Answer:
Is that the entire question? I want to help but I don't see a full question it looks like half of one
Find all rational polynomials p(x) = x3 + ax2 + bx + c such that a, b, c are
roots of the equation p(x)=0
Answer:
p(x) = x³ +0x² +0x +0p(x) = x³ +x² -x -1p(x) = x³ -x² -2xStep-by-step explanation:
If the roots of p(x) are a, b, c, then it factors as ...
p(x) = (x -a)(x -b)(x -c)
and the expanded form is ...
p(x) = x^3 -(a+b+c)x^2 +(ac +b(a+c))x -abc
The requirement that the coefficients match the roots means we have three equations in three unknowns:
a = -(a+b+c)
b = ac +b(a+c)
c = -abc
The attachment shows the solutions to these equations. The solutions are found by making the substitutions ...
b = xc = ya = -(x+y)/2This leaves us with two equations in two unknowns that can be graphed on a Cartesian plane. The graph of the second equation is a circle:
x(1 -a -y) -ay = 0 ⇒ (x +1)^2 +y^2 = 1
The graph of the first equation is the union of the line y=0 and two hyperbolas. The points of intersection between this graph and the circle are ...
(x, y) = (-2, 0), (-1, -1), (0, 0) ⇒ (a, b, c) = (1, -2, 0), (1, -1, -1), (0, 0, 0)
The three polynomials that correspond to these values are shown above and in the attachment.
_____
Additional comment
There is an irrational fourth solution to the requirement that the roots match the coefficients.
Which inequality is true when x = 4?
Answer:
x + 5 < 3
Step-by-step explanation:
One inequality could be x > 3. So when x = 4 this is true because 4 is greater than 3.
what type of solution results in exactly one
x and one y value?
Answer:
An independent system of equations
This figure consists of a rectangle and semicircle.
What is the area of this figure?
Use 3.14 for π.
please help ASAP!
Answer:
46.28
Step-by-step explanation:
rectangle = 10×4 = 40 ft²
semicircle = 1/2×3.14×2×2 = 6.28 ft²
area of this figure is 40+6.28 = 46.28 ft²
PLS HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
R=11cm, r=3cm
Step-by-step explanation:
π(R²-r²) = π(121-9) = 112π cm² = 35.63cm².
hope this helps you.
The graph of y = f(x) is shown below. What are all of the real solutions of f(x) = 0?
x = -8, x = 7. It can also be put into coordinate form based off what the website is looking for.
But solutions to a quadratic equation is essentially where the line crosses the 'x' line.
can someone pls help i need your help
Answer:
12 miles
Step-by-step explanation:
You would have to divide $26.40 by $2.20 which equals 12 so she traveled 12 miles.
PLS HELP ASAP ILL GIVE BRAINLKEST PLS THANKS
Answer:
y = 3x
Step-by-step explanation:
When y = 12, x = 4
When y = 0, x = 0
The y intercept is zero.
The easiest point to see clearly is (4,12)
m = y / x because the y intercept is 0
m = 12/4 = 3
The equation of the line is
y = 3x which is the last one.
56 is what percent of 80
Answer:
70%
Step-by-step explanation:
Therefore, we can conclude that the required percentage is 70% that is 70% of 80 is 56.
Hopes This Helps :)
which ratio is equivalent to 4:10? Choose ALL the equivalent ratios from i-ready
Answer:
2:5 is the simplified form.
Step-by-step explanation:
4:10 => 4/10 => 2/5=> 2:5Conclusion:
Therefore, the simplified form of 4:10 is 2:5.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
Answer:
2:5 and 12:30
I hope this helps!
From: Aug1e
At a glass vase factory, 2 out of the last 10 vases produced were chipped. What is the experimental probability that the next vase will be chipped?
Answer:
there is a 20% chance that a vase will be cracked
Step-by-step explanation:
Answer:
2/10 = 1/5 = 0.2 = 20%
Step-by-step explanation:
What is the slope of the line
tickets at a particular movie theater have different rates for adults and children. On tuesday the theater sold 8 adult tickets and 9 tickets for 174. the next day the theater sold 5 adult tickets and 7 children tickets for 117. What is the price for the adult ticket and the price for the child ticket
Answer:
Adult = $15 pp
Child = 46 pp
Step-by-step explanation:
Let A and C be the price of Adult and Child's tickets, respectively.
We can set up equations for each of the two days, Tuesday and Wednesday. Each equation adds the totals paid for the two ticket levels and set it equal to the total income for that day:
Tues: 8A+9C=174
Wed: 5A+7C=117
We have two equations and two unknowns. Let's manipulate one of the equations in a way that allows us to eliminate one of the two variables, A or C. [One can also solve either equation to isolate one of the variables, and then use that in the second equation.]
I chose to multiply the first by 5 and the second by -8, in order to make the coefficients for A the same value in both equations, but opposite in sign:
Tues: 40A+45C = 870 [Multiply by 5]
Wed: -40A -56C = -936 [Multiply by -8]
-11C = -66 [Add the two equations]
C = 6 [Ta Da. Now use this price for a child's ticket in either of the original equations to find the cost of an adult ticket.]
8A+9C=174
8A+9*(6)=174
8A+54=174
8A = 120
A = 15
====
Use these two prices in the original equations to see if they indeed add up to the correct totals for each day.
Total Sales
Price Tues Wed Tues Wed
A 15 8 5 120 75
C 6 9 7 54 42
174 117 174 117 [The prices are correct]
Adult is $15 and child is $6
What is the value of x in the equation 2
(4x+)-(3x+2)- 8(9-x) = x
Answer:
open the bracket
(4X+)-3X-2-72+X=X
4X+(-3X)-74+X=X
X-74+X=X
2X-74=X
then collect the term
-74=X-2X
-74=-X
divide by negative every side then you get
X=74
finding the distance along a diagonal with the distance formula requires you evaluate a square root. true or false ?
Answer:
true
Step-by-step explanation:
Pythagoras is simply c² = a² + b².
so, it does not matter which side of the triangle we need, we will always have to solve a square root for the final result.
if a line has slope -2/3 and passes through point (-3,7) what is the y intercept
Answer: The y-intercept is 5.
Step-by-step explanation:
We can write what we know in the form of a slope intercept equation,
y=mx + b,
where m is the slope and b the y-intercept (the value of y when x=0).
We are given the slope:
y = -(2/3)x + b
We need a value of b that forces the line through the point (-3,7). Enter the point and solve for b:
y = -(2/3)x + b
7 = -(2/3)*(-3) + b for (-3,7)
7 = 2 + b
b = 5
The equation becomes y = -(2/3)x + 5
The y-intercept is 5.
See attachment.
Determine algebraically if the function is even, odd or neither:f(x)=5x2+2x+1
This function is neither even nor odd.
We have
f(x) = 5x² + 2x + 1
f(-x) = 5 (-x)² + 2 (-x) + 1 = 5x² - 2x + 1
- f(x) = -5x² - 2x - 1
but neither f(-x) = f(x) nor f(-x) = -f(x).
The value of y varies directly with the value of x. When y= 24, x = 4.
-
What is the value of x when y = 48?
O 6
0 8
O 28
0 288
Answer:
8
Step-by-step explanation:
whatever was done to y needs to be done to x.
in this case (y) was 2x so you need to 2x (x) making 4 into 8
Given that 372 × 68 = 25296 find the value of 3720 x 68
Answer:
252960
Step-by-step explanation:
3720 x 68 = 252960
hope it's helpful
[tex]3720 \times 68 = 372 \times 10 \times 68 = 372 \times 68 \times 10 = 25296 \times 10 = 252960[/tex]
7x - 4 = -18?
please give an answer.
Answer:
x=-2
Step-by-step explanation:
7x - 4 = -18
+ 4. +4
7x = -14
÷7. ÷7
x=-2
Answer:
x = -2Step-by-step explanation:
7x - 4 = -18?
7x - 4 = -18
7x = -18 + 4
7x = -14
x = -14 : 7
x = -2
-----------------
check
7 * (-2) - 4 = -18
-14 - 4 = -18
-18 = -18
the answer is good
Parallel, perpendicular, or neither
1. Y=x+6 and x- y=2
2. X-2y=8 and y=-2x+1
Answer:
1. parallel
2. perpendicular
Step-by-step explanation:
−8x−10=4x+14 what’s x
Answer:
x=-2
Step-by-step explanation:
−8x−10=4x+14
-8x-4x=14+10
-12x=24
[tex]\frac{-12x}{-12} = \frac{24}{-12}[/tex]
x = -2
if you add two obtuse angles do they sometimes make supplamentary angles?
Answer:
No, they can NEVER make supplementary angles.
Step-by-step explanation:
Two angles are supplementary when they add to 180 degrees. Since two obtuse angles have their angles greater than 90 degrees, they can never be supplementary. Let's take the angles as 91 degrees (the lowest whole obtuse measure). 91 + 91 = 182, which is more than 180.
Therefore, the answer is no.
Answer:
Adding two obtuse angles can never make supplementary angles.
Step-by-step explanation:
An obtuse angle has a measure of greater than 90°, and less than 180°.
Supplementary angles are two angles whose sum add up to 180°.
We must determine whether adding two obtuse angles can make them supplementary angles through the following example.
Example:Suppose that we have two obtuse angles:
m ∠ 1 = 90.1°
m∠ 2 = 90.1°
Let us add these two obtuse angles together to determine whether their sum is at most 180°.
m ∠ 1 + m ∠ 2 = ?
90.1° + 90.1° = 180.2°
Since their sum is greater than 180°, then it means that they are not supplements.
Conclusion:Adding two obtuse angles will have a sum of greater than 180°, thus making them invalid as supplementary angles.
Write an equation in slope-intercept form for the line with slope 5 and y-intercept -2.
What is the common denominator of y StartFraction y minus 3 Over 3 EndFraction in the complex fraction y StartFraction y minus 3 Over 3 EndFraction divided by five-ninths StartFraction 2 Over 3 y EndFraction?.
The common denominator of the given expression is [tex]5y+6.[/tex]
Given expression,
[tex]\dfrac{y+\frac{y-3}{3} }{\frac{5}{9} +\frac{2}{3y} }[/tex].
We have to find the common denominator.
On solving the numerator and denominator of the given expression,
[tex]\dfrac{y+\frac{y-3}{3} }{\frac{5}{9} +\frac{2}{3y} }= \dfrac{\frac{3y+y-3}{3} }{\frac{5y+6}{9y} }[/tex]
[tex]= \dfrac{\frac{4y-3}{3} }{\frac{5y+6}{9y} }[/tex]
[tex]= \dfrac{4y-3}{3} \times\dfrac{9y}{5y+6}[/tex]
Or,[tex]\dfrac{y+\frac{y-3}{3} }{\frac{5}{9} +\frac{2}{3y} }= \dfrac{3y(4y-3)}{5y+6}[/tex]
Hence the common denominator of the above expression is given by [tex]5y+6.[/tex]
For more details follow the link:
https://brainly.com/question/357568
Answer:
Not A 3y(y – 3)
Not B y(y – 3)
it is either C 3Y or D 3
Someone pls help me with these 4 questions pls asap for BRAINLIEST and 100 points
Answer:
5. (-1,-1)
6. (6,-9)
8. (1,2)
9. (-1,0)
Step-by-step explanation:
5. first you add -6 and 6 to cancel out the x and solve for y..once you have your y plug it back into the equation to find x
6. your going to subtract 7 and 8, and then 2 and 2 (this will cancel your ys). solve for x and then plug back in to solve for y.
7. plug -3x+5 into the second equation to find x then plug your x into the first equation to find y
8. same as above but with x then find y
HELP!!!!!!
Find the length of segment SV.
Answer:
how do u want the formula because there is no numbers
Sophia wants to buy a digital camera for $145.40. She has $ 37.90 and is saving $ 2.50 each week. In how many weeks will she have enough money saved to purchase the camera?
Answer:
43 weeks
Step-by-step explanation:
145.40 - 37.90 = 107.5
107.5/2.50 = 43
What is the x-coordinate of the solution to the system of equations?
3x + 5y = 10
1x + 5y = 2
Answer:
x = 4
Step-by-step explanation:
Use elimination method.
-----------------
3x + 5y = 10
-(1x + 5y) = -1(2)
-1x -5y = -2
------Simiplify------
2x = 8
x = 4
Write
[tex] \frac{10}{12} [/tex]
in simplest form
[tex]\dfrac{10}{12} = \dfrac{10 \times \tfrac 12 }{12 \times \tfrac 12} =\dfrac{5}6[/tex]
Answer:
5/6Step-by-step explanation:
10 ÷ 2/12 ÷ 2=> 5/6Conclusion:
Therefore, the simplified form of 10/12 is 5/6.
Hoped this helped.
[tex]BrainiacUser1357[/tex]