Answers
Step-by-step explanation:
1 result(s) found
x
2
−x−3
Step by Step Solution:
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STEP
1
:
Equation at the end of step 1
STEP
2
:
x3 + 3x2 - 7x - 12
Simplify ——————————————————
x + 4
Checking for a perfect cube :
2.1 x3 + 3x2 - 7x - 12 is not a perfect cube
Trying to factor by pulling out :
2.2 Factoring: x3 + 3x2 - 7x - 12
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -7x - 12
Group 2: x3 + 3x2
Pull out from each group separately :
Group 1: (7x + 12) • (-1)
Group 2: (x + 3) • (x2)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.
Polynomial Roots Calculator :
2.3 Find roots (zeroes) of : F(x) = x3 + 3x2 - 7x - 12
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is -12.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,3 ,4 ,6 ,12
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -3.00
-2 1 -2.00 6.00
-3 1 -3.00 9.00
-4 1 -4.00 0.00 x + 4
-6 1 -6.00 -78.00
-12 1 -12.00 -1224.00
1 1 1.00 -15.00
2 1 2.00 -6.00
3 1 3.00 21.00
4 1 4.00 72.00
6 1 6.00 270.00
12 1 12.00 2064.00
The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms
In our case this means that
x3 + 3x2 - 7x - 12
can be divided with x + 4
Polynomial Long Division :
2.4 Polynomial Long Division
Dividing : x3 + 3x2 - 7x - 12
("Dividend")
By : x + 4 ("Divisor")
dividend x3 + 3x2 - 7x - 12
- divisor * x2 x3 + 4x2
remainder - x2 - 7x - 12
- divisor * -x1 - x2 - 4x
remainder - 3x - 12
- divisor * -3x0 - 3x - 12
remainder 0
Quotient : x2-x-3 Remainder: 0
Trying to factor by splitting the middle term
2.5 Factoring x2-x-3
The first term is, x2 its coefficient is 1 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -3
Step-1 : Multiply the coefficient of the first term by the constant 1 • -3 = -3
Step-2 : Find two factors of -3 whose sum equals the coefficient of the middle term, which is -1 .
-3 + 1 = -2
-1 + 3 = 2
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Canceling Out :
2.6 Cancel out (x+4) which appears on both sides of the fraction line.
Final result :
x2 - x - 3
Terms and topics
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Polynomial root calculator
Polynomial long division
Related links
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Root Finder -- Polynomials Calculator
How to factor five term polynomial - Yahoo Answers
Long Polynomial Division
Polynomial long division - Wikipedia
Polynomial Long Division
Polynomials - Long Division
Related Questions
What is the missing exponent
Answers
Answer:
x^5 is the missing
Workers have been down the street installing two blinking red lights in front of the fire station. The two lights are always turned on at the same time. Both lights blink as they are turned on. One lights blinks after every 8 seconds. The other light blinks every 22 seconds. After how many seconds will they blink together again?
Answers
Answer:
After 88 seconds, they will blink together.
Step-by-step explanation:
Time after which the first light blinks = 8 seconds
Time after which the second light blinks = 22 seconds
Initially, both the lights blink together.
To find:
The time at which they will blink together again.
Solution:
Let us have a look at the time after which each light will blink.
First light will blink after:
8 s, 16 s, 24 s, 32 s, 40 s, 48 s, 56 s, 64 s, 72 s, 80 s, 88 s, 96 s, 104 s, ......
Second light will blink after:
22 s, 44 s, 66 s, 88 s, 110 s, .....
It can be seen that common time is 88 second, at which the both will blink together.
So, the answer is 88 s.
This answer can also be computed by taking the LCM (Least Common Multiple) of both the numbers i.e. 8 and 22.
Using the factorization method:
[tex]8=\underline{2}\times 2\times 2[/tex]
[tex]22=\underline{2}\times 11[/tex]
Common is 2.
Therefore the LCM will be:
[tex]2\times 2\times2\times 11 = \bold{88}[/tex]
So, the answer is 88 s.
Ashley has 6,452 buttons that need to be sorted equally into 25 jars. How many buttons will be in each jar? How many buttons will be leftover??? Pls answer.
Answers
3x−8≤23 AND −4x+26≥63,
Answers
only 1 question!
Please help I’ll mark brainliest!!!
Answers
Answer:
Wouldn’t y be 4 and x be 1?
Answer:
Y = -1X + 5
Step-by-step explanation:
I just solved it, it was a long problem, I don't wanna talk you through it. I think I'm correct.
Hope this helps! Let me know!
Borrow $1,500 at an interest rate of 5% for one year for a total repayment of
Answers
Answer:
1680
Step-by-step explanation:
1500÷100=15
15x12 months =180
1500+180=1680
The graph of an equation intersects the y-axis at some point. What do the coordinates of the intersection indicate?
A. the input when the output is zero
B. the output when the input is zero
C. the input when the output is 1
D. the output when the input is 1
Answers
Answer:
B
Step-by-step explanation:
got stuck on it too lol
The graph of an equation intersects the y-axis at some point. Therefore, the coordinates of the intersection indicate is B. the output when the input is zero.
What is perimeter?Its the sum of length of the sides used to made the given figure. A regular figure with n-sides has n equal sides in it, and they are the only parts of it(that means, nothing more than those equal lengthed n sides).
Since sum of side lengths of the triangle of vertices: 3
Area: ½ × base × height
Number of edges: 3
Internal angle: 60° (for equilateral)
The Sum of interior angles is 180°
Therefore, the coordinates of the intersection indicate will be;
B. the output when the input is zero.
Learn more about perimeter here:
https://brainly.com/question/10466285
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The cost for children under twelve at a certain buffet restaurant is a base charge of a dollar plus twenty-five cents for each year of the child's age. Represent this cost as an expression, using y to stand for the child's age in years. Then use the expression to find the cost for a child who is nine.
Answers
Answer:
[tex]Cost = 1 + 0.25y[/tex]
[tex]Cost =3.25[/tex]
Step-by-step explanation:
Given
[tex]Base\ Amount = \$ 1[/tex]
[tex]Additional = 25cents[/tex] of child's age
Solving (1):
Determine the cost function.
Represent the years as y.
So, we have:
[tex]Additional = 25cents[/tex] * y
Convert 25 cents to dollars.
[tex]25 cents = 25 * \$0.01[/tex]
[tex]25 cents = \$0.25[/tex]
So, we have:
[tex]Additional = \$0.25 * y[/tex]
The cost amount is then:
[tex]Cost = Base\ Amount + Additional[/tex]
[tex]Cost = 1 + 0.25y[/tex] --- This is the cost function
Solving (b): Cost of 9 years old.
In this case;
[tex]y = 9[/tex]
Substitute 9 for y in [tex]Cost = 1 + 0.25y[/tex]
[tex]Cost =1 + 0.25 * 9[/tex]
[tex]Cost =1 + 2.25[/tex]
[tex]Cost =3.25[/tex] --- This is the cost for a child of 9
Answer:
1+0.25y, 2.25
Step-by-step explanation:
You would express the added 25 cents times the age of the child since the age is represented by the variable y, you would put 0.25y
then to find what the cost is for a nine year old you would multiply 9 by 25 and at the end of multiplying you would move the decimal from zero two times to the left. In case you don't understand how you could move the decimal from zero, there is always a decimal to the right of a whole number where the number ends its just not seen because there is no decimal in the number to represent. The decimal would still be there just it would be invisible but it becomes visible when there is a decimal number to represent.
hope this helps someone, keera
help please! show your steps please
Answers
Answer:
x = -9
Step-by-step explanation:
To solve the equation
Simplify each sideSeparate the variable on one side and the numerical term on the other sideMake the coefficient of the variable equal 1Let us do these steps with our question to find x
∵ 4(2x + 7) = 12 - 2(10 - 2x)
→ Simplify each side
∵ 4(2x) + 4(7) = 12 - 2(10) - 2(-2x)
∴ 8x + 28 = 12 - 20 + 4x
→ Add the like terms in the right side
∵ 8x + 28 = (12 - 20) + 4x
∴ 8x + 28 = -8 + 4x
→ Subtract 28 from both sides
∵ 8x + 28 - 28 = -8 - 28 + 4x
∴ 8x = -36 + 4x
→ Subtract 4x from both sides
∵ 8x - 4x = -36 + 4x - 4x
∴ 4x = -36
→ Make coefficient of x equal 1 by dividing both sides by 4
∴ [tex]\frac{4x}{4}=\frac{-36}{4}[/tex]
∴ x = -9
Haddle wrote a check to the grocery store for $156.00. However, when she looks at her check register later that night, she sees she only has
$122.66 In her checking account. Haddle has opted in to the standard overdraft practices at her bank. How many fees is Haddle likely to pay for
writing the check?
Answers
Answer:
she will have one fee for standard overdraft practices and that will prevent a fee from the grocery. store
Step-by-step explanation:
We are told she wrote a check to the grocery store for $156.00.
And that when she looked at her check register later that day, she had only $122.66.
This means she doesn't have sufficient balance for the grocery.
It means the bank will pay the overdraft and it attracts charges which may vary for different banks.
Thus, she will have one fee for standard overdraft practices and that will prevent a fee from the grocery store
C. Assume you are putting 10 gallons of gas a week in your car for 4 weeks at $2.25 a
gallon. How much are you spending on gas every month? |I
Answers
Answer:
22.50
Step-by-step explanation:
Does anyone know what f(x)=-5x-1 when f(-7) i need help with this please.
Answers
Answer:
f(-7) = 34
Step-by-step explanation:
If f(x) = -5x - 1, then . . .
f(x) = -5x - 1
f(-7) = -5(-7) - 1
= 35 - 1
= 34
. . . because in f(-7), the (-7) is the x-value you're supposed to use to find the value of the function.
Arianna is packing scented candles and candle holders into gift boxes. She has 84 candles and 48 holders, and each box must contain both items. She puts the same number of candles in each box, and the same number of holders in each box. What is the maximum number of gift boxes Arianna can pack, and how many scented candles and candle holders will each box have?
Answers
Answer:
Step-by-step explanation:
If she has 84 candles and 48 holders, we can write out the factors of both values as shown
For candles
84 = 2×2×3×7
84 = 12×7
For 48
48 = 2×2×2×2×3
48 = (2×2)×(2×2×3)
48 = 4×12
48 = 12×4
From both factors, we can are that 12 common to both of them. This means that the maximum number of gift boxes Ariana can pack is 12
The other factors will give the amount of scented candles and candle holders that each box will have. This means that each box will have 7scented candles and 4 holders.
y−1=−2(x−2) in slope intercept form
Answers
Answer:
[tex]y = - 2x + 5[/tex]
Step-by-step explanation:
Simply simplify the equation from what it is to the slope intercept format:
[tex]y = mx + b[/tex]
Step-by-step explanation:
Hey there!
We know;
The slope intercept form of equation is;
y = mx+c
So, let's try to take it in this form.
(y-1) = -2(x-2)
Multiply -2 and (x-2)
(y-1) = -2x + 4
Take '-1' to right side.
y = -2x+4+1
y = -2x+5
Therefore, the equation is y = -2x+5.
Hope it helps...
Use the diagram to find the measures of all the angles, given that m< 1 = 76°
Answers
Answer:
m< 3 = 76°, m< 3 = 104°, m< 3 = 76°,
Step-by-step explanation:
360°
m< 1 = m< 3 → 76° (76°*2 = 152°)
360° - 152° = 208°
208°/2 = 104°
m< 2 = m< 4 → 104°
PLEASE HELP QUESTIONS ARE BELOW FIRST TO ANSWER WILL BE VOTED BRAINLIEST
Answers
Answer:
1. 7.5
2. 7
3. 8
4. 1.44
5. 2
6. 4
Step-by-step explanation:
Use cross multiplication and then divide by the coefficient of x.
Here is how to solve number 1. Solve the rest of them like this.
2.5(15) = 5x
37.5 =5x
5 5
x=7.5
Please mark me brainliest and I hope this helps.
Answer:
1. x = 7.5
2. x = 7
3. x = 8
4. x = 1.44
5. x = 2
6. x = 4
Step-by-step explanation:
All you have to do is cross multipy and then solve.
10 Brynlee's monthly cell phone bill
is $60 a month plus $2.50 per
gigabyte used. Raylin's cell phone bill is $450
per month plus $3.25 per gigabyte used.
Determine after how many gigabytes used
would the cell phone plans cost the same
for the month what is the answer??
Answers
Answer:
20 gigabytes
Step-by-step explanation:
Let n represent the amount of gigabytes used.
First make an equation for each senario, Brynlee's would be 60+2.50n and Raylin's would be 45+3.25n.
Set them to equal each other, 60+2.50n=45+3.25n.
Then isolate for n.
60-45=3.25n-2.50n
15=0.75n
Divide both sides by 0.75 to get 20
15+6x=45+8x
what does x equal
Answers
Answer:
X=-15
Step-by-step explanation:
Do simple math
Answer:
-15=x
Step-by-step explanation:
15 + 6x = 45 + 8x
-6x -6x
15 = 45 + 2x
-45 -45
-30 = 2x
/2 /2
-15 = x
Hope this helps!
Which term is coefficient of 1?
Answers
Answer:
the first one.
Answer:
k^7
Step-by-step explanation:
As there is nothing in front of it that means the coefficient is 1
:)
easy?
3x-100 what does x equal?
Answers
Help Me need help please it is due today please help ASAP
Answers
Answer:
87
Step-by-step explanation:
you subtract 3:32-2:45
-16 > -f, if f = 15
True or falsehood
Answers
Answer:
false
Step-by-step explanation:
15 is a larger number than -16
Benjamin must have 120 credit hours of instruction to receive his college degree. Benjamin wants to graduate in 8 semesters without attending summer sessions. How many credit hours must Benjamin take on average each semester to graduate in 8 semesters? (8) Simplify this expression: -4^2
Answers
Answer: See explanation
Step-by-step explanation:
From the question, we are informed that Benjamin must have 120 credit hours of instruction to receive his college degree and that he wants to graduate in 8 semesters without attending summer sessions.
The number of credit hours that Benjamin must take on average each semester to graduate in 8 semesters will be:
= 120/8
= 15 credit hours
(8) Simplify this expression: -4^2. This will be:
= -4 × -4
= 16
find the length indicated
Answers
Answer:
ST = 5
Step-by-step explanation:
RT = 7
Subtract the RS, which is 2.
You get, ST = 5.
1. Which of the following is a pair of parallel lines? W = 1/4x - 7 V=1/44+2 W = 4x - 7 V = 1/4x + 2 W = 1/4x - 7 V= 1/4x + 2 W = 4x - 7 V = -4x + 2 C
Answers
Four pounds of apples cost 3.88. what is the price per pound
I need this done asap!!!!
WILL give brainliest!
Answers
Answer:
0.97 cents
Step-by-step explanation:
4/3.88=0.97
price per pound=0.97 cents
BRAINLIEST APPRECIATED!
HOPE YOU ARE HAVING A GOOD DAY!
Simplify 9 to the 2nd power/ 9 to the 7th power
Answers
Answer:
9^2=81, 9^7=478,296,9
Rectangle ABCDABCDA, B, C, D is graphed in the coordinate plane. The following are the vertices of the rectangle: A(-2, 2)A(−2,2)A, left parenthesis, minus, 2, comma, 2, right parenthesis, B(6, 2)B(6,2)B, left parenthesis, 6, comma, 2, right parenthesis, C(6, 3)C(6,3)C, left parenthesis, 6, comma, 3, right parenthesis, and D(-2, 3)D(−2,3)D, left parenthesis, minus, 2, comma, 3, right parenthesis.
What is the area of rectangle ABCDABCDA, B, C, D?
Answers
The area of rectangle ABCD with the given vertices is: 8 units².
What is the Area of a Rectangle?Area of rectangle = (length)(width).
Given the following vertices:
A(-2, 2)B(6, 2)C(6, 3)D(-2, 3)Area = (length)(width) = (AB)(BC)
AB = |-2 - 6| = 8 units
BC = |2 - 3} = 1 unit
Area of rectangle = (8)(1) = 8 units².
Learn more about area of rectangle on:
https://brainly.com/question/25292087
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Answer: 8
Step-by-step explanation:
Give the place of the digit 1 in 296,518.4
296,518,417
Answers
Answer:
296,518.4 the one is in the tenths place sunce it's after the decimal
296,518,417 the first 1 in 518 is in the tenths place but the 2nd .. 1 is in the tens place bc no decimal
What is y= 1/3x+2 equal to as a slope?
Answers
Answer:
The graph below models the value of a $20,000 car t years after it was purchased.
Value of Car
A graph titled Value of Car has years bbhvb ngc,jon the x-axis and Dollars on the y-axis. A line curves down and goes through points (0, 20,000), (4, 10,000), and (14, 2,000).
Which statement best describes why the value of the car is a function of the number of years since it was purchased?
Each car value, y, is associated with exactly one time, t.
Each time, t, is associated with exactly one car value, y.
The rate at which the car decreases in value is not constant.
There is no time, t, at which the value of the car is 0.
Step-by-step explanation: