I need step by step solution of this question.i will give brainliest to who gives step by step answer.
Answers
Answer:
(- 1, - 2/3, 1/2)
======================
Factorize as below and find roots:
6x³ + 7x² - x - 2 = 06x³ + 6x² + x² - x - 2 = 06x²(x + 1) + x² + x - 2x - 2 = 06x²(x + 1) + x(x + 1) - 2(x + 1) = 0(x + 1)(6x² + x - 2) = 0(x + 1)(6x² + 4x - 3x - 2) = 0(x + 1)(2x(3x + 2) - (3x + 2)) = 0(x + 1)(3x + 2)(2x - 1) = 0x + 1 = 0 or 3x + 2 = 0 or 2x - 1 = 0x = - 1 or x = - 2/3 or x = 1/2Answer:
\(x=-1, \quad x=\dfrac{1}{2}, \quad x=-\dfrac{2}{3}\)
Step-by-step explanation:
Given polynomial:
\(f(x)=6x^2+7x^2-x-2\)
\(\boxed{\begin{minipage}{6 cm}\underline{Factor Theorem}\\\\If $f(x)$ is a polynomial, and $f(a) = 0$,\\ then $(x-a)$ is a factor of $f(x)$.\\\end{minipage}}\)
Since the constant of the given polynomial is -2, the possible factors are ±1 and ±2.
Apply the Factor Theorem to check the possible values:
\(f(1)=6(1)^3+7(1)^2-(1)-2=10 \neq 0\)
\(f(-1)=6(-1)^3+7(-1)^2-(-1)-2=0\)
\(f(2)=6(2)^3+7(2)^2-(2)-2=72 \neq 0\)
\(f(-2)=6(-2)^3+7(-2)^2-(-2)-2=-20 \neq 0\)
Therefore, (x + 1) is a factor of the polynomial:
\(f(x)=(x+1)(ax^2+bx+c)\)
Compare with the original function to find the coefficients of the quadratic:
\(6x^3=ax^3 \implies a=6\)
\(7x^2=(b+a)x^2 \implies b=1\)
\(-2=c \implies c=-2\)
Therefore:
\(f(x)=(x+1)(6x^2+x-2)\)
Factor the quadratic:
\(f(x)=(x+1)(6x^2+4x-3x-2)\)
\(f(x)=(x+1)[2x(3x+2)-1(3x+2)]\)
\(f(x)=(x+1)(2x-1)(3x+2)\)
Set the polynomial function to zero:
\((x+1)(2x-1)(3x+2)=0\)
Apply the zero product property:
\((x+1)=0 \implies x=-1\)
\((2x-1)=0 \implies x=\dfrac{1}{2}\)
\((3x+2)=0 \implies x=-\dfrac{2}{3}\)
Therefore, the solutions are:
\(x=-1, \quad x=\dfrac{1}{2}, \quad x=-\dfrac{2}{3}\)
Related Questions
what is the following coordinates of (2,0) and (0,4)
Answers
Answer:
(2, 0) and (0, 4) are coordinates in the form of (x, y)
(2, 0) -> x = 2, y = 0
(0, 4) -> x = 0, y = 4
joey finds 14 video games that he would like to have. nine of them will run on this operating system and 5 will not. how many ways can joey select 1 that will run on his operating system and 1 that will not?
Answers
There are 45 ways that joey select 1 that will run on his operating system and 1 that will not
To solve this problem the formula and the combination procedure we must use is:
C(n/r) = n! / [(n-r)! *r!]
Where:
C(n/r) = combinationn = total number of objectsr = number of selected objects! = factorial of the numberInformation about the problem:
Run on
n = 9r = 1C(9/1) =?Will not run on
n = 5r = 1C(5/1)=?C(9/1) * C(5/1) = ?
Applying the combination formula we have:
C(n/r) = n! / [(n-r)! *r!]
C(9/1) = 9! / [(9-1)! *1!]
C(9/1) = 9! / [(8)! *1!]
C(9/1) = 9*8! / [(8)! *1!]
C(9/1) = 9/1!
C(9/1) = 9/1
C(9/1) = 9
C(5/1) = 5! / [(5-1)! *1!]
C(5/1) = 5! / [(4)! *1!]
C(5/1) = 5*4! / [(4)! *1!]
C(5/1) = 5/1!
C(5/1) = 5/1
C(5/1) = 5
C(9/1) * C(5/1) = 9*5 = 45
What is a combination?In mathematics, a combination or combinations are all the possible groupings that can be made of a given number of elements, without repeating them and regardless of the order in which they are found.
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Your friend loans you $20,000 for school. In five years he wants
$40,000 back. What is the interest rate he is charging you?
Remember to show your work.
Answers
The interest rate your friend is charging you for the $20,000 loan is 20% per year.
What is the interest rate on the loan?
The simple interest is expressed as;
A = P( 1 + rt )
Where A is accrued amount, P is principal, r is the interest rate and t is time.
Given that;
The Principal P = $20,000
Accrued amount A = $40,000
Elapsed time t = 5 years
Interest rate r =?
Plug these values into the above formula and solve for the interest rate r:
\(A = P( 1 + rt )\\\\r = \frac{1}{t}( \frac{A}{P} -1 ) \\\\r = \frac{1}{5}( \frac{40000}{20000} -1 ) \\\\r = \frac{1}{5}( 2 -1 ) \\\\r = \frac{1}{5}\\\\r = 0.2 \\\\\)
Converting r decimal to R a percentage
Rate R = 0.2 × 100%
Rate r = 20% per year
Therefore, the interest rate is 20% per year.
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If you can solve this i will thank you, rate you 5 stars, and give you brainly. 50 POINTS
Answers
Roll one fair, six-sided die, numbered 1 through 6. Let A be the event you will roll an even number.
Answers
Answer:
P(A) = 1/2
Step-by-step explanation:
The question seems incomplete, I assume that we want to find the probability of event A.
Here we have a fair six-sided dice, so each one of the six numbers has exactly the same probability of being rolled.
Such that the possible outcomes of rolling the dice is:
{1, 2, 3, 4, 5, 6}
Now we define event A as rolling an even number.
The possible outcomes such that the event A is true are the even numbers:
{2, 4, 6}
So we have 3 outcomes out of 6.
Then the probability of rolling an even numbers, is just the quotient between the number of outcomes of even numbers (3) and the total number of outcomes (6).
Then:
P(A) = 3/6 = 1/2 = 0.5
A phone case comes in 8 different colors, and you can also pick from 10 different patterns. If you can only pick one of each, how many different phone cases can there be
Answers
Answer:
80
Step-by-step explanation:
8 different colors multiplied by 10 different patterns
A gallon of water at room temperature weight about 8.35 pounds Lena put 4.5 gallons in a bucket how much is a water weight
Answers
Answer:
(4.5)(8.35)=37.58 lbs should be the answer
Step-by-step explanation:
What is the slope of the line with equation y-3=-1/2 (x-2)
Answers
Given parameters:
Equation of the straight line;
y - 3 = \(\frac{-1}{2}\)(x -2)
We can determine the slope of any straight line from the equation of such lines.
Generally, a straight line has the formula;
y = mx + C
where y is the y-axis coordinate and x is the x-axis coordinate
m is the slope and c is the y-axis intercept
Now let us express the given equation in this format;
y - 3 = \(\frac{-1}{2}\)(x - 2)
Multiply both sides by 2;
2(y - 3) = -1(x -2)
2y -6 = -x + 2
Rearrange to the form y = mx + c
2y = -x + 2 + 6
2y = -x + 8
divide by 2;
y = \(\frac{-1}{2}\)x + 4
y = mx + c
the slope is m and it is equal to \(\frac{-1}{2}\)
If the surface area of a can is 1406.72 cm2, and the radius is 8 cm, the height
Answers
Answer:
20
Step-by-step explanation:
i got it right on a quiz
Height of a can is equal to \(\boldsymbol{6.99\,cm}\).
Surface area of a cylinderSurface area of a cylinder \(=\pi r^2h\) where \(r,h\) denote radius, height of a cylinder respectively.
Surface area of a can \(=1406.72 \,cm^2\)
Radius of a can \(=8 \,cm\)
\(1406.72=\frac{22}{7}(8)^2h\)
\(h=6.99\,cm\)
Therefore, height of a can is equal to \(\boldsymbol{6.99\,cm}\)
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A baseball team plays the same opponent six times in a season. The set {0,1,2,3,4,5,6} describes the possible number of wins for the six games.
Set A contains the number of wins when exactly four games are won.
Set B contains the number of wins when at least four games are won.
Which of these statements are true? Choose all that are correct.
The union of set A and B is an empty set
The complement of the union of set A and B is {0,1,2,3} set A
The complement of set B is {0,1,2,3}
The intersection of set A and set B is an empty set
The complement of set B is {1,2,3}
Answers
- The complement of set B is {0,1,2,3}
- The complement of set B is {1,2,3}
Endure all, a manufacturer of batteries claims that the lifetime of their batteries is normally distributed with a mean of 500 hours and a standard deviation of 40 hours. What is the probability that an endure all battery selected at random will last more than 550 hours?.
Answers
An Endure chosen randomly the likelihood of any battery lasting longer than 550 hours is 10.56%.
What does z score mean?An indicator of how nearly a value relates to the mean of either a set of values is called a Z-score.Z-score is quantified using standard deviations relative to the mean.The data point's entire score is equal to the mean score when the Z-score is 0.The amount that the raw score departs first from mean is determined using the Z score.These steps are used to determine the Z score:
z = (x - μ)/σ
As mentioned in question-
x > 550 and μ = 500, σ = 40:
z = 550 - 500 / 40
z = 1.25
Obtain the p-value from normal distribution chart,
P(z > 1.25) = 1 - P(z < 1.25)
P(z > 1.25) = 1 - 0.8944
P(z > 1.25) = 0.1056
Thus, an Endure chosen at random the likelihood of any battery lasting longer than 550 hours is 10.56%.
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Don buys a car for $22,500. Don gets a loan for a year with an interest rate of 3% per year. How much total money will Don pay in a year?
A. $2.75
B. $583
C. $552.75
D. $23,175
e. $407.78
f. $33
g. $806.25
H. $437.70
i. $443.01
j. $185
*also explain how you got your anwers
Answers
Answer:
To find out how much total money Don will pay in a year, we need to calculate the interest on the loan. The formula for calculating simple interest is Interest = Principal x Rate x Time, where Principal is the amount of money borrowed, Rate is the interest rate per year, and Time is the duration of the loan in years.
In this case, the Principal is $22,500, the Rate is 3%, and the Time is 1 year. So, the Interest = 22,500 x 0.03 x 1 = $675. This means that Don will have to pay $22,500 + $675 = $23,175 in total in a year. However, the options given in the question are different from the calculated answer. Option f is incorrect, and option i is correct. The calculated answer matches option i, which is $443.01.
To calculate the total money Don will pay in a year, you need to find the interest and add it to the principal amount.
Step 1: Calculate the interest
Interest = Principal × Interest Rate × Time
Interest = $22,500 × 3% × 1 year
Interest = $22,500 × 0.03 × 1
Interest = $675
Step 2: Add the interest to the principal amount
Total Payment = Principal + Interest
Total Payment = $22,500 + $675
Total Payment = $23,175
So, Don will pay a total of $23,175 in a year. I found this answer by calculating the interest and then adding it to the initial amount of the car.
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The length of a rectangle is 24" and its width is 7". How long is a diagonal?
(A) 22"
(B) 25"
(C) 28"
(D) 31"
(E) 34"
Answers
Select the correct answer.
Use a graphing tool to solve the equation for x.
-4x - 1 = 5x + 4
A.
X-0.25
B.
X=-1.50
C.
X-1.25
D. X=-1
Answers
The equation -4x + 1 = 5x + 4 can be used to form a system of linear equations
The solution of x is x = -0.33
How to determine the solution?The equation is given as:
-4x + 1 = 5x + 4
Split the equation into a system of equations
y =-4x + 1
y = 5x + 4
Next, we plot the graph of both equations
From the graph (see attachment), we have the solution to be:
(x,y) = (-0.33, 2.33)
Remove the y value
x = -0.33
Hence, the solution of x is x = -0.33
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help in explaining please!
Answers
Hi!
As per graph and question,
a) The most challenging is:-
Examination B
Reason - There are few high scores and many low scores.
b) The least challenging is:-
Examination C
Reason- There are many high scores, few low scores and the lowest mark is not zero.
is the integer k divisible by 4 ? (1) 8k is divisible by 16. (2) 9k is divisible by 12.
Answers
Yes , the integer k is divisible by 4 and statement (1) alone is sufficient to determine that k is divisible by 4.
Given data ,
Let the equation be represented as A
Now , the value of A is
a)
To determine if the integer k is divisible by 4, let's analyze the given statements:
Statement (1): 8k is divisible by 16.
This means that 8k is a multiple of 16. Since 16 is divisible by 4, we can conclude that k must be divisible by 4 as well. Therefore, statement (1) alone is sufficient to determine that k is divisible by 4.
8k = 16
k = 2
b)
This statement does not provide direct information about the divisibility of k by 4. While 12 is divisible by 4, the fact that 9k is divisible by 12 does not guarantee that k itself is divisible by 4.
9k = 12
k = 12/9
k = 4/3
So , it is not an integer
In conclusion, statement (1) alone is sufficient to determine that k is divisible by 4. Statement (2) is not sufficient on its own.
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what proportion of tickets sold are adult tickets? (image)
Answers
100-40=60
60/100=0.6
Maria's penny collection contains three Indian head pennies for every 30 Lincoln pennies. If Maria has 630 Lincoln head pennies, how many Indian head pennies does she have?
Answers
Answer:
63 Indian head pennies
Step-by-step explanation:
3:30 i:L
simplifies to
1:10 so 1 Indian head penny for every 10 Lincoln.
?:630
630 / 10 = 63
find the length of ab? i’ll give brainlist
Answers
Answer:
b
Step-by-step explanation:
draw a right angled triangle and use pythagoras to solve it
The fraction 6/2 describes Kyle's speed in miles per hour. What fraction would
describe Kyle's speed in hours per mile? What is his speed in hours per mile?
Answers
Kyle's speed in hours per mile is \(\frac{2}{6}\) hours/mile.
What is a fraction?A fraction is a component or segment taken from a whole, which can be any number, a certain amount, or an object. Let's use an example to better comprehend this idea. The pizza in the accompanying image has been sliced into 8 equally sized pieces. Now, if we wish to refer to a single portion of the pizza, we can do so by using the notation 1/8, which indicates that we are talking about one portion out of 8 equally sized portions.
Given that,
Kyle's speed in miles/hour = \(\frac{6}{2}\)
Now,
Kyle's speed in hour/mile = \(\frac{2}{6}\)
Hence, Kyle's speed in hours per mile is \(\frac{2}{6}\) hours/mile.
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can someone please help me find the valu of X?
Answers
The midsegment determines a smaller triangle that is similar to the larger triangle. If two triangles are similar, then their side lengths are at the same ratio, so that:
\(\begin{gathered} \frac{5x}{45}=\frac{20}{20+16} \\ \frac{5x}{45}=\frac{20}{36} \end{gathered}\)From this expression, you can determine the value of x:
-First. multiply both sides by 45:
\(\begin{gathered} 45(\frac{5x}{45})=45(\frac{20}{36}) \\ 5x=25 \end{gathered}\)-Second, divide both sides by 5 to determine the value of x:
\(\begin{gathered} \frac{5x}{5}=\frac{25}{5} \\ x=5 \end{gathered}\)The value of x is equal to 5
ply
1:
Kristina receives £5 from her Grandmother.
She gives £1 to her sister.
What percentage of the £5 did she give to her sister?
Answers
Answer:
Step-by-step explanation:
1/5 = 0.2 = 20%
Evaluate 10 + 8 ÷ 2 − 4
Answers
Step-by-step explanation:
we will solve this question according to BODMAS rule...
B for bracket
O for of
D for division
M for multiplication
A for addition
S for Subtraction
10+4-4
14-4
10 Answer..
Answer:
10
Step-by-step explanation:
Using order of operations as stated in PEMDAS , that is
division is performed before addition/ subtraction , then
10 + 8 ÷ 2 - 4
= 10 + 4 - 4
= 14 - 4
= 10
What is the answer when you evaluate m + p - p2 ÷ 6; use m = 5 and p = 6 ?
Answers
Answer:
5
Step-by-step explanation:
m + p - p^2 ÷ 6
Let m = 5 and p=6
5 + 6 - 6^2 ÷ 6
Exponents first
5 + 6 - 36 ÷ 6
Then divide
5 + 6 - 6
Then add and subtract from left to right
11-6
5
f(x)=2x^2-5x-3 g(x)=2x^2+5x+2 find (f/g)(x)
Answers
If f(x)=2x²-5x-3 g(x)=2x²+5x+2 then (f/g)(x) = (x - 3) / (x + 2).
What is function?
In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.
To find (f/g)(x), we need to divide f(x) by g(x) as follows:
f(x) = 2x² - 5x - 3
g(x) = 2x² + 5x + 2
f(x) / g(x) = (2x² - 5x - 3) / (2x² + 5x + 2)
To simplify this expression, we can factor the numerator and denominator:
f(x) / g(x) = [(2x + 1)(x - 3)] / [(2x + 1)(x + 2)]
Now, we can cancel out the common factor of (2x + 1) from both the numerator and denominator:
f(x) / g(x) = (x - 3) / (x + 2)
Therefore, (f/g)(x) = (x - 3) / (x + 2).
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-
If (a + b)² = 80 and ab=12, find the
value of a² +6?
Answers
Answer:
(a+b)²=a²+2ab+b²=80
a²+b²=80-2ab
=80-2(12)
=80-24
=56
Side AC corresponds to side
.
Angle BAC corresponds to angle
Answers
Answer:
???
Step-by-step explanation:
Where's the image?
The difference between two numbers is 5, and 2 times the lesser number is 18 more than the greater number. Find the numbers.
Answers
Answer:
Let x and y be the numbers, with x the larger one.
x - y = 5
2y = x + 18
Then solve this system of equations:
x - y = 5
x - 2y = -18
Subtract bottom equation from top equation and get
y = 23
So x = y + 5 = 23 + 5 = 28
Help ASAP please and thanks
Answers
Answer: 234 - 40 = 2x
194 = 2x
97 = x
x being the amount Trey had before mowing lawns
If a baseball card appreciates exponentially in value by 50% over 10 years, what is its annual appreciation (growth) rate? Please use a calculator, and answer to the nearest whole percent.
Answers
we can use hmmm any value per se for the card, hmmm say let's use $2, if the baseball card was initially 2 bucks, and after 10 years it went up in value by 50%, well 50% of 2 is 1, so the new value is 3 bucks, then
\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill &3\\ P=\textit{initial amount}\dotfill &2\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &10\\ \end{cases} \\\\\\ 3=2(1 + \frac{r}{100})^{10}\implies \cfrac{3}{2}=(1 + \frac{r}{100})^{10}\implies \cfrac{3}{2}=(\frac{100+r}{100})^{10} \\\\\\ \sqrt[10]{\cfrac{3}{2}}=\cfrac{100+r}{100}\implies 100\sqrt[10]{\cfrac{3}{2}}=100+r \\\\\\ 100\sqrt[10]{\cfrac{3}{2}}-100=r\implies 4\approx r\)