Answer:
8, 13, 18
Step-by-step explanation:
If we want the mean to be 13, and there are 3 integers, that means the sum of all 3 integers must be 39. I started at 13 and counted 5 up and 5 down, which already makes sure of the range and the mean is 13 (since it's balanced with 13 being the middle), therefore, 13+5 is 18, 13-5=8.
If a population is ______ , a sample of the population could be _____.
Using sampling concepts, it is found that the sentence is:
C. If a population is all actors, a sample of the population could be movie actors.
A sample is a group taken from the population. It has to come from a more restrict group of the population, that is, an subset of the population.
In option A, baseball players is a subset of all athletes, so all athletes would be the population and baseball players would be the sample. The same can be applied in options B and D.
In option C, movie starts is a subset of all actors, thus the roles of sample and population are correct.
A similar problem is given at https://brainly.com/question/25119689
PLEASE HELP! Select all the correct answers.
Terry is an up-and-coming florist who specializes in weddings. He uses 5 roses, 3 daisies, and 4 bundles of green filler to make one bouquet. If r is the cost of a rose, d is the cost of a daisy, and f is the cost of a bundle of green filler, which expression represents the cost for making 75 bouquets?
Answer:
im sorry this never got answered but you would put the third one i believe
Step-by-step explanation:
Simplify [4a^(-6) b^2]^(-3) write your answer using only positive exponent
For this case we must simplify the following expression:
[tex](4a^{ - 6} * b ^ 2)^{ - 3}[/tex]
By definition of power properties we have:[tex]a ^ {-1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]
Then, rewriting the expression:
[tex](\frac {4} {a ^ 6} * b ^ 2) ^ {- 3} =\\\frac {1} {(\frac {4} {a ^ 6} * b ^ 2)^3} =\\\frac {1} {(\frac {4b ^ 2} {a ^ 6})^3} =[/tex]
By definition we have to:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
[tex]\frac {1} {\frac {64b ^ 6} {a^{18}}}\\\frac {a^{18}} {64b ^ 6}[/tex]
Answer:
[tex]\frac {a^{18}} {64b ^ 6}[/tex]
Which of the following fractions is an improper fraction?
*2/3
*6/11
*21/25
*8/7
Answer:
8/7
Step-by-step explanation:
8/7 is an improper fraction.
8 > 7
A fraction has to have the numerator less than the denominator, in order to be a proper fraction.
In this case, 8/7 is the only fraction with a numerator more than the denominator.
Therefore, 8/7 is an improper fraction.
Answer:
8/7 is an improper fraction.
Step-by-step explanation:
An improper fraction is just a fraction where the numerator (top number) is greater than the denominator (bottom number)
2<3
6<11
21<25
8>7
Hope this helps!!!
The figure is a regular hexagon with side length 26 ft.
What is the length of y?
Answer: the length is 13
Step-by-step explanation:
one side is 26 ft. and y is half of one side so by dividing 26 by 2 you would get 13
System of equations graphed below had How many equations?
Answer:
A. 0Step-by-step explanation:
The solution of the system of equations are the coordinates of the point of intersection.
We have two parallel lines. The intersection point does not exist.
Therefore, this system of equations has no solution.
13, 29, 427, 881
Is the sequence geometric? If so, identify the common ratio.
Final answer:
The sequence 13, 29, 427, 881 is not geometric because each term is not obtained by multiplying the previous term by a constant ratio. The ratios between successive terms vary, so there is no common ratio.
Explanation:
Is the sequence 13, 29, 427, 881 geometric? To determine if a sequence is geometric, each term should be obtained by multiplying the previous term by a constant number, known as the common ratio.
Let's calculate the ratios between successive terms:
Ratio from 13 to 29: 29 ÷ 13 = 2.23077 (approximately)Ratio from 29 to 427: 427 ÷ 29 = 14.72414 (approximately)Ratio from 427 to 881: 881 ÷ 427 = 2.06324 (approximately)Since the ratios are not the same, the sequence is not geometric. Therefore, there is no common ratio.
An ancient artifact was recently discovered, but due to rust and corrosion, only 75 grams of the original item remained. Based on historical dates, scientists believe that this artifact was decaying at a rate of 2% each year. Although the artifact will now be preserved at a museum, scientists wonder: how much of the original artifact would there be if they had not discovered it for another 10 years?
Write an exponential function rule and solve. Round your answer to the nearest whole number (the ones place). Enter both the number and the associated units
namely, what is the leftover amount when the decay rate is 2% for an original amount of 75 grams after 10 years?
[tex]\bf \qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &75\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ t=\textit{elapsed time}\dotfill &10\\ \end{cases} \\\\\\ A=75(1-0.02)^{10}\implies A=75(0.98)^{10}\implies A\approx 61.28\implies \stackrel{\textit{rounded up}}{A=61~grams}[/tex]
Answer with explanation:
The exponential decay function is written as :-
[tex]f(x)=A(1-r)^x[/tex], where f (x) is the amount of material left after x years , A is the initial amount of material and r is the rate of decay.
Given : The amount of original item remained now = 75 grams
The rate of decay = 2% = 0.02
Now, the amount of original artifact would there be left if they had not discovered it for another 10 years is given by :-
[tex]f(10)=75(1-0.02)^{10}[/tex]
Solving the above exponential equation , we get
[tex]=61.2804605166\approx61[/tex]
Hence only 61 grams original artifact would there be left if they had not discovered it for another 10 years .
F(x)=x^2 what is g(x)
Answer:
[tex]\large\boxed{C.\ g(x)=3x^2}[/tex]
Step-by-step explanation:
[tex]f(x)=x^2\to f(1)=1^2=1\\\\g(1)=3\to\text{given point (1,\ 3)}\\\\3=3\cdot1=3\cdot1^2=3f(1)\to g(x)=3f(x)=3x^2[/tex]
Which algebraic expression represents the phrase "four times a number"?
0 4+0
O 0-4
0 4=0
040
Answer:
Step-by-step explanation:
None of them do to me. The last one does not. And certainly the second last one cannot.
In B, you are subtracting 4 from zero which doesn't work.
A adds 0 to 4 which gives 4
Unless I misreading D and O is a variable (sneaky), there is no answer.
Consider the given function. Which statement about the functions is true?
Answer:
the correct answer is D. Funtion 1 and 3 have the same rate of change but funtion 1 has greater y intercept
Step-by-step explanation:
If we organize the funtion 1, we have y= 2x+8
Funtion 2 the need to calculate the slope m = (y2-y1)/(x2-x1) the point on the y represent (y2,x2) and is (4,0) the point onn the x axis is (x1,y1) and is (-2,0)
So, m=(4-0)/(0-(-2) => m=(4/2) => m=2
Then, y=m(X-Xo) + Yo . From the plot, I choose (x2,y2) as (Xo,Yo) So, (0,4)
y=2(X-0) +4 then y= 2x+4
From 3 equation the choose the value x=o and g(x)= 5 and x=1 and g(x)=7 and following the same m=(7-5)/(1-0) the slope is m=2. Following the same procedure before I choose x=0 and y=5
Then the equation is: y=2(x-0) + 5
So, opcion D is true
Select the correct answer from each drop-down menu.
Ashley has 500 songs in his music player. Every week he adds 10 songs to his collection. How many songs will he have in his music player after
20 weeks?
The output of the function (f(n)=500+10n) or (f(n)=10+20n).the output of the function is (700/600)
when the input is 20
Answer:
700
Step-by-step explanation:
he originally has 500 songs which is the constant. He adds 10 songs a week which is the slope. and 20 will be the number of weeks. You can make the equation y=10x+500 and replace the x with 20. 20 times 10 is 200 and 200 plus 500 is 700 which is your answer
THANK U!!✔
for answering
Answer:
-8.95 ,, -8.36 ,, 7/28 ,, 8 22/40
Step-by-step explanation:
Answer:
-8.95, -8.36, 7/28, 8 22/40
Step-by-step explanation:
1,2,and 3 please I really need help
Answer:
1) yes
2) Option B
3) 9200
Step-by-step explanation:
1) yes
The exponential function is: y=-(x)^3
Putting the values of x in the given function we get the values of y.
x =1 , y= -(1)^3, y=-1
x= 2, y= -(2)^3, y = -8
x= 3, y= -(3)^3,y = -27
x= 4, y= -(4)^3,y = -64
2) f(x) = 160.2^x
if value of x = 2
then f(2) = 160.2^(2)
f(2) = 160.4
f(2) = 640
So, Option B is correct.
3) f(x) = 2300.2^x
if value of x = 2 decades then
f(2) = 2300.2^2
f(2) = 2300.4
f(2) = 9200
Since all options are not visible, so correct answer is 9200
What is the volume of the composite figure?
A. 140 cubic inches
B. 147 cubic inches
C. 168 cubic inches
D. 196 cubic inches
Answer:
A. 140 cubic inches
Step-by-step explanation:
The total volume is the volume of the rectangular prism at the bottom plus the volume of the pyramid on top.
The volume of the prism is width times length times height.
V = wlh
V = (3)(7)(4)
V = 84
The volume of the pyramid is one third the area of the base times the height.
V = ⅓ Ah
The base of the pyramid is a rectangle. Its area is the width times length. The height of the pyramid is the total height minus the height of the prism.
V = ⅓ (3)(7)(12−4)
V = 56
So the total volume is:
V = 84 + 56
V = 140
Answer:
140 cubic inches
Step-by-step explanation:
Which functions have an additive rate of change of 3? Select TWO options
Answer:
Second table.
Step-by-step explanation:
A function has an additive rate of change if there is a constant difference between any two consecutive input and output values.
The additive rate of change is determined using the slope formula,
[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]
From the first table we can observe a constant difference of -6 among the y-values and a constant difference of 2 among the x-values.
[tex]m = \frac{ - 9- - 3}{4-2} = - 3[/tex]
For the second table there is a constant difference of 3 among the y-values and a constant difference of 1 among the x-values.
The additive rate of change of this table is
[tex]m = \frac{ - 1 - - 4}{3 - 1} = 3[/tex]
Therefore the second table has an additive rate of change of 3.
Answer: it’s A and E
First and last one
Step-by-step explanation:
Roy wants to make a path from one corner of his yard to the other as shown below. The path will be 4 feet wide. He wants to find the area of lawn that remains.
Roy claims that the area of the lawn is 300 square feet since it covers exactly one-half of the yard. Which statement about his claim is correct?
He is incorrect. The path will have an area of (4)(40)=160 sq ft. The yard has an area of 600 sq ft. The area of the lawn will be the difference of the yard and path, so it is 440 sq ft.
He is incorrect. The path will have an area of 1/2(4)(40)=80 sq ft. The yard has an area of 300 sq ft. The area of the lawn will be the difference of the yard and path, so it is 220 sq ft.
He is incorrect. The path will have an area of (4)(40)=160 sq ft. The yard has an area of 300 sq ft. The area of the lawn will be the difference of the yard and path, so it is 140 sq ft.
He is incorrect. The path will have an area of (9)(40)=360 sq ft. The yard has an area of 600 sq ft. The area of the lawn will be the difference of the yard and path, so it is 240 sq ft.
Answer:
He is incorrect. The path will have an area of (4)(40) = 160 ft². The yard has an area of 600 ft². The area of the lawn will be the difference of the yard and path, so it is 440 ft².
Step-by-step explanation:
1. Original area of yard
A = lw = 40 × 15 = 600 ft²
2. Area of path
The path is a parallelogram.
A = bh = 4 × 40 =160 ft²
3. Remaining area
Remaining area = original area - area of path = 600 - 160 = 440 ft².
Answer:
A is correct
Step-by-step explanation:
I got 100 on edg
ali and jake went on a cross country trip they took a train part of the way and took a bus the rest of the way they traveled a total of 1450 riding on the train 150 more kilometers than on the bus
let x=kilometers traveled by bus
let y = kilometers traveled by train
question how many kilometers did they travel by train?
Answer:
y=800 km
Step-by-step explanation:
Let the distance traveled by train be y and by bus be x.
Bus -x
Train -y
y=x+150 (since they traveled by train for a distance of 150 km more than by bus.)
The sum of the two is equal to 1450
x+y=1450
The two equations form simultaneous equations which when solved simultaneously give the values of x and y.
y+x=1450
y-x=150
Adding the two we get:
2y=1600
Divide both sides by two:
y=800 km
Y is the distance traveled by train= 800 km
Find the midpoint of the line segment with the given endpoints
(10,2) and (8,4)
Answer:
The midpoint of the line segment is (9,3).
Step-by-step explanation:
To find the midpoint of a line segment, we use the midpoint formula, ( (x1 + x2)/2, (y1+y2)/2). This means that to find the midpoint, we must add together both of the x-values of the endpoints and divide by 2 and do the same with the y values, basically finding the average of the two endpoints, or the middle.
x1 + x2 = 10 + 8 = 18
18/2 = 9
y1 + y2 = 2 + 4 = 6
6/2 = 3
Therefore, the midpoint of the line segment is (9,3).
Hope this helps!
If 8(x) is the inverse of f(x) and f(x) = 4x + 12, what is g(x)?
Answer:
[tex]g(x)=\frac{x-12}{4}[/tex]
Step-by-step explanation:
To find the inverse of y=4x+12, all you need to is swap x an y and then remake y the subject.
y=4x+12
Swap x and y:
x=4y+12
Solve for y:
Subtracting 12 on both sides:
x-12=4y
Dividing 4 on both sides:
[tex]\frac{x-12}{4}=y[/tex]
So [tex]g(x)=\frac{x-12}{4}[/tex]
Answer:
[-12 + x]\4 = g(x)
Step-by-step explanation:
x = 4y + 12 [SWAP y and x]-12 + x = 4y [Move -12 to the left side of the equivalence symbol][-12 + x]\4 = g(x) [Divide by 4]If you are ever in need of assistance, do not hesitate to let me know by subscribing to my You-Tube channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.
The graphed line shown below is y=-4x-12. Which equation, when graphed with the given equation, will form a system that has no solution?
I guess one more does not hurt.
Notice that choice D is equivalent to the given equation y = -4x - 12.
The only equation that does not cross the given equation is y = -4x.
They have THE SAME SLOPE. This means they are parallel and thus lead to NO SOLUTION.
ANSWER: y = -4x
Answer:
[tex]y=-4x[/tex]
Step-by-step explanation:
A Linear System with no solution, therefore inconsistent, is graphically represented by a pair of parallel lines.
According to Analytic Geometry, a parallel line shares the same slope.
Given the options, the only parallel line to [tex]y=-4x-12[/tex] is [tex]y=-4x[/tex] Since [tex]y=-4(x+3)[/tex] despite having the same slope, is actually the same line [tex]y=-4x+12[/tex]
So [tex]y=-4x[/tex] will form a system that has no solution.
Which represents the solution set of the inequality 5x-9321?
Answer:
The solution set is the interval (-∞ , 6] OR {x : x ≤ 6}
Step-by-step explanation:
* Lets explain how to find the solution set of the inequality
- The inequality is 5x - 9 ≤ 21
∵ 5x - 9 ≤ 21
- At first add 9 to both sides of the inequality to separate x in one
side and the numbers in the other sides
∴ 5x - 9 + 9 ≤ 21 + 9
∴ 5x ≤ 30
- Lets divide both sides of the inequality by 5 to find the values of x
∴ (5x ÷ 5) ≤ (30 ÷ 5)
∴ x ≤ 6
- The solutions of the inequality is all real numbers smaller than
or equal to 6
∴ The solution set is the interval (-∞ , 6] OR {x : x ≤ 6}
- We can represent this inequality graphically to more understand
for the solution
- From the graph the solution set is the purple area
seven sixteeths wrote as a decimal
Answer:
The answer is 0.4375 .
Hope this helps!
There are 32 students in Jenny's class. If the teacher randomly picks a student to call on, what is the probability that Jenny will be called on twice? (If necessary, round to the nearest hundredth.)
To find the probability that Jenny will be called on twice, we multiply the probabilities of picking her on the first and second calls, which is 1/992.
Explanation:To find the probability that Jenny will be called on twice, we need to consider the total number of possible outcomes and the number of favorable outcomes.
There are 32 students in Jenny's class, so the total number of possible outcomes is 32.
For the first call, the probability of picking Jenny is 1/32. After the first call, there are now 31 students left, with 1 of them being Jenny. So, the probability of picking Jenny again on the second call is 1/31.
To find the probability of both events happening, we multiply the probabilities together: (1/32) x (1/31) = 1/992.
The probability that Jenny will be called on twice is 1/992.
The probability that Jenny will be called twice in a class of 32 students is 0.00098. This rounds to 0.00 when rounded to the nearest hundredth.
To determine the probability that Jenny is called on twice when there are 32 students in the class, we start by finding the probability for one instance and then consider the repeated scenario.
For the first call, Jenny has a 1 in 32 chance of being called, so the probability is 1/32.For the second call, we're still considering a random selection from the entire class, so Jenny again has a 1 in 32 chance.To find the combined probability of both events happening (Jenny being called twice), we multiply the probabilities of each individual event:
(1/32) * (1/32) = 1/1024
Thus, the probability that Jenny will be called on twice is approximately 0.00098 when rounded to the nearest hundredth.
Write a polynomial function of least degree with integral coefficients that has the given zeros. –2, –3,3 – 6i
Answer:
f(x) = (x+2)(x+3)(x-(3-6i))(x-(3+6i))
f(x) = 270 + 189 x + 21 x^2 - x^3 + x^4
Step-by-step explanation:
First of all, we must know that complex roots come in conjugate pairs.
So the zeros of your equation would be
x = -2
x = -3
x = 3 - 6i
x = 3 + 6i
Your polynomial is of fourth degree.
f(x) = (x-(-2))(x-(-3))(x-(3-6i))(x-(3+6i))
f(x) = (x+2)(x+3)(x-(3-6i))(x-(3+6i))
Please , see attached image below for full expression
f(x) = 270 + 189 x + 21 x^2 - x^3 + x^4
Answer:
The required polynomial is [tex]P(x)=a\left(x^4-x^3+21x^2+189x+270\right)[/tex].
Step-by-step explanation:
The general form of a polynomial is
[tex]P(x)=a(x-c_1)^{m_1}(x-c_2)^{m_2}...(x-c_n)^{m_n}[/tex]
where, a is a constant, [tex]c_1,c_2,..c_n[/tex] are zeroes with multiplicity [tex]m_1,m_2,..m_n[/tex] respectively.
It is given that –2, –3,3 – 6i are three zeroes of a polynomial.
According to complex conjugate root theorem, if a+ib is a zero of a polynomial, then a-ib is also the zero of that polynomial.
3 – 6i is a zero. By using complex conjugate root theorem 3+6i is also a zero.
The required polynomial is
[tex]P(x)=a(x-(-2))(x-(-3))(x-(3-6i))(x-(3+6i))[/tex]
[tex]P(x)=a(x+2)(x+3)(x-3+6i)(x-3-6i)[/tex]
[tex]P(x)=a\left(x^2+5x+6\right)\left(x-3+6i\right)\left(x-3-6i\right)[/tex]
On further simplification, we get
[tex]P(x)=a\left(x^3+6ix^2+2x^2+30ix-9x+36i-18\right)\left(x-3-6i\right)[/tex]
[tex]P(x)=a\left(x^4-x^3+21x^2+189x+270\right)[/tex]
Therefore the required polynomial is [tex]P(x)=a\left(x^4-x^3+21x^2+189x+270\right)[/tex].
The complex numbers w
and z satisfy the relation w= (z + i)/ (iz + 2)
Given that z = 1 + i, find w. giving your answer in the form x + iy, where x and y are real.
[tex]w=\dfrac{1+i+i}{i(1+i)+2}\\\\w=\dfrac{1+2i}{i-1+2}\\\\w=\dfrac{1+2i}{1+i}\\\\w=\dfrac{(1+2i)(1-i)}{1+1}\\\\w=\dfrac{1-i+2i+2}{2}\\\\w=\dfrac{3+i}{2}\\\\w=\dfrac{3}{2}+\dfrac{1}{2}i[/tex]
To find the value of w, substitute the given value of z into the equation for w. Simplify the expression to obtain the value of w in the form x + iy, where x and y are real numbers.
Explanation:To find the value of w, we first substitute the given value of z into the equation for w.
Given z = 1 + i, we have:
w = (1 + i + i) / (i(1 + i) + 2)
Simplifying the numerator:
w = (1 + 2i) / (i + i^2 + 2)
Since i^2 = -1, we can rewrite the equation as:
w = (1 + 2i) / (-1 + i + 2)
Simplifying further:
w = (1 + 2i) / (1 + i)
To divide complex numbers, we multiply the numerator and denominator by the conjugate of the denominator.
w = ((1 + 2i)(1 - i)) / ((1 + i)(1 - i))
w = (1 - i + 2i - 2i^2) / (1 - i^2)
Using i^2 = -1 again:
w = (1 + i + 2i + 2) / (1 - (-1))
Simplifying the numerator:
w = (3 + 3i) / 2
Dividing both terms by 2:
w = 3/2 + 3/2i
Therefore, w = 3/2 + 3/2i in the form x + iy, where x = 3/2 and y = 3/2 are real numbers.
The Coffee Counter charges $10 per pound for Kenyan French Roast coffee and $9 per pound for Sumatran coffee.
How much of each type should be used to make a 20 pound blend that sells for $ 9.50 per pound?
10 pounds of each type of coffee should be mixed to make a 20 pound blend that sells for $9.50 per pound.
Charges for Kenyan French Roast coffee = $10 per pound
Charges for Sumatran coffee = $9 per pound
Let the amount of Kenyan French Roast used = K pound
And the amount of Sumatran coffee used = S pound
If the total amount of the mixture = 20 pounds
Equation for the total amount will be,
K + S = 20 ------- (1)
If the cost of this mixture = $9.50
Equation for the cost of the mixture will be,
10K + 9S = 20×9.50
10k + 9S = 190 ------- (2)
Multiply equation (1) by 9 and subtract this equation from equation (2),
(10k + 9S) - (9K + 9S) = 190 - 180
K = 10 pounds
Substitute the value of K in equation (1),
10 + S = 20
S = 10 pounds
Therefore, 10 pounds of each blend of coffee should be mixed.
Learn more,
https://brainly.com/question/17106913
To make a 20 pound blend of coffee that costs $9.50 per pound using Kenyan French Roast coffee ($10 per pound) and Sumatran coffee ($9 per pound), you should use 10 pounds of each type.
Explanation:To solve this problem, we can set up a system of equations to represent the given information. Let x represent the amount of Kenyan French Roast coffee and y represent the amount of Sumatran coffee. We have the following equations:
x + y = 20 (equation 1 - representing the total weight of the blend)
10x + 9y = 9.50 * 20 (equation 2 - representing the total cost of the blend)
To solve this system, we can first multiply equation 1 by 10 to get:
10x + 10y = 200 (equation 3)
We can then subtract equation 3 from equation 2 to eliminate the variable x:
10x + 9y - (10x + 10y) = 9.50 * 20 - 200
9y - 10y = 190 - 200
-y = -10
y = 10
Substituting this value back into equation 1 gives us:
x + 10 = 20
x = 10
Therefore, we should use 10 pounds of Kenyan French Roast coffee and 10 pounds of Sumatran coffee to make the 20 pound blend.
Learn more about Coffee blend here:https://brainly.com/question/26627385
#SPJ11
what is the value of x?
To solve this you must use Pythagorean theorem:
[tex]a^{2} +b^{2} =c^{2}[/tex]
a and b are the legs (the sides that form a perpendicular/right angle)
c is the hypotenuse (the side opposite the right angle)
In this case...
a = 48
b = x
c = 50
^^^Plug these numbers into the theorem
[tex]48^{2} +x^{2} =50^{2}[/tex]
simplify
2304 + [tex]x^{2}[/tex] = 2500
Isolate x^2 by subtracting 2304 to both sides
[tex]x^{2}[/tex] = 196
To remove the square from x take the square root of both sides to get you...
14 = x
Hope this helped!
~Just a girl in love with Shawn Mendes
Write the equation of the line that passes
through the point (3, -3) and has a slope of -2.
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point on a line
We have the point (3, -3) and the slope m = -2. Substitute:
[tex]y-(-3)=-2(x-3)[/tex]
[tex]y+3=-2(x-3)[/tex] - point-slope form
Convert to the slope-intercept form (y = mx + b):
[tex]y+3=-2(x-3)[/tex] use the distributtive property
[tex]y+3=-2x+(-2)(-3)[/tex]
[tex]y+3=-2x+6[/tex] subtract 3 from both sides
[tex]y=-2x+3[/tex] - slope-intercept form
Convert to the standard form (Ax + By = C):
[tex]y=-2x+3[/tex] add 2x to both sides
[tex]2x+y=3[/tex] - standard form
Convert to the general form (Ax + By + C = 0):
[tex]2x+y=3[/tex] subtract 3 from both sides
[tex]2x+y-3=0[/tex] - general form
Find the equation of quadratic function determined from the graph below?
Step-by-step explanation:
The x-intercepts are x = -1 and x = 5, so:
y = k (x + 1) (x − 5)
The vertex is (2, -3), so:
-3 = k (2 + 1) (2 − 5)
-3 = -9k
k = 1/3
y = 1/3 (x + 1) (x − 5)
Simplifying:
y = 1/3 (x² − 4x − 5)
y = 1/3 x² − 4/3 x − 5/3
f(x) = 1 / 3 x² - 4 / 3 x - 5 / 3
using the form:
f(x) = a(x - h)² + k
The vertex coordinates are 2 and -3.
h = 2
k = - 3
therefore,
f(x) = a(x - 2)² - 3
f(x) = a(x - 2)² - 3
let's use the coordinates (-1, 0) to find a. Therefore,
0 = a(-1 - 2)² - 3
0 = 9a - 3
3 = 9a
a = 3 / 9
a = 1 / 3
let's insert the value of a in the equation.
f(x) = a(x - 2)² - 3
f(x) = 1 / 3 ( x - 2)² - 3
f(x) = 1 / 3 (x - 2)(x -2) - 3
f(x) = 1 / 3 (x² - 4x + 4) - 3
f(x) = x² / 3 - 4x / 3 + 4 / 3 - 3
f(x) = 1 / 3 x² - 4 / 3 x - 5 / 3
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