Answers
Related Questions
Find all rational polynomials p(x) = x3 + ax2 + bx + c such that a, b, c are
roots of the equation p(x)=0
Answers
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.
Determine algebraically if the function is even, odd or neither:f(x)=5x2+2x+1
Answers
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).
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
Answers
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 type of solution results in exactly one
x and one y value?
Answers
Answer:
An independent system of equations
finding the distance along a diagonal with the distance formula requires you evaluate a square root. true or false ?
Answers
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.
Write
[tex] \frac{10}{12} [/tex]
in simplest form
Answers
[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]
7x - 4 = -18?
please give an answer.
Answers
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
Which inequality is true when x = 4?
Answers
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.
Given that 372 × 68 = 25296 find the value of 3720 x 68
Answers
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]
Someone pls help me with these 4 questions pls asap for BRAINLIEST and 100 points
Answers
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
What is the slope of the line
Answers
The formula for finding slope using two coordinate pairs is y-y
——-
x-x
In this case, the y values are 10 and 2, and the x values are 6 and 2. If we plug these into our formula the equation is 10-2
———
6-2
10-2 is 8 and 6-2 is 4. So 8 divided by 4 would equal 2
How many groups of are there in 30?
Answers
Answer:
6
Step-by-step explanation:
divide or multiply by 5 to get 30
Answer:
??????????????????????
Parallel, perpendicular, or neither
1. Y=x+6 and x- y=2
2. X-2y=8 and y=-2x+1
Answers
Answer:
1. parallel
2. perpendicular
Step-by-step explanation:
a desk costs $145. what is the total cost of 23 desks?
Answers
Answer:
145*23=3335$
by multiplying cost by sum of desk
What is the x-coordinate of the solution to the system of equations?
3x + 5y = 10
1x + 5y = 2
Answers
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
When Zainab started work, her original hourly wage was ‘y’ dollars. Her wage was then doubled, and then increased by $4. If Zainab now gets paid $17 an hour, what was her original hourly wage?
Answers
Answer:
$6.5 dollars
Step-by-step explanation:
We can make an equation to find out the original total.
2y+4=17
(subtract 4 from both sides)
2y=13
(divide by 2)
y=6.5
Hope this helped :D
can someone pls help i need your help
Answers
hope this is helpful!
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.
which ratio is equivalent to 4:10? Choose ALL the equivalent ratios from i-ready
Answers
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
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
Answers
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
The graph of y = f(x) is shown below. What are all of the real solutions of f(x) = 0?
Answers
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.
HELP!!!!!!
Find the length of segment SV.
Answers
Answer:
how do u want the formula because there is no numbers
Find the difference of (4.2 x 103) - (2.7 x 103) Show work.
-
Answers
Answer:
154.5
Step-by-step explanation:
just inputed the equation in desmos.
Answer: 154.5
Step-by-step explanation:
4.2*103=432.6
2.7*103=278.1
432.6-278.1=154.5
the reataurant started the week with blank quarts the of olive oil
Answers
Answer:
where is the question like background info
Step-by-step explanation:
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?
Answers
Answer:
43 weeks
Step-by-step explanation:
145.40 - 37.90 = 107.5
107.5/2.50 = 43
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?
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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:
−8x−10=4x+14 what’s x
Answers
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
Write an equation in slope-intercept form for the line with slope 5 and y-intercept -2.
Answers
Slope intercept form is y=mx+b
all you have to do is substitute your given
m is your slope (5)
b is your y intercept (-2)
if a line has slope -2/3 and passes through point (-3,7) what is the y intercept
Answers
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.
PLS HELP ASAP ILL GIVE BRAINLKEST PLS THANKS
Answers
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.
if you add two obtuse angles do they sometimes make supplamentary angles?
Answers
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.