what are the roots of the polynomial equation x3-7x=6x-12? Use a graphing calculator and a system of equations.
Answers
x3-7x-6x+12=0
x3-13x+12=0
(x-1)(x2+x-12)=0
Calculate delta of the second bracket:
delta = 1+4*12=49
sqrt(delta)=sqrt(49)=7
x_1=(-1-7)/2=-4
x_2=(-1+7)/2=3
(x-1)(x+4)(x-3)=0
Answear:
Roots: x=1, x=-4, x=3.
The roots of the polynomial equation x³ - 7x = 6x - 12 is x = 1, 3, -4 and graph is shown in the picture.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
We have a polynomial equation:
x³ - 7x = 6x - 12
[tex]\rm x^3-7x+12=6x[/tex]
x³ - 13x + 2 = 0
(x - 1)(x -3)(x + 4) = 0
x = 1, 3, -4
Thus, the roots of the polynomial equation x³ - 7x = 6x - 12 is x = 1, 3, -4 and graph is shown in the picture.
Learn more about Polynomial here:
brainly.com/question/17822016
#SPJ2
Related Questions
What is the product of the rational expressions shown below? Make sure your answer is in reduced form. x+2/x-5 times 8x/x+2
A 8x/x-5
B8x/x-5
C 8/x+2
D8/ x-5
Answers
x+2 cancels out and leaves 8x/x-5
Also, Answer A and B are the same
Factor completely 16a^3b^7 + 2a^6 b4 − 22a ^4 b^5.
2(8a3b7 + a6b4 − 11a4b5)
2a3b4(8b3 + a3 − 11ab)
a3b4(16b3 + 2a3 − 22ab)
8b3 + a3 − 11ab
Answers
so it would become 2a^3b(8b^6 + a^3 * 4 - 11ab^4)
then you would use the communitive property to re order the terms
so your answer is 2a^3b * (8b^6 + 4a^3 - 11ab^4)
Answer:
2a3b4(8b3 + a3 − 11ab)
A school typically sells 500 yearbooks each year for $50 each.
The economics class does a project and discovers that they can sell 100 more yearbooks for every $5 decrease in price.The revenue for yearbook sales is equal to the number of yearbooks sold times the price of the yearbook.
Let X represent the number of $5 decreases in price. If the expression that represents the revenue is written in the form R(X)=(500+ax)(50-bx). Find the values of a and b.
Answers
Answer: a=100 and b=5
Step-by-step explanation:
Given: A school typically sells 500 yearbooks each year for $50 each.
The economics class discovers that they can sell 100 more yearbooks for every $5 decrease in price.
Let x represents the number of $5 decreases in price.
Then the new price (in dollars)=50-5x
Total yearbook sold=500+100x
If the revenue for yearbook sales is equal to the number of yearbooks sold times the price of the yearbook.
Then the revenue function will be [tex]R(X)=(500+100x)(50-5x)[/tex]
On comparing this with the given revenue expression we get
a=100 and b=5.
In this exercise we have to calculate the values of A and B, so we have to:
[tex]A=100\\B=5[/tex]
Since the equation is:
[tex]R(X)=(500+ax)(50-bx)[/tex]
And the following information was given:
A school typically sells 500 yearbooks each year for $50 each.The economics class discovers that they can sell 100 more yearbooks for every $5 decrease in price.So knowing that by increasing 100 more books sold this is equal to A and the decrease in value is going to be equal to b.
[tex]R(X)=(500+100x)(50-5x)[/tex]
See more about equation at brainly.com/question/2263981
Indicate the equation of the line that is the perpendicular bisector of the segment with endpoints (4, 1) and (2, -5).
Answers
the mindpoint of 2 points (x1,y1) and (x2,y2) is
((x1+x2)/2,(y1+y2)/2)
so midpoint is ((4+2)/2,(1-5)/2)=(6/2,-4/2)=(3,-2)
now find the slope of the line
it is perpendicular to the line with (4,1) and (2,-5)
find the slope of th eline passing through (4,1) and (2,-5)
slope between (x1,y1) and (x2,y2) is
(y2-y1)/(x2-x1)
so the slope between (4,1) and (2,-5) is
(-5-1)/(2-4)=-6/-2=3
perpendicular lines have slopes tha tmuliplty to get -1
3 times what=-1
what=-1/3
so what is the equation of a line that passes through the point (3,-2) and has a slope of -1/3
the equation of a line that has a slope of m and passes through (x1,y1) is
y-y1=m(x-x1)
so
y-(-2)=-1/3(x-3)
y+2=-1/3(x-3)
if we want slope intercept form
y+2=-1/3x+1
y=-1/3x-1
if we want standard form
1/3x+y=-1
x+3y=-3
Answer:
The correct answer is x+3y=-3
Step-by-step explanation:
My fist step to solving this question would be to find the mid-point of the given line. The mid point of (4,1) and (2,-5) is (3,-2). The mid point is where the perpendicular bisector connects or bisects the given segment. My second step would be to graph the two given points and to connect them, forming a line. This way, I would know the slope of the line and then I would be able to find the slope of the perpendicular bisector, since the slope for perpendicular lines is the opposite reciprocal of the given line. In doing this, I discovered that the slope of the segment with the given endpoints is 3 which means that the slope of the perpendicular bisector will be x. So, so far we've got a point of intersection and a slope which is all we need to formulate the equation of the line that we are looking for.
In the end, our answer will be x+3y=-3.
The bacteria in a container quadruples every day. if there are initially 100 bacteria, write an equation that models the number of bacteria a after d days. how many bacteria will there be after 1 week?
Answers
16a = 2d
.......
16,384a = 7d
Answer:
[tex]a = 100 * 4^{d}[/tex]
In a 1 week there would be 1,638,400 bacteria
Step-by-step explanation:
Hello, great question. These types are questions are the beginning steps for learning more advanced Algebraic Equations.
Since the amount of bacteria are quadrupling every day this means that the bacteria are compounding, meaning that every time they quadruple the next day the new amount is quadrupled. Thus growing exponentially every time.
So to solve this we would need to create an exponential equation that calculates the amount of bacteria after a certain amount of days, like so...
[tex]a = 100 * 4^{d}[/tex]
If we want to calculate the number of bacteria after 1 week , we would substitute d for 7 and solve for a.
[tex]a = 100 * 4^{7}[/tex]
[tex]a = 100 * 16,384[/tex]
[tex]a = 1,638,400[/tex]
In a 1 week there would be 1,638,400 bacteria
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
The function $f$ satisfies \[f(x) + f(2x + y) + 5 x y = f(3x - y) + 2x^2 + 1\]for all real numbers $x$, $y$. determine the value of $f(10)$.
Answers
One more than 16 times the population density of New Mexico equals the population density of Texas to the nearest whole number , what is New Mexico's populations density ?
Answers
let n represent the population density of New Mexico
To solve for New Mexico's population density, we represent the given condition in a mathematical equation: '1 + 16x = y', where 'x' is the population density of New Mexico and 'y' is the Texas population density. We solve for 'x' by rearranging the equation to: 'x = (y - 1) / 16'. The specific population density of New Mexico can be calculated when the density of Texas is known.
Explanation:The seemingly complicated question is basically one about algebra. It can be expressed as: '1 + 16x = y', where 'x' is the population density of New Mexico and 'y' is the population density of Texas. To find 'x' (New Mexico's population density) given the value for 'y', we need to rearrange the equation by subtracting 1 from both sides to get '16x = y - 1', and then divide both sides by 16 to solve for 'x': 'x = (y - 1) / 16'.
Without specific population density values for Texas ('y'), we cannot compute an actual numeric value for New Mexico's population density. However, we can use this equation to perform the necessary calculations once we know the population density (per square mile, for instance) of Texas.
This focuses on math skills including algebra and application of formulas, important aspects of high school math curriculum.
Learn more about Algebra here:https://brainly.com/question/24875240
#SPJ12
The number of bacteria in a petri dishes 524 and growing at a rate of 7% every month how many bacteria will be there in seven months
Answers
Luckily, there is a quick way of doing this. Just take the original amount and multiply it by 1.07. Since there are a total of 7 months, we must multiply the original amount by 1.07 seven times.
So our answer is:
524 * 1.07^7 =
841.429 bacteria
7% = 0.07
since it is growing add that to 1 = 1.07
now that is to the power of length of time 1.07^7
now multiply
524 x 1.07^7 = 841.429 ( round answer as needed)
A certain forest covers an area of
4000
km2
. Suppose that each year this area decreases by
5.25%
. What will the area be after
14
years?
Answers
A = P(1-r)^t
A = 4000(1-0.0525)^14
A = 4000(0.9475)^14
A = 4000(0.9475)^14
A = 4000(0.470012124)
A = 1880.048
the answer is roughly 1880 square km
Answer:
Step-by-step explanation:
Thast 6% I don’t know why it’s tuping my answers different ?? I need help for this one
A cylindrical tree trunk is 14 yards high from the ground up to the lowest branch, and it measures 4 yards around. What is the volume of wood in this section of the trunk?
Answers
V=πr^2h
Given that the circumference of the figure is 4 yds, the radius will be:
C=2πr
4=2πr
hence;
r=4/(2π)
r=0.64 yds
Therefore the volume of the cylinder will be:
V=π*0.64^2*14
=17.83 cubic yards
What is #3 step by step?
Answers
(-9) - (-7) × [2 - (-9)]^2 + (-7)
-9 + 7 × [2 + 9]^2 - 7
- 9 + 7 * (11)^2 - 7
-9 + 7*121 - 7
-9 + 847 - 7
831
Given triangle JKL.
Write the coordinates of vertex J and its reflection J' across the y-axis.
Answers
When reflected across the y-axis, the y-coordinate remains unchanged. The x-coordinate changes to 5.
Therefore the reflected coordinates of J are (5, -2).
The reflected image is shown in red color in the picture below.
Answer:
After reflection across the y-axis, J' has coordinates (5, -2).
Answer:
(5, -2) = J'(-5, -2) = JStep-by-step explanation:
A hospital gives a survey to all surgical patients asking them to rate the quality of their hospital experience. One month after surgery, the hospital contacts the patients again to ask if there were any complications from the surgery. Last year, the results of the surveys showed that of the patients who had a poor hospital experience, 23% had post-surgical complications. What conclusion can be drawn from this study?
Answers
Solutions:
As given in the question , patients who had a poor hospital experience, 23% had post-surgical complications.
Option (C) appears the right choice from my point of view which is c) Most patients who have a poor hospital experience also have post-surgical complications.
The reason being , that the patients who suffer from these complications have experienced badly in the last hospital where they were diagnosed or cured.
Answer:
a) Some patients who have a poor hospital experience also have post-surgical complications.
Step-by-step explanation:
Given is :
Last year, the results of the surveys showed that of the patients who had a poor hospital experience, 23% had post-surgical complications.
The conclusion that can be drawn from this study is - Some patients who have a poor hospital experience also have post-surgical complications.
If we turn the percentage in figures, we can see that almost 2.3 person or 2 patients out of 10 patients have a poor hospital experience and also have post-surgical complications.
So, this is a low value that is why the correct answer is Some patients who have a poor hospital experience also have post-surgical complications.
given g(x)=Squareroot x-4 and h(x)=2x-8, what are the restriction on the domain of gofh?
x>?
Answers
[tex] = \sqrt{2x - 12}[/tex]
Now, there's a restriction inside the square root
Thus, 2x - 12 ≥ 0
2x ≥ 12
x ≥ 6
The domain of the (goh)(x) will be [6, ∞).
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The functions are given below.
g(x) = √(x - 4) and h(x) = 2x - 8
Then the function f of g (x) will be
(goh)(x) = g(h(x))
(goh)(x) = √((2x - 8) - 4)
(goh)(x) = √(2x - 12)
Then the domain of the (goh)(x) will be
We know that the value under the square root should be greater than zero.
2x - 12 ≥ 0
2x ≥ 12
x ≥ 6
The domain of the (goh)(x) will be [6, ∞).
More about the domain and range link is given below.
https://brainly.com/question/12208715
#SPJ2
George's page contains twice as many typed words as bills page and bills page contains 50 fewer words than Charlie's page. If each person can type 60 words per minute, after one minute, the difference between twice the number of words on bills page and the number of words on Charlie's page is 210. How many words did bills page contain initially? Use a table to organize the information.
Answers
Let:
x = number of words in George's page
y = number of words in Bill's page
z = number of words in Charlie's page
The equations formulated from the relationships would be:
x = 2y
y = z - 50
2(y - 60) - (z - 60) = 210
Simplifying the third equations:
2y - 120 - z + 60 = 210
2y - z = 210 + 120 - 60
2y - z = 270
Substituting eqn 2 to eqn 3:
2(z - 50) - z = 270
z = 370
y = 370 - 50 = 320
x = 2(320) = 640
Therefore, there are 320 words initially in Bill's page.
Please help me!! I really need it (:
Answers
it is a linear equation
if you take the negative of x and subtract 1 you get Y
so the answer is A
The cartesian coordinate system can be used to describe three dimensional space using three axes insyead of two. what are the labels
Answers
Based on its degree, what kind of polynomial is this? h(x)=-x^2+2x-5
Answers
P = 3^7 x 11^2 and Q = 3^4 x 7^3 x 11. Write as the product of prime factors the LCM of P and Q
Answers
The LCM of P and Q is found by taking the highest powers of the common prime factors from both numbers, which results in LCM(P, Q) = 37 x 73 x 112.
Explanation:To find the Least Common Multiple (LCM) of P and Q when given as products of prime factors, we look for the highest powers of the prime factors that appear in either P or Q. In this case:
P = 37 x 112Q = 34 x 73 x 11For prime factor 3, the highest power in P and Q is 37. For prime factor 11, the highest power is 112 (from P). Since prime factor 7 only appears in Q, we include it in its highest power, which is 73. Combining these, the LCM of P and Q as the product of prime factors is:
LCM(P, Q) = 37 x 73 x 112
an air traffic controller spots two planes at the same altitude flying toward each other. Their flight paths form a right angle at point p. One plane is 150 miles from point P and is moving at 450 miles per hour. The other plane is 200 miles from point P and is moving at 450 miles per hour. What is the distance s between the planes as a function of time t?
Answers
The problem states that the paths of the two planes form a right triangle, therefore this means that the distance between the two is the hypotenuse. Given that information, we can use the hypotenuse formula for finding the distance formula:
c^2 = a^2 + b^2 ---> 1
Where c is the hypotenuse, in this case the distance between the two planes.
First let us find the value of a. We know that one plane is 150 miles from point P and this distance is decreasing by a rate of 450 miles per hour, therefore a is:
a = 150 – 450 t ---> 2
We also know that the other plane is 200 miles away and this distance decreases by a rate of 450 miles per hour also, therefore b is:
b = 200 – 450 t ---> 3
Substituting equations 2 and 3 to 1:
c^2 = (150 - 450 t)^2 + (200 – 450 t)^2
c^2 = 22500 – 135000t + 202500t^2 + 40000 – 180000t + + 202500t^2
c^2 = 405,000 t^2 – 315,000 t + 62,500 (ANSWER)
If you take a certain number and add a zero to the right of it and subtract the result from 143, you'll get the tripled imagined number. What is the imagined number?
Answers
Final answer:
To find the imagined number, we need to follow the given steps: add a zero to the original number, subtract it from 143, and set the result equal to the tripled imagined number.
Explanation:
To find the imagined number in this question, we need to follow the given steps. Let's assume the original number is x. Adding a zero to the right of it gives us 10x. Subtracting this result from 143 gives us 143 - 10x. According to the question, this result is equal to the tripled imagined number, so we have 143 - 10x = 3x. To solve for x, we can rearrange the equation as 143 = 13x, and then divide both sides by 13. Therefore, the imagined number, x, is 11.
Given that the two triangles are similar, solve for x if AU = 20x + 108, UB = 273, BC = 703, UV = 444, AV = 372 and AC = 589. You must show all of your work to receive credit.
Answers
If two triangles are similar then the corresponding sides are in proportion. Thus,
AB / AU = BC / UV = AC / AV
AB / (20x+108) = 703 / 444
Where AB is equivalent to:
AB = AU + UB
AB = 20x + 108 + 273
AB = 20x + 381
Therefore going back to the first equation:
(20x + 381) / (20x + 108) = 703/444
444 (20x + 381) = 703 (20x + 108)
8880x + 169164 = 14060x + 75924
14060x - 8880x = 169164 – 75924
5180 x = 93240
x = 93240 / 5180
x = 18
Answer:
x = 18
Step-by-step explanation:
You want the value of x, given similar triangles ABC and AUV with ...
AU = 20x +108AV = 372UB = 273AC = 589Similar trianglesCorresponding sides, or their parts, of similar triangles are proportional. In this geometry, this means ...
[tex]\dfrac{AU}{UB}=\dfrac{AV}{VC}[/tex]
We know that VC = AC -AV = 589 -372 = 217, so we can write the proportion as ...
[tex]\dfrac{20x +108}{273}=\dfrac{372}{217}= \dfrac{12}{7}\\\\7(20x+108)=273(12)\qquad\text{multiply by $273\cdot12$}\\\\140x = 2520\qquad\text{subtract 756}\\\\x=\dfrac{2520}{140}=18[/tex]
The value of x is 18.
PLEASE HELP! A square piece of paper 144 mm on a side is folded in half along a diagonal. The result is a 45 -45-90 triangle. What is the length of the hypotenuse
A:140 mm
B:12 square root 2
C:280mm
D: 140 square root 2
Answers
When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the number. find the number?
Answers
Answer:x equals 12
Step-by-step explanation:
4x+40=100-x
add x to both sides
5x+40=100
Subtract 40 on both sides
5x=60
divide both sides by 5
x=12
The number is 12 from the obtained equation.
Given that, When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the number.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the unknown number be x.
4 times a number is increased by 40
=4x+40
100 is decreased by the number
= 100-x
So, equation is 4x+40=100-x
4x+x=100-40
⇒ 5x = 60
⇒ x=12
Therefore, the number is 12 from the obtained equation.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ5
What is the awnser to -10x+3(4x-2)=6
Answers
In order to solve that equation, you would need to distribute the 3 inside the parenthesis.
-10x + 3(4x - 2) = 6
-10x + 12x - 6 = 6
Then you would need to keep the variable in the left and everything else to the right - in other words, solving for x.
-10x + 12x - 6 = 6
2x = 12
x = 6
Your answer would be 6.
first, distribute
remember that a(b+c)=ab+ac
so
3(4x-2)=3(4x)+3(-2)=12x-6
so
-10x+3(4x-2)=6
-10x+12x-6=6
2x-6=6
add 6 to both sides
2x=12
divide by 2
x=6
find a positive angle less than one rotation that is coterminal with 750 degrees
Answers
To solve this problem, all you have to do is to subtract 360 degrees (equivalent to 1 rotation) from the given angle until the answer is less than 360 degrees.
1st subtraction: 750 – 360 = 390 degrees
2nd subtraction: 390 – 360 = 30 degrees
Therefore the positive angle less than one rotation that is coterminal with 750 degrees is 30 degrees.
What is the value of x?
A. 68°
B. 62°
C. 112°
D. 124°
please show your work
Answers
As the sides that subtend the angle x are of equal lengths and are joined to form a triangle, we know the only other angle (the blank one) is going to also be 56° and since angles in a triangle always add up to 180°, we just have to do:
180 - (2 × 56) = 68°
Find the standard form of the equation of the parabola with a focus at (-8, 0) and a directrix at x = 8
Answers
Answer:
x = -1/32 * y^2
Step-by-step explanation:
John must have at least 289 test points to pass his math class. He already has test scores of 72, 78, and 70. Which inequality will tell him at least how many more points he needs to pass the class
A. 72 + 78 + 70 + x < 289
B. 72 + 78 + 70 + x ≤ 289
C. 72 + 78 + 70 + x ≥ 289
D. 72 + 78 + 70 + x > 289
Answers
72+78+70+x ≥ 289
Answer:
C. [tex]72+78+70+x\geq 289[/tex]
Step-by-step explanation:
Let x represent the number of points John needs to pass the class.
We have been that John must have at least 289 test points to pass his math class. He already has test scores of 72, 78, and 70.
After scoring x points on John's total score would be [tex]72+78+70+x[/tex].
Since John needs at least 289 test points to pass his math class, so the total number of points should be greater than or equal to 289.
We can represent this information in an inequality as:
[tex]72+78+70+x\geq 289[/tex]
Therefore, the inequality [tex]72+78+70+x\geq 289[/tex] represents the number of more points John needs to pass the class.
A certain kind of bacteria growing on your kitchen counter doubles every 30 mins.. Assuming that you start with only one bacterium, how many bacteria could be present at the end of 180 mins.