
y = (x + 16)/2 <----- This is your answer
Hope this helps!
Jack was 14 years older than Priscilla. Together their ages totaled 158 years. What were their ages?
Answer:
Jack's age: 86, Priscilla's age: 72
Step-by-step explanation:
Priscilla's age can be called x, which makes Jack's x + 14. We know that their added ages total 158 years which means that x + x + 14 = 158, which means that 2x + 14 = 158. We can then solve this by subtracting 14 on both sides and getting 2x = 144. We can divide on both sides to get that x = 72. Since Priscilla's age is x and Jack's is x + 14, we already know Priscilla's age and we need to find Jacks by adding 14 to 72. 72 + 14 = 86, so Jack's age is 86.
Answer:
Jack is 86 years old,
and Priscilla is 72 years old
Step-by-step explanation:
j = Jack
p = Priscilla
j - 14 = p $\Rightarrow$ j = p+14
j+p = 158
By subsituting the value of j ( first equation) into the second equation, we get:
p+14+p = 158
2p+14 = 158
2p = 144
p = 72.
So, j = 86
choice one work less than 20 hours per week. Choice two I work more than 20 hours per week good or poor
Answer:
Is this a question? What's your question?
Step-by-step explanation: