The degree 3 polynomial with the zeros {1, 4, 2} and a leading coefficient equal to 1 is:
p(x) = x^3 -7x^2 + 14x - 8
We know that for a polynomial of degree n, with a leading coefficient "a" and the zeros {x₁, x₂, ..., xₙ} can be written as:
p(x) = a*(x - x₁)*(x - x₂)*...*(x - xₙ)
Knowing that here we have a polynomial of degree n = 3, with a leading coefficient a = 1, and the zeros {1, 4, 2}
Replacing these in the above form, we get:
p(x) = 1*(x - 1)*(x - 4)*(x - 2)
Now we can expand that to get:
p(x) = (x^2 - x - 4x + 4)*(x - 2) = (x^2 - 5x + 4)*(x - 2)
p(x) = x^3 - 5x^2 + 4x - 2x^2 + 10x - 8
p(x) = x^3 -7x^2 + 14x - 8
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For brainliest answer this ASAP
The hypotenuse of a right triangle is 4 meters more than three times the length of the shorter . The length of the longer leg is less than that of the hypotenuse. Find the length of the shorter leg of the triangle .
Answer:
The hypotenuse of a right triangle is 4m longer than the shorter leg and 2m longer than the longer leg. What are the lengths of the sides?
Just for variety, consider the hypotenuse = h, the short leg h-4 and the long leg h-2.
c^2 = a^2 + b^2; so h^2 = (h-4)^2 + (h-2)^2; h^2 = h^2 - 8h + 16 +h^2 -4h +4;
h^2 -12h +20 = 0 factors to (h - 10)(h - 2) = 0 so h = 2 or h = 10
Since (h - 2) = (2 - 2) = 0 and a triangle cannot have a side of zero length, 10 is the length of the hypotenuse.
h^2 = (h-4)^2 + (h-2); 10^2 = (10-4)^2 + (10-2); (10)^2 = (6)^2 + (8)
The hypotenuse is 10 cm, short leg 6 cm and long leg 8 cm.
BC has endpoints B(5,9) and C(-4,-3). Find the coordinates of the midpoint of BC.
I need help !!
Answer:
(0.5,3)
Hope this helps..Have a good day!!
what is the angle what it use
Answer:
Which angle are you talking about please?
HURRY!!!!! HELP PLEASE!!!! NO SPAM!!!!!!!!!There are two identical oil tanks. The level of oil in Tank A is 6 ft and is drained at the rate of 0.5 ft/min. Tank B contains 10 ft of oil and is drained at the rate of 1 ft/min. After how many minutes will the level of oil in the two tanks be the same?
Answer:
8 munutes
Step-by-step explanation:
let :
x is the final level for both tanks (in ft) and
t is the time (in minutes)
the equation :
x = 6 - 0.5 t (eq.1)
x = 10 - 1t (eq.2)
eq. 1 = eq. 2
=>
6-0.5t = 10-1t
1t - 0.5t = 10-6
0.5t = 4
t = 4/0.5 = 8
t = 8 minutes
Answer: 8 minutes
Step-by-step explanation:
Write an equation for the level of oil in each tank.
Let t = the number of minutes.
Tank A: y = 6 − 0.5t
Tank B: y = 10 − 1t
Solve the system by using a table of values
When t = 8 minutes, the level in both tanks will be at 2 feet.
Hello! I really need some help with this (:
Answer:
y = 3x + 3
Step-by-step explanation:
As x increases, y increases by 3. Therefore, the slope of the function is 3.
Setting x = 0 will give an output of 3. Therefore, the y-intercept is (0, 3).
Overall, the function rule for the given data set is y = 3x + 3.
Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles.
A. 3.7 yds
B. 5.3 yds
C. 2.6 yds
D. 1.9 yds
The height of the given triangle is 3.7 yds. Therefore option A is the correct answer.
We need to find the height of the given triangle.
What is the formula to find the area of the triangle?The formula to find the area of the triangle is Area=√s(s-a)(s-b)(s-c).
Where s is the semiperimeter, a,b and c are sides of the triangle.
Now, s=6+10+14/2=15 yds
Area of a triangle=√15(15-6)(15-10)(15-14)=25.9
Area of triangle=1/2×14×h=25.9 square yds
⇒h=3.7 yds
Therefore, the height of the given triangle is 3.7 yds.
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Find the value of f(x) at the given value of x: f(x) = (x -4)(x + 3), x = 3
Answer:
-6
Step-by-step explanation:
f(x)= (3- 4)(3+3)
=( -1 )(6)
= -6
If 8x-4=12;then 2x - 1=
Answer: 21
Step-by-step explanation:
Step-by-step explanation:
tbh I have no idea
doing this for points
so yeah
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
Find the following measure for this figure.
12
10
Answer:
13 units
Step-by-step explanation:
Using the right triangle formed by the 2 legs and the slant height s
The legs are 12 and 10 ÷ 2 = 5, with hypotenuse s
Using Pythagoras' identity in the right triangle, then
s² = 12² + 5² = 144 + 25 = 169 ( take the square root of both sides )
s = [tex]\sqrt{169}[/tex] = 13
1:4 of 2,500 what is it???
Answer:
40% of 2500=
100
40
×2500
=1000
Step-by-step explanation:
Write the calculation exactly as you say it:
7000 cm² is the same area as
.......... m².
Answer:
1000cm²=0.1m²
so 7000cm²=0.7m²
Step-by-step explanation:
please mark me as brainliest
Answer:
0.7
Step-by-step explanation:
Make ratio:
1 square centimeter = 0.0001 square meter
x square meters = 7000 square centimeters
Multiply:
0.0001 × 7000 = 0.7
Hope this helped.
Whats the answer
HURRY IM BEING TIMED
Answer:
(C.
I THINK-
Step-by-step explanation:
pls look at the image and solve all.
Answer:
Solution of question number 23
Step-by-step explanation:
Given,
5a - 12
= 5 × 12
= 15 - 12
= 3 answer
[tex]\sqrt{\frac{x-4\sqrt{x}+4 }{x+4\sqrt{x} +4} }[/tex]
Answer:
\begin{bmatrix}\mathrm{Solution:}\:&\:x\ge \:0\:\\ \:\mathrm{Interval\:Notation:}&\:[0,\:\infty \:)\end{bmatrix}
\begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)=1\:\\ \:\mathrm{Interval\:Notation:}&\:f\left(x\right)=1\end{bmatrix}
Step-by-step explanation:
What is the surface area of the cylinder?
•9377 ft2
•5787 ft2
•1,156 ft2
•2891 ft2
Answer:
3631.681108 ft^2
Step-by-step explanation:
The surface area of a cylinder is
SA = 2pi r^2 + 2pi r h where r is the radius and h is the height
= 2pi (17)^2 + 2 pi (17)(17)
= 578pi +578pi
= 1156pi
Approximate pi with the pi button
3631.681108 ft^2
formula of (a^3+b^3)
Answer:
[tex](a+b)(a^2-ab+b^2)=(a^3+b^3)[/tex]
Step-by-step explanation:
f(x)=−4x
2
+5x
\text{Find }f(6)
Find f(6)
Answer:
-114
Step-by-step explanation:
f(x) = -4x^2 +5x
Let x = 6
f(6) = -4(6)^2 +5(6)
= -4(36) +30
- 144+30
= -114
Please help me with this anyone please and thank you
Answer:
w∈ {-1/5, -5/3]
If this is what you were looking for...
If 3r=4t+6, what is the value of t?
I don’t understand how taxes and discounts work in math, could someone explain to me?
Some additional context would be helpful in providing a complete answer. But the basic idea is this:
• Object ABC has a price X set on it.
• Hey, ABC is on sale! Let's say there's a 20% discount. That means 20% of the price X is subtracted from X.
• Boo, there's a 15% sales tax! This means whatever you would pay for ABC, discount included, you will ultimately have to pay an additional 15% of, or 0.15 times, that amount in tax.
Suppose you're looking to buy a T-shirt. The price tag on says it costs $25, but there's a 20% discount and a 15% sales tax.
• The discount has a value of 0.2 ($25) = $5. Subtract this from the original price, and its discounted price is $20.
• The sales tax is applied to this discounted price, and comes out to 0.15 ($20) = $3. This gets added to the discounted price, so you end up paying $23.
4(x — 8)+10 = -10
What is the solution to this equation?
Answer:
x = 3
Step-by-step explanation:
We are given the equation 4(x - 8) + 10 = -10 and are asked to find the solution, solution meaning to get x alone.
To do so, first distribute the 4 on the outside of the parenthesis to both values on the inside of the parenthesis :
4(x - 8)
(4 * x - 4 * 8)
4x - 32
4x - 32 + 10 = -10
Now combine like terms :
4x - 22 = -10
Now it's time to get x alone, first get rid of -22 by adding 22 to both sides :
4x = 12
Now get x alone by dividing both sides by 4 :
x = 3
A sequence starts 0, 5, ...
Give a rule the sequence could follow and the next 3 terms for that rule.
Give a different rule the sequence could follow and the next 3 terms for that rule.
Answer:
0, 5, 10, 15, 20
0, 5, 40, 405, 5,120
Step-by-step explanation:
One rule can be "add 5 to the previous term to get the next term."
0, 5, 10, 15, 20
Second rule:
For each term number 1, 2, 3, ..., n,
each term = 5(n - 1)^n
0, 5, 40, 405, 5,120
The next three terms for the rule Tn = a + (n-1)d will be 10,15 and 20
The next three terms for rule 5(n-1)ⁿ will be 40, 405 and 5120.
Sequences are numbers arranged in a specific pattern.
Given the sequence 0, 5...
This sequence can be an arithmetic sequence with nth term expressed as:
Tn = a + (n-1)da is the first term = 0
n is the number of terms
d is the common difference = 5 - 0 5
If n = 3
T3 = 0 + (3-1)*5
T3 = 2 * 5
T3 = 10
If n = 4
T4 = 0 + (4-1)*5
T4 = 3 * 5
T4 = 15
If n = 5
T5 = 0 + (5-1)*5
T5 = 4 * 5
T5 = 20
Hence the next three terms for the rule will be 10,15 and 20
Also, we can also use the recursive rule f(n) = 5(n-1)ⁿ
If n = 3
f(3) = 5(3-1)³
f(3) = 5(2)³
f(3) = 5 * 8
f(3) = 40
If n = 4
f(4) = 5(4-1)⁴
f(4) = 5(3)⁴
f(4) = 5 * 81
f(4) = 405
If n = 5
f(5) = 5(5-1)⁵
f(5) = 5(4)⁵
f(5) = 5 * 81
f(5) = 1024 * 5
f(5) = 5120
Hence the next three terms for the rule will be 40, 405, and 5120.
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What is the slope of the line?
y
slope = 13
slope = -3
slope =3
Answer:
slope = 3
Step-by-step explanation:
Take a look at the grid, when the x = 0, y = -2, so it means you have a function with form y = a•x - 2
Now, look at the grid lime when x = 2, at this point, y = 4. If the function doesn't had -2, y in x = 2 would be 4 + 2 = 6
Which number you multiply 2 to have 6? Number 3, so this is the slope, and the function is y = 3x -2
Answer:
3
Step-by-step explanation:
Start at the y-intercept
Slope is rise (up/down) over run (move to the right/left)
First you rise 3
And you run 1
3/1 is 3 thus 3
Find the value of x in each case
Answer: x=45
Step-by-step explanation:
To solve for x, we first need to understand the figure. We know TV and RS are parallel lines. If we extend TV to the left, we get a straight line parallel to RS. By Alternate Interior Angles, We know ∠R is equivalent to ∠T on the very left. Therefore, we can set it equal to 180° and solve.
x+2x+x=180 [combine like terms]
4x=180 [divide both sides by 4]
x=45
Now, we know x=45.
A matrix having unequal number of rows and columns is called
A
D
С
B
If mZABD = 60°, then mZDBC = [?]°
Answer:
60
Step-by-step explanation:
Since the angles are shown equal in the diagram, ABD=DBC=60
8. Define transversal lines.
Step-by-step explanation:
In geometry, a transversal is a line that intersects two or more other (often parallel ) lines. In the figure below, line n is a transversal cutting lines l and m . When two or more lines are cut by a transversal, the angles which occupy the same relative position are called corresponding angles
PLEASE HELP, I'LL MARK BRAINLIEST.. Of the 37 teachers at Francesca's high school, 9 are female. What is the ratio of the number of male teachers to the total number of teachers? Please write in decimal form
please help 15 points (picture)
Answer:
the first difference are all 20.
since the first differences of this relation are constant, it is a linear relation
Answer:
Linear because the account balance increases by a constant 20.
Step-by-step explanation:
→ The first difference is 20 for all values because :
20 - 0 = 20
40 - 20 = 20
60 - 40 = 20
80 - 60 = 20
100 - 80 = 20
