Answers
x = -1
x = 0
Equation at the end of step 1 :
((3 • (x3)) - 32x2) - 12x = 0
Step 2 :
Equation at the end of step 2 :
(3x3 - 32x2) - 12x = 0
Step 3 :
Step 4 :
Pulling out like terms :
4.1 Pull out like factors :
3x3 - 9x2 - 12x = 3x • (x2 - 3x - 4)
Trying to factor by splitting the middle term
4.2 Factoring x2 - 3x - 4
The first term is, x2 its coefficient is 1 .
The middle term is, -3x its coefficient is -3 .
The last term, "the constant", is -4
Step-1 : Multiply the coefficient of the first term by the constant 1 • -4 = -4
Step-2 : Find two factors of -4 whose sum equals the coefficient of the middle term, which is -3 .
-4 + 1 = -3 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 1
x2 - 4x + 1x - 4
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-4)
Add up the last 2 terms, pulling out common factors :
1 • (x-4)
Step-5 : Add up the four terms of step 4 :
(x+1) • (x-4)
Which is the desired factorization
If you factor 3x from the expression, you have
[tex]3x^3+9x^2-12x=3x(x^2+3x-4)[/tex]
So, we have
[tex]3x(x^2+3x-4)=0 \iff 3x=0\lor x^2+3x-4=0[/tex]
We easily have
[tex]3x=0\iff x=0[/tex]
So, one solution is x=0.
The other solutions depend on the quadratic equation:
[tex]x^2+3x-4=0 \iff x=-4 \lor x=1[/tex]
So, the solutions are [tex]x=-4,\ 0,\ 1[/tex]
Related Questions
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
Find S5 for the sequence 3, 13, 23, 33, 43, 53, 63, 73.
Answers
Answer: B) 115
Step-by-step explanation:
S₅ means the sum of the first 5 numbers in the sequence.
3 + 13 + 23 + 33 + 43 = 115
What can you conclude from the diagram below?
Answers
Explanation:
E is the midpoint of ABF is the midpoint of CBEF is the midline of ΔABC, hence ║ACH is the midpoint of ADG is the midpoint of CDGH is the midline of ΔACD, hence ║AClength of EF = length of GH = 1/2 length of ACEFGH is a parallelogramΔEBF ~ ΔABCΔHGD ~ ΔACDarea relationships can be derived from the fact that the similar triangle scale factors are 1:2___
Similar relationships pertain to the diagonal BD and segments EH and FG. You can also conclude that area EFGH is half of area ABCD by considering the various triangles you get by connecting midpoints different ways.
The sum of the first 12 terms of an arithmetic progression is 156. What is the sum of the first and twelfth terms?
Answers
[tex]\bf \qquad \qquad \textit{sum of a finite arithmetic sequence} \\\\ S_n=\cfrac{n}{2}(a_1+a_n)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\[-0.5em] \hrulefill\\ n=12\\ S_{12}=156 \end{cases}\implies 156=\cfrac{12}{2}(a_1+a_{12}) \\\\\\ 156=6(a_1+a_{12})\implies \cfrac{156}{6}=a_1+a_{12}\implies 26=a_1+a_{12}[/tex]
Final answer:
The sum of the first and twelfth terms of an arithmetic progression, whose first 12 terms sum to 156, is 26. This is determined by using the arithmetic progression sum formula and understanding that the sum of equidistant terms from the beginning and end of the series is constant.
Explanation:
To determine the sum of the first and twelfth terms of an arithmetic progression (AP) given the sum of the first 12 terms, we can use the properties of AP. The sum of an arithmetic progression can be expressed using the formula Sn = n/2(2a + (n-1)d), where Sn is the sum of the first n terms, a is the first term, n is the number of terms, and d is the common difference.
For this question, the sum of the first 12 terms (S12) is given as 156, and we want to find the sum of the first and twelfth terms. By properties of AP, the sum of equidistant terms from the beginning and end (first and last terms in this case) is the same. So the sum of the first and twelfth terms is equal to the sum of the second and eleventh terms, and so on. This sum is consistent and equals a + a + 11d, which simplifies to 2a + 11d.
Since S12 = 12/2(2a + 11d) and we know S12 = 156, we can simplify the formula to get 156 = 6(2a + 11d). However, to solve for 2a + 11d directly, we do not need the value of d; we only need the fact that the sum of the first and last terms will be constant and equal to the sum of 2a + 11d. Therefore, the sum of the first and twelfth terms is 156/6, which equals 26.
Ava is solving a geometry problem. The length of a side of a triangle is 36. A line parallel to that side divides the triangle into two equal area parts. She solved for the length of the segment dividing the triangle and got 25.455. How did Ava get that answer?
Answers
The ratio of areas of similar triangles is the square of the ratio of their linear dimensions. If the smaller triangle is 1/2 the area of the larger, then its linear dimensions are √(1/2) those of the larger triangle.
smaller side length = √(1/2) × larger side length
= (√2)/2×36 = 18√2 ≈ 25.4558
Please help me with this please
Answers
If you extend the lines of the triangle, the angles formed are cut by the same transversals. therefore the angles of the two triangles are all congruent. If the two triangles have congruent angles, they are similar.
The sum of two numbers is 27. The larger number is 6 more than twice the smaller number. What is the number?
Answers
Answer:
Step-by-step explanation:
Let's say the numbers are x and y, and y is larger than x.
x + y = 27
y = 6 + 2x
Substitute:
x + (6 + 2x) = 27
3x + 6 = 27
3x = 21
x = 7
So x = 7 and y = 20.
If the search item is the 500th item in the list, how many key comparisons does the sequential search make to find the search item?
Answers
Answer:
500
Step-by-step explanation:
A sequential search starts with the first item on the list, making a comparison with every item until the desired one is found. It takes 500 comparisons to find the 500th item.
What is the approximate value of 2π -√ 3 ?
Answers
Answer:
Step-by-step explanation:
2*pi - sqrt(3)
pi = 3.14159
2pi = 6.283184
sqrt(3) = 1.73205
Answer
6.283184 - 1.73205
4.51133
Answer:
Sorry about being so late, but the answer is
4.55
OR
4.55113449961
Step-by-step explanation:
What is the sum of the coefficients of the expression 3x^4 + 5x^2 + x?
9
7
8
6
Answers
Answer:
9
Step-by-step explanation:
coefficients = numbers in front of variables (x, x^2 etc)
so 5 + 3 + 1 = 9
In the expression 3x^4 + 5x^2 + x, the coefficients are 3, 5, and 1. Adding these values together gives a sum of 9.
Explanation:In the expression 3x^4 + 5x^2 + x, the coefficients are 3, 5, and 1 respectively. The term x is implied to have a coefficient of 1 though it is not written explicitly. We find the sum of the coefficients by simply adding all these values together. So the sum would be 3 + 5 + 1 = 9.
The term x is implied to have a coefficient of 1 though it is not written explicitly. We find the sum of the coefficients by simply adding all these values together.
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True or False?
When researchers incorrectly interpret the responses to a survey question,
this is poor analysis.
Answers
Answer:
I think it would be true
The provided statement "When researchers incorrectly interpret the responses to a survey question, this is poor analysis" is true.
What is an analysis of a survey?The practice of assessing client insights is known as survey analysis. It could be customer satisfaction scores or other customer experience measures.
We have a statement:
When researchers incorrectly interpret the responses to a survey question,
this is a poor analysis.
The above statement is true because when we have survey data that is incorrectly interpreted, it will create a problem in the final phase or implementation phase.
Thus, the provided statement "When researchers incorrectly interpret the responses to a survey question, this is poor analysis" is true.
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You have 5 different trophies to arrange on the top shelf of a bookcase. How many ways are there to arrange the trophies?
A. 120
B. 24
C. 720
D. 25
Answers
Answer:
120
Step-by-step explanation:
5x4x3x2x1 =120
The number of ways to arrange the trophies is 120. The correct answer is option A.
What is the combination?The arrangement of the different things or numbers in a number of ways is called the combination.
Given that:-
You have 5 different trophies to arrange on the top shelf of a bookcaseThe number of the ways will be calculated as:-
N = 5!
N = 5 x 4 x 3 x 2 x 1
N = 120 ways
Therefore the number of ways to arrange the trophies is 120.
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Can the polynomial in the numerator of the expression x2-5x+7/x-9 be factored to derive (x − 9) as a factor?
Answers
Answer:
No.
Step-by-step explanation:
Because x²-5x+7, as x = 9 is 9²-5·9+7 = 81-45+7 ≠ 0
f(x) = x²-5x+7 is divisible by x-9 only if f(9) = 0.
Function 1: y = 4x + 5
Function 2: The line passing through the points (1, 6) and (3, 10).
Which of these functions has the greater rate of change?
Answers
Answer:
B
Hope this helps!
Answer:
B
Step-by-step explanation:
The rate of change is the slope. Function 1 has a slope of 4. Function 2 has a slope of:
m = Δy / Δx
m = (10 - 6) / (3 - 1)
m = 4 / 2
m = 2
So function 1 has the greater rate of change. Answer B.
The ages of Hari and Harry are in the ratio 5:7. Four years from now the ratio of their ages will be 3:4. Find their present ages
Answers
Answer:
Hari is 20; Harry is 28
Step-by-step explanation:
The ratio in 4 years is equivalent to the ratio 6:8, which has each of the original ratio unit numbers increased by 1. That means each of those ratio units stands for 4 years, and the present ages are ...
Hari: 5·4 = 20
Harry: 7·4 = 28
_____
Conventional method of solution
If you like, you can write equations for the ages of Hari (x) and Harry (y):
x/y = 5/7
(x+4)/(y+4) = 3/4
These can be solved a variety of ways. For some methods, it may be useful to write them in standard form:
7x -5y = 04x -3y = -4These have solution (x, y) = (20, 28).
I need help with this please
Answers
Answer:
D
Step-by-step explanation:
The difference in the x-coordinates is Δx = 6 - 3 = 3.
The difference in the y-coordinates is Δy = 8 - 2 = 6.
One third the difference is Δx/3 = 3/3 = 1 and Δy/3 = 6/3 = 2.
So the one-third point is at (3 + 1, 2 + 2) = (4, 4).
In general the segment from A to B has parametric equation
X = (1-t)A + tB
t=0 gives point A, t=1 gives point B, and in between we move linearly with t from A to B.
So if we want AX:BX=1:3, that's 1/(1+3)=1/4 of the way along from A to B, so corresponds to t=1/4. So the point we seek is
X = (1 - 1/4)(3, 2) + (1/4)(6,8) = ((9+6)/4, (6+8)/4)=(15/4, 7/2)
Answer: Choice C
A Package of 10 pens cost $5. Ms.Jackson spent $45 on pens for her office. How many pens did she buy?
Answers
Each pack costs 5 dollars so you take 5 times 8 to get 45 dollars. Then you take to 8 and times it by 10 to get a total of 80 pens
The function f(x) is the total amount spent at a store, when purchasing x items that are $5 each and the items are not taxable.
What is the practical domain for the function f(x)?
A. all positive integers that are multiples of 5
B. all whole numbers
C. all positive integers
D. all real numbers
Answers
Answer:
B
Step-by-step explanation:
The domain is all possible values of x. Here, x is the number of $5 nontaxable items. So x must be an integer, and it can't be negative. It is possible for x to be 0. So x is all whole numbers.
The practical domain for the function f(x) which represents the total amount spent at a store is all whole numbers. Option B is correct.
What is domain of function?Domain of a function is the set of all the possible input values which are valid for that function.
The function f(x) represents the total amount spent at a store. The purchasing number of x items which are $5 each and the items which are not taxable is represented by x.
Thus, this function can be given as,
f(x)=5x
Now the domain of a function is the set of all the possible input values which are valid for that function. Thus, for this case the domain is,
-∞<x<∞
(-∞,∞)
For the practical domain, the numbers should be whole number to avoid negative amount value and integer amount.
Hence, the practical domain for the function f(x) which represents the total amount spent at a store is all whole numbers. Option B is correct.
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The Environmental Protection Agency is attempting to revive 3 acres of contaminated soil by replacing the top 24 inches of the soil. Trucks with a hauling capacity of 28 cubic yards of soil are hired to remove the contaminated soil. How many full truckloads of contaminated soil will be hauled away?
Answers
Answer:
346 trucks are needed
Step-by-step explanation:
We know that one acre equals 43560 feet ^ 2
In this case the area is 3 acres. So:
[tex]3\ acres * \frac{43,560\ ft^2}{1\ acre} = 130,680\ ft^2[/tex]
We know that 1 foot equals 12 inches. So:
[tex]24\ in * \frac{1\ ft}{12\ in} = 2\ ft[/tex]
So the volume of the contaminated area is:
[tex]V = 2* 130,680\ ft^3\\\\V = 261,360\ ft^3[/tex]
In a cubic yard there are 27 cubic feet. So:
[tex]28\ yard^2 * \frac{27\ ft^3}{1\ yard^3} = 756\ ft^3[/tex]
Finally if we have a volume of [tex]261,360\ ft ^ 3[/tex] and each truck can transport [tex]756\ ft ^ 3[/tex] then the amount of trucks x we need is:
[tex]x = \frac{261,360\ ft ^ 3}{756\ ft ^ 3} = 346\ trucks[/tex]
Write an equation that represents Boyle’s law (the volume of air varies inversely with the pressure). Use k for the variation constant.
Answers
[tex]\bf \qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{\textit{\underline{v}olume varies inversely with \underline{p}ressure}}{V=\cfrac{k}{p}}~\hfill[/tex]
For which values of x, rounded to the nearest hundredth, will x 2 − 9 | | | | − 3 = log3 x?
Answers
Answer:
2.3 and 3.6
Step-by-step explanation:
Final answer:
To solve the equation x^2 - 9|||-3 = log3 x, simplify both sides of the equation and then find the values of x that satisfy the equation.
Explanation:
To find the values of x that satisfy the equation, we can start by simplifying both sides of the equation.
On the left side, we have x^2 - 9|||-3. To simplify this, we first evaluate the absolute value of -3, which is 3. Then we have x^2 - 9(3), which simplifies to x^2 - 27.
On the right side, we have log3 x.
Setting the two sides equal to each other, we have x^2 - 27 = log3 x.
To solve this equation, we can graph both sides and find the intersection points, or we can use numerical methods like iteration or Newton's method to find the approximate solutions.
Karen finished watching a movie at 1:10 pm. The movie lasted 1 hour 38 minutes what time did Karen started watching the movie
Answers
well, the movie lasted 1:38 so.... and she finished it at 1:10pm.
1:10pm minus 1 hour? 12:10pm.
12:10 pm minus 10 and minus 28 minutes? 12:10 - 00:10 = 12:00pm, 12:00 - 00:28 minutes = 11:32am.
Answer: 11:32
Step-by-step explanation:
Sydney needs 70cm of feinge for each scarf she makes. How many scarves can she make if she has 6 meters of fringe?
Answers
Answer:
8
Step-by-step explanation:
First Step
Convert meters to centimeters
For every meter there are 100 (centi)meters
6 meters ×100=600 cm
Second Step
Find how many scarves can be made
We have 600 cm of fringe
It takes 70 cm to make 1 scarf
Divide 70 into 600
600÷70=8.571
Rounding down we get 8
Katie is going to rent an apartment and has to choose the number of bedrooms the apartment has, the type of parking she will use, and the length of the lease that she will sign. She has three options for the number of bedrooms (one, two, or three bedrooms), three options for the type of parking (street, assigned, or garage spots), and four options for the length of the lease (1, 6, 12, or 24 months.) How many possible combinations are there for the number of bedrooms, parking options, and the length of the lease that Katie could select?
How many possible combinations are there for the number of bedrooms, parking options, and the length of the lease that Katie could select?
72
36
27
48
10
Answers
Answer:
36
Step-by-step explanation:
The total number of options is the product of the numbers of independent options: 3×3×4 = 36.
__
For each of the bedroom options, she can choose any parking option, so can have ...
1 br, street parking
2 br, street parking
3 br, street parking
1 br, assigned parking
2 br, assigned parking
3 br, assigned parking
1 br, garage spots
2 br, garage spots
3 br, garage spots
That is, 3×3 = 9 options. Any of these can be put with any of the four lease options, for a total of 9×4 = 36 options altogether.
The answer would be 36
Solve the equation by completing the square. Round to the nearest hundredth if necessary. x^2 – 2x = 24
Answers
Answer:
x=6,-4
Step-by-step explanation:
Use the formula (b/2)^2 in order to create a new term. Solve for x by using this term to complete the square.
x=6,-4
Which of the following expressions are equivalent to 48a^3-75a? Select all that apply.
Answer 1) 3(48a^3-75a).
Answer 2) 3a(16a^2-25)
Answer 3)3a(4a+5)(4a+5)
Answer 4) 3a(4a+5)(4a-5)
Answer 5) -3a(25-16a^2)
Answer 6) -3a(5-4a)(5+4a)
Answers
Answer:
Answer 2) 3a(16a^2-25)Answer 4) 3a(4a+5)(4a-5)Answer 5) -3a(25-16a^2) Answer 6) -3a(5-4a)(5+4a)Step-by-step explanation:
The factors of each term are ...
2·2·2·2·3·a·a·a3·5·5·aSo, the greatest common factor is 3a. Factoring that out gives ...
3a(16a^2 -25) . . . . . . matches answer 2
The factor in parentheses is the difference of squares, so it can be factored. You have memorized the form for the difference of squares ...
p^2 -q^2 = (p -q)(p +q)
so you know the factoring of this with p=4a and q=5 will be ...
3a(4a -5)(4a +5) . . . . . . matches answer 4
__
Any pair of factors can be multiplied by -1 without changing the value of the expression. So, two more answers are equivalent:
(-3a)(-(16a^2 -25) = -3a(25 -16a^2) . . . . . . matches answer 5
(-3a)(-(4a -5)(4a +5) = -3a(5 -4a)(5 +4a) . . . . . . matches answer 6
Answer:
2 4 5 6
Step-by-step explanation:
The highest common factor is 3a That means that 48a^3 must be divided by 3a which means 48a^3 / 3a = 16a^2. Notice what happened. 48/3 = 16. a^3/a = a^2.
Now you have to pull out 3a from 75a. That wasn't done to Answer 1. So answer one is incorrect.
75a/3a = 25
So far what you answer looks like is
3a(16a^2 - 25) which is answer 2
===========================================
Answer 3 is wrong because one of the factor has to be - 5. Neither one is.
===========================================
Answer 4 is correct
16a^2 - 25 factors into (4a - 5)(4a + 5)
So what is written reflects those factors + the 3a
==============================================
Now we come to the brutal ones.
If you take out a minus sign from the brackets, it has the effect of turning the two terms inside the brackets around.
-3a(25 - 16a^2) is what the above sentence means. so 5 is correct
==============================================
The two terms inside the brackets still factor
-3a ( 5 - 4a)(5 + 4a) It is just that they are turned around.
6 is correct.
===============================================
WILL MARK BRAINLEST
The graph shows two lines, A and B.
A graph is shown with x- and y-axes labeled from 0 to 6 at increments of 1. A straight line labeled A joins the ordered pair 0, 6 with the ordered pair 6, 3. Another straight line labeled B joins the ordered pair 0, 0 with the ordered pair 6, 6.
Part A: How many solutions does the pair of equations for lines A and B have? Explain your answer. (5 points)
Part B: What is the solution to the equations of lines A and B? Explain your answer. (5 points)
Answers
Answer:
Part A) The system has one solution
Part B) The solution is the point (4,4)
Step-by-step explanation:
step 1
Find the equation of the line A
we have
(0,6) and (6,3)
Find the slope
m=(3-6)/(6-0)
m=-0.5
Find the equation of the line into slope intercept form
y=mx+b
we have
m=-0.5
b=6 -----> the point (0,6) is the y-intercept
substitute
y=-0.5x+6 ------> equation A
step 2
Find the equation of the line B
we have
(0,0) and (6,6)
Find the slope
m=(6-0)/(6-0)
m=1
Find the equation of the line into slope intercept form
y=mx+b
we have
m=1
b=0 -----> the line represent a direct variation
substitute
y=x ------> equation B
step 3
Find how many solutions does the pair of equations for lines A and B have
we have
y=-0.5x+6 ------> equation A
y=x ------> equation B
Solve the system of equations by graphing
Remember that the solution of the system of equations is the intersection point both lines
using a graphing tool
There is one point of intersection
therefore
The system has one solution
see the attached figure
step 4
What is the solution to the equations of lines A and B?
we know that
The solution of the system of equations is the intersection point both lines
The intersection point is (4,4)
therefore
The solution is the point (4,4)
so
x=4,y=4
Domain and Range...
Answers
The domain is the X values and the range is the y values.
The blue line starts at X 0 and Y 0 and moves up and to the right.
This means the range and domain are equal to or greater than 0.
The 3rd choice is the correct one.
someone please help me
i’ll give brainliest
Answers
Answer:
[tex]x^{1/4} y^{1/2}[/tex]
Step-by-step explanation:
When you have a power then a root like that, you have to divide the power by the root.
So, in this case, you have (x^2y^4) and a 8th root (8√).
So, you take your exponents from (x^2y^4) and divide them by the root (8), to get new powers of 2/8, or 1/4, and 4/8 or 1/2
As I already explained you in other questions, that leaves a fractional exponent that is equivalent to the regular exponent then rooted.
Answer is then: [tex]x^{1/4} y^{1/2}[/tex]
Please help me out with this!!!!! Help is much needed !
Answers
here the centre of circle(h,k) is (-2,4)
and its radius(r) is 6 uints.
now the equation of circle is,
(x-h)^2 +(y-k)^2 =r^2
or, (x+2)^2 + (y-4)^2=6^2
or, x^2 + 4x + 4+y^2 -8y+16=36
or, x^2 +y^2 + 4x -8y -16=o
The equation y=15x+30 describes the relationship between the number of months since a customer began renting a storage unit and the total amount of money, in dollars, the customer has paid to the storage facility. Which statement describes a solution of the equation based on the number of months of customer has rented the storage unit
Answers
This function starts at 30 where x=0, and then gains 15 units each time x is increased by 1.
So, we deduce that renting the storage has a fixed price of 30, and then you have to pay 15 each month.
It will add 15 dollar for each month.