Answer:
x = 2, -2
explanation:
[tex]\sf y=x^4+3x^3+x^2-12x-20[/tex]
Find a factor for this equation:
-5 < x < 5
-------------
f(-3) = 25
f(-2) = 0
f(-1) = -9
f(0) = -20
f(1) = -27
f(2) = 0
f(3) = 115
Hence found that ( x -2) and ( x + 2) are the factor of the following equation.
Divide both by the following equation:
[tex]\sf \rightarrow \dfrac{x^4+3x^3+x^2-12x-20}{\left(x-2\right)\left(x+2\right)}[/tex]
[tex]\sf \rightarrow \dfrac{\left(x-2\right)\left(x+2\right)\left(x^2+3x+5\right)}{\left(x-2\right)\left(x+2\right)}[/tex]
[tex]\sf \rightarrow x^2+3x+5[/tex]
Using quadratic formula: [tex]\sf x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ \ when \ \ ax^2 + bx + c = 0[/tex]
[tex]\sf \hookrightarrow x_{1,\:2}=\dfrac{-3\pm \sqrt{3^2-4\cdot \:1\cdot \:5}}{2\cdot \:1}[/tex]
[tex]\hookrightarrow x=-\dfrac{3}{2}+i\dfrac{\sqrt{11}}{2},\:x=-\dfrac{3}{2}-i\dfrac{\sqrt{11}}{2}[/tex]
Thus the zero's of the function are:
x = 2, -2
Answer:
[tex]x=2, x=-2[/tex]; [tex]\frac{-3\pm i\sqrt{11}}{2} \in \mathbb{C}[/tex]
Step-by-step explanation:
Zeroes are found by setting the RHS = 0.
Since the quantity [tex]x^4+3x^3+x^2-12x-20[/tex] is a 4th degree polynomial there isn't a formula that gives us the solution, so we're stuck having to divide: to do so we make THE LIST: you list the divisors of the constant term without its sign (20: 1,2,4,5,10,20), the divisor of the lead coefficient (1), and you divide the first by the second in any possible way, adding a plus or minus:
[tex]\pm1, \pm2, \pm4, \pm5,\pm10,\pm20[/tex]. At this point you just have to check, replacing each one in the equation until you find two values that work (why two? You need to lower the degree of the polynomial by two, if you found only one you'd be stuck with a third degree equation which doesn't have an "easy" solving formula).
After some adding and multiplying you find that both 2 and -2 make the expression to zero. At this point you have two options
First is to divide the given expression by[tex](x-2)(x-2)=(x^2-4)[/tex] or, as I did in the image, notice that you will end up with a 2nd degree polynomial, whose coefficient you find by multiplying and confronting with the original equation.
Either way, you will end up with
[tex](x+2)(x-2)(x^2+3x+5)=0[/tex]
First two factors will give [tex]x=-2; x=2[/tex] respectively, while the third term has no real solutions (it still offers a pair of solutions in [tex]\mathbb{C}[/tex] which I'll add for the sake of completeness, but you're most likely required to look for real solutions only).
A town's population is currently 20,000. If the population doubles every 34 years, what will
the population be 68 years from now?
Answer:
80,000
Step-by-step explanation:
20,000 x 2 = 40,000
40,000 x 2 = 80,000
(I'm pretty sure it's right if not let me know.)
Is it graph 1, 2 or 3
Solve each equation x+2y=1 and -x+y=2
Answer:
x = -1, y = 1
Step-by-step explanation:
x + 2y = 1
Subtract 2y from both sides
x + 2y - 2y = 1 - 2y (simplify) -> x= 1 - 2y
----
-x + y = 2
Subtract y from both sides
-x + y - y + 2 - y (simplify) -> -x = 2 - y
Divide both sides by -1
[tex]\frac{-x}{-1}[/tex] = [tex]\frac{2}{-1}[/tex] - [tex]\frac{y}{-1}[/tex] (simplify) -> x = -2 + y
Help asap!
Monica is making a candle by pouring melted wax into a mold in the shape of a cylinder. The radius of the cylinder’s base is 6 cm, and the height of the cylinder is 12 cm. To get the wax for the candle, Monica melts cubes of wax that are each 5 cm by 5 cm by 5 cm. How many of the wax cubes will Monica need to purchase to make the candle? (Note that Monica is not able to purchase partial
cubes). Show all your work
Answer:
Volume of the cylinder=3.14×6×6×12=1356.48
volume of one cube=5×5×5=125
divide1356.48÷125=10.85
since she can't buy partial cubes, she'll have to purchase 11 cubes
here is my question: Find the rule which gives the number of matchsticks required to make the following matchstick patterns?
Find the supplement of each angle. If the angle does not have a supplement, write None.
1.) 147
2.) 105
3.) 38
4.) 87
5.) 90
6.) 170
Answer:
{33, 75, 142, 93, 90, 10}°
Step-by-step explanation:
Two angles are supplementary when their sum is 180°. That means the supplement of an angle is the difference between that angle and 180°.
180° -{147, 105, 38, 87, 90, 170}° = {33, 75, 142, 93, 90, 10}°
an oil spill spreads 25 square meters every 1/6 hour. How much area does the oil spill cover after 2 hours?
Answer:
300 [tex]m^{2}[/tex]
Step-by-step explanation:
The spread has a rate of 25 [tex]m^{2}[/tex] per every 1/6 hour. That can be expressed as 25 [tex]m^{2}[/tex] per every 1/6 hour:
25 [tex]m^{2}[/tex]/ (1/6 hour), or
150 [tex]m^{2}[/tex]/hour
After 2 hours, the spread would be (150 [tex]m^{2}[/tex]/hour)*(2 hours) = 300 [tex]m^{2}[/tex]
need help with inscribed angles
Answer:
m∠A = 79°
m∠B = 112°
Step-by-step explanation:
A+C=180
A=180-C=180-101=79
B+D=180
B=180-D=180-68=112
What is the volume of a cylinder with a height of 4xy^4 and a radius of 2x? (The formula fo
the volume of a cylinder is V = pie r^2 h.)
Answer:
volume: [tex]\sf 16\pi x^3y^4[/tex]
given:
height: [tex]\sf 4xy^4[/tex]radius: [tex]\sf 2x[/tex]cylinder volume:
[tex]\hookrightarrow \sf \pi r^2h[/tex]
[tex]\hookrightarrow \sf \pi (2x)^2(4xy^4)[/tex]
[tex]\hookrightarrow \sf \pi (4x^2)(4xy^4)[/tex]
[tex]\hookrightarrow \sf 16\pi x^3y^4[/tex]
help me solve it please
Answer:5
Step-by-step explanation:
the lenglength of 2x2x is 10 so 2x2x. Means that x is 5
HELP ME PLEASE!!!!!!
Answer:
53 people
Step-by-step explanation:
[tex]\frac{2}{5}[/tex] × 120 = = 48
48 + 5 = 53 people
____
You've made your grade level high school, lower it to Grade 4. Thank you!
Which of the following
represents this inequality?
|3x – 4| < 6x
Answer:
x>
4
9
Step-by-step explanation:
|3x−4|<6x
Let's find the critical points of the inequality.
|3x−4|=6x
We know either3x−4=6xor3x−4=−6x
3x−4=6x(Possibility 1)
3x−4−6x=6x−6x(Subtract 6x from both sides)
−3x−4=0
−3x−4+4=0+4(Add 4 to both sides)
−3x=4
−3x
−3
=
4
−3
(Divide both sides by -3)
x=
−4
3
3x−4=−6x(Possibility 2)
3x−4+6x=−6x+6x(Add 6x to both sides)
9x−4=0
9x−4+4=0+4(Add 4 to both sides)
9x=4
9x
9
=
4
9
(Divide both sides by 9)
x=
4
9
Check possible critical points.
x=
−4
3
(Doesn't work in original equation)
x=
4
9
(Works in original equation)
Critical points:
x=
4
9
Check intervals in between critical points. (Test values in the intervals to see if they work.)
x<
4
9
(Doesn't work in original inequality)
x>
4
9
(Works in original inequality)
Answer:
x>
4
9
find the LCM of 9 and 54 using prime factorization
Find the domain and range. Show solution.
[tex]y = \frac{2}{2x} [/tex]
Domain:
Range:
We are given with a function y =2/(2x) . So , if we cancel the 2 from both numerator and denominator we are left with y = 1/x . Now , here we need to find the domain , bur let's Recall that Domain is the set of all values for which the given function is defined .Now , here , if we put x = 0 , then y will be not defined , but as for domain we need only the set of values for which the function is defined , so domain willn't include 0 , and for all real numbers except 0 , the given function is defined . So Our domain is [tex]{\boxed{\bf{(-\infty,0)\cup (0,\infty)}}}[/tex] and as this interval contains all real numbers except 0 , so domain can be further written as [tex]{\boxed{\mathbb{R}-\bf \{0\}}}[/tex] . Now , Range is the set of all output values of the function when we put the values of domain as input . So , now here when we put values of domain as input like let's put x = -1 , -2 , -3 , -4 , 1 , 2 , 3 ,..... we will get y = -1 , -1/2 , -1/3 , -1/4 , 1 , 1/2 , 1/3 and so on , now , the input will give output as 0 , iff input is Infinite , but as input can never be infinite, so output will never comes to 0 as the intervals of real numbers is [tex]{\bf{(-\infty,\infty)}}[/tex] it's an open interval so Infinity and -ve infinity is not concluded in the above interval because whenever we think a number as large as much we can think , their exists infinitely large numbers greater than it , assume you're thinking 10¹⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰ as the largest number you can think , but if we add 1 in that i.e 10¹⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰ + 1 comes to be greater than it , Hence , we don't include Infinity and -ve Infinity in the interval which represents the set of all real numbers. So now the range is same as the Domain i.e [tex]{\boxed{\bf{(-\infty,0)\cup (0,\infty)}}}[/tex] or [tex]{\boxed{\mathbb{R}-\bf \{0\}}}[/tex]
Hence , we concluded that :
[tex]{\bf Domain=\mathbb{R}-\bf \{0\}}[/tex][tex]{\bf Range=\mathbb{R}-\bf \{0\}}[/tex] Range = DomainWhat is 45% of 32? can u also help me out with 8
Answer:
the answer is x=14.4
Step-by-step explanation in the photo :)
Solve the two-step equation.
3
4
(x) − 1.72 = −6.82
1. The first step is to
on both sides.
2. The second step is to
on both sides.
The solution is x =
Answer:
1. The first step is to
✔ add 1.72
on both sides.
2. The second step is to
✔ multiply by 4/3
on both sides.
The solution is x =
✔ -6.8
Step-by-step explanation:
Answer
The first step is to
add 1.72
on both sides.
2. The second step is to
multiply by 4/3
on both sides.
The solution is x =
-6.8
.
.
Step-by-step explanation:
The diameter of a circle is 2 centimeters. What is the circle's circumference? d=2 cm
Answer: pi (3.14)
Step-by-step explanation:
The circumference formula is pi*radius squared. Radius is half the diameter so radius is 1.
1 squared is still 1.
The answer is 3.14 or pi
i need help quick!! its due in 10 mintunes helpp!!!!!
Answer:
b) 10
Step-by-step explanation:
(3×10+46)+14 = 90
Hope this helps!!!!!
What is the value of a?
Answer:
62 i think
Step-by-step explanation:
What is the probability that a number selected from the numbers 1 to 15 is a multiple of 4?
Answer:
1/5
Step-by-step explanation:
probability = favorable outcomes/total outcomes
4, 8, 12 are multiples of 4, so there are 3 favorable outcomes.
There are 15 total outcomes.
Make the fraction
3/15
reduce by 3
1/5
Given that f(x) = 2000(1. 2) 5^x, Find
3. f(0)
4. f(2)
The graph of f (z) -x^2 was translated 4.5 units to the left to create the graph of function g.
which function represents g?
If the function is translated 4.5 units to the left to createe the graph of function g(x), hence the resuting function will be g(x) = (x + 4.5)^2
Translation of coordinatesGiven the function expressed as
f(x) = x^2
If the function is translated 4.5 units to the left to createe the graph of function g(x), hence the resuting function will be:
g(x) = (x + 4.5)^2
Note that translation to the left means addition of the factor
Learn more on translation here: https://brainly.com/question/1046778
23
Select the correct answer
Two manufacturers of sport utility vehicles claim that the sharpness of the turning radius for their SUV is better than all other SUVs on the
market. John randomly selected 30 professional sports car drivers to test the manufacturers claims. The drivers were all experienced in driving
both manufacturers' SUVs as well as competing SUVs on the market. He asked 15 drivers their opinion of vehicle A and 15 drivers their opinion
of vehicle B. The drivers' opinions on both SUV manufacturers claims are shown in the table.
Vehicle A Vehicle B
11 13
Agreed
Disagreed
4
2
Given John's data collection method and findings, what conclusion can be made?
ОА
Both SUV manufacturers' claims are true, but the turning radius of vehide B is sharper than the turning radius of vehicle A.
OB. Only the claim for vehicle B is true because more people agree with their claim.
OC. Neither of the claims are correct.
OD. Only the claim for vehicle A is true because 11 out of 15 people agree with their claim
Reset
Next
2022 Edmentum. All rights reserved.
Answer:
a.) both suv manufractures claims are true
Step-by-step explanation: got it right on edmentum
Evaluate 4x + 5y, when x = 7 and y = 10
My Explanation:
So, I picked 78. But the whole issue is that I can’t specifically “work it out”.
Question: How do you get 78? If you can give a kind answer, thank you very much. :)
Answer:
78
Step-by-step explanation:
4(x) = 4(7) = 28 5(x) = 5(10) = 50
28+50=
78
Module 13 area and polygons answer key please help.
Answer:
Parallelogram - B.
Trapezoid - C.
Rhombus - A.
Step-by-step explanation:
If the product of two numbers is 14 and one of the numbers is 3 1/2 times the other, then what is the sum of the two numbers?
Answer:
x=number1 and y=number2
product of the two numbers is 14 which translates to
xy=14
either x or y are 3.5 times big as the other one
so 3.5x=y
substituting in xy=14
x(3.5x)=14
[tex]3.5x^2=14\\x^2 =\frac{14}{3.5}=4[/tex]
then x must be equal to 2 or -2
x+y=
by substituting
x+3.5x=
if x =2 then 2+7=9 or if x=-2 then -2-7=-9
(1,-4), (8,2) , (2,9) and (-5,3) Which formula can be used to determine the coordinates of the point at which the diagonals of this square intersect?
Answer:
The midpoint formula
Step-by-step explanation:
(x,y)=(x1+x2)/2,(y1+y2)/2 ..(Take any two points that are opposite to each other in this case first and third points)
(x,y)=(1+2)/2,(-4+9)/2
(x,y)=3/2,5/2
As the diagonals of a square are equal, their intersection point will be the midpoint.
Please answer quickly, I will give Brainlist and lots of points.
An ellipse has vertices along the major axis at (0, 1) and (0, −9). The foci of the ellipse are located at (0, −1) and (0, −7). The equation of the ellipse is in the form below.
Which is a correct value for one of the variables shown in the equation?
a = 10
b = 4
h = 3
k = 0
Answer:
A. A=10
Step-by-step explanation:
you’re welcome
The equation of the ellipse is required \frac{(x)^2}{16} +\frac{(y+4)^2}{25}=1
The required equation is
[tex]\frac{x^2}{16} +\frac{(y+4)^2}{25}=1[/tex]
It can be seen that the major axis is parallel to the y axis.
The major axis points are
[tex](h,k+a)=(0,1)\\(h,k-a)=(0,-9)\\k+a=1\\k-a=-9[/tex]
Subtracting the equations
[tex]2a=10\\\implies a=5[/tex]
The foci are
[tex](h,k+c)=(0,-1)\\(h,k-c)=(0,-7)[/tex]
[tex]k+c=-1\\k-c=-7[/tex]
Subtracting the equations
2c=6
c=3
k+c=-1 implies that k=-1-c
k=-1-3
k=-4
What is the equation of the ellipse?[tex]\frac{(x-h)^2}{b^2} +\frac{(x-h)^2}{a^2}=1[/tex]
So we get,
[tex]\frac{(x-0)^2}{4^2} +\frac{(y+4)^2}{5^2}=1[/tex]
[tex]\frac{(x)^2}{16} +\frac{(y+4)^2}{25}=1[/tex]
Therefore the equation is, [tex]\frac{(x)^2}{16} +\frac{(y+4)^2}{25}=1[/tex].
To learn more about the ellipse visit:
https://brainly.com/question/450229
If I have a 78 and I got a 93.1 on a test that counted for 5 percent of my grade what would my grade be?
Answer
It might be 88%
Step-by-step explanation:
Roy borrows $60 from his sister. She charges him 5% simple interest per month. How
much does Roy owe his sister if he pays her back after 4 months?
a. )
$72. 93
b. )
$60
c. )
$72
d. )
$120
Оа
Ob
Submit Answer
Ос
Od
Answer:
C.) 72
5% x 60 = 3
It's 4 months, so 4 x 3
4 x 3 = 12
12 + 60 = 72