Write the equation of the graph shown below in the factored form f(x) = (x + 2) (x - 1) (x - 3) f(x) = (x - 2) (x + 1) (x + 3) f(x) = (x + 2) (x + 1) (x + 3) f(x) = (x - 2) (x - 1) (x - 3)
Answers
Answer:
[tex]f(x)=(x-1)\,(x-3)\.(x+2)[/tex]
which agrees with the first answer shown in the list of possible options.
Step-by-step explanation:
Notice that there are three roots for this polynomial clearly shown on the graph's crossings of the x axis: x = 1, x = 3, and x = -2.
Therefore, based on such, we can write three binomial factors of the form [tex](x-root)[/tex] for the polynomial:
[tex]f(x)=(x-1)\,(x-3)\.(x-(-2))=(x-1)\,(x-3)\.(x+2)[/tex]
Related Questions
Select the correct answer from each drop-down menu. The graph represents the piecewise function.
Answers
Answer:
1). f(x) = x² if ∞ < x < 2
2). f(x) = 5 if 2 ≤ x < 4
Step-by-step explanation:
The graph attached shows the function in two pieces.
1). Parabola
2). A straight line parallel to the x-axis.
Standard equation of a parabola is,
y = a(x - h)² + k
where (h, k) is the vertex.
Vertex of the given parabola is (0, 0).
Equation of the parabola will be,
y = a(x - 0)² + 0
Therefore, the function will be,
f(x) = ax²
Given parabola is passing through (-1, 1) also,
1 = a(-1)²
a = 1
Therefore, parabolic function will be represented by,
f(x) = x² if ∞ < x < 2
2). Straight line parallel to the x-axis,
y = 5 if 2 ≤ x < 4
Function representing the straight line will be,
f(x) = 5 if 2 ≤ x < 4
Answer:
Please mark me as Brainliest :)
Step-by-step explanation:
A cryptarithm is a math puzzle in which the digits in a simple equation are replaced with letters. Each digit is represented by only one letter, and each letter represents a different digit. So, for example, we might represent 51+50 = 101 as AB + AC = BCB. In the cryptarithm SEND + MORE = MONEY, what digit does the letter Y represent?
Answers
Answer:
[tex]\large \boxed{\sf \begin{aligned}9567&\\+1085&\\----&-\\10652&\\\end{aligned}}[/tex]
Step-by-step explanation:
Hello, let's do it step by step and see what we can find.
[tex]\begin{aligned}\text{ SEND}&\\+\text{ MORE}&\\-----&-\\\text{ MONEY}&\\\end{aligned}[/tex]
We assume that M is different from 0, otherwise we could find several different solutions I would think.
It means that S + M is greater than 10, otherwise the number of digit of the result would have been 4 and not 5.
The only possible number for M is then 1. M = 1
[tex]\begin{aligned}\text{ SEND}&\\+\text{ \boxed{1}ORE}&\\-----&-\\\text{ \boxed{1}ONEY}&\\\end{aligned}[/tex]
But then, S can only by 9, otherwise S + 1 < 10. S = 9
S + 1 = 10 + O if there is no carry over, so S = 9 + O
1 + S + 1 = 10 + O if there is a carry, so S = 8 + O
So O = 0 or O = 1. Wait !? M is already equal to 1 so O must be 0
E cannot be equal to N so 1 + E = N, meaning that there must be a carry over from column second from the right.
and E < 9 as we know that there is no carry over from column 3 from the right.
N + R = 10 + E => 1 + E + R = 10 + E => R = 9, impossible, as S=9
or 1 + N + R = 10 + E => 1 + 1 + E + R = 10 + E => R = 8
And there is a carry over from the column 1 from the right, so:
Y cannot be 0 or 1, as already used so D + E > 11
8 and 9 are already taken so we could have 7 + 5 = 12, 7 + 6 = 13 and that's it.
It means that E is 7 or D is 7.
If E is 7 then E+1=9=N, impossible, so D = 7
Then, E is 5 or 6
if E = 6 E + 1 = N = 7, impossible, so E = 5 and N = 6.
And 7 + 5 = 12 so Y = 2.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Which expression is equivalent to 0.83¯ ?
Answers
Answer:
Hello There!!
Step-by-step explanation:
Your answer will be 83/99. Because, We have to expressed the 0.83¯ as a fraction in simplest form. Let x = 0.83¯ = 0.8383. Then, We have to multiply by 100 to both sides we have: 100x = 83.8383. After, Subtract (One) to (Two) we will have: 99x = 83. Then, We will divide both sides by 99 we have: x = 83/99. Therefore, the 0.83¯ as a fraction in simplest form is, 83/99. Hope This Helps!!~ Sorry, If the example confusing...
The original price of a 2018 Honda Shadow to the dealer is $17,715, but the dealer will pay only $16,985 after rebate. If the dealer pays Honda within 15 days, there is a 2% cash discount.
Answers
Answer:
The final price to be paid after the 2% discount has been made will be $ 16,645.30.
Step-by-step explanation:
Since there is a 2% discount on the price of the Honda Shadow in the event that the dealer pays Honda within 15 days, and that after a rebate the price of the vehicle is $ 16,985, to obtain the value of the discount and the final amount to be paid must be calculated as follows:
16,985 x 2/100 = X
33,970 / 100 = X
339.70 = X
Thus, the discount to be made will be $ 339.70, with which the final price to be paid after the 2% discount has been made will be $ 16,645.30.
Assume the weight of Valencia oranges is normally distributed with a mean 9 oz and standard deviation 2 oz. What is the probability that a sample of 100 units show a mean weight of less than 9.5 oz?
Answers
Answer:
0.99379
Step-by-step explanation:
The first thing to do here is to calculate the z-score
mathematically;
z-score = x-mean/SD/√(n)
From the question x = 9.5 ,
mean = 9, SD = 2 and n = 100
Plugging the values we have;
z-score = (9.5-9)/2/√(100) = 0.5/2/10 = 0.5/0.2 = 2.5
So the probability we want to calculate is;
P(z<2.5)
We use the standard table for this
and that equals 0.99379
Solve the equation.
y + 3 = -y + 9
y= 1
y=3
y = 6
y = 9
Answers
Answer: y=3
Step-by-step explanation:
To solve the equation, we want to get the same terms onto the same side and solve.
y+3=-y+9 [add y on both sides]
2y+3=9 [subtract 3 on both sides]
2y=6 [divide 2 on both sides]
y=3
Answer:
y=3
Step-by-step explanation:
A sample of radioactive material disintegrates from 6 to 4 grams in 100 days. After how many days will just 3 grams remain?
Answers
Answer:
150 days
Step-by-step explanation:
6-4=2
100/2=50
50*3=150
The number of days for the radioactive material to disintegrate to 3 grams is 173.077 days.
The rate of disintegration varies directly proportional to the quantity of the material.
As such, we can say:
[tex]\mathbf{=\dfrac{dN}{dt}\ \alpha \ N}[/tex]
[tex]\mathbf{\implies \dfrac{dN}{N}\ = k dt}[/tex]
Taking the integral form;
[tex]\mathbf{\implies \int \dfrac{dN}{N}\ =\int k dt}[/tex]
[tex]\mathbf{\implies In N =kt+ C---- (1)}[/tex]
When t = 0, N = 6 grams
In(6) = C
∴
When t = 100, N = 4 grams
In (4) = 100k + In6
100 k = 1n (4) - In(6)
[tex]\mathbf{100 k = In (\dfrac{4}{6})}[/tex]
[tex]\mathbf{k = \dfrac{1}{100} In(\dfrac{4}{6})}[/tex]
∴
From equation (1):
[tex]\mathbf{In N = \dfrac{t}{100} In(\dfrac{4}{6})+ In 6}[/tex]
when,
n = 3 grams; we have:[tex]\mathbf{In (3) = \dfrac{t}{100} In(\dfrac{4}{6})+ In 6}[/tex]
[tex]\mathbf{\implies \dfrac{t}{100} In(\dfrac{4}{6}) = In \dfrac{ 3}{ 6}}[/tex]
[tex]\mathbf{t = 100\times \Big ( \dfrac{In (\dfrac{ 3}{ 6})}{ In(\dfrac{4}{6}) }\Big) }[/tex]
[tex]\mathbf{t = 100\times \Big ( \dfrac{0.69314}{ 0.40048}\Big) }[/tex]
t = 173.077 days
Therefore, the number of days for the radioactive material to disintegrate to 3 grams is 173.077 days.
Learn more about radioactive materials here:
https://brainly.com/question/24339152?referrer=searchResults
Which statement is true about figures ABC D & ABCD
Answers
Answer:
it's option b that is the right answer
A group of 10 students participate in chess club, karate club, or neither.
Answers
Answer:
P(A︱B) =0.50
Step-by-step explanation:
That's the answer
A certain forest covers an area of 2100 km². Suppose that each year this area decreases by 3.5%. What will the area be after 5 years
Use the calculator provided and round your answer to the nearest square kilometer.
Answers
Answer:
[tex]\large\boxed{\sf \ \ \ 1757 \ km^2 \ \ \ }[/tex]
Step-by-step explanation:
Hello,
I would recommend that you checked the answers I have already provided as this is the same method for all these questions, and maybe try to solve this one before you check the solution.
At the beginning the area is 2100
After one year the area will be
2100*(1-3.5%)=2100*0.965
After n years the area will be
[tex]2100\cdot0.965^n[/tex]
So after 5 years the area will be
[tex]2100\cdot0.965^5=1757.34027...[/tex]
So rounded to the nearest square kilometer is 1757
Hope this helps
Answer: 1757 km²
Step-by-step explanation:
Because 3.5% = 0.035, first do 1-.035 to get .965. Then do 2100*.965*.965*.965*.965*.965 to get 1757.34027.
If sinθ = 12/13 and θ is an acute angle, find cotθ.
Answers
Answer:
[tex]\displaystyle \cot \theta = \frac{5}{12}[/tex]
Step-by-step explanation:
We are given that:
[tex]\displaystyle \sin \theta = \frac{12}{13}[/tex]
Where θ is an acute angle, and we want to find cot(θ).
Recall that sine is the ratio of the opposite side over the hypotenuse. In other words, our opposite side is measures 12 units and our hypotenuse measures 13 units.
Find the adjacent side:
[tex]\displaystyle \begin{aligned} a^2 + b^2 & = c^2 \\ \\ (12)^2 + b^2 & = (13)^2 \\ \\ b & = 5\end{aligned}[/tex]
Hence, our adjacent side is 5, our opposite side is 12, and our hypotenuse is 13.
Recall that cotangent is the ratio of the adjacent side to the opposite side. Therefore:
[tex]\displaystyle \cot \theta = \frac{5}{12}[/tex]
In conclusion:
[tex]\displaystyle \cot \theta = \frac{5}{12}[/tex]
Answer:
-5/12
Step-by-step explanation:
I just completed Quiz 2: Evaluation of Functions. Of which, this was one of the questions.
PLEASE HELP ?
A: 111.6 square centimeters
B: 323 square centimeters
C: 7.75 square centimeters
Answers
Answer:
B. 323 square centimeters
Step-by-step explanation:
multiply the inches by the conversion number
50 x 6.45 = 322.5
Answer:
[tex]\boxed{Option \ B}[/tex]
Step-by-step explanation:
[tex]1 \ inch^2 = 6.45 \ cm^2[/tex]
Multiplying both sides by 50
[tex]1 * 50 \ inch^2 = 6.45 * 50 \ cm^2\\[/tex]
[tex]50 \ inch^2 = 323 \ cm^2[/tex]
Here is a sample distribution of hourly earnings in Paul's Cookie Factory:
Hourly Earning $6 up to $9 $9 up to $12 $12 up to $15
Frequency 16 42 10
The limits of the class with the smallest frequency are:_________
A) $6.00 and $9.00.
B) $12.00 and up to $14.00.
C) $11.75 and $14.25.
D) $12.00 and up to $15.00.
Answers
Answer:
The correct answer is:
$12.00 and up to $15.00 (D)
Step-by-step explanation:
Let us arrange the data properly in a tabular format.
Hourly Earnings($) 6 - 9 9 - 12 12 - 15
Frequency 16 42 10
The frequency of a distribution is the number of times that distribution occurs in a particular group of data or intervals.
From the frequency table above the following observations can be made:
Highest frequency = 42 (hourly earnings of $9 - $12)
smallest frequency = 10 ( hourly earnings of $12 - $15)
This means that among a total of 68 workers (16 + 42 + 10), the people earning $12 - $15 form the smallest group (only 10 people), while 42 workers earn $9 - $12, forming the largest majority
Select the correct text in the table. Use the fundamental theorem of algebra to determine whether each statement is sometimes true, always true, or never true.
1. A quadratic function has 2 distinct roots. always sometimes never
2. A cubic function has at least 1 real root. always sometimes never
3. A function with a degree of 5 has 5 roots. always sometimes never
4. A quadratic function can have only 1 complex solution. always sometimes never
Answers
Answer:
1. Sometimes
2. Sometimes
3. Always
4. Sometimes
Step-by-step explanation:
1. Quadratic function : in which maximum power of [tex]x[/tex] is two.
The roots of quadratic function can be either equal or different.
For example:
[tex]x^{2} -2x+1[/tex] will have two equal roots i.e. 1 and 1.[tex]x^{2} -3x+2[/tex] will have two different roots i.e. 1 and 2.So, sometimes is the correct answer.
2. Cubic function has atleast 1 real root.
Cubic function has maximum power of [tex]x[/tex] as 3.
If the coefficients are real numbers then atleast 1 real root.
If the coefficients are imaginary in nature, then this is not true.
For example:
Cubic equation [tex]x^3 +i = 0[/tex] does not have any real root.
Cubic equation [tex]x^3 +1 = 0[/tex] has a real root x = -1.
So, it is sometimes true.
3. A function with degree 5 i.e. maximum power of [tex]x[/tex] as 5 will have 5 roots.
It is always true that a function will have number of roots equal to its degree.
4. Quadratic function can have only 1 complex solution.
Two complex solutions are also possible for a quadratic function.
For example:
[tex]x^{2} +1=0[/tex] will have two imaginary roots: [tex]x=i, -i[/tex]
It is also possible to have 1 complex solution,
For example:
[tex](x-1)(x-i) = 0[/tex] will have one complex root and one real root.
So, the statement is sometimes true.
Answer:
MY ANSWER IS CORRECT IN PLATO!!!
1. Sometimes
2. Always
3. Always
4. Never
Step-by-step explanation:
1. A quadratic function has 2 distinct roots SOMETIMES
2. A cubic Function has at least 1 root ALWAYS
3. A function with a degree of 5 has 5 roots ALWAYS
4. A quadratic function can have only 1 complex solution NEVER
I JUST GOT 100% on the quiz in PLATO
Which value of x makes the equation 0.75( x + 20) = 2 + 0.5(x - 2) true?
Answers
Answer:
0.75x+15=2+0.5x-1
0.25x=1-15
0.25x=-14
x=-56
Step-by-step explanation:
Edgar accumulated $5,000 in credit card debt. If the interest rate is 20% per year and he does not make any payments for 2 years, how much will he owe on this debt in 2 years by compounding continuously? Round to the nearest cent.
Answers
Answer:
$7200
Step-by-step explanation:
The interest rate on $5,000 accumulated by Edgar is 20%.
He does not make any payment for 2 years and the interests are compounded continuously.
The amount of money he owes after 2 years is the original $5000 and the interest that would have accumulated after 2 years.
The formula for compound amount is:
[tex]A = P(1 + R)^T[/tex]
where P = amount borrowed = $5000
R = interest rate = 20%
T = amount of time = 2 years
Therefore, the amount he will owe on his debt is:
[tex]A = 5000 (1 + 20/100)^2\\\\A = 5000(1 + 0.2)^2\\\\A = 5000(1.2)^2\\[/tex]
A = $7200
After 2 years, he will owe $7200
Answer:7,434.57
Explanation: A= 5000(1+0.2/12)^12•2
f(x) = x + 2
g(x) = x - 4
(fg)(x) =
Answers
Answer:
Step-by-step explanation:pleased to help u....
jogged the track 5/9 miles long and jogged around it 4 times
Answers
Answer:
The answer is 2 1/5 miles.
Step-by-step explanation:
You have to multiply 5/9 with 4 since you are going around 4 times. You could also use addition which is 5/9 + 5/9 + 5/9 + 5/9.
Answer:
Hey there!
The person jogged a total of 20/9 miles.
Hope this helps :)
Evaluate the expression. 1/2 x (4+8)
Answers
Answer:
Hey there!
1/2 x (4+8)
1/2 x (12)
6
Hope this helps :)
Answer: 6x
Step-by-step explanation:
.5x*(4+8)
.5x*(12)
6x
Hope it helps <3
Simplify 3 (2x + 1) - 2 (x + 1)
Answers
Let's simplify step-by-step.
3(2x+1)−2(x+1)
Distribute:
=(3)(2x)+(3)(1)+(−2)(x)+(−2)(1)
=6x+3+−2x+−2
Combine Like Terms:
=6x+3+−2x+−2
=(6x+−2x)+(3+−2)
=4x+1
4x+1 is the answer to the question
What is the measure of ∠BCD?
Answers
Answer: 77 degrees
Step-by-step explanation:
interior angles on the same side of transversal are supplementary. Thus,
103+x=180
x = 77
Hope it helps <3
Answer:
Hey there!
This is a parallelogram, and we have the angles next to each other add to 180 degrees. Angle ABC+Angle BCD=180
103+x=180
x=77
BCD=77 degrees.
Let me know if this helps :)
if ade has 23hand bag and he sells one for 409$ and he sells 22 for toby what will be the amount
Answers
Step-by-step explanation:
Hello there!
Its simple,
Given that, Ade had 23 hand bags.
selling price of each bag=$409
total sold bags= 22.
now, total amount he got was = no.of sold bag×sp of each bag.
so, total amount = 22×$409
=$8998.
Therefore, he has $ 8998 now.
Hope it helps...
Which system type is a linear system with infinitely many solutions?
Answers
Answer:
down b3low
Step-by-step explanation:
The point where the two lines intersect is the only solution. An inconsistent system has no solution. Notice that the two lines are parallel and will never intersect. A dependent system has infinitely many solutions.
Help Please! Solve this problem without the law of cosines.
Answers
Answer:A
Step-by-step explanation:
Find the value of x.
Answers
Answer:
[tex]\huge\boxed{y=\sqrt{55}}[/tex]
Step-by-step explanation:
ΔADC and ΔDBC are similar (AAA)
Therefore the cooresponging sides are in proportion:
[tex]\dfrac{AC}{CD}=\dfrac{CD}{BC}[/tex]
Substitute:
[tex]AC=6+5=11\\BC=5\\CD=y[/tex]
[tex]\dfrac{11}{y}=\dfrac{y}{5}[/tex] cross multiply
[tex](11)(5)=(y)(y)\\\\55=y^2\to y=\sqrt{55}[/tex]
Can you help me with this.
Answers
Answer:
You would basically expand all the equations!
1. 7(4z+8b) is equal to 28z+56b.
2. 8(2x+3^2) is equal to 16x+72
3. 4(r+r+r+r) is equal to 4r+4r+4r+4r
4. 9(3+8x) is equal to 27+72x
5. 4^2(3+6f) is equal to 48+96t
6. (t+t+t)/4 is equal to t/4+t/4+t/4
7. 2(4s^3+2) is equal to 8s^3+4
8. 30(3x+4) is equal to 90x+120
9. 6(5a+9b) is equal to 30a+54b
10. 9(3x+5^4) is equal to 27x+5625
11. 7(c+c+c) is equal to 7c+7c+7c
12. 9(2+7f) is equal to 18+63f
13. 7^5(4g-8d) is equal to 67228g-134456d
Step-by-step explanation:
Simplify the rate:
46 cans of Soda / 8 people
Only enter the numeric amount:
Answers
Answer: 23 cans of soda/4 people.
or (23/4) cans of soda per person.
Step-by-step explanation:
So we have the rate:
46 cans of soda/ 8 people
First, 46 and 8 are multiples of 2, so we can divide both numerator and denominator by 2:
46/2 = 23
8/2 = 4
Then the rate can be:
23 cans of soda/4 people.
Now 23 is a prime number, so we can not simplify it furthermore
15x - 30 x 0 + 40 = 89
Answers
Answer:
x = 49/15
Step-by-step explanation:
15x - 30 x 0 + 40 = 89 PEMDAS
15x + 40 = 89 Isolate the variable
15x = 49
x = 49/15
━━━━━━━☆☆━━━━━━━
▹ Answer
x = 49/15 or 3 4/15 or 3.26
▹ Step-by-Step Explanation
15x - 30 * 0 + 40 = 89
15x - 0 + 40 = 89
15x + 40 = 89
15x = 89 - 40
15x = 49
x = 49/15 or 3 4/15 or 3.26
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
3
Easton mixed
kg of flour with
kg of sugar.
6
Determine a reasonable estimate for the amount of flour and sugar combined.
Choose 1 answer:
1
Less than
2
kg
B
More than
1
kg but less than 1 kg
2
More than 1 kg
Answers
Find the value of EB
Answers
Answer:
31Step-by-step explanation:
Given,
AD = 38
EB = 7x - 4
FC = 6x - 6
Now, we have to find the value of X
[tex]eb \: = \frac{1}{2} (ad \: + fc \: )[/tex] ( Mid segment Theorem )
Plug the values
[tex]7x - 4 = \frac{1}{2} (38 + 6x - 6)[/tex]
Calculate the difference
[tex]7x - 4 = \frac{1}{2} (32 + 6x)[/tex]
Remove the parentheses
[tex]7x - 4 = \frac{32}{2} + \frac{6x}{2} [/tex]
[tex]7x - 4 = 16 + 3x[/tex]
Move variable to L.H.S and change its sign
Similarly, Move constant to R.H.S and change its sign
[tex]7x - 3x = 16 + 4[/tex]
Collect like terms
[tex]4x = 16 + 4[/tex]
Calculate the sum
[tex]4x = 20[/tex]
Divide both sides of the equation by 4
[tex] \frac{4x}{4} = \frac{20}{4} [/tex]
Calculate
[tex]x = 5[/tex]
The value of X is 5
Now, let's find the value of EB
EB = 7x - 4
Plug the value of X
[tex] = 7 \times 5 - 4[/tex]
Calculate the product
[tex] = 35 - 4[/tex]
Calculate the difference
[tex] = 31[/tex]
The value of EB is 31
Hope this helps..
Best regards!!