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
Graph the exponential function.
f(x) = 4^x
Plot five points on the graph of the function. Then click on the graph-a-function button.
Answers
Exponential Function doesn't have a graph that intercepts x-axis only if it is f(x) = a^x (when a>0 and a ≠ 1)
If you want to plot five points to graph the function then. I'd rather do from negative number to positive number.
Substitute from -3≤x≤1 (We get 5 points)
f(-3) = 4^-3
f(-3) = 1/4^3
f(-3) = 1/64 (First point) (-3,1/64)
f(-2) = 4^-2
f(-2) = 1/4^2 = 1/16 (Second point) (-2,1/16)
f(-1)=4^-1 = 1/4 (Third point) (-1, 1/4)
f(0) = 4^0 = 1 (Fourth point) (0, 1)
f(1) = 4^1 = 4 (Fifth point) (1,4)
I need help with this question.
-3(k+5)>-7-3k
Answers
Answer:
no solution
Step-by-step explanation:
-3(k+5)>-7-3k
Distribute
-3k -15 > -7-3k
Add 3k to each side
-3k+3k -15 > -7-3k+3k
-15 > -7
This is not true so there is no solution
Rectangle A measures 8 inches by 5 inches. Rectangle B is a scaled copy of Rectangle A. Select all the measurement pairs that could be the dimensions of Rectangle B. 1. 4 inches by 2.5 inches 2. 15 inches by 10 inches 3. 24 inches by 15 inches 4. 9 inches by 6 inches
Answers
Answer:
C. 24 inches by 15 inches
Step-by-step explanation:
Given
[tex]Rectangle: 8\ by\ 5\ inches[/tex]
Required
Determine the scale copies
To do this, we calculate the ratio.
[tex]Ratio = \frac{Actual}{Measured}[/tex]
Analyzing A.
Sides: 1.4 by 2.5 inches
We start by calculating ratio of each sides;
Length:
[tex]Ratio =\frac{8}{1.4}[/tex]
[tex]Ratio = \frac{40}{7}[/tex]
Width:
[tex]Ratio = \frac{5}{2.5}[/tex]
[tex]Ratio = 2[/tex]
Analyzing B.
Sides: 15 inches by 10 inches
Length
[tex]Ratio = \frac{8}{15}[/tex]
Width:
[tex]Ratio = \frac{5}{10}[/tex]
[tex]Ratio = \frac{1}{2}[/tex]
Both ratios are not equal
Analyzing C.
24 inches by 15 inches
Length
[tex]Ratio = \frac{8}{24}[/tex]
[tex]Ratio = \frac{1}{3}[/tex]
Width:
[tex]Ratio = \frac{5}{15}[/tex]
[tex]Ratio = \frac{1}{3}[/tex]
Both ratios are equal
Analyzing D.
Sides: 9 inches by 6 inches
Length
[tex]Ratio = \frac{8}{9}[/tex]
Width
[tex]Ratio = \frac{5}{6}[/tex]
Both ratios are not equal
Option C answers the question because both ratio are equal
HELP ASAP
Jason has $2.25 worth of dimes and quarters. He has twice as many dimes as quarters. Determine the number of dimes and the number of quarters that Jason has.
Answers
Answer:
Step-by-step explanation:
let the number of dimes=x
and number of quarters=y
x=2y
0.10 x+0.25 y=2.25
or 10x+25y=225
divide by 5
2x+5y=45
2 ×2y+5y=45
4y+5y=45
9y=45
y=45/9=5
x=2y=2×5=10
Hence dimes=10
quarters=5
Dairy Delight offers a free ice cream every time that the saleperson does not greet the customer with a smile. Last year Dairy Delight gave away free ice cream 3.8% of the time. What is the probability of randomly selecting 3 customers from last year who all received a free ice cream? Round the answer to 6 decimals. Show your work below.
Answers
Answer:
0.000055
Step-by-step explanation:
Given that:
Percentage of free ice cream Given last year = 3.8%
From a total population of 1 ; proportion of those who received free ice cream = 3.8/100 = 0.038
Hence,
Probability of selecting a customer who received free Ice cream = 0.038
Hence, if 3 people are picked randomly from last year who received free ice cream:
(0.038 * 0.038 * 0.038) = 0.000054872
= 0.000055 ( to 6 decimal places)
Solve the system of equation
Answers
Fort the first equation just click on the photo and for the second it’s x-y=-1
Answer:
x= 3, y= 8
or x= -1, y= 0
Step-by-step explanation:
y= 2x² -2x -4 -----(1)
y -2x= 2
y= 2x +2 -----(2)
Substitute (1) into (2):
2x² -2x -4= 2x +2
2x² -2x -4 -2x -2= 0 (bring all terms to the left)
2x² -4x -6= 0 (simplify)
x² -2x -3= 0 (÷2 on both sides)
(x -3)(x +1)= 0 (factorise)
x -3= 0 or x +1= 0
x= 3 or x= -1
Substitute into (2):
y= 2(3) +2 or y= 2(-1) +2
y= 6 +2 or y= -2 +2
y= 8 or y= 0
x-(x(x-y to the power of 3)) ; use x=9 and y=1
Answers
Answer:
-4599
Step-by-step explanation:
x-(x(x-y)^3) , x=9, y=1
=9-(9(9-1)^3)
=9-(9(8)^3)
=9-(9*512)
=9-4608
= -4599
Does the point (1,2) lie on the locus whose equation is 2x+4y = 10?
Answers
Answer:
Yes, the point lies on the line.
Step-by-step explanation:
Given coordinate of the locus = (1,2)
Equation of the line 2x+4y = 10
Unknown:
Does the given coordinate lie on the line?
Solution:
The equation given is that of a straight line. To solve this problem, we simply plug the coordinates of the point back into the equation and check if solves it.
x = 1 and y = 2;
2x+4y = 10
So;
2(1) + 4(2) gives 2 + 8 = 10
Yes, the point lies on the line.
3/5 ÷ 1 1/4. plz help
Answers
Answer:
12/25 (0.48 in decimal form)
Step-by-step explanation:
3/5 divided by 1 1/4
Make 1 1/4 an improper fraction:
1 1/4 = 5/4
Now we flip 5/4 (the second fraction) when we divide and then multiply it by the first fraction.
Our equation now:
3/5 x 4/5
After multiplying across, you get 12/25 (0.48 in decimal form).
Hope this helps!
this is urgent i’ll get a F.... and my momma is crazy so please help it’s my last question
Answers
Answer:
Step-by-step explanation:
The measure of angle BCD is 22 degrees
The measure of angle DCE is 158 degrees
The measure of angle BCF is 158 degrees
The measure of ECF is 22 degrees
Answer:
BCD = 22
DCE = 158
BCF = 158
ECF = 22
Step-by-step explanation:
first one is alternate interior angles
second one is 180 - 22
third one is congruent to second one
last one is congruent w/ BCD
The equation of y-axis is of the form
Answers
Answer:
x=0
Step-by-step explanation:
The equation of the y axis corresponds to the equation of every point that lies and constitute the y-axis. As the horizontal distance from every point lying on the y-axis with the main y-axis remains 0, hence, its abscica (x-coordinate) also will be zero.
Hence, x=0
Integers on number lines
Answers
what is 8.8x10^5 in standard notation?
Answers
Answer:
880,000
Step-by-step explanation:
Move the decimal in 8.8 five places to the right.
Plz help with this question
Answers
Answer:
A
Step-by-step explanation:
Given
6 ([tex]\frac{x}{2}[/tex] + 4) ≥ 9 ( distribute the parenthesis by 6 )
3x + 24 ≥ 9 ( subtract 24 from both sides )
3x ≥ - 15 ( divide both sides by 3 )
x ≥ - 5 → A
Answer:
A
Step-by-step explanation:
First, divide both sides by 6:
6(x/2 + 4) ≥ 9
x/2 + 4 ≥ 9/6
x/2 + 4 ≥ 3/2
Now, subtract 4 from both sides:
x/2 ≥ 3/2 - 4
x/2 ≥ -5/2
Finally multiply both sides by 2:
x ≥ (-5/2) * 2
x ≥ -5
The answer is thus A.
~ an aesthetics lover
Check all fractions equivalent to 2⁄8.
Check all that are true.
1⁄2
1⁄6
4⁄16
1⁄4
4⁄12
Answers
An airplane is flying at an altitude of 2.7 miles and is 8.3 miles from the runway. Find the angle of depression that the airplane must make to land safely.
Answers
Answer:
-8.72811548... i think
Step-by-step explanation:
a² + b² = c²
8.3² + 2.7² = c²
68.89 + 7.29 = c²
76.18 = c²
√76.18, -√76.18 = c
c = 8.72811548…, −8.72811548…
I think because it's depression, it's -8.72811548...
Simplify. Express your answer as a single fraction in simplest form.
9v/4v- (w - 2)
Answers
i’m pretty sure this would be your answer
explanation:
Reduce the fraction with v
When there is a in front of an expression in parentheses, change the sign of each term in the expression
then calculate the sum
You and your friend share a paper route. You can deliver 4 papers in one minute and your friend can deliver 3 papers in one minute. Seventy-five papers have to be delivered each day on the route. Let n be the number of papers you deliver. A) use the verbal model to write an equation that you can use to find out how long it will take the two of you working together to deliver the papers.
Answers
Answer:
[tex]n\times \frac{1}{4}+(75-n)\times \frac{1}{3}[/tex]
Step-by-step explanation:
Given that:
4 papers are delivered by first person in one minute.
Rate of delivering one paper
or
Time taken to deliver one paper can be calculated by the formula:
[tex]\dfrac{\text{Total Time taken}}{\text{Number of papers delivered}}[/tex]
Time taken to deliver one paper by first person = [tex]\frac{1}{4}[/tex]
3 papers are delivered by second person in one minute.
Time taken to deliver one paper by second person = [tex]\frac{1}{3}[/tex]
Total number of papers = 75
Number of papers delivered by first person = [tex]n[/tex]
So, number of papers delivered by second person = ([tex]75-n[/tex])
Time taken to deliver [tex]n[/tex] newspapers = Number of newspapers delivered multiplied by Time taken to deliver one newspaper
Time taken by first person = [tex]n\times \frac{1}{4}[/tex]
Time taken by second person = [tex](75-n)\times \frac{1}{3}[/tex]
So, Total time taken can be written as:
[tex]n\times \frac{1}{4}+(75-n)\times \frac{1}{3}[/tex]
There are 2 computers for every 3 iPads in this technology room
Answers
Answer:
The Ans Is 2:3
Step-by-step explanation:
at the beginning of grade 6 the number of advanced math to the number of regluar math students was 3:8 however after taking placement tests students were moved around chaning the ratio of the number of advanced math students to the number of regluar math students was 4:7 how many student students started in reglaur math and advanced math if there were 92 students in advanced math after the placement test. Please tell me how to do this on a tape diagram
Answers
Answer:
There were 69 students in advanced math and 184 students in regular math before the placement tests
Step-by-step explanation:
The correct question
At the beginning of 6th grade, the ratio of the number of advanced math students to the number of regular math students was 3:8. However, after taking placement tests, students were moved around changing the ratio of the number of advanced math students to the number of regular math students to 4:7. How many students started in regular math and advanced math if there were 92 students in advanced math after the placement tests?
Let
x ----> the number of advanced math students
y ----> the number of regular math students
we know that
At the beginning of grade 6
----> equation A
After taking placement tests
----> equation B
----> equation C
Remember that
The total number of students at the beginning of grade 6 is the same that the number of students after taking placement tests
step 1
Find out the total number of students after taking placement tests
we have
----> equation B
----> equation C
substitute the value of x in equation B and solve for y
The total number of students after taking placement tests is
step 2
Find out how many students started in regular math and advanced math
we have that
At the beginning of grade 6
----> equation A
-----> equation D
Solve the system of equations by graphing
The solution is the intersection point both graphs
using a graphing tool
The solution is the point (69,184)
see the attached figure
therefore
There were 69 students in advanced math and 184 students in regular math before the placement tests
Answer:
:o
Step-by-step explanation:
I need help with these I also would like it if you showed your work.
Answers
Answer:
1. n=11 2. n=5 3. n=15 4. n=4 5. n=4 6. n=27
Step-by-step explanation:
1. Subtract 2 from 13 to get your answer of 11
2. Divide 15 by 3 to get your answer of 5
3. Multiply both sides by 3 to cancel out the division of 3 and you'll get 30, then divide both sides by 2 to get your answer of 15
4. Add 5 to both sides to cancel out the negative 5 and you'll get 4
5. Subtract 3 from both sides to cancel out the 3 and you'll end up with 2n=8, then you wanna divide both sides by 2 to get your final answer of 4
6. Add 2 to both sides to cancel out the negative 2 and you'll be left with 1/3n=9, next you wanna multiply both sides by 3 to cancel out the 1/3 and you'll get your final answer of 27
- 2 -2
subtract 2 from both sides in order to isolate the variable (n) , 2 then crosses out and you are left with n= 11
2. 3n = 15
\ 3 \3
divide by three on both sides in order to isolate the variable (n), 3 crosses out and you are left with 15\3 = 5 . therefore n=5 .
3. 2n/3 = 10
2/3 n = 10
you need to reciprocate by doing this you multiply 2/3 by 3/2 , this cross cancels. you then must do the same for the other side (10) , 10/1 * 3/2 . 10x3 = 30 1*2 =2 , 30/2 therefore n=15 .
4. n -5 = -1
+5 +5
add five to both sides:) , 5 cross cancels and you are left with -1 + 5, this equals 4
therefore n=4.
5. 2n + 3 = 11
this is a two step equation so you need to subtract & multiply. first subtract three from both sides leaving you with 2n = 8
then divide by 2, this isolates the variable. 2/2 you’re left with n and 8/2 is 4, therefore n=4 .
6. 1/3n - 2 = 7
two step equation so you need to multiply and add. first add 2 to both sides -2 + 2 crosses out = 0 and 7 + 2 = 9 . the equation should now be 1/3n = 9
you then need to reciprocate and multiply , 1/3 * 3/1 crosses out and you’re left with n , then do the other side 3/1 * 9/1 , 3*9 = 27 and 1*1 = 1 . therefore n = 27/1 or 27 .
i hope this helped a little :) sorry i couldn’t show all work so i did my best to explain, good luckk .
Ivan is getting ready for a long road trip. He wants to pack a few books from his collection of 5 novels and 7 collected short stories books. He asks his friend to select a book without showing. From the remaining books, Ivan then himself picks a random book, which turns out to be a novel. The third book that he randomly selects from the remaining ones is also a novel. Find the probability that Ivan will have 3 novels to read during the road trip.
Answers
Answer:
The probability that Ivan will have 3 novels to read during the road trip is 0.0455
Step-by-step explanation:
Given;
number of novels = 5
number of short stories = 7
total number of books = 12
The probability that Ivan's friend pick's a novel = 5 / 12
The probability of Ivan's first pick to be a novel = 4 / 11
The probability of Ivan's second pick to be a novel = 3 /10
The probability that Ivan will have 3 novels to read during the road trip is given by;
= p(Ivan's friend pick) and P(Ivan's first pick) and P(Ivan's second pick);
[tex]= \frac{5}{12}*\frac{4}{11}*\frac{3}{10}\\\\ = \frac{1}{22}\\\\ = 0.0455[/tex]
Therefore, the probability that Ivan will have 3 novels to read during the road trip is 0.0455
if there are 689 turtles flying on clouds and 90 turtles fall and die how much turtles are flying on clouds find the answers yourself I know you can do it! :)
Answers
Answer:
599
Step-by-step explanation:
uh just subtraction
Answer:
599
Step-by-step explanation:
689-90=599
Thats pretty sad...
which expressions are equivalent to 4b?
b+2(b+2b)
3b+b
2(2b)
Answers
Answer:
3b+b and 2(2b)
Step-by-step explanation:
BRAINLIEST APPRECIATED!
THANKS!
Consider the equation and its solution. 8 (x minus 2) = 64. 8 x minus 16 = 64. 8 x = 80. X = 10. Which property is used in the last step to find that x = 10? Distributive property addition property of equality subtraction property of equality division property of equality
Answers
Answer:
Division property of equality
Step-by-step explanation:
Consider the equation and its solution. 8 (x minus 2) = 64.
8 x minus 16 = 64.
8 x = 80.
x = 10.
Which property is used in the last step to find that x = 10
The property used in the last step to find that x = 10 is called the DIVISION PROPERTY OF EQUALITY
The Division property of equality states that , when two sides of a quadratic equation are divide by the same integer that is greater than zero, both sides will be equal to one another
Let c be the integer greater than zero
ac = bc
Divide both sides by c
a = b
From the above question
8 x = 80
This is also written as:
8x = 8 × 10
Division property of equality
Divide both sides by 8
Hence,
x = 10
Answer:
division property of equality
Step-by-step explanation:
since the equation before our answer was a multiplication equation, you must counteract that with the division property of equality.
Solve 5(x + 3) = 3x - 4
Show clear algebraic working,
Answers
Answer:
5(x + 3) = 3x - 4
=> (5 * x ) + (5 * 3) = 3x - 4
=> 5x + 15 = 3x - 4
=> 5x = 3x - 4 - 15
=> 5x - 3x = -4 - 15
=> 2x = -19
=> x = -19/2
=> x = -9.5
If my answer helped, kindly mark me as the brainliest!
Thank You!!
Leah bought a dress for the school dance that was priced ar $98.25. If the sales tax is 7.25%, how much money is added to the price?
Answers
Answer:
105.37
Step-by-step explanation:
Write an algebraic expression for the area of the conference room
Answers
Answer:
I like yo cut gggggggggggg
Use the greatest common factor to write each answer in simplest form what is 3/4 • 2/3?
Help ASAP
Answers
Answer:
1/2
Step-by-step explanation:
Please help me!!
Geometry
Answers
Answer:
3
Step-by-step explanation:
M is the midpoint of AB. That means that 2 binomials are equal.
4n - 40 = 7* (-2n + 2) Remove the brackets
4n - 40 = - 14n + 14 Add 14n to both sides
4n+14n - 40 = -14n+14n + 14 Combine
18n - 40 = 14 Add 40 to both sides
18n = 14 + 40 Combine
18n = 54 Divide by 18
18n/18 = 54/18 Combine
n = 3