Step-by-step explanation:
Example 1
Solve the equation x3 − 3x2 – 2x + 4 = 0
We put the numbers that are factors of 4 into the equation to see if any of them are correct.
f(1) = 13 − 3×12 – 2×1 + 4 = 0 1 is a solution
f(−1) = (−1)3 − 3×(−1)2 – 2×(−1) + 4 = 2
f(2) = 23 − 3×22 – 2×2 + 4 = −4
f(−2) = (−2)3 − 3×(−2)2 – 2×(−2) + 4 = −12
f(4) = 43 − 3×42 – 2×4 + 4 = 12
f(−4) = (−4)3 − 3×(−4)2 – 2×(−4) + 4 = −100
The only integer solution is x = 1. When we have found one solution we don’t really need to test any other numbers because we can now solve the equation by dividing by (x − 1) and trying to solve the quadratic we get from the division.
Now we can factorise our expression as follows:
x3 − 3x2 – 2x + 4 = (x − 1)(x2 − 2x − 4) = 0
It now remains for us to solve the quadratic equation.
x2 − 2x − 4 = 0
We use the formula for quadratics with a = 1, b = −2 and c = −4.
We have now found all three solutions of the equation x3 − 3x2 – 2x + 4 = 0. They are: eftirfarandi:
x = 1
x = 1 + Ö5
x = 1 − Ö5
Example 2
We can easily use the same method to solve a fourth degree equation or equations of a still higher degree. Solve the equation f(x) = x4 − x3 − 5x2 + 3x + 2 = 0.
First we find the integer factors of the constant term, 2. The integer factors of 2 are ±1 and ±2.
f(1) = 14 − 13 − 5×12 + 3×1 + 2 = 0 1 is a solution
f(−1) = (−1)4 − (−1)3 − 5×(−1)2 + 3×(−1) + 2 = −4
f(2) = 24 − 23 − 5×22 + 3×2 + 2 = −4
f(−2) = (−2)4 − (−2)3 − 5×(−2)2 + 3×(−2) + 2 = 0 we have found a second solution.
The two solutions we have found 1 and −2 mean that we can divide by x − 1 and x + 2 and there will be no remainder. We’ll do this in two steps.
First divide by x + 2
Now divide the resulting cubic factor by x − 1.
We have now factorised
f(x) = x4 − x3 − 5x2 + 3x + 2 into
f(x) = (x + 2)(x − 1)(x2 − 2x − 1) and it only remains to solve the quadratic equation
x2 − 2x − 1 = 0. We use the formula with a = 1, b = −2 and c = −1.
Now we have found a total of four solutions. They are:
x = 1
x = −2
x = 1 +
x = 1 −
Sometimes we can solve a third degree equation by bracketing the terms two by two and finding a factor that they have in common.
Step-by-step explanation:
mark up as brainliest
Commutative law under addition says- p + q = q + p. Commutative law under multiplication says p x q = q x p. Note- Rational numbers, integers and whole numbers are commutative under addition and multiplication. Rational numbers, integers and whole numbers are non commutative under subtraction and division.0
HELP 1 QUESTION.... Write a plan for proving that <1 is congruent to <2
Answer:
corresponding angles
Alternate angle
cointerior angle
4. Line r is mapped onto line m by a dilation centered at the origin with a
scale factor of 4. The equation of line r is 6x – 3y = 12. What is the
equation for line m?
3x - y = 8
Step-by-step explanation:
Since, if a line having points represented by (x,y) is dilated about origin with a scale factor k,
Then the coordinates of the dilated line is obtained by the rule,
Here, line L is,
3x - y = 4
The x-intercept and y-intercept of line L are (4/3,0) and (0,-4) respectively,
If the line L is mapped onto line M by a dilation centered at the origin with a scale factor of 2,
Then by the above definition,
The points of the line M are,
(2×4/3, 2×0) and (2×0, 2×-4) ⇒ (8/3,0) and (0,-8)
Hence, the equation of line M passes through the points (8/3,0) and (0,-8)
Find the root of the following equation: (6+x)2−x2=168
Answer:
No solutions (roots)
Step-by-step explanation:
The root of an equation is basically the solution of the equation. If I'm reading the problem correctly, the equation is (6+x)*2 - x*2 = 168.
We distribute the (6+x)*2 part and get 12+2x - 2x = 168. Uh oh.. the 2x terms cancel each other out and we are left with 12=168. Either I'm reading the equation wrong or the equation has no solutions.
PLEASE HELP MIDDLE SCHOOL MATH
Answer:
x>=5
Step-by-step explanation:
If x is less than five, then there will be a negative in the square root, which will yield x an imaginary number.
What value of x makes this equation true?
15 –
1
2
x = 21
Answer:
x= -0.5
Step-by-step explanation:
You want to isolate x on one side of the equation
15-12x=21
-15 -15
-12x=6
/-12 /-12
x= -0.5
help me someone solve this
Do you know the answer
Answer:
y=2x+2
Step-by-step explanation:
The * stands for multiplication.
0*2+2=2
3*2+2=8
6*2+2=14
All of these statements are true, so this should be the correct answer.
BRAINLIEST
PLS HELP ASAP IM FAILING
Quadrilateral ABCD has coordinates A(-2,0), B(0,4), C(4.6), and D(2,2). If it is
reflected over the x-axis, what are the coordinates of B'? (Answer as an ordered pair without spaces)
pair without spaces)
Answer:
B' (0,-4)
Step-by-step explanation:
When a point undergoes a reflection across the x-axis, it follows this transformation:
(x, y) --> (x, -y)
(0, 4) --> (0, -4)
i need help answer it correctly
Answer:
(1) when x is 0 y=5/2 and when y is 0 x=5
(2)Graph the points : (0 , 5/2) and (5 , 0)
(3)the slope is -1/2
Step-by-step explanation:
Helppp!!!!!!!!this for a test
Answer:
Step-by-step explanation:
A,because it goes diagonally which (with the fraction) means that the fraction should be equal to the problem
Answer:
A
Step-by-step explanation:
I believe this is the right answer becasue all the other lines and curved (not constant) and the other goes in different directions.
a 6 ounce package costs $2.10 a 16 ounce package costs $5.28 a 26 ounce package costs $9.36 which package is the best buy
Answer:
The better buy is the 16 ounce package for $5.28.
Step-by-step explanation:
First divide each price with their ounce,so 2.10 ÷ 6 = 2.1 per 1 ounce , 5.28 ÷ 16 = 0.33 per 1 ounce , 9.35 ÷ 26 = 0.36 per 1 ounce.
Next compare the prices for 1 ounce and see which on is lower. The 16 ounce package has a better price because the price for each ounce is lower than the other prices.
PLEASE HELP URGENT!!!!!!
Tom, Sam and Victor are painting the rooms in their new house. It takes Tom 4 hours to paint one room, but Sam and Victor take 3 hours each. If all of them work together, how long does it take them to paint one room?
9514 1404 393
Answer:
12/11 = 1 1/11 hours
Step-by-step explanation:
The total rate is the sum of the individual rates in rooms per hour.
Tom can paint 1/4 room per hour.
Sam and Victor can each paint 1/3 room per hour.
Their total rate is ...
1/4 +1/3 +1/3 = 11/12 . . . rooms per hour
The rate in "hours per room" is the inverse of this.
It takes them 12/11 = 1 1/11 hours to paint one room.
Which of the following equations has infinitely many real solutions?
A. 4x + 1 = x-1
B. 4(x - 5) = 4x – 20
C. 4(x – 5) = 4x + 20
D.4x + 1 = 4x - 1
995² evaluate and answer
Answer:
Step-by-step explanation:
995 2 = 990025
Thia is the correct answer
z2 + 5z - 3z2 + z
Terms
Like Terms
trey had 440 songs on his mp3 player.now he has 473 songs.what is the percent of increase in the number of songs on his mp3 player?
round to the nearest tenth if necessary.
Answer:
There is 7.5% increase in the number of songs on his mp3 player.
Step-by-step explanation:
Original Songs in mp3= 440 songs
Final Songs in mp3= 473 songs
We need to find percent of increase in the number of songs on his mp3 player.
The formula used is: [tex]Percent \ of \ increase = \frac{Final \ Value \ -\ Original \ Value}{Original \ Value} \times 100[/tex]
Now putting values and finding percent of increase
[tex]Percent \ of \ increase = \frac{Final \ Value \ -\ Original \ Value}{Original \ Value} \times 100\\Percent \ of \ increase = \frac{473-440}{440} \times 100\\Percent \ of \ increase = 7.5\%[/tex]
So, there is 7.5% increase in the number of songs on his mp3 player.
. There are 200 different pieces of fruit in a barrel. There are 42 apples, 82 oranges, and 76 pears. Which of the following events have a probability that is less than 0.4? * Select all that apply. A. Randomly selecting an apple B. Randomly selecting an orange C. Randomly selecting a pear D. Randomly selecting an apple or an orange E. Randomly selecting an apple or a pear F. Randomly selecting an orange or a pear
Answer:
A and C
Step-by-step explanation:
42/200 = .21
76/200 = .38
Answer:
Apples and Pears
Step-by-step explanation:
21 % = Apples
41 % = Oranges
38 % = Pears
Probablity of less than 40% = pears and apples
HOPE THIS HELPS
PLZZ MARK BRAINLIEST
which numbers is equivalent to 75%?
Answer:
in fraction form it would be 3/4
Step-by-step explanation:
6th one....pls help me out
Now , For 12n to end with 0, it should have 2 as well as 5 in its Prime factors to end with 0, Also to end with 5 , it requires at least a single multiple of 5 in its Prime Factors, So 12n cannot end with the digit 0 or 5.
I WILL MARK BRAINIEST
please answer question 5
Answer:
a = 150
Step-by-step explanation:
The sum of the internal angles of an octagon is 1080°.
[tex]4a+4(120)=1080[/tex] (There are four [tex]120^{\circ}[/tex] and 4 [tex]a^{\circ}[/tex], they sum to 1080°)
[tex]4a + 480 = 1080[/tex]
[tex]4a = 600[/tex]
[tex]a = 150[/tex]
Hope this helps :)
Answer:
a = 150
Step-by-step explanation:
A octagon is 1080 degrees. The half circles are showing which angles are the same. So all the red circles are 120 degrees. To find the green circles, multiply 120 by 4 for the total of the four angles and then subtract it from 1080:
120(4) = 480
1080 - 480 = 600
So 600 is the total of all the green half circles added together, so divide 600 with 4 because there are four green half circles.
600/4 = 150
What will be the max height of the ball?
Answer:
(2, 6)
Step-by-step explanation:
I used my graphing calculator and I just got finished with this topic in my Math 2 class.
Pls help me
Question 10 (1 point)
Which of the following measurements, could be the side lengths of a right triangle?
a
8 inches, 10 inches, and 12 inches
9 inches, 12 inches, and 15 inches
b
с
10 inches, 5 inches, 11 inches
d
6 inches, 12 inches, 14 inches
Submit
Answer:
9in 12in 15in
Step-by-step explanation:
M/4=-13
Find the value of M?
Brainliest 5 stars and thank you! (correct answers only)
What divisor is represented by the synthetic division below?
Answer:
Answer - -5
Step-by-step explanation:
Answer:
The correct answer is 2
5x + 5x - 5what are the measures of angles 1,2,3, and 4?
Answer:
I know that 2 is 18
I need help with solving for x. Then find the measure of the base angle. Please
Answer:
x = 8 base angle = 81 degrees
Step-by-step explanation:
Answer:
x = 8
base angle = 81 deg
Step-by-step explanation:
we observe that because the given triangle is a isosceles triangle, the base angles must be the same.
Hence the missing base angle must also be (10x+1)°
recall that all internal angles of an triangle must add up to 180 deg,
hence
180° = sum of all internal angles
180° = 18° + (10x+1)° + (10x+1)°
180° = 18° + 2(10x+1)° (subtracting 18 from both sides)
180 - 18 = 2(10x+1)
162 = 2(10x+1) dividing both sides by 2)
162 / 2 = 10x + 1
81 = 10x + 1 (subtracting 1 from both sides)
81 - 1 = 10x
10x = 80 (divide both sides by 10)
x = 80/10
x = 8 (answer)
substituting x = 8 into the expression for the base angle
base angle = (10x+1)
= 10(8) + 1
= 10 + 1
= 81
r=4/3(p-q)
solve for p
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[tex]r = \frac{4}{3} (p - q) \\ [/tex]
Multiply sides by 3
[tex]3r = 4(p - q)[/tex]
Divide sides by 4
[tex] \frac{3r}{4} = p - q \\ [/tex]
Add sides q
[tex] \frac{3r}{4} + q = p \\ [/tex]
[tex]p = \frac{3}{4} r + q \\ [/tex]
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Please answer correctly !!!!!!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!!
Which expression is equivalent to (−3n+18m)−(112m−n)?
Answer:
I believe it is -94m-2n
∫ ⊃øℕτ ωΛℕℕΛ βΣ ℏΣℝΣ βℝ∪ℏ
Answer:
same
Step-by-step explanation:
heheh
